|-/ ^,: : " v -60UGHT WITH THE INCOME ' '^ . FR(|M THE SA(ffc -ENDOWMENT /UND THE GIF« ©P* _.**' '"- v-' ;■ * '^SUnrg 1$. Sage V ^ ^/ fyjUujjz ¥ Cornell University Library VM145 .W58 1894 A manual of naval architecture for the u olin 3 1924 030 901 403 The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924030901403 JSTAVAL ARCHITECTURE. A MANUAL OP NAVAL ABCHITECTUBE FOR THE USE OF OFFICERS OF THE EOYAL NAVY, OFFICEBS OF THE MEECANTILE MAEINE, YACHTSMEN, SHIPOWNEES, AND SHIPBUILDEES., By W. H. WHITE, C.B., LL.D., ASSISTANT CONTROLLER AND DIRECTOR OF NAVAL CONSTRUCTION, ROYAL NAVY ; FELLOW OF THE ROYAL SOCIETIES OF LONDON AND EDINBURGH; VICE-PRESIDENT OP THK INSTITUTION OF NAVAL ARCHITECTS ; PAST PRESIDENT OF THE INSTITUTE OF MAEINE ENGINEERS; MEMBER OF THE COUNCILS OF THE INSTITUTIONS OF CIVIL ENGINEERS AND MECHANICAL ENGINEERS ; HONORARY MEMBER OF THE SOCIETY OF ENGINEERS, THE INSTITUTION OF ENGINEERS AND SHIPBUILDERS IN SCOTLAND, AND THE NORTH-EAST COAST INSTITUTION OF ENGINEERS AND SHIPBUILDERS ; FELLOW OF THE ROYAL SCHOOL OF NAVAL ARCHITECTURE. THIRD EDITION, REVISED AND ENLARGED. The Lords Commissioners of the Admiralty have been pleased to authorize the issue of this book to the Ships of the Royal Navy. LONDON : JOHN MUEEAY, ALBEMARLE STREET. 1894. LONDON : NilNTED BY WILLIAM OI.OWKS AND SONS, LIMITED, STAMFORD' STBKIJT AND OBABINO CROSS. PREFACE The first edition of this book, published in 1877, grew out of lectures delivered at the Eoyal Naval College to naval officers and others studying there. In these lectures it was my endeavour to popularize and explain some of the many problems of naval architecture in a manner which should be intelligible to those who were interested in or connected with shipping, but not engaged as naval architects or shipbuilders. Many officers who attended the lectures requested that they might be published ; and from shipowners, yachtsmen, and other persons came inquiries for a book containing, in popular language, a comprehensive summary of the theory of naval architecture. Existing treatises had been written mainly for the use of those who desired to obtain an acquaintance with the subject which would fit them for the practice of ship-designing. To benefit by these treatises a considerable knowledge of mathematics was necessary. There was obviously a want in the literature of naval architecture ; and, in its original form, this book was intended to supply that want, and to enable persons, outside the profession of the naval architect, to obtain a general acquaintance with the principles of the construction, propulsion, and behaviour of ships. The book was written, therefore, in popular language ; and the mathematics introduced were of the simplest character. Explana- tions were given of many terms and mechanical principles, which required no explanations to readers possessing a good knowledge of mathematics. The details of theoretical investigations were omitted, but the general modes of procedure were sketched, and the practical deductions fully explained and illustrated. From this point of view, the survey of the theory of naval architecture was made as complete as possible. The principal deductions from theory respecting the buoyancy, b VI PREFACE. stability, behaviour, resistance, and propulsion of ships, were set forth at length. Practical rules were given for regulating the draught and stowage of ships, estimating their tonnage, and approximating to their stability. Writing largely for the information of seamen, it was my endeavour to awaken in their minds an intelligent interest in the observations of deep-sea waves and the behaviour of ships. Such observations, carefully made and properly recorded, are of the greatest value to future ship-designing, and, from the nature of the case, can only be made by seamen. Practical shipbuilding was not treated in any detail, but a comprehensive sketch was given of the structural arrangements in various types of ships, of the relative qualities of the principal materials used in shipbuilding, and the principles which govern the work of the shipbuilder in providing the strength neces- sary to resist the action of the various straining forces to which the hulls of ships are subjected during service at sea. It was anticipated that such a book, while primarily designed for the use of naval officers — in the Eoyal Navy and the Mercantile Marine — shipowners, and yachtsmen, would prove useful also as an introduction for students of naval architecture to more formal and mathematical treatises, while it would serve as a book of reference for naval architects, shipbuilders, and marine engineers. These anticipations were realized. The book has had a wide circulation in this country and abroad. The Admiralty has approved it as a text-book for officers of the Eoyal Navy, and it has been issued to H.M. ships. The naval authorities of Italy and Germany have similarly approved of translations of the work. It has been extensively used by the classes for whom it was originally undertaken — naval officers, shipowners, yachtsmen, and others interested in ship- ping. It has become a text-book for students of naval architecture, and has been welcomed by professional men engaged in the design and construction of ships and propelling machinery. A second edition was issued in . 1882, revised and enlarged. Since that time the work has been reprinted without revision. Pressure of other work prevented me from undertaking a task which became increasingly necessary as time passed and progress was made in shipbuilding. At length the demand for a new edition became imperative ; and under very .difficult conditions, arising out of re- sponsible and heavy official duties, the task now completed has been carried out, occupying my scanty leisure for nearly two years. . PREFACE. Vll In this edition the general arrangement previously adopted has been maintained. A large portion of the book has been rewritten, and it has been considerably increased in size. All the sections have been carefully revised and brought up to date. The notable advance made during recent years in the application of scientific methods to merchant-ship construction has made it possible to add greatly to the information given in regard to the stability, strength, and pro- pulsion of vessels of various types. Important inquiries and legisla- tion have taken place also since the previous edition appeared, dealing with the load-line, the tonnage, and the watertight sub- division of merchant ships. These subjects have been summarized and discussed in the following pages, and the information brought together will be of interest to many readers. The section dealing with steamship propulsion is practically a new and much extended treatment of this important subject. An endeavour has been made to summarize and digest the most recent and valuable theoretical and experimental investigations bearing on steamship performance and the efficiency of propellers. In the chapter on sailing ships will be found a careful resume of the latest investigations of the laws of wind pressure. I venture to hope that in its new form the book will be of greater value to naval architects and shipbuilders, while it will losejnothing of its interest for other classes of readers. Much of the informa- tion contained herein has necessarily been drawn from the work of other writers. The substance of various papers of my own, pre- viously published, has been used. I am indebted also to many friends for valuable information not previously published, especially in regard to ships of the mercantile marine. In all cases it has been my endeavour to acknowledge the sources of information, and these references may be of value to students desiring to follow up the complete treatment of subjects which are only briefly touched upon in the following pages. To Mr. W. E. Smith, of the Constructive Staff, my thanks are due for valuable assistance in the passage of this edition through the press. W. H. WHITE. January, 1894. CONTENTS CHAPTER I. THE DISPLACEMENT AND BUOYANCY OP SHIPS. PAGE Definitions of displacement and buoyancy 1 Useful displacement, or carrying power 2 Approximate rules for estimating displacement 3 Curves of displacement : their construction and uses 5 Curves of tons per inch immersion : their construction and uses 6 Changes in draught of water produced by the passage of ships from the sea to rivers and docks 7 Reserve of buoyancy for various types of ships 9 Rules for freeboard 10 Load-line legislation for merchant ships 12 Load-line committee, conclusions 15 Load-line for vessels with deck erections 18 Submarine and surface vessels : fundamental principles of construction ... 19 Foundering of ships which are " swamped." Water-logged ships 21 Foundering of ships which have bottoms penetrated 23 Principles of watertight subdivision of ships :— By transverse bulkheads 25 By longitudinal bulkheads 28 By decks or platforms 30 Watertight subdivision in modern war-ships 31 Cellular double bottoms 34 Wing passage bulkheads 35. Examples of foundering caused by collision 36 "Unsinkable" ships 38 Watertight subdivision in merchant ships 39 Bulkheads committee, work of 41 CHAPTER II. THE TONNAGE OF SHIPS. Early systems of tonnage measurements 45 Legal tonnage of coal-carrying vessels 46 Early rules for estimating tonnage 47 Builders' old measurement tonnage 47 Tonnage legislation, 1821-1853 50 CONTENTS. CHAPTEE III. THE STATICAL STABILITY OF SHIPS. l'AOX New measurement tonnage, 1836 51 Moorsom tonnage system, 1854 52 Royal Commission of 1881 •■ 53 Tonnage deck defined by House of Lords 55 Approximate rules for gross tonnage 56 Register tonnage 59 Deductions permitted from gross tonnage 60 Danube rule 63 Tonnage Act of 1889 64 International tonnage "5 Suez Canal rule 65 Alternative systems of tonnage for merchant ships 67 Dead-weight tonnage 68 Displacement tonnage 70 Parallelopipedon tonnage 71 Freight tonnage 72 War -ship tonnage 73 Yacht-measurements : for time allowances 74 Thames rule 75 Yacht Racing Association ml e 75 Corinthian rule ••• 76 American rules ... ... ••• •■■ ... 78 Condition of ships floating in still water 80 ,, „ inclined by mechanical couple 81 Stable, unstable, and indifferent equilibrium 82 Statical stability defined 83 Metacentre for transverse inclinations ... ... ... ... ... ... 83 Stiffness, crankness, and steadiness ... ... ... ... ... ... 84 Effect of metacentric height on stiffness 85 Approximate rules for positions of centre of buoyancy and metacentre ... 87 Metacentric diagrams : construction and uses of 89-94 Stability of cigar and submerged vessels ... ... ... ... ... 95 Metacentric heights : for war-ships 97 „ „ for merchant steamships 100 Inclining experiments 103 Metacentric heights for sailing ships and yachts 105 Heel produced by tra versing weights 107 Stability with shifting cargoes , ... HO Water ballast, effect on stability Ill Oil cargoes, precautions as regards stability Ill Stability not always reduced by free water in hold 114 Central citadel ships : metacentric height when riddled 115 Effect of adding or removing weights 117 Metacentre for longitudinal inclinations 119 Estimates for change of trim 119 Stability of ships partially waterborne 124 CONTENTS. XI FAGK Curves of stability 126 Atwood's formula » 127 Effect of freeboard and beam on stability 129 Earliest curves of stability on record 131 Curves of stability for typical war-ships 132-134 „ ., „ merchant steamers 135 „ „ „ sailing vessels 138 „ „ ,, torpedo-boats 139 Stability of ships when launched 141 Cross-curves of stability 144 Use of Amsler's Integrator 146 CHAPTER IV. THE OSCILLATIONS OP SHIPS IS STILL WATER. Comparison of ship with a pendulum 147 Angular velocity, accelerating force, and moment of inertia 149 Instantaneous axis for unresisted rolling 151 Curve of flotation 152 Motion of metacentre during rolling ... ... ... ... ... ... 153 Formula for unresisted rolling ... ... ... ... ... ... ... 154 Changes in period produced by changes in distribution of weights ... ... 155 Isochronous rolling ... ... ... ... ... 157 Dynamical stability : modes of estimating ... ... ... ... ... 158 Moseley's formula 160 Dipping oscillations • 162 Effect of fluid resistance on rolling 163 Rolling experiments in still water 164 Curves of extinction of rolling 167 Still- water periods for typical war-ships 169 Coefficients of extinction 172 Resistance to rolling mainly due to surface disturbance... ... ... ... 175 Usefulness of bilge keels 176 Extinctive effect of " Water chambers " 181 Thornycroft's automatic steadying apparatus 183 Resistance to rolling when sides are damaged 184 Effect of gusts or squalls of wind on rigged ships in still water 185 Captain compared with Monarch ... ... ... ... ... ... 186 Cases of capsizing in smooth water by squalls 190 CHAPTER V. DEEP-SEA WAVES. Fundamental conditions of trochoidal theory 191 Construction of trochoidal profiles 192 Orbital motions of particles and advance of wave form 194 Internal structure of wave 196 Xll CONTENTS. Variations in direction and intensity of fluid pressure incidental to wave motion 199 Heaving motion on wave surface t 201 FormulsB for dimensions and speeds of waves 202 Observations of waves: methods of conducting ... ... ... ... ••• 204 Summary of maximum dimensions recorded ... ... ... ... ... 209 Comparison of observation with theory 212 Conditions of a confused sea ... ... ... ... ... ... ... 215 The genesis of waves 216 Relation of force of wind to dimensions of waves ... ... ... ... 219 Prevalent waves in different regions ... ... ... ... ... ■•• 220 Utilization of wave power 223 CHAPTER VI. THE OSCILLATIONS OF SHIPS AMONG WAVES. Early theories of rolling ... ... ... ... ... ... ... ... 224 Principal features of modern theory of rolling 225 The "virtual upright" 226 The " effective wave slope " 227 The importance of ratio of period of rolling to half period of wave 229 Fundamental assumptions for mathematical investigation of unresisted rolling 231 Critical cases of rolling of ships : — Amongst waves of synchronizing periods 233 Variation of period of rolling due to variation in angle of swing 235 ■" Permanent " oscillations 236 " Phases " of oscillation ... 238 Examples of actual rolling ... ... ... ... ... 239 Practical deductions from investigation of unresisted rolling, compared with observations of the rolling of ships at sea 240 Importance of rate of rolling on strength of structure 244 Effect of changing course and speed relative to waves 245 Influence of fluid resistance upon rolling 247 Graphic integration for resisted rolling : Mr. Froude's method 249 M. Berlin's investigation for resisted rolling 251 Influence of bilge keels in steadying ships 253 Influence of projecting armour and low freeboard 255 " Water-chambers " in armoured ships, extinctive effect of 255 Rolling of ships with sail set 257 Effect of heaving motion 258 „ gusts and squalls of wind < 260 Ranges of stability in certain classes of vessels 261 Steadying effect of sails 262 Longitudinal oscillations : pitching and 'scending 263 Influence of length on pitching 265 „ distribution of weight on pitching 268 „ fluid resistance on pitching 269 Effect of low ends 270 Heaving oscillations 271 CONTENTS. Xlll CHAPTER VH. METHODS OF OBSERVING THE ROLLING -VXD PITCHING MOTIONS Or SHIPS. FAGB Necessity for such observations ... ... ... ... ... ... ... 274 Pendulum observations, and their errors 276 Spirit-levels and clinometers ... ... ... ... ... ... ... 279 Gyroscopic instruments and their drawbacks ... ... ... ... ... 281 Admiral Paris's instrument 283 M. Normand's instrument 284 Batten instruments, various arrangements of ... ... ... ... ... 285 Photographic apparatus 288 Description of Mr. Froude's automatic instrument ... ... ... ... 290 Towers'" Steady platform" 292 Simultaneous observations of behaviour of ships and character of waves much needed 294 CHAPTER VHI. THE STEAMS EXPERIENCED BY SHIPS. Necessity for careful study of subject Classification of principal strains ... Longitudinal bending moments (hogging and sagging) : — Due to unequal distribution of weight and buoyancy Method of estimating bending moments ... Curves of weight, buoyancy, loads and bending moments, construction uses of, with examples for typical ships ... ... Bending moments due to longitudinal fluid pressure Extreme cases of support for ships among waves ... Corresponding bending moments for typical ships ... Influence of wave structure on bending moments ... „ pitching and 'scending upon longitudinal strains Bending moments of ships ashore Transverse strains experienced by ships when — Resting on the keel only in dock or ashore ... Afloat in still water ... Rolling among waves Strains incidental to propulsion : — By sails By screws or paddles ... Straining due to vibration ... Local strains produced by — Concentrated load or support Grounding: with special reference to iron ships Loads on decks Collision : with special reference to ramming Propulsion Dismasting of large sailing ships and 301- 296 297 299 299 310 310 311 315 317 319 320 322 323 324 327 328 328 330 333 335 335 339 341 XIV CONTENTS. CHAPTER IX. THE STRUCTURAL ARRANGEMENTS AND STRENGTH OF SHIPS. FAQK Gradual development of structural arrangements *>'** Features common to structures of all ships ... . . •■• ••■ ••■ "" Ultimate effect of longitudinal bending strains 34v> Construction of " equivalent girder " sections "4b Principles of the strength of beams and girders 349 Application of these principles to longitudinal strength of ships 353 Influence of form, proportions, and local requirements upon the scantlings of ships 35& Longitudinal strength contributed by — Upper decks of ships 361 Skins and riders of ordinary wood ships 361 Bottoms below the bilges 363. Longitudinal framing and cellular construction ... ... ■•• 367 Skins of composite ships 373 „ diagonally built wood ships 374 „ iron and steel ships 374 Special arrangements of shallow-draught vessels 375 Maximum longitudinal strains on war-ships ... ... ... ••• ... 379 „ „ „ merchant ships 381 Provision of transverse strength 383 Strength of transverse frames or ribs in wood and iron ships 384 Partial bulkheads of iron ships 384 Bracket frames in cellular double bottoms 385 Transverse framing of ironclads and swift cruisers ... ... ... ... 385 Decks, beams, and pillars as transverse strengtheners 387 Beam-knees and beam-end fastening ... ... 389 Transverse bulkheads considered as strengtheners 391 CHAPTER X. MATERIALS FOE SHIPBUILDING : WOOD, IRON, AND STEEL. Remarkable progress of iron and steel shipbuilding, 393 Aluminium and bronzes ... ... ... ... ... 395 Relative strengths and weights of timber, iron, and steel 396-402 Forms of beams in common use 403 Comparison of strength between wood and iron beams ... ... 404 Relative strengths of combinations of wood, iron, and steel 405- Scarphing of wood beams 406 Comparative weights of wood, iron, and steel ships 409 Weights of hull in wood-built ships 411 „ „ iron and steel ships 413. Distribution of weights in battle-ships 41 5. „ „ „ a swift protected cruiser ... 416 Comparative durability of wood, iron, and steel ships ... 417 Iron and steel not subject to internal sources of decay 418 CONTENTS. xv Preservation of iron hulls 419 Corrosion of iron and steel ships 420 Increase of corrosion due to galvanic action 422 Admiralty regulations for the preservation of iron and steel ships 425 Fouling of ships 426 Copper sheathing to prevent fouling 426 Muntz metal and naval brass 427 Zinc sheathing 428 Prevention of fouling ... ... ... ... ... ••• 429 Wood-sheathed ships 430 Nickel steel as a material for bottoms 433 CHAPTER XI. THE RESISTANCE OF SHIPS. Early theories of resistance 434 Classification of water resistance ... ... ... ... 435 Resistance to direct and oblique motion of plates 436-438 Modern formulae for direct resistance on front of plates 438 Recent experiments on oblique resistance 439 Froude's experiments on frictional resistance 440 Effect of length on frictional resistance 441 Stream-line theory of resistance 443 Rankine's rules for constructing stream lines 445 Motion of a perfect fluid through a bent pipe 447 " Augmented surface " 450 Eddy-making resistance 451 Characteristics of wake of ships 452 Modem experiments on stream lines at sterns of ships 453 Wave-making resistance ... ... 454 Scott Russell's rules for length of entrance and run 457 Waves accompanying ships 458 Effect of varying lengths of middle body 460 Summary of chief features of resistance 464 Effect of shoal water 464-467 Recent advance in speeds ... ... ... ... ... ... ... ... 468 Tow-rope strains in typical cases 469 Resistance of torpedo-boats at very high speeds 469 Ship-design as influenced by form and resistance 472 Greyhound towed by Active ... 473 Influence of Suez Canal on forms and proportions 476 Model experiments on resistance 477 Scale of comparison between models and ships 478-485 Air resistance 485 Resistance when motion is not uniform 487 Resistance in a seaway 488 XVI CONTENTS. CHAPTER XII. PROPULSION BY SAILS. l'AGK Laws of wind pressure 489 Results of experiments on wind pressures and velocities 491 Effect of size of structure on average pressure 493 Experiments on wind pressure on Forth bridge 495 Wind pressure on oblique plates ... ... ••• ••• 496 Wind pressure on curved surfaces and sails ... ... •■• ••• ••• 497 Classification of winds (Beaufort scale) 500 Propulsive effect of wind on sails ■•• ••■ 501 Actual and apparent direction and velocity of wind relatively to sails 502 Leeway •■■ ••• ••■ 504 Speeds of ice yachts 507 Ardency and slackness 507 Case of ship sailing close hauled 508 French experiments on Jean Bart 509 Preparation of sail plans 510 Plain sail for various rigs ••• ••• ••• ••• 511 Ratio of sail area to area of immersed surface 513 Sail spread in terms of (displacement)' 515 Sail areas of yachts ... ••• ••• •■• ••• 517 Distribution of sail ••■ ••• ■•• 518 Positions of masts and length of base of sail 521 Sail spread on each mast ... ... ... ... ... 523 Vertical distribution of sail 524 Angle of heel under sail 525 Sail-carrying power ... ... ... 527 Dimensions and proportions of modern sailing ships 528 Propulsion under steam and sail ... ... ... ... 530 Proportions of yachts ... ... ... ... 531 CHAPTER XIH. STEAM PROPULSION — MEASURES OF HORSE-POWER, AND PROPULSIVE COEFFICIENTS. General problem 532 Joint responsibility of naval architect and marine engineer 532 Tentative character of first stages of design 533 Effective horse-power 534 Indicated horse-power 535 Duration of steam trials in various vessels 536 French horse-power 537 Nominal , 537 Normal , 539 Lloyds'rule 539 Propulsive coefficients 540 Efficiency of mechanism 541 Constant friction 542 CONTENTS. XVll PAGE Iris trials 543 Waste work 544 Augmentation of resistance by action of propeller .. 544 Efficiency of a well-designed screw 545 CHAPTER XIV. PROGRESS IS MARINE ENGINEERING — ITS INFLUENCE UPON STEAMSHIP DESIGN. General outline of subject 546 Effect of increase in steam pressure 546 Combustion of coal in boilers 547 Kates of expansion of steam ... ... ... ... ... ... ... 518 Efficiency of condensers ... ... ... ... ... 549 Feed heaters and super-beating 549 Single, compound, triple, and quadruple expansion . 550 Effect of increase in piston speed and rate of revolution 550 Use of gearing 551 Types of marine boilers ... 552 Tank boilers ... 553 Locomotive boilers ... ... ... ... ... ... ... ... 553 Water-tube boilers... ... ... ... ... ... ... ... ... 554 Trials of Speedy 555 Methods of accelerating evaporation in boilers 557 Use of steam blast 557 „ air blast 558 Induced draught 558 Forced draught 558 Closed ash-pit system 559 „ stokehold system ... ... ' 559 Forced draught with groups of locomotive boilers 560 Fan draught open stokeholds 561 Weights of machinery and rates of coal consumption for war-ships 562 „ „ „ „ „ „ merchant ships ... 563 Economy in coal consumption ... ... ... ... ... 564 Eecent case of Thunderer ... ... .. ... ■■• ... ... ... 565 Use of liquid fuel 566 Influence of engine design upon ship design 567 Ocean steaming at high speeds 568 Eecent cargo-steamers 569 Cross-channel steamers 570 CHAPTER XV. MARINE PROPELLERS— FUNDAMENTAL PRINCIPLES OF ACTION: WATER-JETS AND PADDLE-WHEELS. Types of propellers 571 Difficulties in use of paddle-wheels in seagoing vessels 571 Early paddle vessels °* 2 Position of single screws 573 XVlll CONTENTS. FAGE Early use of twin screws ■■■ ■•■ 57o Use of twin screws in mercantile marine 574 Single screws not more efficient than twin screws ••• 575 Use of two screws on one shaft 576 Triple and multiple screws ... ... ... ••• ■■■ ••• ••• "77 Triple screws with respect to economy of coal at low speeds ... ... ... 578 Screw turbine propeller ... ... ... ... ■■■ ••• 579 Fundamental principles of action of propeller, thrust and efficiency 580 Water-jet propeller 585 Waterwitch trials 588 Jet-propelled torpedo-boats 589 Hydromotor trials ... ... ... ... ■•• •■■ ■■• ••• •■• 591 Paddle-wheels, general principles 592 „ „ practical rules for design 596 CHAPTER XVI. THE SCREW PROPELLER. General definitions ... ... ... ... ... •■■ 597 Efficiency diagram ... ... ... ... ... ... 599 Effect of wake on screw propulsion 601 Thrust horse-power ... ... ... ... ... ... 602 Sufficient immersion necessary for efficiency 603 Theories relating to screw propulsion ... ... ... ... 603 Professor Eankine's investigations 604 „ Greenhill's „ 605 Mr. W. Froude's „ 606 Mr. Calvert's „ 608 Professor CotterilTs „ ' 608 „ Mamice Fitzgerald's and Mr. R. E. Froude's investigations 609 Determination of dimensions for screw propeller 609 Sea trials 610 Progressive trials , 611 Special experimental trials on iris 613 Experiments with model screws ,,, ... ... ... ... ... ... 614 Mr. Thornycroft's trials 616 Messrs. R. and W. Hawthorn's trials 617 Mr. Blechynden's deductions 620 General conclusions 622 CHAPTER XVII. ESTIMATES FOR THE HORSE-POWER AND SPEED OF STEAMSHIPS — STEAMSHIP EFFICIENCY. " Admiralty " coefficients g23 Ordinary calculations for I.H.P g25 Rankine's " augmented surface " method 627 Early progressive steam trials g28 CONTENTS. XIX PAGE Variation of I.H.P. with size of ship 631 I.H.P. of Hercules based on that of Greyhound 633 Steamship efficiency 635 Economical propulsion favoured by increase in size 636 Examples of economy of propulsion ... ... ... ... ... ... 638 Economy of propulsion as affected by suitable form and proportions ... ... 639 Hercules compared with longer ship 641 Central citadel ships and circular ironclads ... ... ... ... ... 642 Devastation compared with circular ironclad ... ... ... ... ... 643 Speed of Livadia 644 Recent developments of speed 647 Speed and I.H.P. for typical ships 647 CHAPTER XVIII. THE STEERING OF SHIPS. Various modes of steering 649 Most advantageous position for rudder 649 Ordinary and balanced rudders 650 " Turn-about " system 652 Eluid pressure on rudders : causes and measures of ... ... 653 Relative effects of upper and lower portions of rudders 655 Special features of screw-ship steerage ... ... ... ... 655 British Association Committee's experiments 657 Length required for stopping ships 658 Effect of reversing engines on steering 659 Force required on tillers 661 Joessel's rudder 663 Calculations for strengths of rudder heads and steering gear 664 Mechanical work done in putting rudders over 665 Balanced rudders : their advantages ... ... ... ... 666 Steam and hydraulic steering gear 667 Turning effect of rudders 668 Causes affecting readiness to answer helm 670 Steerage in shallow water 672 Paths traversed by ships in turning 673 French experiments 674 Turning trials of Thunderer 675 Drift angles for ships turning, and their effects 678 Heeling of ships in turning 682 Deductions from turning trials of ships 685-691 Determination of rudder areas 691 Forms of rudder 695 Special rudders 696 Auxiliary appliances for steering. 697 Bow rudders 698 Torpedo-gunboat turning trials with typical forms of rudders 699 Thornycroft's steering paddle 701 XX CONTENTS. Comtis class auxiliary rudders ... ... ... ... ... ... ... 702 Steering by propellers ... ... ... ... ... ... 703 Mallory propeller 705 Fowler's propeller 706 Erratic steering of Ajax, and how remedied 707 General conclusions for twin-screw ships ... ... ... ... ... 708 Special case of Faraday telegraph ship 710 Wateruritck steering trials ... ... ... ... 711 Manoeuvring in a seaway 712 Index 713 NAVAL AKCHITECTUBE. CHAPTEE I. THE DISPLACEMENT AND BUOYANCY OP SHIPS. A ship floating freely and at rest in still water must displace a volume of water having a weight equal to her own weight. The truth of this fundamental condition may he easily demonstrated. Let Fig. 1 represent the ship (in profile view and athwartship section), WL being the surface of the water. If it is supposed that the water surrounding the ship becomes solidified, and that the ship is then removed, there will remain a cavity representing in form and volume the water displaced by the ship : this is termed the " volume of dis- placement " (or, shortly, the " displacement ") of the ship, being- represented in the diagrams by WKL. If the cavity is then filled up to the level of the surface WL with water of the same density FIG. 1. Unfile as that in which the ship floated, and afterwards the surrounding water again becomes liquid, there will obviously be no disturbance or change of level in consequence of the substitution of the water for the ship. Therefore the total weight of water poured into the cavity — that is, the total weight of water displaced by the ship — must equal her weight. This fundamental law of hydrostatics applies to all floating bodies, and is equally true of wholly submerged vessels floating at any depth as of ships of ordinary form, having only a portion of their volume immersed. Ships which are of equal weight may differ greatly in form and 2 NA VAL ARCHITECTURE. [chap. i. dimensions, and consequently the forms of their respective displace- ments will differ ; but when they are floating in water of the same density, the volumes must be equal to one another, because the weights of the ships are equal. On the other hand, when a ship passes from water of one density to water of another density, say from the open sea to a river where the water is comparatively fresh, her volume of displacement must change, because the weight of water displaced must be the same in both cases. Under all circum- stances the volume of displacement, multiplied by the weight per unit of volume of the water in which the ship floats, must equal the weight of the ship. It is usual to express the volume in cubic feet, and for sea-water to take 64 lbs. as the weight of a cubic foot ; so that the weight of the ship in tons multiplied by thirty-five gives the number of cubic feet in the volume of displacement when she floats in sea-water. At every point on the bottom of a ship floating freely and at rest in still water, the water pressure acts perpendicularly to the bottom. This normal pressure at any point is proportional to the depth of the point below the water surface ; and it may be regarded as made up of three component pressures. First, a vertical pressure ; second, a horizontal pressure acting athwartships ; third, a horizontal pressure acting longitudinally. Over the whole surface of the bottom a similar decomposition of the normal fluid pressures may be made ; but of the three sets of forces so obtained, only those acting vertically are important in a ship at rest. The horizontal components in each set must obviously be exactly balanced amongst themselves, other- wise the ship would be set in motion either athwartships or length- wise. The sum of the vertical components must be balanced by the weight of the ship, which is the only other vertical force ; this sum is usually termed the " buoyancy ; " it equals the weight of water displaced, and the two terms " buoyancy " and " displacement " are often used interchangeably. The total weight of a ship may be subdivided into the " weight of the hull," or structure, and the " weight of lading." The latter measures the " carrying power " of the ship, and is therefore fre- quently termed the " useful displacement." Useful displacement for a certain degree of immersion is simply the difference between the total displacement and the weight of the hull ; so that any decrease in the weight of hull leads to an increase in the carrying power. If the ship is a merchantman, savings on the hull enable the owner either to carry more cargo in a vessel of a specified size or else to build a smaller vessel to carry a specified cargo. If the ship is a man-of-war, such savings on the hull render possible increase in the offensive or defensive powers, or in the coal supply, engine power, chap. i.J DISPLACEMENT AND BUOYANCY OF SHIPS. 3 or speed ; or else enable certain specified qualities to be obtained on smaller dimensions than would otherwise be practicable. Hence appears the necessity for careful selection of the best materials and most perfect structural arrangements, in order that the necessary- strength may be secured in association with the minimum of weight. It is in this direction that all recent improvements in shipbuilding have tended ; the use of iron hulls instead of wood greatly facilitated progress, and further advances are now being made by the substitu- tion of steel for iron. These improvements in ship-construction are described in Chapter X. Having given the draught of water to which it is proposed to immerse a ship, the volume of her immersed part determines the corresponding displacement, and this displacement can be calculated with exactitude from the drawings of the ship. This is the method adopted by the naval architect ; but any details of the method would be out of place here. At the same time an approximate rule by which an estimate of the displacement of the ship may be rapidly made may have some value. Assuming that the length of the ship at the load-line is known (say L), also the breadth extreme (B), and the mean draught (D), the product of these three dimensions will give the volume of a parallelopipedon. This may be written : — Volume of parallelopipedon = V (cubic feet) = L x B x D. The volume of displacement may then be expressed as a percentage of the volume (V) of the parallelopipedon. The technical term for such percentages is " coefficient of fineness," expressing, as it does, the extent to which the immersed part of a ship is reduced from the parallelopipedon, or " fined." The following table gives values for several classes of ships : — Classes of steam-ships. Coefficient of fineness. Displacement -4- volume V. 1. Swift steamers (fine forms) ; her Majesty's yachts ; 2. Swift steam-cruisers, corvettes and sloops, Royal Navy ; first-class ocean passenger steamers of very high 3. Steam gun-vessels, etc., Royal Navy; passenger steamers 4. Latest classes of wood steam line-of-battle ships and frigates, and early types of sea-going ironclads, Royal 5. Recent sea-going battle-ships; later types of rigged 6. Earlier mastless sea-going ironclads of moderate speed ; cargo and passenger steamers of moderate speed 7. Cargo-carrying steamers, ordinary types, low speed Percentage. 40 to 50 45 to 55 55 to 65 50 to 55 55 to 65 62 to 70 65 to 78 4 NAVAL ARCHITECTURE. [chap. i. To these approximate rules for steamers, a few corresponding rules for sailing ships may be added. In the obsolete classes of war- ships the displacements ranged from 40 per cent, of the volume of the parallelopipedon, in brigs, to 45 per cent, in frigates and 50 per cent, in line-of-battle ships. It is to be observed that these vessels had comparatively deep keels and false keels, especially the smaller classes ; which circumstance tended to make their " coefficients of fineness " (or percentages) appear smaller than they would otherwise have done. In modern racing yachts, with very deep keels, the percentages vary from 22 to 33 ; in modern merchantmen the per- centages usually lie between 60 and 70. These approximate rules cannot be substituted for exact calcula- tions of displacement — they are of service only in enabling a fairly accurate estimate to be made when the principal dimensions and character of a ship are known ; and in selecting the appropriate co- efficient of fineness regard must be had to the qualities of a vessel, particularly her speed if she is a steam-ship. The coefficients in the table are sometimes styled " block-coefficients," to distinguish them from other coefficients used in tabulating or comparing the forms of ships. As measures of comparative fineness, naval architects commonly use so-called prismatic coefficients, which express the ratios of the volumes of displacement to the volumes of the right cylinders, described upon the greatest immersed athwartship sections (or mid- ship sections) of ships, the lengths of these cylinders being identical with the lengths of the ships at the water-line. As an example of the application of the foregoing tabulated coefficients, a first-class cruiser of the Edgcw type may be taken. These vessels have maximum smooth-water speeds of from 20 to 21 knots, their forms are very fine, and 50 per cent, is an appropriate coefficient. Length (L) = 360 feet ; breadth (B) = 60 feet ; mean draught (D) = 23-75 feet. Volume of parallelopipedon (V) = 360 x 60 x 23-75 = 513,000 cub. ft, „ „ displacement = 50 per cent, of V = 256, 500 cub. ft. Displacement (in tons) by rule = 256, 500 -r- 35 = 7328 tons. Actual displacement = 7350 tons. Ships vary in their draught of water and displacement as the weights on board vary. In cargo-carrying merchant vessels this variation is most considerable, their displacement without cargo, coals, or stores often being only one-third of the load displacement. In ships of war the variation in displacement is not nearly so great, but the aggregate of consumable stores reaches a large amount, and when they are out of a ship, she may float 2 or 3 feet lighter than when fully laden. Naval architects have devised a plan by which, chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 5 without performing a calculation for every line at which a ship may float, it is possible to ascertain the corresponding displacement by a simple measurement. Fig. 2 illustrates one of the " curves of displacement " drawn for this purpose ; it is constructed as follows. The displacements up to several water-lines are obtained by direct calculation from the drawings of the ship, in the manner before mentioned. Then a line AB is drawn, the point A representing the under side of the keel, and the length AB representing the " mean draught " of the ship when fully laden ; this mean draught being half the sum of the draughts of water forward and aft. Through B a line BO is drawn at right angles to AB, the length BC being made to represent, to scale, the total displacement of the ship when fully laden ; an inch in length along BC representing, say, 1000 FIG. 2. tons of displacement. Suppose the displacement to have been also calculated up to another water-line (represented by DE in the diagram) parallel to and at a known distance below the load- line (BO). Then on DE a length is set off representing this second displacement on the same scale as was used for BO. Similarly the lengths FG-, HK, and so on, are determined, and finally the curve CEG ... A is drawn through the ends of the various ordinates. When this curve is once drawn, it becomes available to find the approximate displacement for any draught of water at which the ship may float, supposing that she does not very greatly depart in trim from that at which she floats when fully laden.* For instance, suppose the mean draught' for which the displacement is required to be 4 feet lighter than the load-draught. Set down Bx representing the 4 feet, on the same scale on which AB * By " trim " the naval architect means the difference in draught at the bow of a ship from that at the stern. NA VAL ARCHITECTURE. [chap. i. represents the mean load-draught. Through x draw xy perpen- dicular to AB to meet the curve, and the length xy (on the proper scale) measures the displacement at the light draught. This brief explanation will render obvious the great practical usefulness of curves of displacement, which always form part of the calculations attached to the designs of ships. Another problem that frequently occurs is the determination of the increased immersion which will result from putting a certain weight on board a ship when floating at a known draught, or the decreased immersion consequent on removing certain weights. Here again the naval architect re- F,G - 3 - sorts to a graphic method in order c to avoid numerous independent calculations. The diagram, Fig. 3, Jr represents a "curve of tons per L inch immersion;" the horizontal J measurement from the base-line AB representing (on a certain scale) the number of tons which would immerse 1 K the ship one inch when she is floating at the draught corresponding to the ordi- nate along which the measurement is made. The construction of this curve is very similar to that of the curve of displacement in Fig. 2, the successive points on the curve being found for the equidistant water-lines, BO, DE, FG, etc., by direct calculation from the drawings of the ship ; and the length of the ordinate xy determining the number of tons required to immerse the ship one inch when floating at any mean draught, A*. In this case also it is to be understood that at the various mean draughts considered there are no considerable departures in trim from that of the fully laden ship. It will be observed in the diagram that the upper part of the curve of tons per inch is very nearly parallel to the base-line AB ; this arises from the well-known fact that, in the neighbourhood of the deep load-line of ships of ordinary form, the sides are nearly upright, and there is little or no change in the areas of the horizontal sections. For all practical purposes, in most ships, no great error is involved in assuming that twelve times the weight which would sink the ship one inch below her load-line will sink her one foot, or that a similar rule holds for the same extent of lightening from the load-draught. In fact, it is very common to find this rule holding fairly for 2 feet or more on either side of the fully laden water-line. A rule which gives a fair approximation CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. to the tons per inch immersion at the load-line, in terms of the length and breadth of the ship, has therefore considerable value. Using the same symbols as before, viz. — Length of the ship at the load-line = L (feet), Breadth extreme „ „ = B „ we should have — Area of circumscribing parallelogram = L x B = A (square feet). The following rules express, with a considerable amount of accuracy, the number of tons required to immerse or emerse the ship one inch when floating at her load-draught : — Tons per inch. 1. For ships with fine ends = B $ ff x A. 2. For ships of ordinary form (including probably^ _ 1 v a the great majority of vessels) / — T8U 3. For ships with bluff ends, such as cargo steamers = -gj^ x A. In vessels of exceptionally fine forms the divisor rises to 620, and falls to 470 in vessels of very full forms. As an example of these rules take the Invincible class of the Boyal Navy, which are ships coming under rule 2, being of ordinary form. Their dimensions are : Length = L = 280 feet ; breadth = B = 54 feet. Area of circumscribing parallelogram = A = 280 X 54 = 15,120 sq. ft. .*. Tons per inch at load-line = 5 ^ x 15,120 = 27 tons. This is nearly exact for these vessels. It is easy to see how curves of tons per inch, and curves of displacement constructed for the case of ships floating in sea-water, may be made use of in order to determine the change of draught produced by the passage of a ship into a river, estuary, or dock, where the water is comparatively fresh. For example, sea-water weighs 64 lbs. per cubic foot, whereas in the London docks the water weighs about 63 lbs. per cubic foot — or ^ 4 - part less than sea- water. Since the total weight of water displaced by the ship must remain constant, it is only necessary to make the following corrections — Difference between weight of sea-water and river-water for the volume immersed up to the draught at which the ship floats at sea = B * 4 x weight of ship = ^VW. Tons per inch immersion at this draught in river-water = $£ tons per inch for sea-water = § |T. .-. Increase in draught of water when ship floats in river-water W = &xW-H2T = gg^(inehes). 8 NA VAL ARCHITECTURE. [chap. i. For any other density of water than that assumed above, the correction would be made in a similar manner. As a numerical example, take a ship having the following particulars : Weight = W = 6000 tons ; tons per inch at load-draught in sea-water = T = 30. Increased draught on entering London \ rc\(\(\ docks as compared with her draught \ = — jn, = 3ii inches. attheNore I 63 X 30 The draught being observed when the vessel is about to leave the sea, the curves of displacement and tons per inch will furnish the corresponding values of W and T in the foregoing expressions. The converse case, where a ship, on passing from a dock or river to the sea, floats at a less draught, is of considerable importance to merchant ships, exercising an appreciable effect upon their freeboard when deeply laden. This variation in draught is provided for in the tables prepared by the Load-line Committee of 1884-85, and em- bodied in the Merchant Shipping Act of 1890. Samples of water were weighed in the various ports, harbours, and rivers of the United Kingdom, and were found to vary from 1000 ounces per cubic foot of fresh water, to 1025 ounces for the densest sea-water on the British coast. The diminution in draught, or "rise," of ships in passing from the lightest to the densest water is expressed in terms of the "moulded depths" of the ships, ranging between 2 inches for a moulded depth of 9 feet, to 6 inches for a depth of 34 feet in vessels without erections on deck. Suitable rules are laid down also for other types of vessels and for intermediate densities of water at loading-berths. Reserve of Buoyancy. — The buoyancy of a ship has already been denned, and shown to be measured by the displacement up to any assigned water-line. " Eeserve of buoyancy " is a phrase now commonly employed to express the volume, and corresponding buoyancy, of the part of a ship not immersed, but which may be made watertight, and which in most vessels would be enclosed by the upper deck, although in many cases there are watertight enclosures above that deck — such as poops, forecastles, bridge-houses, etc. The under-water, or immersed, part of a ship contributes the buoyancy ; the out-of-water part the reserve of buoyancy, and the ratio between the two has a most important influence upon the safety of the ship against foundering at sea. The sum of the two, in short, expresses the total " floating power " of the vessel, and the ratio of the part which is utilized to that in reserve is a matter requiring the most careful attention. In Figs. 4-9 are given illustrations of the very various ratios which the reserve of buoyancy bears to the volume of displacement FIG. 5. ^J w FIG. 6. FIG. 7. chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 9 in different classes of war-snips. As this is only a matter of ratio, a box-shaped form has been employed instead of a ship-shaped, and in all cases the volume of displacement is the same, so that the out-of- water portions can be com- pared with one another as well as with the displace- ment. Fig. 4 represents the condition of low-freeboard American monitors, such as the Canonieus or Pas- saic, which were employed on the Atlantic coast durin.gr the civil war. The upper decks of these vessels are said to have been between 1 and 2 feet only above water; their reserve of buoyancy was only about 10 per cent, of the dis- placement. Fig. 5 represents the condition of the American monitor Miantonomoh, with a reserve of buoyancy of about 20 per cent, of the displacement; this approxi- mately shows her state when she crossed the At- lantic in 1866, but all openings on her upper deck, which was about 3 feet above water, were care- fully closed or caulked. Fig. 6 represents the Cyclops class of breastwork monitors in the Royal Navy as first completed. The upper decks of these ves- sels were originally about the same height above water as that of the Miantonomoh, but, by means of an armoured breastwork standing upon the upper deck, the reserve of buoyancy was increased to 30 per cent, of the displacement. For sea-service, FIG. 9. IO NAVAL ARCHITECTURE. [chap. I. when making passages, the conditions of stability were not con- sidered satisfactory, and light superstructures have been added, bringing the vessels into practically the same category as the Devastation class (Fig. 7), in which the reserve of buoyancy is 50 per cent, of the displacement. Tig. 8 represents armoured and other vessels of high freeboard, in which the reserve of buoyancy reaches 80 or even 90 per cent, of the displacement. Fig. 9 represents ships of high freeboard and fine under-water form, in which the reserve of buoyancy is equal to, or even greater than, the displacement. In the foregoing examples the ratios of reserve of buoyancy to volume of displacement have been given. This is usual for war- ships. In merchant ships it is customary to express the reserve of buoyancy as a percentage of the whole buoyant volume ; that is, of the sum of the buoyancy and reserve of buoyancy. The case of merchant ships is not nearly so simple as that of war-ships ; chiefly for two reasons. First, in war-ships certain specified weights have to be carried in definite positions, and a fixed load-line forms part of the design ; whereas, in merchant ships, with few exceptions, a vary- ing cargo has to be provided for, and until recently there was no generally accepted rule for fixing maximum load-lines, nor any legal enactment on the subject. Second, there are very great varieties in the character and extent of superstructures and deck-erections in different types of merchant ships ; and considerable difficulties have to be overcome in assigning values to such erections when estimating reserves of buoyancy or assigning freeboards. Rules for freeboard. — Freeboard, in its common use, means the height of the upper deck amidships at the side, above the water-line. If a thick " water-way " is fitted on the edge of the deck, the excess of its thickness above the ordinary thickness of the deck-plank would not be reckoned into the freeboard; in other words, freeboard is measured from a continuation to the side of the upper surface of the deck-planking or plating. In some special types, with light superstructures, freeboard is measured to the main deck. Ordinarily, freeboard is expressed in feet and inches. Fixing the minimum freeboard, of course, determines the maximum load-line for a ship. The oldest rules for freeboard were based on " depth of hold," ships to which these rules applied being of simple types with nearly flush upper decks. Probably these rules were intended to roughly pro- portion the relative volumes of the in-water and out-of -water parts of ships when floating in still water. " Lloyd's Eule," for example, was — Freeboard = from 2 to 3 inches per foot depth in hold. chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. II Although this rule was commonly used, it had no legal force, and took no. account of varying degrees of " fulness " of form, nor of the influence upon relative freeboard which increase in the sizes of ships should have. The Liverpool underwriters attempted to correct these faults, by directing their surveyors to make allowance for form and strength when assigning freeboards, and by providing graduated scales of freeboard, ranging from 2j inches per foot depth in hold of small vessels, to as much as 4 inches in large vessels. Similar rules for freeboard were also employed in foreign countries, and in some cases associated with tonnage measurements. The results in working were not satisfactory, especially after the period when steam-propulsion and iron gave rise to rapid developments in the sizes and types of merchant ships. In 1867 the council of the Institution of Naval Architects took up this question, proposing to make the freeboard of ships mainly dependent on the beam. Their rule was as follows : — Freeboard = one-eighth the beam, with the addition of one-thirty- second part of the beam, for every beam in the length of the ship, above five beams. For example, a ship 160 feet long, and 32 feet beam, is five beams in length ; freeboard = ^ x 32 = 4 feet. If she were 192 feet in length, or six beams (one beam in excess of the five) ; freeboard = £ x 32 + 3^ x 32 = 5 feet. If she were 224 feet long, or seven beams ; freeboard = £x32-)-^x32 = 6 feet. And so on. This rule obviously fails by the omission of any reference to the depth of the ship ; deep, narrow ships, which would require exceptional freeboard in consequence of their bad proportions, would by this rule gain upon better-proportioned vessels, and have a relatively low freeboard granted to them. Moreover, in the very long vessels now commonly employed, say with a length ten times the beam, the allowance for the additional five beams would be proportionately very great — in fact, the freeboard required by the rule might be excessive. On the whole, therefore, in spite of the authority on which the proposed rule rested, it is not surprising that it never came into use. The freeboard of war-ships is regulated largely by considerations of fighting efficiency, such as height of guns above water, dis- tribution of armour, and intended service. No fixed rule applies to all classes. In a coast-defence vessel, such as the Glatton, the freeboard (to upper deck) is only about 3 feet ; there is also a " breastwork " with its deck about 10 feet above water. In seagoing turret ships of moderate freeboard the upper decks are from 9 to 10 feet above water. The low ends of the barbette ships of the 12 NAVAL ARCHITECTURE. [chap. I. Admiral class have a freeboard of about 10| feet, while the central portions have a freeboard of 17 feet. The latest first-class battle- ships (Royal Sovereign class) have freeboards of 17 feet 3 inches. It is now generally accepted that high freeboard at the extremities is essential to the maintenance of speed in a sea-way. Cruisers of the latest types and largest size have their continuous upper decks from 15 to 18 feet above water, associated in some cases with long forecastles rising about 7 feet higher. For the smaller classes of cruisers, long and high poops and forecastles are usually associated with upper decks at moderate heights above water. No fixed rules are followed in assigning freeboards to yachts ; in competing designs considerable variations occur. According to Mr. Dixon Kemp, good practice may be represented by the empirical rule — Freeboard (in feet) = factor ,y/ beam (in feet). The " factor " in this rule varies considerably. In a sailing yacht of about 4£ beams in length, or a steam-yacht of 6 beams in length, the factor is said to be roughly T 7 ff ; in a sailing yacht 7 beams in length, or a steam-yacht 8 beams in length, the factor becomes unity. No coal is supposed to be on board the steam-yachts when the freeboards are measured. This attempt at methodical treatment of yacht freeboards is interesting, but no doubt differences in design will continue to prevail. Load-line legislation for merchant ships. — During the period 1870-90 many inquiries were made by commissions and com- mittees into matters affecting the safety and seaworthiness of merchant ships. In all cases the question of depth of loading necessarily came into prominence, and the desirability of rules for fixing freeboards was acknowledged. The difficulties involved were considered insuperable for a time, and the Eoyal Commission of 1874 reported that no general rules could be laid down. Ship- owners as a body were averse to legislation on the subject, and preferred to retain freedom even if associated with responsibility. By Acts of Parliament in 1875-76 their responsibility was affirmed, and they were compelled to mark on the sides of all ships engaged in oversea trade the load-line which was not to be exceeded, as well as the positions of the decks. Official surveyors had authority to detain ships considered to be overladen, subject to claims for damages by the owners. Naturally friction arose under these conditions, no authoritative or generally accepted rules being available for the guidance of either owners or surveyors. Many attempts were made to frame such rules, without success. A settlement was finally reached on the basis of action taken by the Committee of Lloyd's CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 13 Register of Shipping, on the initiative of their chief surveyor, Mr. Martell.* For nearly ten years Mr. Martell and his colleagues persevered in the compilation of data respecting the loading of various types of ships, the scientific analysis of these facts, and the framing of tables of freeboard. In 1882 Lloyd's committee issued these tables, which were soon extensively used in assigning free- boards. A strong and representative committee was appointed by the Board of Trade at the end of 1883 to consider the practicability of framing general rules for freeboard, which would prevent dangerous overloading without unduly interfering with trade. Sir Edward Heed was chairman; the Board of Trade, the Registry Societies, the Admiralty, the Institution of Naval Architects, shipowners, and shipbuilders were all represented. In August, 1885, the committee reported in favour of adopting Lloyd's tables with limited modifi- cations. The Board of Trade acted on this recommendation. From 1886 to 1890, certificates of freeboard issued by Lloyd's were accepted by the Board of Trade surveyors. Shipowners, therefore, who obtained Lloyd's certificates, and had their ships properly marked, were freed from the possibility of detention for overloading, pro- vided the assigned minimum freeboards were maintained. By July, 1890, two thousand two hundred vessels had been granted Lloyd's certificates on the voluntary application of the owners. In June, 1890, an Act of Parliament was passed which made compulsory on all British vessels of above 80 tons register the assignment and marking of a maximum load-line, determined in accordance with the tables framed by the Load-line Committee. Provision was also made in the Act for " such modifications, of any of the tables and the application thereof, as may from time to time be sanctioned by the Board of Trade." Under the terms of the Act freeboards may be assigned and certified by the Committee of Lloyd's Register ; or, at the option of shipowners, any other corporation or association for the survey or registry of shipping approved by the Board of Trade, or any officer of the Board specially selected for the purpose. Up to the present time (1893), two registries besides Lloyd's have been approved by the Board of Trade ; viz. the Bureau Veritas and the British Corporation. As might naturally be expected, however, from the facts above stated, the officials of Lloyd's Register have continued to perform by far the largest portion of the work of assigning freeboards. Reference must be made to the published report of the Load- line Committee, and to the freeboard tables appended thereto, by * See Mr. Marteil's " Keview of the We have to thank Mr. Martell for much Load-line Question." London : 1887. valuable information on the subject. 14 NAVAL ARCHITECTURE. [chap. I. readers desirous of obtaining full particulars of their procedure.* The objects of the committee may be briefly summarized in the statement that they aimed at fixing load-lines so as to secure — (1) a regulated minimum percentage of the total buoyant volume as a reserve of buoyancy ; (2) a sufficient height of deck above water ; (3) a freedom from excessive stresses being brought upon the materials in the structures of laden ships. Although not expressly mentioned in the report, it is understood that the committee also considered the relation of the load-line to stability. In the free- board tables, only cargo-carrying vessels are dealt with. In passenger vessels, of course, the provision of good accommodation in portions of the ships situated above water, necessitates relatively high freeboards. All classes of cargo-carriers are provided for, consideration having been given to various types, dimensions, pro- portions, forms, and structural arrangements. Experience gained in the actual loading and working of different classes of ships was largely drawn upon in framing the tables ; but scientific analysis and investigation were also fully employed in dealing with data obtained from experience. As standards of strength, the committee took scantlings such as would satisfy the highest class at Lloyd's, or be equi- valent thereto. For ships more lightly built, it was laid down that their depths of lading were to be suitably diminished, and the freeboards correspondingly increased; so that the material of the hull might not be subjected to severer stresses than are accepted for vessels of the same dimensions and forms, but of the standard strength. The freeboards tabulated are understood to apply to vessels having such a relation of breadth to depth as will ensure safety at sea when homogeneous cargoes are carried. For vessels of less relative breadth, it is stipulated that either the freeboards shall be increased so as to provide a sufficient range of stability, or other means adopted to ensure that range (see Chapter III.). Detailed directions are given for dealing with unusual conditions of sheer of deck, round of beam, trim, etc., and with extreme proportions of length to depth, as well as with deck erections and superstructures. The committee, while recording the opinion that their tables could be adopted for existing types of vessels for some years, were careful to emphasize the necessity for allowing to responsible authorities * The Board of Trade has also issued ments and extensions of previous rules various memoranda for the guidance of with a view to securing uniformity of authorities assigning load-lines. The practice. It is impossible here to give latest of these (November, 1892) was details of these matters, which leave the based on the work of a departmental principles explained above unchanged, committee, who made various amend- chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 15 assigning freeboards a large discretion in future applications of the tables. This is obviously essential, if there is to be no undue inter- ference with trade, or with the development of ship-construction, in years to come. The tabulated freeboards are for sea-water and for winter voyages. For summer voyages specific reductions of freeboard are made, and for winter voyages in the North Atlantic greater freeboards are required. Certain standard proportions of length to depth are assumed for vessels of which the tabulated freeboards are given. There are four sets of tables, all for flush-deck vessels, and deck erections or superstructures are dealt with independently. Tables A relate to steam-vessels (such as Fig. 10) not having spar or awning decks, FIG. 10. FLUSH DECK VESSEL. 5 with the full strength of structure carried to the upper decks. Tables B relate to " spar-deck " steam-vessels (such as Fig. 11), in FIG. 11. SPAR DECK VESSEL. 3 which the scantlings throughout are somewhat lighter than for the preceding class, and the scantlings from the spar to the main deck may be relatively lighter than those below the main deck. Tables C relate to " awning-deck " steam-vessels (such as Fig. 12), which FIG. 12. AWNING DECK VESSEL. ] D are more lightly built aloft than the spar-deck class. Tables D relate to sailing vessels, distinguishing between wood, composite, and iron or steel. In the first and fourth tables, " moulded depths " are measured, in iron or steel vessels, from the top of upper deck beam at side at the middle of the length to the top of keel ; in spar or awning deck vessels, the corresponding depth is measured from the top of the main-deck beam. The standard ratios of length to J 6 NAVAL ARCHITECTURE. [chap. I. moulded depth assumed in the tables are : In classes A and C, 12 to 1 ; and in class D, 10 to 1. For spar-deck ships, assuming that the spar deck is 7 feet above the main deck, the standard length is assumed to be twelve times the depth to the spar deck. Provision is made for departures from these standard ratios, by corrections for each change of 10 feet in length stated at the foot of the tables. Freeboard has to be increased if the actual length for a certain moulded depth exceeds the standard, and may be diminished if the actual length is below the standard. For class A, the correction for a change of 10 feet in length varies from -8 inch for ships of 10 feet moulded depth, to 1-7 inch for ships of 34 feet moulded depth. Similar corrections are specified for other classes. In spar and awning deck vessels, the corrections are less than for flush-deck vessels ; that for an awning-deck ship 34 feet in moulded depth and 408 feet long being only *8 inch, whereas a spar-deck vessel of the same length would have a correction of 1-4 inch. For vessels of standard proportions, the Tables A, C, and D give the minimum percentages of reserve buoyancy. In Table A, these percentages vary from 22 per cent, for ships of 10 feet moulded depth, up to 35 per cent, of the total buoyancy in ships where that depth is 34 feet. Awning-deck vessels have their " reserves of buoyancy " estimated to the main deck only. Although a large volume is enclosed and made watertight by the light superstructure and awning deck, such ships cannot, with safety, be nearly so deeply laden as flush-deck ships under Table A. For awning-deck ships of 14 feet moulded depth, the percentage of buoyancy is specified as 15 per cent., and for vessels where that depth is 34 feet, it is 28 per cent. It will be seen, therefore, that a considerable allowance is made for the increased buoyant volume enclosed by the light superstructure. For sailing ships, the reserves of buoyancy vary from 23 - 5 per cent, in vessels of 10 feet moulded depth, to 33 per cent, in vessels 31 feet deep. Spar-deck vessels have no specified percentages of buoyancy, heights of freeboard only being tabulated. It may be interesting to compare the freeboards assigned to vessels in classes A, B, and C, alike in length, breadth, and form, but differing in structure. Taking 360 feet as the length, a vessel of standard proportions in Table A would be 30 feet in moulded depth, and should have a minimum winter freeboard of 7 feet 3£ inches, measured to her upper deck. A spar-deck ship of the same external dimensions and form would be required to have a freeboard of 7 feet 11£ inches to her spar deck ; that is to say, she would have 8 inches less draught of water allowed her because of her lighter construction. An awning-deck ship of the same length and form up to the main deck, would have the light superstructure rising about 7 feet above chap. i. J DISPLACEMENT AND BUOYANCY OF SHIPS. 17 the main deck. Her freeboard to the main deck would be about 5 feet, although her apparent freeboard (to awning deck) would be fully 12 feet, as against an apparent freeboard of 7 feet 3£ inches in the more strongly built vessel. By means of a " curve of displacement " like that described on p. 5, but constructed so as to include the whole external volume of a ship up to the upper surface of the deck, which is assumed to bound the reserve of buoyancy, it is a very easy process to fix the load-line giving any specified percentage for that reserve. For newly designed ships this method will doubtless be followed com- monly. In order to deal with existing ships when the system was introduced, and to economize labour, Mr. Martell devised an ap- proximate method, which was adopted by the Load-line Committee, and embodied in their tables. It has been found, on investigation, that the internal volumes of ships under the upper decks bear a closely defined ratio to the external hulk. This internal capacity is known from the tonnage measurements (see p. 56), and represents the " under-deck tonnage " multiplied by 100. As a fairly accurate measure of the form of a ship, Mr. Martell therefore took — ~ „, . , „ „ under-deck tonnage X 100 Coefficient of fineness = — ^ — — - - — length x extreme breadth x depth of hold These coefficients of fineness are tabulated, and the freeboards increase with increase in the coefficients. For instance, a flush-deck vessel 240 feet long, and 20 feet moulded depth, with a coefficient -68, would have a minimum freeboard of 3 feet' 1\ inches ; whereas, if the coefficient rose to -82, the freeboard would have to be 4 feet, in order to give the required reserve of buoyancy. Deck-erections in merchant ships, as already explained, vary greatly in extent and character. The ingenuity of shipbuilders and shipowners has been, and no doubt will continue to be, exercised in modifying practice, and endeavouring to increase earning power in relation to tonnage, while maintaining seaworthiness.* In dealing with these erections, the Load-line Committee undertook a very difficult and laborious duty. The explanations of their freeboard tables contain rules for guidance in making allowances for erections of all classes of ships in existence at that time. Details must be sought in the rules themselves. The broad principle followed is to take each class separately, and have regard to the length, height, * See inter alia Mr. Martell's paper Jordan and Marlborough, on " Types " On the Alterations of Types and Pro- and Proportions of Mercantile Steamers," portions of Mercantile Vessels : " Trans- in the Transactions of the North-Bast actions of the Institution of Naval Coast Institution of Engineers and Ship- Architects, 1892 ; and a paper by Messrs. builders, 1892-93. C 1 8 NAVAL ARCHITECTURE. [chap. i. strength, and character of the several erections. The ratio of the combined length of the erections to the length of the vessel is generally used as a guide in assessing the reduction to be allowed in the freeboard and reserve buoyancy under deck. Comparing flush-deck vessels in Table A with awning-deck vessels of the same dimensions and form (to main deck) in Table C in the manner above explained, the total diminution in freeboard corresponding to a complete awning deck can be ascertained. Then a proportion of this diminution is taken for erections covering a certain part of the length only. As an example, take the case of a vessel having a long poop, at least 4 feet in height, extending to a bridge-house amid- ships, and a forecastle (Fig. 13). If the combined length of these FIG. 13. VESSEL WITH ERECTIONS CONSISTING OF FORECASTLE, BRIDGE HOUSE, RAISED QUARTER DECK AND POOP. fir H erections is 90; per cent, of the ship's length, the freeboard may be reduced from that required for a flush-deck vessel by 85 per cent, of the reduction which by the tables would be permitted if a complete awning deck were fitted. Supposing the erections to aggregate only 60 per cent, of the ship's length, the reduction in freeboard may be 50 per cent, of the reduction corresponding to an awning deck. Other combined lengths of erections carry proportionate reductions in the type of vessel used as an example. If the height of poop above the upper-deck line is less than 4 feet, the reductions in freeboard have to be suitably diminished. These rules for deck-erections are obviously empirical to a great extent. They have been carefully framed in view of existing types of cargo-carriers, and constitute a fairly satisfactory solution of a problem for which no strictly scientific solution can be found. Eevisions of these rules and of other portions of the rules and tables will be required as ship-construction is developed and new types introduced. The Act of 1890 provides the necessary powers. For certain classes of ships owners have already asked for revision, alleging that the freeboards assigned are unnecessarily great, and that earning powers are unduly diminished. To meet these difficulties and provide for necessary revisions, a majority of the Load-line Com- mittee recommended that the scientific staff of the Board of Trade should be strengthened, and that an advisory council of shipowners and shipbuilders should be formed. The Act of 1890, however, does not affirm this recommendation ; it simply specifies that the Board CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 19 of Trade shall have regard to representations made by any corpora- tion or association for the survey or registry of shipping appointed or approved by the Board for the purposes of the Act. Action has already been taken on this provision as explained above. At present foreign nations have not adopted laws for compulsory load-lines. It is stated that some of the most important maritime powers are considering the matter with a view to action.* Obviously it is of the highest importance that British shipping should not be unduly hampered in its competition with foreign shipping. The Load-line Committee emphasized this principle, and advised that, if compulsory load-lines should be enforced, all foreign as well as all British ships, loading in British and colonial ports, should come under the same law. The Act of 1890 was passed primarily with a view to increased safety of life and property at sea. A careful analysis of losses in 1885-89, since the freeboard tables came into use, is said to indicate a sensible increase in safety and diminution in loss. This is satisfactory, and may tend to encourage similar legisla- tion abroad. An international agreement for fixing load-lines has been suggested. Such an agreement practically exists for tonnage measurement. If an agreement is eventually arrived at, ships of different nationalities would compete on fairly equal terms as regards depth of loading. Submarine arid Surface Vessels. — Submarine or " surface " vessels, such as have been built or proposed for use in war, are subject to the same laws as other vessels when floating freely or at rest in still water, either at the surface or at any depth below it. The second class are not designed to be wholly submerged, but are intended to show little above-water and to have an extremely small reserve of buoyancy in fighting condition. For making passages it may be desired to give them greater freeboard, in which case the fighting draught is reached by admitting water into compartments or tanks built for the purpose. Submarine vessels also are sometimes con- structed similarly, so that they may associate the power of making passages at lighter draught, or of operating with a very small exposure, with a capability for diving when required. The last- mentioned operation involves arrangements by which the crew may control the vertical motions, either rising to the surface when necessary or sinking to any desired depth. Supposing the vessel to have been brought by admission of water to the condition where only a very small reserve of buoyancy remains, the operator may totally submerge her by various arrangements. If she has no onward * A special commission is dealing report is not available at the time of with the question in France, but the writing. 20 NA VAL ARCHITECTURE. [chap. i. motion, submergence may be attained either by admitting a quantity of water just a little in excess of the small reserve of buoyancy, or by slightly diminishing the volume of displacement by withdrawing " plungers " which protruded when the vessel floated at the surface. In either case the weight of the vessel and its contents is made to slightly exceed, the weight of water displaced by the total volume of the vessel. This excess in weight will cause a downward motion, rapidly accelerating unless checked ; and the control of the descent so as to limit it to a specified depth is not easily effected by appli- ances which simply vary the displacement. Assuming this difficulty to be overcome, and the vessel to be floating (without vertical motion) at any depth, the general law must hold good that her total weight must equal the weight of water displaced. Consequently some of the water admitted for sinking must have been expelled, or the "plungers" must have been again thrust out to a certain extent. For all practical purposes, within the greatest depths at which submarine vessels are intended to operate, water may be treated as practically incompressible. As a very simple example of the arrangements which may fulfil the foregoing objects, take the following. Conceive a small cavity to be formed in the bottom of the vessel, and that, when this cavity is about half full of water, the total displacement of the vessel, when entirely submerged, just corresponds to the total weight. The other half of the cavity may be then kept filled with compressed air, which is in communication with an air-chamber in the interior of the vessel. The air in the air-chamber would be compressed sufficiently to have a considerable excess of pressure over that corresponding to the maximum depth of immersion at which the vessel is to be employed. When the compressed air is withdrawn from the upper half of the cavity, by an apparatus worked within the vessel, the water rises into the vacated space, the volume of displacement becomes decreased by that space, and is therefore less than will balance the weight; as a result, the vessel sinks. The desired depth being reached, com- pressed air stored within the vessel may be made use of to force the water once more from the upper half of the cavity, thus restoring equality between the weight and displacement; the vessel then remains at that depth. Lastly, when it is required to rise, by means of compressed air the water is wholly expelled from the cavity ; the displacement then exceeds the weight, and consequently the vessel rises. It will be obvious that if a vessel acquires a considerable velocity while descending to any assigned depth, as she may do if the opera- tion is performed quickly, she will probably be carried much beyond that depth, even though her original displacement be restored by chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 21 expelling water from the balancing cavity. Conversely, if to make her rise again still more water be expelled, there is a risk of too great a vertical motion being produced; and so oscillatory move- ments may take place about the desired depth, or she may sink to a depth which will involve a dangerous pressure on the structure. Accidents of the kind have occurred, and in some of the best examples of this class of vessel precautions have been taken against them. One simple plan adopted in a French design and by Mr. Nordenfelt is to fit small screw propellers worked by power and carried on vertical shafts. These propellers may be used either to control vertical oscillations only, or to overcome the small reserve of buoyancy left before the vessel is submerged, and to keep the vessel at any depth. If the latter plan is followed, as soon as the propellers are stopped, the small excess of buoyancy over weight causes the vessel to begin to move towards the surface. Detachable ballast has been provided in some vessels, so as to ensure coming to the surface in case of accident to the controlling arrangements ; and pumps for ejecting water-ballast have also been suggested for the same purpose. The greatest care in management as well as design is obviously necessary, in order to minimize the risks incidental to service in such vessels. In other examples the submergence has been effected by giving onward motion to the vessels. Horizontal rudders have been fitted, under the control of the operators within the vessel. By placing these rudders in suitable positions, when the vessels are moving ahead an unbalanced vertical pressure is obtained, and the vessels are made to move upwards or downwards. When the rudders are horizontal, this vertical pressure disappears. In locomotive torpedoes similar rudders are fitted and automatically governed so as to keep the torpedoes at the desired depth below the surface. Causes of foundering. — Ships founder when the entry of water into the interior causes a serious and fatal loss of floating power. There are two cases requiring notice. The first, and less common, where the bottom of the ship remains intact, but the sea breaks over and " swamps " the vessel. The second, that in which the bottom is damaged or fractured, and water can enter the interior, remaining in free communication with the water outside. Damage to the under-water portion of the skins of iron and steel ships is by far the most fruitful source of disaster ; but many ships have foundered in consequence of being swamped, seas breaking over them, and finding a passage down through the hatchways into the hold. The older sailing brigs of the Eoyal Navy are believed by many competent authorities to have been specially exposed to this danger. Very many of them were lost at sea ; and their loss was believed 22 NAVAL ARCHITECTURE. [chap. i. to liave resulted from the lowness of their freeboard, the height of their bulwarks, and the insufficiency of the "freeing scuttles " in the top-sides to clear rapidly the large masses of water which lodged on the decks. In consequence, water accumulated, passed into the interior, and swamped them. The case of the steam-ship London furnishes another illustration. She is said to have been lost in consequence of a very heavy sea having swept away the covering of the engine hatchway, and left open a large aperture, down through which the water poured, putting out the fires, and leaving the ship a log on the water. Other seas washing over the unfortunate vessel completed: the disaster, and she gradually sank. The United States monitor Weeluiioken also appears to have been lost in this manner. While forming part of the blockading squadron, and lying at anchor off Charleston with her hatchway forward uncovered, the weather being comparatively fine, a sea broke on the deck, poured down the open hatchway, and caused the vessel to sink rapidly — it is said in three minutes — her extreme lowness of freeboard and small reserve of buoyancy conducing to this end. Another, and slightly different, case in point may be found amongst vessels engaged in the timber trade. When these ships have been laden very deeply, and have carried deck cargoes, large quantities of water have been shipped, and the vessels have become " water-logged," and utterly unmanage- able, even if they did not sink. The condition of a water-logged ship naturally leads to the remark, that in any ship the maximum quantity of water that can enter the interior may or may not suffice to sink her, according as it is: greater or less in weight than the reserve of buoyancy which the ship possesses. The maximum quantity of water that can enter the interior is determined by the unoccupied space; for to space which is already occupied by any substances — cargo, coals, engines, etc. — the water can obviously find no access. If the cargo be, like timber, very light, occupying a very large portion of the internal space, then it may happen that the total volume of the space unoccupied is less than that of the reserve of buoyancy, and the ship remains afloat; but this is not the common case, and if a vessel becomes swamped, and the sea finds access into all parts of the interior through the hatchways, she will most probably founder. Properly constructed and well-laden vessels are not, however, likely to founder in this fashion. Their hatchways and openings in the decks are carefully secured, and protected by high coamings and covers; while the interior is so subdivided into compartments, especially in iron and steel ships, that, if a sea breaks on board and finds its way down a hatch, it does not gain free access from the space thus entered to all other parts of the interior. Free water chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 23 which passes thus into a ship must considerably affect her behaviour in a seaway, although it may not jeopardize her safety : this case is considered in Chapter VI. Turning next to the case of the ship of which the skin is pene- trated below water, it is needless to cite examples of the possibly serious nature of such an accident. Very many illustrations will at FIG. 14. Main Deck a e & W I h L ~£omr>~I)eek \r f 111 £ ' ) f' A once occur to the mind of every reader, this being a very common source of loss now that iron or steel is generally used in building merchant ships. The causes of under-water damage may be various — such as accidental collision, local wear and tear, grounding, ram- ming, torpedo explosions, etc. — but in all cases water can enter the ship, and this water remains in free convm/mication with the water outside. So long as that communication is maintained, water will FIG. 15. m Detik a, e A I ■ ■! » Wr .-fmz=?^ff lower JJeeJr fcr=^ __ -J Hi a continue to pass into the ship until it can find access to no further space. If the water enters in such quantities as to exceed the reserve of buoyancy, the vessel sinks. A simple illustration will render these statements clear. Take a box-shaped vessel, such as in Eigs. 14 and 15, and suppose a hole to be broken through the skin under water. The water at once passes into the interior in quantities depending upon the area of the 24 NAVAL ARCHITECTURE. [chap. i. hole and the depth it is below the water-level. A simple rule approximately expresses the initial rate of inflow. Let A = area of the hole (in square feet). ., d = the depth below water in feet (taken about the centre of the hole will be near enough for practical purposes). Then, if v = velocity of inflow of the water in feet per second ■y 2 = 64d (approximately) ; and v = Sy/d ; so that, immediately after an accident, the volume of water passing into the vessel in each second = Sy/d X A (cubic feet). Suppose, for example, the hole is 2 square feet in area, and has its centre 12 feet under water : v = 8\/l2 = 27| feet per second. Water flowing in per second = 27| x 2 = 55J cubic feet. If the vessel floats in sea-water — Tons of water flowing in per second = 55J -f- 35 = T58. Similarly, for any other depth or area of hole in the bottom of a ship, this rule will enable the rate of inflow to be determined very nearly. Reverting to Fig. 14, it is obvious that, if the water can find free access to every part of the interior — which would be true if there were no partitions forming watertight compartments — the ship must sink : unless the power of her pumps is sufficient to overcome the leak ; or some means is devised for checking the inflow, by employ- ing a sail, or a mat, or some other " leak-stopper ; " or the total unoccupied space in the interior is less than the reserve of buoyancy, a condition not commonly fulfilled. A consideration of the preced- ing formula for the rate of inflow will show that it is hopeless to look alone to the pumps to overcome leaks that may be caused by grounding, collision, ram attacks, or torpedo explosions ; the area of the holes broken in the skin admitting quantities of water far too large to be thus dealt with.* Hence attention is directed to two other means of safety : the first, minute watertight subdivision of the interior of the ship, to limit the space to which water can find access ; the second, the employment of leak-stoppers, which can be hauled over the damaged part, and made to stop or greatly reduce the rate of inflow. This latter is a very old remedy, Captain Cook having used a sail as a leak-stopper during his voyages, and many ships having * For a full discussion of this point the author to the Journal of the Royal see a paper " On the Pumping Arrange- United Service Institution (1881). ments of War Ships," contributed by chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 25 been saved by similar means. It has acquired renewed importance of late, and various inventors have proposed modifications of the original plan, but all these are based upon the old principle of " stopping " the leak. Such devices are not embodied in the structure or design of ships, but form simply part of their equip- ment ; whereas watertight subdivision is a prominent feature in the structure of a properly constructed modern iron or steel ship. It will be well, therefore, to sketch some of its leading principles. In doing so, we shall, for the sake of simplicity, make use of box-shaped vessels for purposes of illustration; but the conclusions arrived at will, in principle, be equally applicable to less simple forms, like those of ships. Systems of Watertight Subdivision. — There are three main systems of watertight subdivision : (1) by vertical athwartship bulkheads ; (2) by longitudinal bulkheads ; (3) by horizontal decks or platforms. Besides these there is the very important feature of construction known as the " double bottom," the uses of which will be described further on. In Figs. 14 and 15 the hole in the skin, admitting water to the hold, is supposed to lie between two transverse bulk- heads (marked ab and ce) which cross the ship and form watertight partitions rising to some height above the load-draught line (WL) and terminating at a deck marked " Main Deck." The great use of these bulkheads will be seen if attention is turned to Fig. 15, which represents the condition of the box-shaped vessel after her side has been broken through. The vessel has sunk deeper in the water than when her side was intact ; and it is easy to determine what the increase in draught has been when one knows the volume (fgeb, in Fig. 14) of the damaged compartment, as well as the volume in that space which is occupied by cargo, or machinery, or other substances. To simplify matters, suppose this compartment to be empty ; and assume the length ac to be one-seventh of the total length AA : then the volume fgeb will be about one-seventh of the total dis- placement ; and when this compartment is bilged and filled with water up to the height of the original water-line WL, one-seventh of the original buoyancy will be lost. In fact, the compartment between the bulkheads no longer displaces water ; in it the water- level will stand at the height of the surface of the surrounding water ; and since the weight of the ship remains constant, the lost buoyancy must be supplied by the parts of the ship lying before and abaft the damaged compartment. For this reason we must have — f original water-line area X increase in draught = } X displacement = } X original water-line area x original draught. Increase in draught = \ original draught. 26 NAVAL ARCHITECTURE. [CHAP. I. This very simple example has been worked out in detail because it illustrates the general case for ship-shape forms. The steps in any case are — (1) The estimate of loss of buoyancy due to water entering a compartment ; this loss being equal to the part of the original displacement which the damaged compartment contributed, less the volume in the compartment occupied by cargo, etc. (2) The estimate of the increased draught which would enable the still buoyant portions of the vessel to restore the lost buoyancy if the entry of water were confined to the damaged compartment. And to these, in practice, must be added — (3) The change of trim (if any) resulting from filling the damaged compartment. Eeverting to Figs. 14 and 15, it will be obvious that, if the transverse bulkheads ah and ce did not rise above the original water- line WL, more than one-sixth of the original draught, they would be useless as watertight partitions (unless the deck at which the bulkheads end forms a watertight cover to the compartment) ; because, when the compartment was bilged, their tops would be under water before the increase of draught had sufficed to restore the lost buoyancy. And when their tops are under water, the water is free to pass over the tops, or through hatchways and openings in the deck, into the adjacent compartments, thus depriving them also of buoyancy, and reducing the ship to a condition but little better than if she had no watertight partitions in the hold. Fig. 16 FIG. 16. illustrates this serious defect. The main deck at which the trans- verse bulkheads ab and ce end is lower than in Figs. 14 and 15, all other conditions remaining unchanged ; and consequently, when the compartment is bilged, the water can pour over the tops of the bulkheads into the spaces before and abaft. Hence this practical deduction. Watertight transverse bulk- heads can only be efficient safeguards against foundering when care chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 27 is taken to proportion the heights of their tops above the normal load-line to the volumes of the compartments, allowing for spaces occupied by cargo, stores, propelling apparatus, etc. ; or else to make special provisions for preventing water from passing into adjacent compartments by means of watertight plating on the decks at which the bulkheads end, in association with watertight covers or casings to all hatchways and openings in the decks. The midship compartments of a ship are usually the largest, and claim most attention; but those near the extremities are also important, because, although their volume may be small, when they are filled they cause a considerable change of trim. Eeverting once more to our box-shaped vessel in Fig. 14, instead of supposing an empty midship compartment equal to one-seventh of the length to be filled, and to cause a loss of one-seventh of the buoyancy, let it be supposed that a compartment only half as long and half as large at one end (shown by m&LA in the diagram) is filled. The increase in the mean draught due to this accident would be only one- thirteenth of the original draught, but the trim would be altered very considerably (as shown in Fig. 17) ; and the top of the bulk- FIG. 17 Jt t- - 2s ^3ejr = =j||ifi head hhm, although as high as those amidships, would be put under water by the change of trim. Consequently, unless the main deck is made watertight as far aft as the bulkhead hm, this very small compartment forward might, from its influence on the trim, be large enough to sink the ship ; for when it is filled, if the deck does not form a watertight top to it, the water will pass over (at h) into the next compartment, the bow will gradually settle deeper and deeper, and at last the vessel will go down by the head. It will be in the recollection of many readers that ships which founder very commonly settle down finally either by the head or the stern, and the foregoing 28 NAVAL ARCHITECTURE. [chap. i. simple illustration will furnish an explanation of some such occurrences. It should be added that the assumptions made in the box-shaped vessel are fairly representative of actual ships. For example, in her Majesty's ship -Devastation, if one of the large compartments amid- ships were filled, the ship would have an increased draught of about 15 or 16 inches, and her trim would be practically unaltered. If the aftermost compartments were filled, so as to give the ship an increase of 7 or 8 inches in the mean draught, the trim would be changed from 4£ to 5 feet, and the tops of the bulkheads bounding these extreme compartments would be put under water. No evil would result, however, for these bulkheads are ended at a watertight iron deck. Passing from transverse to longitudinal bulkheads, the same prin- ciples apply. The heights to which the bulkheads are carried should be carefully proportioned to the sizes of the compartments of which the bulkheads form boundaries ; and watertight decks are no less useful as tops to such compartments when the bulkheads cannot be carried high enough to secure the restoration of the lost buoyancy. In this case, however, the longitudinal partitions, supposing only one side of the ship to be damaged, destroy the symmetry of the true " displacement," and the result is that the vessel heels over towards the damaged side. Transverse inclination takes place without change of trim if the damaged compartment is amidships ; but if it be near the bow or stern, both change of trim and transverse inclination will result from the same accident. It is needless to do more than deal with the latter, as the influence of change of trim has already been described; and in this case the box-shaped vessel will once more furnish a simple illustration of what may happen in ships. In Fig. 18, suppose the large midship compartment bounded by transverse bulkheads, ab and ce (in profile view), to be subdivided by longitudinal bulkheads, pq, rs (in section) ; in the positions shown, these longitudinal bulkheads fairly represent the coal-bunker bulk- heads of an ironclad, being rather less than one-fourth of the breadth of the ship within the side. The " wing compartment " lying out- side the bulkhead, marked rs in section, and rr in plan, Fig. 18, may be supposed to contain three-sixteenths of the total volume of the compartment between the transverse bulkheads ab and ce ; reckoning up to the load-line WL, this will give — Loss of buoyancy when wing^ compartment is filled with 1= ^ x | total displacement water J = r | j total displacement. Increase in mean draught = T fa original draught. CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 29 But this will be accompanied by a heel towards the damaged side, as indicated in the lower section (Fig. 18), amounting, in the FIG. 18. Section Profile H/lkm, Deck 'Main. Deck W Lower Deck $- r Section eefter accident. Flam, rv- example chosen, to the immersion of the damaged side to about four times the extent of the increased mean draught due to loss of buoyancy. Hence it is clear that, in arranging longitudinal bulk- heads, care must be taken either to carry them high enough to provide against heeling, or else to have watertight plating forming a top to the compartments. The amount of heel which may be produced by filling compartments bounded by such bulkheads must also be considered in connection with calculations of stability. Lastly, attention must be directed to the usefulness of horizontal watertight decks or platforms in preventing loss of buoyancy. It is unnecessary to repeat what has been said respecting decks lying- above the normal load-draught line, and forming tops to spaces enclosed by longitudinal or transverse bulkheads ; consequently atten- tion will be confined to the cases where a deck or platform lies below the load-line. In such cases either one of two accidents may be assumed to have happened : viz. the side has been broken through below the platform, or else above it. Turning to Fig. 19, let it be supposed that the large midship compartment bounded by the transverse bulkheads db and ce has a watertight platform pq worked in it, at mid-draught. The volume of this compartment up to the load-line being one-seventh of the displacement, the buoyancy con- tributed by either of the parts into which it is divided by the plat- form will be one-fourteenth the displacement. If the side is broken 3Q NAVAL ARCHITECTURE. [chap. i. through below the platform, the whole of the water-line area WL contributes buoyancy when the vessel is immersed more deeply ; FIG. 19. Morn, Beck a e w ■ ........ Jl & i — L i i i T \ A therefore, if the whole space is considered accessible to water (as shown in Fig. 20) — FIG. 20. Increase in mean draught due to ~i . . bilging compartment below n \ = h™%™& draught. But if the side is broken through above the platform, only -fi the water-line area contributes buoyancy; therefore (as shown in Fig. 21)— FIG. 21. Main Beck '~W= -f f- CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 3 I Increase in mean draught due to } bilging compartment above pq ) =A ori ginal draught. This contrast shows how important a thing it is to take all pos- sible measures to maintain the buoyancy of the ship at the load-line • for any decrease of that buoyancy not merely affects the draught of water, but also decreases the stability of a ship, as will be shown hereafter. It may be added that, in all cases where openings have to be made in a watertight deck or platform, either watertight covers must be fitted to the openings ; or water-tight trunks, carried to a sufficient height above the load-line, must be built around them. Watertight Subdivision in War-ships. — All the methods of water- tight subdivision illustrated above are associated in war-ships ; and the minuteness of subdivision attained when care is taken is well exemplified in Figs. 22-29, which represent the arrangements of the water-tight partitions in a modern ironclad of the Koyal Navy. Such vessels have the great safeguard of a " double bottom," formed by a watertight inner skin fitted some distance within the outer skin. This inner skin extends from two-thirds to three-fourths of the total length of the ship ; its terminations are marked c c in the profile view (Fig. 22), and the " plan of double bottom " (Fig. 24). From the keel up to the turn of the bilge, the inner skin is worked about 3 or 4 feet within the outer, as shown in the sections (Figs. 25-29), from the points a downwards. At a there is a watertight longitudinal partition (or frame), and the keel is also made water- tight. Above the turn of the bilge, the inner skin (w, w in the sections) is usually worked vertically up to the height of the main- deck, thus enclosing " wing-spaces " in the region of the water-line, or, as it is termed, " between wind and water." The inner skin is here often 8 or 10 feet within the outer. In addition to the longi- tudinal partitions at the bilges (a, in sections) and at the keel, the double bottom is subdivided by numerous watertight transverse par- titions (shown by // in Fig. 24), about 20 feet apart ; compartments, of very moderate size, being thus formed between the two skins. Within the limits of the double bottom, the hold-space is sub- divided by means of transverse bulkheads (b b, Fig. 22), and longi- tudinal bulkheads (I I, Fig. 23). Before and abaft the double bottom there is only a single skin, and the subdivision is effected by means of transverse bulkheads and horizontal platforms (p p, Fig. 22) Although there is no inner skin at the extremities, the subdivision there is very minute, and the compartments are small owing to the fineness of form of the bow and stern. The " plan of hold " in Fig. 23, taken in connection with the profile (Fig. 22), will give a very complete view of the subdivision of the hold-space. Besides the main partitions already alluded to, it will be observed that, in NAVAL ARCHITECTURE. [CHAP. I. many cases, partitions required primarily for purposes of stowage or convenience are made watertight in order to make the subdivision (N A ° // \ U. /I Yv II «j \\ r r U k ^ v ^ •s •*» "K H, •s I * II \ W 1 more minute. Examples will be found in the coal-bunker bulkheads, the chain-lockers (immediately before the boiler-rooms), the maga- zines and shell-rooms, and the shaft-passages. Slight increase of CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 33 cost and workmanship, with a very small increase in weight, are thus made to contribute to much greater safety. It will be noted that the principal bulkheads either run up to the main-deck, situated some 5 or 6 feet above water, or are ended at a watertight platform. The spaces occupied by the machinery almost necessarily form large compartments amidships; but in recent war-ships the stoke- holds have each been divided into two by means of a middle-line bulkhead (I I in Fig. 23) ; and in vessels propelled by twin-screws, as is the case in our example, the engine-room compartment is similarly halved. The great advantages resulting from this middle- line division are too obvious to need comment, especially in ships which are mainly or wholly dependent upon steam power for propulsion, and exposed to damage under water by shot or shell, ramming, and torpedo explosions. ■* The following table gives the number of compartments in several important ships of the Eoyal Navy : — Armoured ships of Eoyal Navy. Watertight compartments. Classes. Names. In hold- space. In double bottom and wings. Total. Largest early J types 1 Smaller early ( types \ Largest I rigged types \ Smaller ( masted types \ Belted ships { Sea-going J battle-ships I (no sails) 1 Bams { Monitors j Warrior Achilles Minotaur Hector . Besistance Monarch Hercules Sultan . Alexandra . Temeraire Invincible Triumph Shannon Nelson . Devastation . Dreadnought Inflexible Royal Sovereign . Hotspur Bwpert . Gorgon . Glatton 35 40 40 41 47 33 21 27 41 44 23 26 44 83 68 61 89 90 26 40 19 37 57 66 49 52 45 40 40 40 74 40 40 40 32 16 36 40 46 55 32 40 20 60 92 106 89 93 92 73 61 67 115 84 63 66 76 99 104 101 135 145 58 80 39 97 34 NA VAL ARCHITECTURE. [chap. i. The Devastation, as originally built, may be taken as a good example of a modern war-ship, although she had no middle-line bulkhead in her engine and boiler rooms. Her double bottom and wings were divided into thirty -six compartments; the hold-space into sixty-eight compartments. If the three largest compartments of the hold (viz. the engine and boiler rooms) were filled, the vessel would only be immersed about 3f feet. With a middle-line bulk- head, like the later ships, each of these large compartments would be halved, and it would be improbable that both halves of any compartment would be filled simultaneously. The total number of compartments in the hold would then be seventy-one, and filling any six compartments amidships would immerse the vessel as before. The largest compartment in the double bottom holds only about fifty tons of water, corresponding to an increased immersion of only 1£ inch ; and the whole double bottom space will carry 1000 tons of water-ballast, the additional immersion being 28 inches. Similar watertight subdivision is carried out in the unannoured war-ships of the Eoyal Navy having iron or steel hulls ; and to some extent it is applied also in composite ships. The Iris steel despatch vessel, for example, is built in sixty-one separate compartments ; the Edgar class of cruiser in 140 compartments. In foreign war-ships of recent design the same principles have been applied, and in some instances carried even further than in English ships. For instance, the large armoured frigate Admiral Duperre, of the French Navy, is said to have nearly two hundred separate compartments ; and it would appear that equally minute subdivision has been secured in the large Italian ships Italia and Lepanto. Nor are unarmoured ships exceptions to the prevalent foreign practice. In Figs. 22-29 the double-bottom arrangements of war-ships are illustrated. Double bottoms are advantageous (1) as a means of safety, (2) as a source of economy when fitted to carry water-ballast, (3) as an efficient arrangement of the thin materials in the lower part of the structure, enabling them to resist longitudinal strains. The last-mentioned feature is discussed in Chapter IX. ; respecting the other two a few remarks may be added. The lower part of any ship is most liable to injury by touching the ground, the thin bottoms of iron or steel ships being peculiarly liable to serious damage. If there be an inner skin, however, and the damage does not extend to it, fracture of the outer skin may be very extensive, but no water will enter the hold. Very many cases are on record, showing the great usefulness of the inner skin ; two only will be mentioned. The first is that of the Great Eastern, which had a complete double bottom. Off the American coast the vessel ran ashore, and tore a hole 80 feet long in her outer, skin, but the inner skin remained intact, and no chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 35 water entered the hold. The second is that of her Majesty's ship Agincourt, which ran on the Pearl Eock at Gibraltar ; this ship has a partial double bottom, and fortunately grounded at a part where the inner skin existed, so that no serious consequences followed. Considerations of safety and structural strength chiefly influence the adoption of double bottoms in war-ships : their use as receptacles for water-ballast is unfrequent, although they are generally arranged for such use when required, and often used to carry fresh water for use in the boilers. In merchant ships, however, the chief induce- ments to use double bottoms have been found in the commercial advantages of water-ballast. Instead of having to incur delays and considerable expense in shipping and discharging rubble-ballast, the commander of a ship fitted for water-ballast can readily admit or discharge such ballast. In some trades the consequent gains are greater than in others, but it is now generally agreed that the balance of advantage is in favour of ships built with improved forms of double bottom. The older forms of water-ballast tanks ; used before the adoption of the cellular system were objectionable in some respects, raising the cargoes high in the ships, and decreasing the space available for stowage ; yet the experience gained with these imperfect arrangements has largely influenced subsequent practice.* The parts of the inner bottom situated above the bilges in war- ships (see sections in Figs. 25-29) are often termed "wing-passage bulkheads," and are so far inside the outer skin that they can only be broken through by heavy blows on the side. It is at this part that the greatest damage is likely to be done by ramming or torpedo explosions ; and the best known remedy against either is undoubtedly internal subdivision. To attempt to keep out either a ram or a torpedo attack is hopeless ; the outer skin is certain to be broken through and possibly the inner also. But whereas a grazing blow at low speed would suffice to tear a large hole in the outer skin, only the direct blow of a ram moving at good speed would be likely to penetrate the inner skin of an armoured ship. An illustration of the usefulness of the wing-passage bulkhead against ramming or collision was afforded in the accidental collision of the Minotaur and Bellerophon ; the outer skin of the Bellerophon was broken, and the armour driven in, but the ship remained on service for some time before the repairs were completed. Again, when the Hercules and Northumberland came into collision, a very similar advantage resulted from the existence of the wing-passage in the latter ship. In the case of the Vanguard, although the vessel * See a valuable paper " On Water- to Lloyd's Register), in Transactions of Ballast," by Mr. Martell (chief surveyor Institution of Naval Architects for 1877. 36 NAVAL ARCHITECTURE. [CHAP. I. was lost, the existence of the inner skin was an immense advantage to the ship, keeping her afloat for seventy minutes after the collision, whereas, had there been no inner skin, the vessel must have sunk in a very few minutes. So much misapprehension has existed on this matter that it may be well to adduce a few facts in support of the foregoing statement. Fig. 30 shows a cross-section of the Vanguard, with the bow of the Iron Duke in the position which it probably occupied at the time of the collision. It will be noted that, although the armour was driven in, and the armour shelf (a) damaged, the inner skin (s) was not pierced. This the divers asserted after careful examination, and there is conclusive corroborative evidence that their report is correct. Evidence given before the court-martial proves that at first the vessel sank at the rate of only 8 inches in fifteen minutes, and at last at the rate of 1 inch per minute ; this maximum rate of sinking corresponds to a total inflow of only 27 tons of water per minute, which would have been admitted by an CHAP. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 37 aperture less than one square foot in area. But the divers, after measurement, reported that the hole in the outer skin was 10 feet in depth, varying in breadth from 2 feet to 3 feet. Assuming the area to have been 20 square feet (which is probably less than the truth), the initial rate of inflow of water per minute, had there been no inner skin, would probably have been at least 1000 tons, or nearly fortyfold what it actually was at the last. It seems certain, there- fore, that the damage to the armour shelf, and other parts of the ship, admitted into the hold in the aggregate no more water than a hole one square foot in area in the skin of an ordinary ship with no double bottom would have admitted, notwithstanding the fact that the Iron Duke struck the Vanguard, a blow much exceeding in force that delivered by the projectile of a 35-ton muzzle-loading gun. It is noteworthy also (see Fig. 30, and the sections in Figs. 25-29), that in the Vanguard the inner skin terminated about 4 feet under water, whereas in most of her Majesty's ships it is carried to the main deck, several feet above water — a preferable arrangement. Even her loss supplied, therefore, a most striking example of the utility of watertight subdivision, for she was kept afloat more than an hour by this means, instead of foundering in a very few minutes, as an ordinary iron ship similarly damaged in the outer skin must have done. This case also illustrated the necessity for taking all possible care in maintaining the integrity of bulkheads and other partitions intended to be watertight, as well as for keeping in thorough working order the doors or covers fitted to any apertures cut in bulkheads or platforms for ventilation or for convenient access to compartments in the hold. The more recent case of the Grosser Kurfurst has been treated, by some writers, as a proof of the small value attaching to watertight subdivision. This vessel sank in less than ten minutes after her collision with the Konig Wilhelm, notwithstanding the fact that she was extensively subdivided. The circumstances of Jher loss are well known. She was proceeding in company with her consorts, with watertight doors open in bulkheads and no precautions taken to provide for rapidly closing the doors, such as would have been taken in action. In the endeavour to cross the bows of the Konig Wilhelm, when a collision seemed imminent, the Grosser Kurfurst was driven at nearly full speed ; and this rapid motion aggravated greatly the injury consequent upon the entry of the spur of the Konig Wilhelm into her side, the skin-plating being torn away for a considerable distance. The access of water to the hold-space was thus made easy, and the ship sank rapidly. Possibly the damage done might have caused her to founder had all possible precautions been taken— doors closed and all watertight partitions secured. But it is clearly 38 NA VAL ARCHITECTURE. [chap. i. unfair to omit consideration of the exceptional circumstances above- mentioned, or to depreciate the value of watertight subdivision because the Vanguard and Grosser Kurfurst were sunk. On the other side, numerous cases can be mentioned in which ships, which would otherwise have foundered, have been kept afloat by their watertight bulkheads. It cannot be claimed for the most minutely subdivided war-ship that she is absolutely unshakable. Comparatively large spaces have to be provided for engines, boilers, and equipment ; and this puts a practical limit on the minuteness of watertight subdivision. More- over, the damage inflicted by ramming or torpedo attacks may be so extensive as to throw several compartments open to the sea simultaneously. On the other hand, the chances of escape are obviously increased, as the subdivision is made more thorough. If the primary consideration in the design of a ship were to make her as nearly as possible unsinkable, it would clearly be desirable to associate extensive subdivision into watertight compartments with the use of cork, or other packing materials of small specific gravity. By this means, if there were no limitations of size or cost, it might be possible to produce a vessel which could sustain a very consider- able amount of damage before it ceased to be buoyant. The internal spaces to which water could find access would, in the aggregate, bear a small proportion to the reserve of buoyancy ; and when damaged the condition of the vessel would resemble that of a water-logged timber-laden ship. The drawbacks to this system are great; size, cost, and propulsive power would all require great increase, and it is scarcely probable that the plan will ever find favour, except on a limited scale. The system is applied, to some extent, in lifeboats, and to certain limited portions in special classes of war-ships, wherein the whole or a portion of the length is protected by a strong deck. For example, in the Inflexible and other " central-citadel " ships of the Eoyal Navy, cork packing and extensive watertight subdivision are adopted before and abaft the citadel and above the under-water armour deck. Similar methods have been used in vessels designed for torpedo service in foreign navies. In the Italian ships Italia and Lepanto, which are protected below water by strong decks, extremely minute watertight subdivision of the Mater-line region above those decks is trusted to preserve the buoyancy and stability. In some protected cruisers, water-excluding materials (cork, cellu- lose, etc.), have been fitted along the sides in the region of the water-line for the purpose of maintaining buoyancy and stability, or assisting in stopping the inflow of water through shot-holes. Sug- gestions have also been made to construct horizontal decks at a moderate distance under water, and to attach to the upper surfaces chap, i.] DISPLACEMENT AND BUOYANCY OF SHIPS. 39 a considerable thickness of light buoyant material. As a rule, however, such special arrangements for excluding water are not adopted in warships. In the Polyphemus, of the Eoyal Navy, a different system is applied; the hold-space is very minutely sub- divided, and any loss of buoyancy which may occur in action can be met, either wholly or partially, by letting go iron ballast carried for that purpose. The reserve of buoyancy in this vessel is small, if measured in the manner described on p. 9; but the detachable ballast represents a further reserve of about 10 per cent, of the displacement. Watertight Subdivision in Merchant Ships. — The principles of watertight subdivision above described apply to merchant ships as well as to war-ships. In merchant ships, however, facilities for the stowage and working of cargoes as a rule exercise great influence upon the extent to which subdivision is adopted. Except in passenger steamers carrying relatively small cargoes, it is usually considered that spacious, easily accessible holds, are essential to successful working. Consequently the increase of safety admittedly attainable by the multiplication of watertight partitions has been subordinated in most iron and steel cargo-carriers to considerations of stowage. In certain special trades, for many years past, extensive subdivision has been practised. It has been maintained also by some authorities that in general trades the subdivision of holds does not prejudicially affect commercial success ; but the balance of opinion lies, at present, on the opposite side. The value of water- tight subdivision has, however, been increasingly recognized of late in merchant-ship construction. Various causes have contributed to this result. One which deserves mention is the action taken by the Admiralty from 1875 to 1886 in forming an official list of merchant steamers suitable for state purposes, and making a certain degree of subdivision essential to entry on that list. The condition laid down was that every ship should be so divided as to remain afloat in moderate weather with any one compartment thrown open to the sea ; proper allowance being made for the space occupied by cargo, and for the load-draught of the ship. At first this very moderate condition was not fulfilled in many vessels. By modifi- cations in existing ships and improved arrangements in new ships, the number of vessels qualified for admission became very large, including many cargo-carriers. Passenger-steamers were readily brought into the qualified class, and in a large proportion of the largest and swiftest vessels on the Admiralty list, the extent of subdivision suffices to keep them afloat with any two compartments thrown open to the sea. Since 1887 the earlier official list has not been continued, the Admiralty having instituted a system of sub- 40 NAVAL ARCHITECTURE. [chap. l - vention for the largest and swiftest mail steamers, with a view to their employment as auxiliary armed cruisers. The condition of efficient subdivision remains in force. For merchant ships generally there is no legal enforcement of watertight subdivision with iron or steel hulls. Prior to 1862 there were legal conditions. All iron steamers were required to have watertight bulkheads enclosing the engine-rooms ; in other words, two bulkheads were essential. In 1854 it was provided that these two bulkheads should be made to divide ships into three parts, approximately equal to one another, or as nearly so as possible. A small watertight compartment was also made essential at the after end of the shaft in screw steamers. For passenger steamers at the present time, Board-of-Trade surveyors are instructed to insist on a collision bulkhead forward, an after watertight compart- ment in screw steamers, and the watertightness of the shaft tunnels. If more bulkheads are fitted, their condition and that of any water- tight doors has to be ascertained. The officials of the Board of Trade have been strong supporters of the view that efficient water- tight subdivision is of supreme value as a means of saving life and property at sea.* The department has, however, hitherto maintained the position that shipowners should deal with this matter inde- pendently, or nearly so, of legal or official restrictions. The registration societies, while encouraging subdivision, and recording in their registers the number of bulkheads actually fitted in ships, have not insisted on the maintenance of flotation with any specified number of compartments thrown open to the sea. Lloyd's rules at present provide that all ships shall have a collision bulk- head near the bow. This is the only bulkhead required by the rules in iron or steel sailing ships. In all steamers the machinery- space has to be enclosed by bulkheads ; and a fourth bulkhead has to be built at a reasonable distance from the stern. In steamers 280 feet in length and above, the fore-hold has to be further sub- divided by another bulkhead ; and for lengths of 330 feet and above, the after hold has to be similarly subdivided. Regulations are also laid down for the heights to which the bulkheads must be carried, and for their structural arrangements. These rules are obviously framed with reference to the provision of roomy holds, facilitating the stowage and working of cargo. The rules of the Bureau Veritas give 90 feet as the length of hold it is undesirable to exceed in any one compartment, except in vessels built to carry special cargoes of unusual length. They also recommend, but do not make obligatory, * See, inter alia, the Report of Evidence taken by a Parliamentary Committee on Saving Life at Sea, C. 249, 1887. chap. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 4 1 such a spacing of bulkheads as would enable ships to keep afloat with any one hold flooded. The Council of the Institution of Naval Architects, in 1867, proposed, as a standard of efficient subdivision for merchant ships, that they should be able to keep afloat with any two compartments laid open to the sea. The Committee of 1889 on Life-saving Appliances endorsed this standard for the highest class of ships; and so did the Committee on Bulkheads appointed by the Board of Trade, whose report was presented to Parliament in 1891.* Although this subdivision goes far beyond common practice, it is much inferior to that of war-ships, in which from three to six of the largest compartments may be filled simultaneously without bringing the tops of the bulkheads under water, or allowing water to pass into compartments adjacent to those filled. The inquiry of the Bulkheads Committee (1890-91) is the most important step taken since iron and steel merchant ships came into use, with a view to placing on a sound and scientific basis the important questions of " the spacing and construction of watertight " bulkheads in ships of the mercantile marine." The committee had regard to the exigencies of trade in various classes of ships, as well as to the provision of safety from foundering. They reported that a careful classification of ships was necessary ; and a graduated system of subdivision in ships of different sizes and types. The highest standard of subdivision — flotation with two compartments bilged — they reserved for first-class ocean passenger steamers not less than 425 feet in length, and cross-channel passenger steamers. Passenger steamers from 350 feet to 425 feet in length they con- sidered should be made capable of floating in moderate weather, with any two adjoining fore-body compartments, or any one after- body compartment, in free communication with the sea. Passenger steamers 300 to 350 feet in length should keep afloat with any two of the three foremost compartments, or with any one of the other compartments, in free communication with the sea. For passenger steamers less than 300 feet in length, and for sailing ships irrespective of length, carrying more than one passenger per 33 tons of registered tonnage, the subdivision recommended is identical with the preceding grade; except that the two foremost compartments are named instead of any two of the three foremost compartments. Cargo-steamers and sailing ships are still more leniently treated. The old Admiralty condition of floating with any one compartment bilged is recommended for steamers not less than 300 feet, and sailing ships not less than 275 feet, in length. For * See Parliamentary Papers, C. 5762-89 ; C. 6405-91. 42 NAVAL ARCHITECTURE. [chap. I. smaller vessels, any one compartment in the fore-body is substituted for any one compartment. Omitting the last grade, including cargo-steamers from 260 to 300 feet in length, and sailing ships from 225 to 275 feet in length, the committee's recommendations, therefore, take as a minimum of subdivision the old Admiralty condition, and rise by easy stages to the condition of floating with any two compartments bilged. In other words, they confirm the view that, except in the smallest classes of ocean-going cargo-carriers, the requirements of trade are not hampered unduly by the condition that ships shall be made capable of keeping afloat with any one compartment bilged ; whereas in passenger-steamers of the highest class twice that degree of sub- division is considered reasonable. These conclusions and recommendations cannot but have great weight on future practice, even if they receive no legal sanction. They indicate a considerable advance in the appreciation of the importance of subdivision amongst shipowners. Furthermore, they emphasize a principle often previously enunciated, viz. that it is proper to make fuller provision for safety in vessels carrying pas- sengers than can be accepted in cargo-carriers. Exception may be taken to details in the scheme proposed by the committee, but its main features will doubtless eventually command general approval. A powerful incentive to more extensive subdivision is now to be found in the fact that the Board of Trade permits a very great reduction in the outfit of boats and life-saving appliances in well- subdivided vessels, as compared with what is required (under the Life-Saving Appliances Act of 1889) in iron or steel vessels of ordinary construction. From what has been said on p. 13, it will be obvious that the legislation of 1890 on the load-line question, fixing a maximum draught for every British merchant vessel above 80 tons, will enable the subject of spacing bulkheads to be dealt with in a more exact fashion. This spacing also requires some assumption to be made as to the densities of cargoes carried, and the spaces occupied by them, when a ship is floating at her load-line. On successive voyages a cargo-steamer, for example, may carry widely differing cargoes. After full consideration, the Committee on Bulkheads recommended that coal, occupying 47 cubic feet per ton, should be taken as the standard cargo, and they assumed that with such a cargo water could find access to 40 per cent, of the hold-space occupied by the coal. The committee further pointed out that if bulkheads were so closely spaced as to provide for keeping ships afloat with very heavy cargoes, such as iron, the holds would be made too short for general trade. Tables are given in the Appendix to the Eeport, enabling the bulk- chap. I.] DISPLACEMENT AND BUOYANCY OF SHIPS. 43 head spacing to be determined approximately in various classes of ships, so as to fulfil the conditions laid down. These tables are likely to be of much assistance to designers of merchant ships ; but the process of direct calculation is very simple, and is already fre- quently applied in determining the positions of bulkheads, so as to estimate " sinkage " or " change of trim," with cargoes of different densities in the holds, when selected compartments are assumed to be laid open to the sea. In merchant ships transverse watertight bulkheads naturally form the most convenient partitions. Deck-plating also, in many instances, is made to assist subdivision, particularly where necessities for accom- modation in passenger-steamers cause the upper portion of a bulk- head to be carried up at some distance before or abaft the lower portion. Shaft-tunnels in screw steamers are always formed into watertight compartments. Longitudinal bulkheads are not common. They are fitted in the engine-room of some of the largest twin-screw steamers. Cellular double bottoms are very largely adopted, primarily for water-ballast, although they add greatly to safety. As a rule this cellular construction ceases at the bilges. In some cases, however, coal-bunkers are formed at the sides of boiler-rooms, and the bulkheads made watertight. There is not the same definite assignment of hold-spaces for purposes of stowage in merchant ships as in war-ships ; consequently the formation of subsidiary compart- ments in the hold — corresponding to the magazines, shell-rooms, store-rooms, etc., of a war-ship — is not possible in merchant ships. Outside the machinery and boiler compartments, the only subdivision of the hold is usually effected by transverse bulkheads, the inter- mediate spaces being kept free for stowage of cargo. This circumstance makes the provision of adequate strength in the bulkheads of merchant ships a matter of greater difficulty than the corresponding provision in war-ships, where the transverse bulk- heads are succoured and supported by longitudinal bulkheads, plat- forms, decks, etc., abutting against them or carried through them. It is essential to effective subdivision that all partitions, in all classes of ships, shall be sufficiently strong to bear the stresses brought upon them when compartments are in free communication with the sea. The Bulkhead Committee deal with this branch of the subject very thoroughly. Efficiency of subdivision also requires, as above mentioned, that all watertight doors or covers in partitions shall be kept in good order and be perfectly under control. Many trials have been made of plans for dispensing with such doors low down in ships, and maintaining the integrity of bulkheads. Experience has been adverse, however, to this method. In ships originally so constructed 44 NA VAL ARCHITECTURE. [chap. i. doors have subsequently been formed, the requirements of super- vision and ready communication in the engine and boiler rooms having necessitated this change. The drill in war-ships makes the rapid closing of watertight doors in case of accident or emergency a practical certainty ; similar arrangements in merchant ships are obviously desirable, and are recommended by the Bulkhead Com- mittee. ( 45 ) CHAPTEK II. At a very early period trie necessity must have been felt for some mode of measuring the sizes of ships, either for purposes of com- parison, or for estimating the cost of construction, or for determining the carrying capacity, or for computing the various dues and duties from time immemorial levied upon shipping. In some ancient documents statements occur of the "tonnage," or "portage," of ships ; but it is not possible to settle how this tonnage was calculated. The term " tonnage " probably originated in connection with dues levied on ships carrying wine in casks, or " tuns ; " these dues being regulated by the number of tuns carried, and the sizes of ships being roughly measured by the number of tun-casks which could be stowed in their holds. In the fifteenth century, the tun had become a fixed measure of capacity, and the subject of legislation in this country ; and it is interesting to note that in France also the earliest tonnage measurements were similarly connected with the stowage of wine- casks. By an Act of Parliament of 1423, a tun of wine was not to measure less than 252 gallons old English measurement ; but the standard measures of that early period were not very definitely fixed. At a much later date it is on record that two gallons, each accepted as a standard, were found to differ by as much as 18 per cent. Taking the mean of these, a tun of wine would apparently have roughly approximated in weight to a ton of 2240 lbs. avoirdupois. * For fuller information, the follow- Nautical Magazine, 1889-90. ing works may be consulted, to which we " Instructions to Measuring Surveyors are indebted for many of the facts stated of Board of Trade." 1891. in the text : — " Report of Eoyal Commission on Moorsom's "Laws of Tonnage." Tonnage:" Parliamentary Papers, C. London: 1852. 3074 and C. 3074 I. 1881. " Observations respecting admeasure- Memoir by MM. Kiaer and Salves- ment of Tonnage." 1867. sen : prepared for the International Con- " Tonnage, Past and Present : '' gress at Christiania. 1876. 46 NA VAL ARCHITECTURE. [chap. ii. When tonnage measurements were first used for fiscal purposes, ships, according to present standards, were little more than large open boats, undecked except for platforms near the stem and stern. The number of tuns of wine that could be stowed in the hold was, roughly, a measure of the internal capacity ; and the original tonnage was therefore based on capacity, and not dead-weight. For wine- cargoes, capacity and dead-weight were, however, convertible terms. With many other descriptions of cargo the limit of earnings, and the dues levied, must have been fixed by the maximum dead-weight which could be safely carried. For such cargoes the dues, reckoned by weight, were known as " poundage." Some approximate but recognized system of expressing the sizes of ships in tuns clearly existed before any legal enactments of methods of measurement for fiscal purposes. Until 1694 no Act of Parliament enforced a rule for tonnage measurement on English ships, with the exception of " keels " and vessels loading coals on the Tyne and Wear. Yet in statements relating to naval forces, to taxation, and to trade, dating many centuries before the Tonnage Act of 1694, tonnage statistics appear. These early tonnages were probably only rough approximations made in terms of the principal dimensions of the ships, and not according to any established rule. They were usually stated in " round figures ; " and for the earlier ships of the Eoyal Navy, considerable discrepancies appear between the nominal tonnage given for the same ship in different documents. Legal Tonnage of Coal-carrying Vessels. — The earliest English ton- nage law was passed in 1422, and applied exclusively to " keels " used in carrying coals at Newcastle-on-Tyne. Its object was to measure accurately the " portage " of each keel, and to mark that portage on the vessel, so that the king's due of " two pence " per chaldron might be secured. The " chaldron " was a measure of capacity, or " heap measure," and not of weight. With coal-cargoes the two modes of measurement, of course, were convertible; and with the stipulated number of chaldrons on board, any keel would float at a certain draught of water, which could be marked on the stem or stempost. In 1679 another Act was passed, applying the law to the Wear as well as the Tyne, and in 1694 dead-weight was substituted for chaldron-measure. Actual weights of iron or lead were then directed to be put on board each keel, 26£ tons being the maximum load permitted; and the load water-line corresponding was marked with nails on the stem, stern, and each side amidships. An Act of 1775 extended this law to vessels used in loading coal in all ports of the United Kingdom, the vessels coming under the law being limited to harbour or river service, and fairly described as barges rather than seagoing ships. CHAP. II.] THE TONNAGE OF SHIPS. 47 Early Rules for estimating Tonnage. — Apart from legislation, and by gradations of which no sufficient record remains, the necessities of shipowners and shipbuilders led to the gradual acceptance of rules for estimating tonnage in terms of the principal dimensions of ships. Early in the seventeenth century such rules are known to have been in use, and to have been intended to express approximately the maximum dead-weight of the cargoes which could be carried. In 1694 the first Act of Parliament embodying such a rule for English seagoing and coasting ships was passed, but repealed in 1696. It ran as follows : — L = length of keel (so much as she treads on the ground). B = breadth amidships (inboard from plank to plank). D = depth of hold (from plank below keelson to under part of plank of upper deck up to which cargo is stowed). L x B xD Tonnage = — This rule was known to be approximate only, and instructed writers of the period remarked that the displacement of a ship between her light and load lines could be estimated, and would give the true "dead- weight capability." Another Act, passed in 1719-20, was intended to prevent smug- gling of spirits in small vessels of "thirty tons burthen and under ; " and contained a rule for estimating tonnage which differed from that of 1694 chiefly in substituting half the breadth for the measured depth of hold. This assumption of the ratio of depth to beam was probably fairly accurate at the time, but it eventually led to very evil results, which are indicated hereafter. Builders Old Measurement Tonnage.— The next English tonnage law, enacted in 1773, applied to all classes of merchant ships. It continued in force until 1835, and its employment by shipbuilders for their own purposes was common long after it ceased to have legal sanction, while it remained in use as the official mode of measure- ment for ships of the Koyal Navy until 1872. This mode of estimating tonnage is known as " Builder's Old Measurement " (B.O.M.), and closely resembled the rules embodied in the two pre- ceding Acts, being, like them, intended to express approximately the dead-weight capability of ships, that being the basis of tonnage universally regarded as the fairest when the law was passed. Up to that time, also, there is reason to believe that the intention was fairly well fulfilled; but subsequently it was the object of ship- builders and shipowners to increase, as much as possible, the ratio of the dead-weight capability to the legal tonnage, and the empirical 4-8 NA VAL ARCHITECTURE. [chap. ii. character of the rule made this an easy matter. The rule may be briefly stated as follows : — (a) The length was taken on a straight line along the rabbet of the keel of the ship from the back of the main sternpost to a per- pendicular line from the fore part of the main stem, under the bowsprit. Fig. 31 shows this; CA is the perpendicular line, and FIG. 31. AB is the length required. If the ship was afloat when the measure- ments for tonnage were made, the length AB could not be taken ; and to allow for the rake of the sternpost (BE), and the consequent shortening of the keel, as compared with the length along the deck or water-line, a reduction was permitted (by an Act passed in 1786) of 3 inches for every foot of draught of water from the length measured along the water-line from the perpendicular line AC to the back of the sternpost. Long after raking sternposts ceased to be used in war-ships, a deduction continued to be made for the "rake" of a post which was upright, in order to secure a small diminution of the tonnage. By an additional Act, passed in 1819, the length of the engine-room was also deducted in ascertaining the length for tonnage of merchant steamers ; but no similar deduction was made in steamships of war. (b) The breadth was taken from the outside of the outside plank in the broadest part of the ship, exclusive of any additional thick- ness of plunking or doubling strakes that might be wrought at that part. This reduction from the extreme breadth to obtain the " breadth for tonnage " amounted to 10 or 11 inches in large vessels, decreasing to 3 or 4 inches in small vessels ; it expressed the excess in thickness of the "wales," worked in the neighbourhood of the water-line, over the ordinary bottom planking. In iron ships the breadth extreme and breadth for tonnage would usually be identical. (c) From the length obtained as described in (a) was deducted three-fifths of the breadth for tonnage, the remainder being termed the " length for tonnage." This was multiplied by the breadth, and their product by half the breadth, and dividing by 94, the quotient expressed the tonnage — In algebraical language, if L = the measured length along the rabbet of keel ; B = breadth for tonnage — CHAP, n.} THE TONNAGE OF SHIPS. 49 Length for tonnage = (L — f B) ; (L - -p) x B x ~ Tonnage B.O.M.= - . f 94 As an example, take a ship for which L = 200 feet, B = 50 feet ; Tonnage B.O.M.= ^"^ X ^> X 50 ^° 170 x 50 x 25 __„ AAn = ^ = 2260§£ tons. The continued product in the numerator expresses capacity ; and it is prohable, as remarked above, that the divisor 94 was chosen with reference to the carrying power of the ships in tons of dead-weight. The following explanation has been suggested as to the choice of the divisor. In the older classes of sailing ships the length was . commonly about four times the breadth ; consequently the " length "for tonnage " was about 34 times the breadth. The mean draught was about one-half the breadth; and the coefficient of fineness for displacement (see p. 4) was about one-half. Hence it followed that the displacement in cubic feet was not very different from the product — •5 X length x breadth x "5 breadth ; Introducing the value for the length for tonnage stated above, this expression was supposed to resolve itself finally into the approximate equation — Displacement (in cubic feet) = -$2 g x length for tonnage breadth X breadth x — ■- A < .•. Displacement in tons = 3§^o x length for tonnage , breadth X breadth X — x — A The hulls of these vessels are said to have weighed about 40 per cent, of the displacement, 60 per cent, representing the carrying power. Hence — Approximate carrying power > fo tonnage (in tons, dead-weight) j " * X **ov X len g tn tor tonna g e . n . breadth X breadtn x — » — = g\- x length for tonnage breadth X breadth x — x — A which agrees with the B.O.M. rule. This investigation will be seen E 50 NA VAL ARCHITECTURE. [chap. ii. to proceed upon certain fixed proportions of breadth to length and draught, as well as of weight of hull to displacement. Departures from these proportions rendered the rule useless as a measure of carrying power, and it was evaded when its legal enactment supplied a motive for so doing. In order to produce vessels of small nominal tonnage but great carrying power, raking sternposts and other small devices were employed ; but the adoption of great depth, in associa- tion with very full forms under water, was most influential. Instead of the depth of hold being 50 per cent, of the breadth, it was increased to 70 or 75 per cent, in many cases ; and such full forms were adopted that the dead-weight capability ordinarily exceeded the tonnage by one-third. These deep heavy-laden " box-shaped " vessels were, of course, far inferior to vessels of good proportions as regards speed, safety, and good behaviour at sea. The numerous disasters which resulted, and the obvious inferiority of British to foreign merchant ships, being distinctly traceable to the bad influence of the tonnage law, led to an agitation for its repeal. Tormage Legislation and Enquiries, 1821-53. — An Admiralty com- mittee investigated the subject in 1821, and reaffirmed the principle that dead-weight capability was the fairest basis for tonnage. They clearly understood that this could be exactly determined for any ship if the light and load lines were fixed ; but they reported that it was impossible " to ascertain the position of these lines in a "satisfactory manner," and suggested the estimate of dead-weight capability by means of an approximate rule, based on a few internal measurements. This rule would have been easily evaded, and was not adopted. A second commission was appointed in 1833, and reported in favour of "internal capacity as the fairest standard of "measurement, including all those parts of a vessel which, being " under cover of permanent decks, are available for stowage." Great opposition was raised to any change in the law ; but finally, in 1835, another tonnage law was enacted known as the New Measurement, in general accordance with the recommendations of the commission. The change of basis from dead-weight to internal capacity thus made was a step of the highest importance, having been accepted in all subsequent legislation. It will be seen, from the explana- x tions given above, to have been a reversion to the earliest system of estimating the sizes and earnings of ships. All English tonnage laws from 1694 to 1836 had been designed to approximate to dead-weight capability, but at a very early date French laws had based tonnage on internal capacity. The Ordonnance de la Marine of 1681 fixed 42 cubic feet of internal space, as 1 ton of tonnage; this unit corresponding to the space required for the stowage of four wine-casks. In finding the internal volume three CHAP. II.] THE TONNAGE OF SHIPS. 5 1 cross-sections were taken in the ships ; the areas of these sections were estimated roughly, and a mean area found, which, multiplied by length, and divided by forty-two, gave the tonnage. The process was rough, and it appears that here also the final result gave a tonnage fairly approximating to the dead-weight capability of the ships to which the rule applied when it was framed. Bouguer, with his usual discrimination, pointed out the weak points of this system, and proposed improved methods, anticipating by his suggestions (made in 1746) most of the proposals for tonnage measurements since made. If internal capacity was to be the basis of tonnage, he proposed to make the measurements in a strictly scientific manner, much as is done under the Moorsom system now in use; and, if dead-weight capability was to be used, he proposed to determine it by estimating the displacement between the light and load-lines. For port dues he proposed to take the volume of the parallelopipedon circumscribing the ship, since that practically measured the space she occupied.* The "New Measurement" was the legal tonnage for British merchant ships from 1836 to 1854. The rules for estimating internal capacity were intended to give a fair approximation to the volume of " all those parts of a vessel which, being under cover of permanent " decks, are available for stowage," on the basis of the smallest number of measurements which would yield trustworthy results. Taking a considerable number of ships as examples, it was arranged that their aggregate tonnage should be about the same under the old and new systems, by selecting an appropriate division for use in the new measurement. For steam-ships, the estimated cubic contents of the part between the engine-room bulkheads divided by 924 gave the deduction allowed from the gross tonnage. It is unnecessary to reproduce the rules for this measurement, but it may be stated that they involved the measurement of certain lengths, breadths, and depths in a few specified positions, and were, consequently, open to evasion. By means of various devices, shipbuilders were able to secure a considerable excess in the true capacity over the nominal capacity, amounting to as much as 15 per cent, in some cases. Mr. Moorsom summed up his review of the operation of this law as follows : " Although it has suppressed the premium hitherto given to " the building of short, deep ships, and although great improvements " in our commercial navy have accrued under it, yet as it offers so " many facilities for evasion, and is not, from the very nature of its " constitution, to be depended on generally in its results, it cannot " be expected to possess either the confidence or approbation of the * See the Traite du Navire. 5 2 NAVAL ARCHITECTURE. [chap, n. " public." A third commission on tonnage was appointed in 1849, and it recommended that the " entire cubic contents of all vessels " externally " should be carefully measured, and made the basis of dock, light, harbour, and other dues. Poops, forecastles, and other covered-in spaces were also to be measured and included in the tonnage. The total volume in cubic feet was to be divided by 35, and 27 per cent, of the quotient was to be the register tonnage, of sailing vessels. In steamers the tonnage due to the engine-roOm was to be deducted; this was to be done because corresponding deductions had been made in preceding laws, but the commission expressed a doubt as to the propriety of making any such deduction. This proposal was not adopted, and it is mentioned here chiefly because it has been many times repeated since it was first made. The principal objection urged to this system of external measure- ment was, that the fairest measure of the earnings of a ship was to be found in her internal capacity, as affirmed by the commission of 1833. This view received the support of leading shipowners, whose views were pithily expressed by Mr. Moorsom in the following passages : " It is alleged," he writes, " that light merchandise " (meaning thereby such merchandise as fills the hull of the vessel " without wholly loading her to the load-draught of water) forms the " predominant cargoes of commerce, and constitutes for the most part " the profits of the ship ; and, therefore, it is maintained that the " internal capacity, on which the stowage of this merchandise entirely " depends, must be the fair and proper basis for assessment. Besides, "the poops, spar-decks, etc., which are appropriated entirely to " passenger traffic, frequently form a large item in the profits of the " ship." Again he says, " Having assumed, as affirmed to be the case " by the generality of shipowners, . . . that the profits of a vessel "are, for the most part, directly dependent on the quantity of space " for the stowage of cargo and accommodation of passengers — having " assumed this as an incontrovertible condition of the question all " further investigation of the subject has gone to prove the superior " eligibility and desirableness of internal measurement." Tonnage Law of 1854 (Moorsom System), and its Amendments.— The rules for tonnage measurement devised by Mr. Moorsom and embodied in the Merchant Shipping Act of 1854, were intended to give a practically correct estimate of the internal cubic capacity of vessels under their upper decks, and of the "permanent closed-in "spaces on the upper decks available for cargo or stores, or for the " berthing or accommodation of passengers or crew." Mr. Moorsom had been trained in the Admiralty School of Naval Architecture, and his rules, while simple in character and involving only a moderate amount of labour, rest upon scientific principles of CHAP; ii.] THE TONNAGE OF SHIPS. 53 mensuration, and make evasion difficult. They have now been in use for nearly forty years, and have been accepted, with certain modifications in detail, by all the maritime nations of the world, as well as for international purposes on the Danube and the Suez Canal. A Eoyal Commission in 1881, after reviewing the working of the Act of 1854, almost unanimously recorded the opinion that the Moorsom system of tonnage had been favourable to the progress of merchant shipping, and was preferable to any other system that had been tried or suggested. Certain modifications were recom- mended by the commission in matters of detail, and in regard to deductions from gross tonnage ; to some of these reference is made hereafter. In the main, however, the Moorsom system of measure- ment is almost universally approved as having practically fulfilled the intentions of its framer. This is the more remarkable when it is remembered that in 1854 iron shipbuilding was in its earlier stages, and that steam propulsion for seagoing vessels was but little developed. Since that date there have been remarkable changes and improvements in the sizes, speeds, types, and structures of merchant ships ; and there has been a great advance in scientific knowledge on the part of persons engaged in shipbuilding. Under these circumstances, it was inevi- table that differences of opinion should from time to time arise in the interpretation of the rules. The technical terms in the Act of 1854 related to wood ships such as were then chiefly built ; and the rules were devised for vessels of moderate size and simple types as compared with present practice. There have been appeals to the law courts in typical cases, and decisions as to the applications of the rules which have been much discussed. Exception has been taken to the deductions made on account of propelling machinery in steamers, and many proposals have been submitted to Parliament for amendment. In the main, however, the Act of 1854 still stands, and the amending Acts of 1867, 1876, and 1889 only deal with a few i points of importance that have arisen in working the original Act. Details of the rules for estimating internal capacity cannot be given here. A brief summary of the principal steps must suffice. Moorsom arranged to calculate separately : (a) Capacity under the " tonnage " deck ; (b) capacity of space (if any) between the tonnage deck and the upper deck ; (e) capacity of all " permanent closed-in " spaces on upper deck available for cargo or stores, or for the berthing "or accommodation of passengers or crew." The sum of these capacities in cubic feet, divided by 100, expressed the " gross "tonnage." A ton of Moorsom tonnage is 100 cubic feet, or 2 - 83 cubic metres. The divisor 100 was chosen because of its con- 54 NAVAL ARCHITECT URE. [chap. H. venience, and because it was found to give a close approximation to the tonnages of a number of ships under both the preceding law and the new law. The " tonnage " deck was defined as the upper deck in ships of ^less than three decks, and the second deck from below in all other ships. Most of the ships of 1854 had no more than two decks. The conditions are entirely different in large ships now built. Moorsom's rules for under-deck tonnage closely resemble those adopted by naval architects in calculating the volume of displacement for a ship. Actual half-breadth measurements are taken by the surveyors of the Board of Trade, at specified positions in the interior of the ship, if that is accessible. The longitudinal and the vertical intervals between these measurements are varied with the length and depth of the ship, the intention being to space them sufficiently close to indicate fairly the true shape of the interior, and to prevent evasions of the law by any local thickening of the inside lining or other devices. Having obtained these measurements, the first step in the calculation is to find the areas of a series of equidistant vertical transverse sections of the hold- space below the tonnage-deck; and, secondly, to use these areas in estimating the volume of hold-space. When the Act of 1854 was framed, ships were of moderate dimensions and simple construction. The developments which have since taken place could not have been foreseen, but it was provided that the department administering the Act should have power " to make such modifications and alterations as may from time " to time become necessary in the tonnage rules, ... in order to " the more accurate and uniform application thereof, and the effectual " carrying out of the principle of admeasurement therein adopted." This was undoubtedly a wise provision, since a close approach to the true internal capacity ought to be secured, and stereotyped methods of calculation might introduce difficulties or favour evasion. The competent officials of the Tonnage Department under the Board of Trade, whose duty it is to closely scrutinize the working of the rules, appear to have satisfied themselves that no wide departures from Moorsom's methods were necessary. Until March, 1890, those methods remained unaltered. Amended rules were then issued for securing greater accuracy in the computation of the transverse sectional areas in tonnage measurements, and for sepa- rately calculating the volumes, of subdivisions of the hold when "break or breaks" occur "in a double bottom for water-ballast." In other respects Moorsom's rules still hold good. He provided that in ships of "225 feet and above" only thirteen equidistant transverse sectional areas should be measured. Jfo more are chap, ii.] THE TONNAGE OF SHIPS. 55 measured now, even in ships 600 feet long, unless there is a break in the double bottom. It has been urged that more transverse sections should be measured in ships of great length. Several foreign nations have acted on this view, and made from 16 to 20 intervals obligatory in long ships instead of 12. No doubt this closer spacing of measured sections gives somewhat greater accuracy ; but the fact that the Board-of-Trade officials have not insisted on the change indicates that it has no great relative importance, as the subject has been carefully investigated. Manyi disputes have occurred respecting the fair assessment of under-deck tonnage in ships fitted for water-ballast. The matter occupied the attention of the Eoyal Commission of 1881, which made a recommendation thereon. By the Act of 1889 the question has been settled, in a sense contrary to that recommendation, but apparently in agreement with the spirit of the Act of 1854. The law now provides that "in the case of a ship constructed with a " double bottom for water-ballast, if the space between the inner and " outer plating thereof is certified by a surveyor appointed by the " Board of Trade to be not available for the carriage of cargo, stores, " or fuel, then the depth . . . shall be taken to be the upper side " of the inner plating of the double bottom." In other words, the volume of the ballast-tank is not included in the under-deck tonnage ; and shipbuilders are left free to choose their methods of constructing the hulls for water-ballast purposes. The estimate for capacity of spaces between the tonnage deck and the upper deck ('tween-deck tonnage) is a very simple matter, requiring no description. Differences of opinion have arisen, how- ever, as to which was the wpjper deck in certain types, and a definite decision on the point was given by the House of Lords in 1875 : " The kind of upper or spar deck mentioned in the Act of Parlia- " ment is a continuous deck from stem to stern, fastened up and water- " tight, sealing up the cylinder formed between the two decks, and " making it a fit place for the stowage of cargo like a hold." Before the commission of 1881, evidence was given that this decision bore hardly on " awning-decked " ships (Fig. 12, p. 15), in which a light covering-deck is built all fore-and-aft, and carried by light bulwarks extending down to the true upper deck. Such vessels are not loaded so deeply in relation to their total depth as would be done if the full scantlings were carried to the uppermost deck. It is asserted that this arrangement is chiefly favoured because it prevents the lodgment of water on the decks, gives a greater free- board and increased stability, thus adding to the safety as well as the comfort of ships. Further, it is stated that the internal spaces between the awning and upper decks cannot be fully utilized even 50 NAVAL ARCHITECTURE. [chap. n. when the lightest cargoes are carried. On these grounds it is main- tained that the total internal space is not a measure of the earnings in such ships, but unfairly raises their tonnage upon which dues are paid, as compared with the tonnage of ships in which the erections above the upper deck are discontinuous — such as poops, bridge^ houses, forecastles, etc. On the other side it is argued that increased comfort and safety ought to result in larger earnings, and that if the spaces are permanently enclosed there can be no effectual guarantee that cargo or passengers will not be carried above the upper deck. The Board of Trade, therefore, have resisted the endeavour to obtain some reduction of the tonnage of the spaces between upper and awning decks, and, the majority of the Koyal Commission having supported this action, no change in the law has been made. So long as a space is not permanently closed in, gaps being left in a deck, or openings in the sides, it is not included in the tonnage, even though it may be readily, but temporarily, closed after admeasurement. The sum of the tonnages under the tonnage deck and in the 'tween decks is commonly termed the " under-deck tonnage," repre- senting the gross tonnage of a ship exclusive of deck-erections. Under the Act of 1854, an approximate rule was given for measuring the gross under-deck tonnage of laden ships or foreign ships entering British ports, in terms of their external dimensions. It runs as follows according to an amendment made in 1858 : The length is taken at the upper deck from the fore point of the rabbet of the stem to the after point of the rabbet of the post. The extreme breadth of the ship is also taken, and a chain is passed under her at this place in order to determine the girth of the ship as high up as the upper deck. Then the approximate gross tonnage under the upper deck is estimated by the formulae — (1) For wood and -i _ 17 / girth + breadth ^ composite ships . j ~~ 10000 \ 2 ) * en S t ^ 1, /o\ t? • t,- 18 / girth + breadth V (2) For iron ships . = — Q (& — j x length. In the Act of 1854, larger coefficients were given, namely, r oVW for wood ships, and j-tf^ for iron ships ; but enlarged experi- ence led, many years ago, to the substitution of the coefficients still in use. This approximate rule for the gross under-deck tonnage is now but seldom used, for two reasons— First, all new British ships are measured by the more exact method ; and, secondly, so many foreign nations, including all the most important mercantile marines, have now adopted the Moorsom system for gross tonnage, that their legal tonnage, inscribed on the certificates of foreign ships, can be accepted. chap.il] the tonnage of ships. 57 Other approximate rules hare been given for estimating gross under-deck tonnage. Mr. Moorsom proposed the following rules : If L be the inside length on upper deck from plank at bow to plank at stern ; B, the inside main breadth from ceiling to ceiling ; D, the inside midship depth from upper deck to ceiling at liraber-strake : then the gross tonnage under deck may be approximately expressed by the equation — Tonnage =LxBxDxa decimal factor -~ 100, wherein the decimal factor has the following values : — Sailing ships of usual form . „, ., , .. ( two-decked bteam vessels and clippers < ,, -, , j rr (three-decked v , f above sixty tons jl acn is i n i (small vessels .... Decimal factor. •7 •65 •68 •5 ■45 These factors cannot be regarded as applying to ships of the present day. It may be interesting, therefore, to give another approximate rule for gross under-deck tonnage in the form most useful in making rough estimates of the tonnage in new steam-ships, for which the principal dimensions are known. Let L be the length, at the load-line, from the front of the stem to the back of the stern- post ; B, the extreme breadth to the outside of the plating ; D, the depth from the top of the upper-deck amidships to the top of the keel : then, if ordinary methods of construction are followed, the following rules hold fairly well for iron or steel steam-ships of modern types : — Gross tonnage under deck = L X B X D X decimal factor -4- 100. Wherein the decimal factor has the following values : — Decimal factor. Passenger steamers of high speed and sailing ships *6 to "65 Passenger and cargo steamers . . . . "7 to "72 Cargo steamers and oil-tank steamers . . . *72 to '8 Special structural arrangements may sensibly modify the values of these factors ; and it will be understood that they are useful only in rough estimates, not as substitutes for exact calculations of tonnage. All deck-erections coming under the terms of the Act of 1854 are separately measured, and the sums of their capacities divided by 100 gives the tonnage to be included in the gross tonnage. In this case also permanent enclosure is a necessary condition for the measurements, and facilities for temporary enclosure do not bring 58 NAVAL ARCHITECTURE. [chap. n. erections under the terms of the Act. There have been differences of opinion in many cases between the Board of Trade and shipowners, especially for new types of ships, as to the inclusion or exclusion of particular erections ; and there have been instances where two official surveyors have treated sister ships differently as regards erections. Shipowners and shipbuilders naturally desire to obtain the greatest carrying capacity and comfort on the smallest register tonnage, and consequently ingenious devices and modifications of previous methods are continually being introduced in the upper works of ships. The Eoyal Commission of 1881 fully considered the matter, and proposed to amend the law of 1854 as follows : " Gross tonnage should be " made to include all permanently covered and closed-in spaces above " the uppermost deck ; and erections, with openings either on deck " or coverings or partitions that can readily be closed in, should also " be included in the gross tonnage ; but the skylights of saloons, " booby hatches for the crew, light and air-spaces for the boiler and " engine-rooms when situated above the uppermost deck, as well as " erections for the purposes of shelter, such as turtle-backs open at "one end, and light decks supported on pillars and unenclosed, " should not be measured for the purpose of their contents forming " part either of the gross or register tonnage." The Act of 1889 does not give effect to these recommendations, and leaves the question of deck-erections as before, except in rela- tion to crew-space and the casing above engine-rooms. As the law now stands, crew-spaoes, whether situated on deck or ' not, will be measured, and included in the gross tonnage. Under the Act of 1854, these spaces, if situated on deck, were not included in the gross tonnage, unless they exceeded 5 per cent, of the remaining tonnage, and in case of such excess, the excess only was added to the gross tonnage. Under the Act of 1867, it was provided that if crew- spaces did not fall below 72 cubic feet per man, or 12 square feet of deck area, and were officially approved as regards sanitation, light, and ventilation, as well as kept free from cargo or stores, the total tonnage of the crew-spaces should be deducted from the gross tonnage. Although the clauses in the Act of 1854 were not formally repealed, the Board-of-Trade officials acted as if they were, and from 1867 to 1879 included the crew-spaces on deck in gross tonnage, making the deduction subsequently in accordance with the Act of 1867. This action was challenged in the law courts, and it was decided that the non-repeal of the clauses of 1854 left both Acts in force. Consequently for ten years the curious anomaly existed that, in many ships with crew-spaces on deck, they were not included in the gross tonnages, and yet were deducted therefrom in estimating nett tonnages. The Act of 1889 repealed the clauses of 1854, and chap, ii.] THE TONNAGE OF SHIPS. 59 provided that in future, when estimating register tonnage, no deduc- tion shall be allowed in respect of any space, which has not first been included in the measurement of gross tonnage. Certain specified classes of ships are exempt from the application of the Act until 1894, but it is unnecessary to give details of temporary exceptions. The Act of 1854 remains in force respecting shelters for deck- passengers, in river or coasting steamers, which shelters are exempted from measurement, if approved by the Board of Trade. Hatchways over cargo holds are also measured, and if their total tonnage exceeds one-half per cent, of the remaining gross tonnage, the excess is included in the gross tonnage. As to other casings over engines, etc., explanations are given hereafter. The foregoing items of tonnage : (1) under " tonnage-deck ; " (2) between tonnage and upper decks ; and (3) deck-erections, make up the gross tonnage in the Register of British merchant ships. By the Act of 1876, however, if a ship engaged in the over-sea trade carries cargo in any space on the upper deck which has not been measured into the tonnage under the Act of 1854, the tonnage of the space occupied is to be measured and added to the taxable tonnage. This law aimed at the discouragement of deck-cargoes, and the increase of sea-worthiness. Its effect is to give a possible variation in the taxable tonnage from one voyage to another. Passing from gross tonnage to the " nett " or " register " tonnage of British merchant ships, a short statement must be made of the deductions from the gross tonnage allowed by the existing law. Many authorities have supported the view that there should be no deductions, and that gross tonnage should be the legal measurement on which dues should be assessed. Mr. Moorsom is said to have favoured this view, only he had to face the fact that deductions had been permitted under earlier laws. The Suez Canal Company attempted at first to levy dues on gross tonnage, but were over- ruled. The United States also, from 1865 to 1882, used the Moorsom system on a gross tonnage basis, but since the latter date allow deductions similar to those of other nations. Certain dock-dues in this country and abroad are still based on gross tonnage. For fiscal purposes generally the system of deductions is now universally accepted, and its continuance was supported by the weight of evidence given before the Royal Commission of 1881. It may be accepted, therefore, that the system is practically fair in its operation, taken in association with existing methods of charging dock and harbour dues. These methods might be revised, of course, if the tonnage laws were altered; but dockowners do not appear to desire such legislative revision and its accompanying inconveniences. 60 NAVAL ARCHITECTURE. [chap. u. Deductions for crew-spaces are permitted in all ships. The character of these deductions, and the conditions on which they are allowed, have already been explained. From a careful analysis it has been estimated that the actual deduction for crew-space varies from nearly 10 per cent, in small sailing-ships to 3£ per cent, in sailing vessels of 2000 tons gross tonnage ; the average deduction being from 4 to 5 per cent, in both sailing ships and steamers. The Act of 1889 legalizes the following deductions from " the " space included in the measurement of the [gross] tonnage : " — (a) In the case of a ship wholly propelled by sails, any space set apart and used exclusively for the storage of sails. (b) In the case of any ship — (1) Any space used exclusively for the accommodation of the master. (2) Any space used exclusively for the working of the helm, the capstan, and the anchor gear, or for keeping the charts, signals, and other instruments of navigation, and boatswain's stores. (3) The space occupied by the donkey-engine and boiler, if connected with the main pumps of the ship. These deductions are to be allowed subject to the following provisions : — (a) The space deducted must be certified by a surveyor appointed by the Board of Trade, as reasonable in extent, and properly and efficiently constructed for the purpose for which it is intended. (b) There must be permanently marked in or over every such space a notice stating the purpose to which it is to be applied, and that whilst so applied it is to be deducted from the tonnage of the ship, (e) The deduction on account of space for the storage of sails must not exceed 2£ per cent, of the tonnage of the ship. This legislation is a practical endorsement of the recommenda- tions made by the Eoyal Commission of 1881, and is generally approved. The most important deductions made from gross tonnage are those for spaces occupied by or necessary for the working of the machinery in steamships. Such allowances have been made by law from 1819 onwards ; their justice has been questioned repeatedly, but the principle has been maintained so far, and probably will be adhered to. The Act of 1854 still remains in force, notwithstanding many attempts to amend its provisions. The Commission of 1881 dwelt upon the anomalies of the existing law, and proposed important changes, but no action has been taken to embody their recommenda^- chap, ii.] THE TONNAGE OF SHIPS. 6 1 tion in the Act of 1889. The provisions of the Act of 1854 may be briefly summarized. Spaces "solely occupied by and necessary " for the proper working of the boilers and machinery " are measured. These spaces include the internal volume of the ship, below the deck forming the " crown " of the engine and boiler-rooms ; the casings for engine-hatches, ventilation, funnels, etc., from this crown to the upper deck ; and the shaft trunks in screw-steamers. The sum of these volumes in cubic feet, divided by 100, gives the tonnage of the machinery -space. If this tonnage, in screw-steamers, is above 13 per cent, of the gross tonnage and under 20 per cent., the total deduction permitted, for machinery and coal-space, is 32 per cent, of the gross tonnage. In paddle-steamers, if the measured space has a tonnage above 20 per cent, and under 30 per cent, of the gross tonnage, the total deduction permitted is 37 per cent. This is the first, or " percentage," method supposed to be applicable to all ordinary steamers. A second method is applied where the space occupied for the machinery falls below 13 per cent, or above 20 per cent, of the gross tonnage ; the space may then be measured (as before), and the total deduction from the gross tonnage is to be 50 per cent, more than the measured space in paddle-steamers, and 75 per cent, in screw-steamers. Mr. Moorsom explained that the intention of the law of 1854 was to make a fair allowance for the space occupied by propelling machinery and fuel ; or unfitted for other purposes, such as stowage of cargo or accommodation of passengers, because of the presence of the propelling machinery. This intention was not realized, and the failure soon became apparent. In 1860 the Board of Customs made a rule for engine-room allowance, which was intended to give effect to the original idea, and to deduct a tonnage representing the actual machinery-space. This rule was applied until 1866, when it was decided by the law courts to have no legal force, and the law of 1854 has since continued in operation. Under it shipowners have every inducement to arrange the machinery-space in the majority of ocean-going screw-steamers, so as to bring it a little above 13 per cent, of the gross tonnage, and to secure the 32 per cent, deduction. Take, for example, two screw-steamers, each of 3000 tons gross, and suppose that in one the machinery-space is 12| per cent, of the gross tonnage, while in the other it is 13£ per cent. The deductions would be as follows : — First, steamer : Tons. Actual machinery-space . . . 380 Add 75 per cent, of ditto . . .285 Total deduction 665 62 NAVAL ARCHITECTURE. [chap. ii. Second steamer : Tons. Actual machinery-space . . . 400 Deduction allowed (32 per cent, of) q~q gross tonnage) . . . j That is to say, the shipowner, by increasing the machinery-space 20 tons, and diminishing the cargo-space equally, secures an increase in the deduction from the gross tonnage of 295 tons, and saves largely on the dues paid on nett tonnage. It has been estimated that in ocean-going cargo-steamers coming under this percentage rule, the actual tonnage-space available for stowage exceeds the space corresponding to the register tonnage by from 10 to 12 per cent. ; and the owners of sailing ships, as well as the proprietors of docks, have not failed to complain of these anomalies. No practical result has followed these criticisms ; and the Act of 1889 provides that for existing screw-steamers, the present allowance of 32 per cent, for engine-room shall be continued, even in cases where the addition of the crew-spaces on deck to the former gross tonnage, would make the engine-room space less than 13 per cent, of the amended gross tonnage. This allowance, taken with the crew-space deduction above described, gives a register tonnage of about 64 to 65 per cent, of the gross tonnage to the great majority of sea-going screw-steamers built for cargo-carrying. The second rule for engine-room deductions in the Act of 1854 is also open to serious objection as applied to certain classes of steam- ships. For steamers making passages of 3000 to 4000 knots between coaling-stations, 75 per cent, of the measured machinery-space is said to be a fair average allowance for the space actually occupied by coals. It will be obvious that if this is true now, it could not have been true when the law was framed, marine engineering having been so greatly developed in the direction of economy in coal-consumption (see Chapter XIV.) ; and it is also evident that further improvements may sensibly affect the space required for coals or fuel. Passing this difficulty by, however, and accepting the foregoing statement, it will appear that for many steamers employed on coasting or short sea voyages, the coal-space actually required falls much below 50 or 75 per cent, of the machinery-space. In channel or river passenger- steamers of high speed and in tugs the anomaly is greatest. By an interpretation of the Act of 1854, which has been upheld in the law courts, cases have occurred in which the nett tonnage of swift pas- senger-steamers has been reduced to little more than 22 per cent, of their gross tonnage, and 30 to 40 per cent, is quite a common value. Tugs of considerable gross tonnage, by the application of the same rules, have had less them no register tonnage assigned to them, entirely escaping the payment of many dues, although enjoying chap, ii.] THE TONNAGE OF SHIPS. 63 the privileges of harbours, rivers, etc., and earning large sums by towing. It has been estimated by competent authorities that in sea-going screw-steamers, where the measured machinery-space falls below 13 per cent, of the gross tonnage, the nett tonnage averages about 77 per cent, of the gross. In swifter vessels, having machinery-space exceed- ing 20 per cent, of the gross tonnage, the nett tonnage averages about 57 per cent. In passenger-steamers of the first class and highest speed the corresponding percentage varies from 44 to 54. Individual vessels may, of course, depart considerably from these averages. Various proposals have been made by the Board of Trade for the purpose of removing these anomalies ; and it is but right to add that the officers of that department have consistently endeavoured to improve the law of 1854, while maintaining its fundamental prin- ciple in the directions indicated by experience of its working. In 1866 the department issued a circular requesting consideration of a proposal to make the deduction for engine-rooms as follows : To measure the machinery-space, exclusive of bunkers, and to allow \\ times that space in all paddle-steamers, and If times in all screw- steamers, the total deduction in any case not to exceed 50 per cent, of the gross tonnage, except in tugs. This method was afterwards accepted by the Commissioners for the Danube Navigation, and is usually termed the " Danube Eule." Again, in 1867, the Board of Trade submitted for consideration a proposal to measure coal-bunkers as well as machinery-space, and to make the total space thus occupied the allowance for engine- room, etc., it being provided that such allowance should not exceed 50 per cent, of the gross tonnage, excepting in tugs. This proposal was embodied in the Merchant Shipping Code of 1871, which was introduced into Parliament, but not proceeded with. It was subsequently adopted in Germany, and is now commonly termed the German Eule. This plan is specially applicable to ships with permanent coal-bunkers ; but many cargo-carrying steamers are con- structed with shifting coal-bunker bulkheads ; the space assigned to the coal varying with the quantity required to be carried for the particular voyage, and the space sometimes included in, and at others excluded from, the bunkers being respectively unavailable or available for cargo-stowage. Since the nett register tonnage cannot be allowed to vary with the coal-space, some modification of the rule would be necessary. The Danube Eule meets such cases. The majority of the Eoyal Commission in 1881 reported in favour of a combination of the Danube and German Eules, with certain modifications, as will appear from the following extract: "The " deduction for propelling space in steamers should be the actual space 64 NAVAL ARCHITECTURE. [chap. n. " set apart by the owner at his discretion for the engine and boiler " room and permanent bunkers, provided that such space be enclosed, " separated from the hold of the ship by permanent bulkheads, and " that the bunkers be so constructed that no access can be obtained " thereto otherwise than through the ordinary coal-shoots on deck or " in the ship's side, or from the openings in the engine-room or stoke- " hold ; but that to meet the varying requirements as to fuel of " steamers engaged in long voyages, and to encourage ample ventila- " tion to boiler and engine rooms in hot climates, owners of steamers " should have the option to claim as deduction for propelling-space the " actual contents of engine and boiler space, plus 75 per cent, thereon " in the case of screw-steamers and 50 per cent, in the case of paddle- " steamers, without restriction as to extent, construction, and use of " bunkers, provided always that the deduction for propelling-space " shall not exceed 33 per cent, of the gross tonnage of any screw- " steamer, and shall not exceed 50 per cent, of the gross tonnage of " any paddle-steamer." It will be remarked that the limit of deduc- tion for screw-steamers is made considerably lower than in the German or Danube Eules, and that clauses are introduced with the intention of preventing cargo from being carried in the permanent bunkers. The Act of 1889 touches the question of engine-room allowances only in two points. That relating to the retention of 32 per cent, allowance in cargo steamers has been mentioned above ; the second amendment deals with a difficulty which has arisen in recent years in connection with casings over the machinery -spaces, and above the level of the upper deck. The Board-of-Trade surveyors, under the Act of 1854, measured the volumes of the cased-in spaces from the crown of the engine and boiler rooms up to the level of the upper deck. They did not measure the continuations of these cased-in spaces situated above the upper deck, or include the corresponding tonnage in the gross; neither did they reckon the corresponding tonnage into the machinery-space when estimating the percentage allowance, under the second rule of 1854. An appeal was made to the law courts, whose decision was that the whole volumes of the cased-in spaces, although not included in the gross tonnage, must be reckoned into the machinery-space ; in other words, that the register tonnages, as estimated by the Board of Trade, must be diminished by \\ times in paddle-steamers and 1| times in screw-steamers, the tonnage of closed-in spaces above the upper deck not reckoned into the gross tonnage. This blemish in the law is corrected by two clauses in the Act of 1889. The first, already quoted with refer- ence to crew-spaces, provides that in future no deduction shall be allowed in respect of any space which has not first been CHAP. II.] THE TONNAGE OF SHIPS. 65 included in the measurement of tonnage. The second provision is as follows : — " In the case of any ship built or measured after the passing of " this Act, such portion of the space or spaces above the crown of the " engine-room and above the upper deck as is framed in for the machi- " nery, or for the admission of light and air, shall not be included in ** the measurement of the space occupied by the propelling power, " except in pursuance of a request in writing to the Board of Trade " by the owner of the ship, and shall not be included in pursuance of " such request unless — " (a) That portion is first included in the measurement of the " gross tonnage ; and " (6) A surveyor appointed under the fourth part of the Merchant " Shipping Act of 1854 certifies that the portion so framed in " is reasonable in extent, and is so constructed as to be safe " and seaworthy, and that it cannot be used for any purpose "other than the machinery, or for the admission of light " and air to the machinery or boilers of the ship." International Tonnage. — This extract completes all that need be said respecting existing tonnage laws for British merchant ships, and attention will next be directed to the use of the Moorsom system for international purposes. This was first done in connection with the Danube navigation. In 1860 the English law of 1854 was adopted, factors being used to convert the tonnages of other than English ships into approximate English measure. Subsequently the allowances for propelling machinery-space were modified as above described. In 1873 an International Commission on Tonnage met at Constantinople, specially with reference to the assessment of Suez Canal dues, and the settlement of the tonnage on which dues should be paid. While adopting the Moorsom system, the Commission pro- posed stricter regulations in regard to deck-erections and a different method of engine-room allowance than are contained, in the English law. The Suez Canal Eules respecting enclosed spaces are as follows : — " By permanently covered and closed-in spaces on the upper deck " are to be understood all those which are separated off by decks, or " coverings, or fixed partitions, and therefore represent an increase of " capacity, which might be used for stowage of merchandise, or for the " berthing and accommodation of the passengers or of the officers or " crew. Thus any one or more openings either on the deck or cover - " ings, or in the partitions, or a break in the deck, or the absence of a " portion of the partition, will not prevent such spaces being com- " prised in the gross tonnage if they can easily be closed in after " admeasurement, and thus better fitted for the transport of goods " and passengers." 66 NA VAL ARCHITECTURE. [chap. h. The essential difference from the English law will be seen to lie in the addition to gross tonnage of spaces which " can easily be closed " in." It was also provided that " spaces under awning decks without " other connection with the body of the ship than the props necessary "for supporting them, and which are permanently exposed to the "weather or the sea, will not be comprised in the gross tonnage, •' although they may serve to shelter the ship's crew, the deck pas- " sengers, and even merchandise known as deck-loads." The regula- tions for deck-loads under the Act of 1876 are therefore in excess of Suez Canal measurement. The spaces measured for the gross tonnage in all ships are : Space under the tonnage deck ; space or spaces between tonnage deck and uppermost deck; all covered or closed-in spaces, such as poop, forecastle, officers' cabins, galleys, cook-houses, deck-houses, wheel-houses, and other enclosed or covered-in spaces employed for working the ship. The deductions permitted in all ships are : Berthing accommodation for the crew in forecastle and elsewhere — not including spaces for stewards and passengers' servants ; berthing accommodation for the officers, except the captain; galleys, cook- houses, etc., used exclusively for the crew; covered and closed-in spaces above the uppermost deck employed for working the ship. In none of these spaces must cargo be carried or passengers berthed, and the total deduction under all these heads must not exceed 5 per cent, of the gross tonnage. In steamers with fixed coal-bunkers the German Eule (see p. 63) may be followed, or the owners may choose to have their vessels measured by the Danube Eule. Vessels with shifting bunkers would be measured by the Danube Kule. In no case, except in tugs, must the deduction for the propelling power exceed 50 per cent, of the gross tonnage ; so that the minimum tonnage upon which a vessel can pay dues in passing through is 45 per cent, of her gross tonnage. The actual average deduction from the gross tonnage of merchant steamers using the canal is estimated at about 30 per cent. Owing to the different methods of making the deductions, a British ship has to pay Suez Canal dues upon a tonnage exceeding by about 10 to 12 per cent, that on which she is assessed in home ports. War-ships, as well as merchantmen, use the canal, and have to pay dues. For this purpose all the ships of the Eoyal Navy are measured by surveyors of the Board of Trade, and furnished with special tonnage certificates. In them the deductions from the gross tonnage vary from 30 to 50 per cent., according to the class of ship. In 1876 the Danube Com- mission officially adopted the Suez Canal Eules, so that the same certificates are now available for both navigations. In 1874 a bill was introduced into the House of Commons to chap, ii.] THE TONNAGE OF SHIPS. 67 assimilate the English tonnage law to the Suez Canal Eules, but it did not pass. Some of the recommendations of the Eoyal Commis- sion of 1881 were in the same direction ; these have not been acted on. It is curious to note that the Suez Canal Eules are, in the main, based on proposals made by our own Board-of-Trade officials, many of which have been presented to but not accepted by Parlia- ment. International tonnage has many obvious advantages, and if ever a universal law is arranged by maritime nations, it will probably be" based on the Suez Canal regulations. Even as matters now stand, much advance has been made during the last thirty years by the general adoption of the Moorsom system. The United States, Denmark, Austro-Hungary, France, Germany, Italy, Spain, Sweden, the Netherlands, Norway, Finland, Greece, Eussia, Hayti, Belgium, Japan, Chili, and the Argentine Eepublic have followed the lead of this country, although they have dealt with engine-room deductions, enclosed spaces, etc., in a manner differing from the Act of 1854, and in some cases have laid down different rules for computing under-deck tonnage. Crew-space deductions for nearly all these countries are limited to 5 per cent, of the gross tonnage. According to the latest information in our possession, engine-room deductions are dealt with as follows : Austria, Italy, Finland, France, Hayti, and Japan use the English Eules ; Germany, Sweden, Norway, Eussia, and Belgium adopt the " German " Eule ; the United States, Den- mark, Spain, the Netherlands, and Greece use the " Danube " Eule. For convenience, and the avoidance of the necessity for remeasure- ment, the tonnage of the measured machinery-spaces and permanent coal-bunkers (if any) might be officially recorded by all countries, as they are on the Suez Canal certificates. It is stated on good authority that for steamers above 1000 tons (gross tonnage) the nett registered tonnages by British Eule have been found to average about 10 per cent, less than the corresponding tonnage by the Danube Eule, and about 16 per cent, less than by the German Eule. Alternative Systems of Tonnage for Merchant Ships.— Although the Moorsom system of tonnage is now almost universally accepted, there are not wanting advocates of change, on the ground that internal capacity is not a fair basis for taxation. These views were strongly expressed in evidence given before the Eoyal Commission of 1881, in dissentient reports by two eminent commissioners, and have been endorsed by French writers of repute. Undoubtedly the greatly preponderating weight of opinion amongst shipbuilders and shipowners is contrary to change in the basis of measurement ; and the inconveniences attaching to such a change are very serious. This feeling has had much to do, no doubt, with the opposition shown 68 NA VAL ARCHITECTURE. [chap. ii. to the amendments in the Act of 1854, above described, although they are undoubtedly desirable on many grounds. To an entire alteration in the basis of tonnage, which has worked well, on the whole, for nearly forty years, much greater opposition may be antici- pated. It may be interesting, however, to indicate briefly the nature of some of the alternative proposals which have been brought forward in recent years. The first, supported by the late Mr. Waymouth, then secretary to Lloyd's Eegister, and a member of the Commission of 1881, was to return to a dead-weight basis of measurement. Mr. Waymouth maintained that, as the great majority of ships are engaged in carrying cargo and not passengers, the tonnage laws should be especially suitable to them. Freights, as a rule, are now. based upon the dead-weight capability of ships; and when light measurement goods are carried, the rates are raised pro- portionately. In other words, it is asserted that the fundamental principle laid down by Mr. Moorsom no longer holds good ; that internal capacity in the present conditions of the shipping trade is not the fair measure of the possible earnings of ships under most circumstances, whereas dead-weight capability is. This view of the matter is disputed, but the question cannot be discussed here. It may be observed, however, that the special mechanical appliances for packing in small compass many descriptions of light goods, have produced remarkable reductions in the space required for their stowage since the date when Mr. Moorsom wrote ; while the change from wood to iron and steel, and the modifications introduced in modern types, have tended to increase the internal capacity available for stowage. Starting from this assumption, Mr. Waymouth proposed to ascertain the light-line to which a ship would be immersed when equipped for sea, but without cargo on board. For sailing vessels, no consumable stores would be on board ; for steamers, the engines would be complete, and the water in the boilers, but no coals would be on board when the light-line was ascertained. A maximum load- line would be fixed by some central authority for each ship. The dead-weight capability would then be easily and accurately estimated, being the number of tons of sea water displaced by the ship between her light and load-lines. For passenger-ships it was proposed to place the load-lines exactly as if they were cargo-ships, and at the maximum height above the keel compatible with safety ; although it is admitted that these vessels would never in their regular service load so deeply. The reason given is "that no shipowner will carry " light freight, passengers, or cattle unless he earns at least as much " as if he were carrying a dead-weight cargo." A "register ton" according to this system would be 20 cwt. CHAP. II.] THE TONNAGE OF SHIPS. 69 avoirdupois, and it may be interesting to inquire how it would be related to the register ton under the existing system. There is, of course, no constant ratio between the two, the relative accommodation assigned to cargo or passengers in different classes of ships, the variations in the relative weights of machinery in various types of steamers, and other circumstances affecting the ratio. In 1860 Mr. Moorsom gave the following rule : " To ascertain approximately the " dead-weight cargo which a ship can safely carry on an average " length of voyage, deduct the tonnage of the spaces appropriated to "passenger accommodation from the nett register tonnage, and " multiply the remainder by the factor \\" At present in iron and steel sailing ships the corresponding ratio usually lies between \\ and 1^ ; in cargo steamers, If is a fair average, but 2 to 1\ is said to occur. For passenger steamers the ratio of dead weight to nett tonnage varies greatly with differences in the speed as well as in the proportionate importance of cargo and passengers, and in some of the swiftest seagoing vessels is less than unity. Hence it will appear that difficulties would arise in changing from the present basis to a dead-weight basis, if it were desired for statistical purposes to leave unchanged the nominal aggregate tonnage of the British mercantile marine. This has been considered a matter of some importance in all revisions of the tonnage laws so far made. Mr. Waymouth did not have regard to this consideration : his system would make the aggregate tonnage considerably greater than at present. It would be possible, no doubt, to keep the aggregate register tonnage of the mercantile marine unchanged, if the labour of determining the total dead-weight tonnage were incurred, and a divisor found expressing the ratio of that total to the present total register tonnage. But it would still remain true, for the reasons given above, that the nominal tonnage of different classes of ships would be very differently affected by the use of this divisor in all cases, because the ratio of the dead-weight capability to the present register tonnage varies so greatly. Since Mr. Waymouth made his proposal, one of the great objec- tions raised to his scheme has been removed by the settlement of the load-line question for merchant ships (see p. 13). This does not dispose, however, of the objection that for passenger-steamers and for vessels built to carry light cargoes he proposed to have a " tonnage load-line " deeper than the vessels would ever be sailed at, and based upon perfectly hypothetical conditions. Here lay the novel feature of the scheme, and it does not commend itself. In other respects the plan is identical with that favoured by writers of the seventeenth century. Another method of estimating tonnage by dead-weight has been 70 NA VAL ARCHITECTURE. [chap. ii. proposed at different times, but never adopted. The tonnage on which dues were to be paid was to be governed by the number of tons of cargo carried on each voyage ; and to assist in ascertaining the dead-weight on board, an officially guaranteed " curve of dis- " placement " was to be carried by each vessel (see p. 5). It will be seen, therefore, that the tonnage of a ship would be a variable quantity. Moreover, the attempt to assess earnings by the dead- weight carried could not possibly succeed, since it leaves almost untaxed the extremely valuable earnings obtained from the carriage of passengers, and treats too favourably the cases where light cargoes are carried. As regards statistical uses, this form of dead- weight tonnage would be more objectionable than that described above. The second proposal for a change in the tonnage law was embodied in a separate report by the late Mr. Eothery (Wreck Commissioner), who was also a member of the Eoyal Commission of 1881. It may be shortly described as a proposal to make "dis- " placement tonnage " the basis of all dues. This also was a revival of a proposal made years ago, and, like dead-weight measurement, it required the fixing of a load-line for each ship, either by the ship- owner or by some central authority. It was further suggested that, for the purpose of bringing the register tonnage obtained on the new basis into approximate agreement with the present register tonnage, the actual displacement (in tons avoirdupois) should be divided by some factor. Here, however, difficulties must arise, corresponding to those mentioned in connection with the attempt to deal similarly with dead-weight measurement and the present register tonnage. The factor to be used would have very different values in different classes of ships, with different structural arrangements, and different reserves of buoyancy. Even in comparisons between the gross tonnages and the displacements of ships considerable variations occur, due to the wide divergencies in reserves of buoyancy and methods of construction. In ocean-going steamers the gross tonnage may vary from two-thirds to one-half of the displacement (in tons) ; in sailing ships, between one-half and five-elevenths of the displace- ment. When we pass from gross to nett tonnage on the present system, these ratios of tonnage to displacement are very little altered in sailing ships, but very considerably and unequally affected in different classes of steamers, owing to the nature of the deductions for propelling-space. For statistical purposes, therefore, the change to a displacement basis would involve some difficulty. Mr. Eothery advocated a displacement basis for tonnage, on the grounds that, if the load-line is fixed, the tonnage can be accurately estimated, without difficulties arising as to structural arrangements, chap, ii.] THE TONNAGE OF SHIPS. 71 propelling-space, erections on deck, etc. ; and that this tonnage is the fairest for assessing dock and harbour dues, because it corresponds to the water-space actually occupied. Eecognizing the fact that in both the Moorsom system and in dead-weight measurement, an endeavour is made to roughly assess the earnings of ships, Mr. Eothery contended that the true basis for canal, river, dock, and harbour dues is to be found, not in the earnings of ships, but in the service rendered to them.* This service is supposed to be measurable by the space occupied by a ship, represented by her displacement, and by the time during which it is occupied. Light dues are treated as of minor importance when compared with dock and harbour dues. Turning to the objections to this proposal, independently of those connected with fixing the load-line, which have been removed by recent legislation, it must first be noticed that the displacement is not a fair measure of the space required by a ship in dock or harbour. That space is more fairly measured by the parallelo- pipedon of which the length equals the length of the ship " over " all," the breadth is her extreme breadth, and the depth her mean draught, unless she trims excessively by the stern. For it is evident that if these three leading dimensions are the same, the possibility of berthing other ships in a dock or harbour is not altered by variations in the "coefficient of fineness" for displace- ment (see p. 3). And we have seen that the coefficients of fineness may vary from 78 down to 40 in ships of different classes, but with the same extreme dimensions. Next, it is said that a displacement basis would furnish strong inducements to the construction of excessively light hulls and engines, in order that on a given displacement the greatest dead- weight carrying power might be secured. There is force in this argument, but it applies with practically equal force to ships built to carry dead-weight cargoes under the present tonnage law. The tendency to undue lightness of construction is always kept in check by careful surveys, such as are made on nearly all merchant ships by officers of the great registration societies. A third proposal put before the Royal Commission was to base dock-dues, etc., upon either the area of the rectangle having the length over all and breadth extreme of a ship, or upon the volume * The reader interested in this sub- mittee on the Tonnage Bill of 1874, ject may turn with advantage to the where this distinction between the two evidence given by Sir Thomas Farrer, systems of taxation is admirably stated late secretary to the Board of Trade, and illustrated, before the House of Commons Com- 7 2 NAVAL ARCHITECTURE. [chap. II. obtained by multiplying that area by the draught. This class of proposal will be seen to approximate to that made by Bouguer in 1746. It proceeds upon the assumption that dock and harbour dues should be paid on service rendered, and not on the earning powers of ships ; and this assumption, as has been shown, is not generally admitted. While the circumscribing parallelopipedon is a moderately fair measure of water-space occupied, it is very properly urged that varying circumstances affect the cost of construction of docks greatly, making quay-space very expensive of provision in some cases, or depth of water in others. In other words, a complete revision of dock dues and much legislation would have to be effected if on other grounds such a radical change of system were made. These and international obligations are the most serious objections raised. It has been urged, further, that for statistical purposes the change would be objectionable, and this must be admitted. The objection that the parallelopipedon system would encourage the production of box-shaped vessels does not seem to have much force ; for it is not probable that under existing conditions shipowners would sacrifice speed, economy under steam, and good behaviour at sea simply to increase the ratio of dead weight or capacity to nominal tonnage. In view of the full discussion of the subject in 1881, and the recommendations of the Eoyal Commission, as well as the continuous extension of international obligations, it is obvious that the Moorsom system is now more thoroughly established than ever, and that no change seems probable, except as regards improvement in details. Freight Tonnage.— A. few words will suffice respecting another kind of tonnage measurement commonly employed in the mercantile marine. Freight tonnage is simply a measure of cubical capacity. Merchants and shipowners make considerable use of this measure- ment, although it has no legal authority; it is also used in the Admiralty service in connection with store-ships and yard-craft. A freight-ton, or " unit-of-measurement cargo," simply means in most cases 40 cubic feet of space available for cargo, and is therefore two- fifths of a register ton. In some cases the internal capacity of a ship available for freight is expressed in tons of 50 cubio feet, this unit having especial reference to import goods loaded in India. The freight- ton is, of course, a purely arbitrary measure, but has a definite meaning, and is of service in the stowage of ships. Mr. Moorsom estimated that in the ships built thirty years ago for an average length of voyage the nett register tonnage, less the tonnage of the passenger space, when multiplied by the factor If, CHAP. II.] THE TONNAGE OF SHIPS. 73 would give a fair approximation to the freight-tons for cargo stowage. This rule cannot be applied to ships of the present day, which differ greatly from their predecessors in structural arrangements and propelling apparatus. It is now the practice of shipbuilders, however, to furnish drawings showing the capacity of the several holds in cubic feet ; and this information, taken in association with the form and structure of a ship, is of great value in dealing with stowage. War-ship Tonnage. — It has been stated above that until 1872 the official tonnages of British war-ships continued to be estimated by " Builder's old measurement ; " this was simply for Navy List and statistical purposes. The defects of the old measurement were fully recognized, and often taken advantage of in giving small nominal tonnages to ships of large displacements. For example, deductions were made for " rake " of stern-posts long after these were upright. In other cases the "breadth for tonnage," when armour projected beyond the hull, was made 4 feet less than the extreme breadth. Similar action was taken to even a later date in the United States navy; but in most foreign navies displacement tonnages (for the fully laden and equipped condition) had been used for many years previously to our change of system in 1872. The designers of British war-ships had also long worked on a displacement basis, although bound to the official measurement in published lists. For a few years both displacement and B.O.M. tonnages appeared in the Navy List ; now only displacements are given. Displacement tonnage, as explained on p. 2, expresses the total weight of a ship (in tons) when immersed to her maximum draught or "load-line." For war-ships this measurement is especially suited, since they are designed to carry certain maximum weights, and to float at certain load-lines, which are fixed with reference to the character of the service. It will be obvious, however, that a simple comparison of displacements affords no means of judging the relative powers of two war-ships. A displacement of given amount may be very differently distributed in different ships. For example, one may be an armoured coast-defence vessel of low speed, small free-board, heavily protected and armed, but carrying small weights of coal or equipment. Another may be a sea-going armoured ship with high sides, large coal-supply and equipment, higher speed, with lighter armour and armament. A third may be an unarmoured cruiser of very high speed, intended to keep the sea for long periods with large coal-supply, good equipment, and light armament. In each of these cases and others which might be mentioned the distribution of the constant displacement into the various per- centages assigned to hull, machinery, coals, armament, armour, and 74 NA VAL ARCHITECTURE. [chap. 11. equipment will necessarily vary greatly. Consequently it is desirable, when using displacement tonnage as a means of comparison for war-ships, and in order to estimate the skill displayed by designers, to restrict the comparison to ships of similar types, built for similar service. Since the opening of the Suez Canal all British war-ships have been measured by surveyors of the Board of Trade, and furnished with official certificates of their " gross " and " nett " tonnages according to Suez Canal Kules. Dues in passing through are paid on the " nett " tonnage of a ship. When war-ships are docked in private docks abroad, the charges are usually based on the " gross " tonnage. Prior to the financial year 1874-5 the programmes for tonnage of new ships building or to be built appeared in the Navy Estimates, as "Tons B.O.M." From 1875 to 1885 another tonnage-unit appeared in the Estimates ; it has now been abolished, but it may be useful to explain what this statistical "ton" meant. When a new ship is designed, an estimate is made of the total weight (in tons) of her hull and fittings, as well as the cost of the labour to be expended on her construction. The average cost of the labour to be expended in building one ton weight of hull was ascertained from these estimates ; and in the period 1875-85 that "average expen- "diture per ton " was called a "ton " in the shipbuilding programmes. It is unnecessary to criticize an arrangement which was open to grave misconception, and has been abandoned. For purposes of information, it may be added that on an average a " ton " in the shipbuilding programmes 1875-84 about equalled 91 per cent, of a " ton " for armoured ships in preceding programmes, and 144 per cent, of a " ton " for unarmoured ships. Yacht Tonnage. — All British yachts are measured by surveyors of the Board of Trade, and their " register tonnages " are determined. For the purposes of regulating time allowances in racing, or classify- ing yachts, special tonnage rules are employed. A brief description of some of the most important of these rules will now be given. Up to the year 1880 the "Thames Bule," or some modifica- tion thereof, was generally adopted in this country. It ran as follows : — (a) The length is measured on the deck from the fore part of the stem to the after part of the stern-post (CD in Fig. 31, p. 48) ; let this be called L. (b) The breadth is measured to the outside of the outside plank at the broadest part wherever found ; let this be called B. (c) From the length the breadth extreme is deducted, the remainder being the " length for tonnage." This.length for tonnage CHAP, ii.] THE TONNAGE OF SHIPS. 75 is multiplied by the breadth, and their product by half the breadth ; the result divided by 94 gives the tonnage. In algebraical language — (L - B) x B x | Tonnage (Thames measurement) = 94 As an example, take the case of a yacht for which the length (L) is 102 feet ; breadth extreme (B) 21 feet. (102-21) x 21 x 2 ^ Tonnage (Thames measurement) = 94 81 X 21 x 21 94 x 2 = 190 tons. The Yacht Bacing Association adopted the Thames Bule in 1876, and up to 1882 used it with the following modification : The length was measured from out to out on the load-line, it being provided that " if any part of the stern or stern-post or other part of the vessel " below the load water-line project beyond the length taken as men- "tioned, such projection or projections shall, for the purposes of " finding the tonnage, be added to the length taken as stated." It will be noted that these rules were based upon the B.O.M. rule ; only the yacht-owner, naturally seeking to secure speed, and conse- quently favouring good form and ample stability, had not the same inducements to malform his vessel which the owner of the cargo- ship had under the B.O.M. rule. These rules put a severe penalty on beam as compared with length; and, since they took no account of depth, designers were not slow to avail themselves of the possibility afforded them to use large weights of ballast placed low down for the purpose of securing large sail-carrying power on vessels of great length, small beam, and small nominal tonnage. It is admitted that this deep, narrow type of vessel is practically uncapsizable and very well-behaved at sea (see Chapter III.). It is also claimed for the Thames Bule, and its modification, that it brought the type of yacht built specially to sail under it into fair competition with other types of yachts, such as the American, built to sail under other tonnage rules. Further- more it appears that the Thames Bule approximately expressed the sail-carrying power of yachts (see Chapter XII.). But notwith- standing all these considerations, and the dislike of many yachts- men to a change of rule, the Yacht Bacing Association have introduced new systems of measurement, designed especially to check the tendency to greater length, narrower beam, and more ballast in yachts of different classes. 7 6 NA VAL ARCHITECTURE. [chap. ii. The Yacht Kacing Association Kule of 1882 measured the length and breadth as before, and expressed the tonnage by the equation — m _ (length + breadth) 2 X breadth onnage - ^^ A fraction counts as a ton. The divisor was so chosen as to keep the tonnage of existing yachts very nearly the same as under the previous rule. It will be observed that no actual measurement of depth appears in the amended rule, which is in this respect no improvement upon its predecessors. It continued in use until 1886, and was then cancelled in favour of a rule proposed by Mr. Dixon Kemp, which estimates " rating " (or tonnage for racing purposes) in terms of the water-line length and sail-area only. This amended rule is — m / . • \ length on water-line x sail-area 1 onnage (rating) = ^ 5 v &J 6000 Length measured in feet ; sail-area in square feet. The fundamental ideas on which it rests are that speed is largely dependent upon length, and also upon " driving-power," or sail-area. It is claimed for this rule that it gives greater latitude to designers in the choice of proportions of yachts which may be fairly sailed together if of equal rating, and that it encourages greater ratios of breadth to length than under previous rules. At the end of 1892, after six years' experience of the working of this rule, and a thorough inquiry conducted by a special committee, the council of the Association came to the conclusion that "no " sufficient reason has been given for at present altering the existing " rule," and recommended its retention. They decided, further, not to tax " overhangs " at the bow and stern above water, nor to inter- fere in any way with the forms of yachts. They recommended that the load water-line which is to be measured for rating should be marked at the bow and stern, and proposed certain amended methods for measuring the sails. In all essentials they maintained the rule of 1886, which may be expected, therefore, to remain in use for some time longer, as it has given satisfaction on the whole. Besides these rules for yacht-tonnage, there are many others which have been proposed or employed to a limited extent. None of these are free from objection, but a few of the principal alternative rules may be described. In 1874, the Corinthian and New Thames Yacht Clubs adopted the following rule for a short time, but eventually abandoned it, in consequence of the objections raised by yachtsmen : — Tonnage = length x breadth x depth S 200 chap, ii.] THE TONNAGE OF SHIPS. 77 In this rule the length and breadth for tonnage were measured as in Thames measurement, the depth being the total depth up to the top of the covering board. One obvious objection to the use of the total depth is that owners desiring to decrease the nominal tonnage would be tempted to decrease the height out of water to an objection- able, although not to a dangerous, extent. Displacement tonnage has been advocated for British yachts, and was formerly in use for American yachts. It is urged in favour of this mode of measurement that it would bring yachts into the same category as other classes of ships, for which economical pro- pulsion is measured by the power required to drive a given weight at a given speed. Also that the designer would then have absolute freedom in choosing forms and proportions. On the other hand, it is argued that displacement tonnage favours the construction of mere "racing machines," vessels broad in relation to length, with shallow hulls, deep keels, and small range of stability, although exceedingly stiff (see Chapter III.). These objections are emphasized by reference to the yachts actually built in America to sail under displacement rules, which had a very small displacement in pro- portion to their extreme dimensions, great "stiffness," large sail- areas, and high speed in smooth water, but which proved inferior to the English type of yachts when sailing in strong winds and heavy seas. This displacement rule has now been abandoned in America, and there is no probability of its adoption in this country. Minor objections to its use have been raised on the grounds that variations in the amount of ballast carried at different times would necessitate variations in time-allowance ; also that many owners would object to having their yachts measured accurately, fearing that their forms might be reproduced or improved upon. Little weight attaches to these objections, however, as compared with those stated above. Another proposal which has found much favour, and has even been temporarily adopted, is to base time-allowances upon the sail- areas of yachts. One of the strongest advocates of this method used the following arguments: "If, with smaller sails, we outsail our " rival, who can say that an improvement in the form of the vessel is " not the cause ? we have given the owner a yacht of equal size and " greater velocity." Further, it is asserted as an observed fact that, when two well-designed yachts of dissimilar forms are sufficiently near to equality of size to permit of competitive sailing, their speeds will be about equal under most conditions, if the sail-spreads are of equal area. A very common practice has been to proportion the total sail-spread of yachts to the area of the load water-plane, or to the product of the extreme length and breadth of that plane. The New York Yacht Club, therefore, formerly based time-allowances 78 NAVAL ARCHITECTURE. [chap. n. upon the product of these two extreme dimensions, instead of upon sail-area, which would have involved greater difficulties in measure- ment. It will be observed, however, that the reasoning upon which the proposal is based takes account of size or displacement as well as sail-areas ; and that some definite regulation would be needed as to the "classes" in which yachts should be ranged for competitive sailing. Hence would arise considerable difficulty in practically applying the proposal. The Seawanhaka Yacht Club of New York and the New York Yacht Club have used rules based upon length on water-line (L), and sail-area (S), but differing from the Yacht Association Kule. Seawanhaka " corrected length " = — New York „ „ - GjJS^ti* These are clearly empirical rules, although they may serve the purpose intended for a time. The French Union des Yachts during 1892 held a congress for the consideration of the rules for tonnage-rating. After considering a large number of proposals, the congress approved, the following rule : — (l - 1) x P x VS Tonnage = 6 130 In this formula — L = the length at the water-line (in metres), with any projec- tions under water, except the rudder, added. This water- line has to be marked on the yacht. " Overhangs " (knees of the head and counters) are not to be reckoned except the sums of their lengths (taken at the deck) exceed half the lengths at the water-line. All such excesses to be added to the length. P = the perimeter (in metres), measured as follows : A chain to be passed under the yacht at the place where the girth (measured to top of deck) is greatest. To this add the greatest beam to outside of planking (excluding speoial projections or thick strakes). S = area of sails (in square metres) measured in a manner of which the details are prescribed. There is an obvious intention here to take account of depth as well as beam, length, and sail-spread. It will be interesting to see how this new rule works. chap, ii.] THE TONNAGE OF SHIPS. 79 Some eminent authorities in yacht-construction have favoured the determination of time-allowances on the basis of the "sail- carrying powers." It is clearly of the greatest importance to the speed of yachts that they should be capable of " standing-up " under their canvas ; but before any rule of this kind could be used, much more care would have to be bestowed upon the exact determination of the stability of yachts. Other methods for estimating yacht-tonnage for time-allowances proceed on the assumption thati the length, or some function of the length, should be the basis of measurement. Kules of this kind have been used in America, but in this country they have been applied only to boats or small yachts. External bulk, measured to the top of the upper deck planking, has also been used in America and advocated here. Another proposal has been to use the register (or fiscal) tonnage of yachts — a measure of their internal capacity. This last suggestion is simple ; but variations in the structures of yachts, affecting the thicknesses of their sides, would make the " register tonnage " a very unfair comparison of their external bulk, and there would be a temptation to decrease the freeboard, in order to lessen the tonnage, whether measured by internal capacity or by accurate determination of the outside shape. Besides these various rules there are many others in force, for small boats, canoes, and yachts. Space fails, however, for the further discussion of this in- teresting subject ; and it must suffice to add that each rule inevitably tends to produce its special type of vessel, adapted to derive the greatest advantage by the combination of small nominal tonnage with large driving-power.* * The reader desirous of pursuing estimating time-allowances in Mr. Dixon the subject further will find a full dis- Kemp's "Manual of Yacht and Boat cussion of existing tonnage-rules used in Sailing," and " Yacht Architecture." 8o NA VAL ARCHITECTURE. [chap. hi. CHAPTEE III. THE STATICAL STABILITY OF SHIPS. A ship floating freely and at rest in still water must fulfil two con- ditions : first, she must displace a weight of water equal to her own weight ; second, her centre of gravity must lie in the same vertical line with the centre of gravity of the volume of displacement, or "centre of buoyancy." 1 ' In the opening chapter the truth of the first condition was established, and it was shown that the circum- stances of the surrounding water were unchanged, whether the cavity of the displacement was filled by the ship or by the volume of water displaced by the ship. When the ship occupies the cavity, the whole of her weight may be supposed to be concentrated at her centre of gravity, and to act vertically downwards. When the cavity is filled with water, its weight may be supposed to be concentrated at the centre of gravity of the volume occupied (i.e. at the centre of buoyancy), and to act vertically downwards ; the downward pressure must necessarily be balanced by the equal upward pressures, or "buoyancy," of the surrounding water; therefore these upward pressures must have a resultant also passing through the centre of buoyancy. In Fig. 32, a ship is represented (in profile and trans- FIG. 32. Profile Seetion I vG «B \ k. } —I verse section) floating freely and at rest in still water. Her total weight may be supposed to act vertically downwards through the centre of gravity G-, the buoyancy acting vertically upwards through the centre of buoyancy B. If (as in the diagram) the line joining the centres G- and B is vertical, it obviously represents the common line of action of the weight and buoyancy, which are equal and chap, in.] THE STATICAL STABILITY OF SHIPS. 8l opposite vertical forces ; in that case the ship is subject to no dis- turbing forces, and remains at rest, the horizontal fluid pressures which act upon her being balanced amongst themselves. But if (as^ represented in Fig. 33) the centres G and B are not in the same vertical line, the equal and opposite forces of the weight and buoyancy do not balance each other, but form a " mechanical couple," tending to disturb the ship, either by heeling her or by producing change of trim or causing both these changes. If D = total weight of the ship (in tons), and GZ = perpendicular distance between the parallel lines of action of the weight and buoyancy (in feet) — Moment of couple = D x GZ (foot-tons). If the vessel is left free to move from this position, not being subjected to the action of external forces other than the fluid pressures, she will either heel or change trim, or both heel and change trim until the consequent alteration in the form of the dis- placement brings the centre of buoyancy into the same vertical with the centre of gravity G. It is important to note that, for any specified distribution of weights in a ship, supposing no change of place in those weights to accompany her transverse or longitudinal inclinations, the centre of gravity is a fixed point in the ship, the position of which may be correctly ascertained by calculation. On the contrary, the centre of buoyancy varies in position as the ship is inclined, because the form of the displacement changes. Hence, in treating of the stability of ships, it is usual to assume that the position of the centre of gravity is known, and to determine the place of the centre of buoyancy for the volume of displacement corresponding to any assigned position of the ship. The value of the " arm " (GZ) of the mechanical couple formed by the weight and buoyancy can then be determined. If it is zero, the vessel floats freely and at rest, in other words, occupies a " position of equilib- " rium ; " if the arm (GZ) has a certain value, the moment of the couple (D X GZ) measures the effort of the ship to change her position in order to reach a position of equilibrium. In this latter case the vessel can only be retained in the supposed position by G 82 NAVAL ARCHITECTURE. [chap. hi. means of the action of external forces ; and if her volume of dis- placement is to remain the same as when she floats freely, these external forces must also form a mechanical " couple," the equal and opposite forces acting in parallel lines. For example, suppose a ship to be sailing at a steady angle of heel, and the resultant pressure of the wind on the sails to be represented by the pressure P in Fig. 33 (section) acting along a horizontal line. When the vessel has attained a uniform rate of drift to leeward, the resistance of the water will contribute a pressure, P, equal and opposite to the wind-pressure ; and if d be the vertical distance between the lines of action of these pressures, we have — Moment of couple formed by horizontal forces = Pxd (foot-tons) ; which moment will be balanced by that of the couple formed by the weight and buoyancy. Hence — D x GZ = P x d, is an equation enabling one to ascertain the angle of steady heel for a particular ship, with a given spread of sail, and a certain force of wind. Supposing a ship, when floating upright and at rest, to be in a position of equilibrium, which is the common case : let her be in- clined through a very small angle from the initial position by the action of a mechanical couple. If, when the inclining forces are removed, she returns towards the initial position, she is said to have been in stable equilibrium when upright; if, on the contrary, she moves further away from the initial position, she is said to have been in unstable equilibrium when upright ; if, as may happen, she simply rests in the slightly inclined position, neither tending to return to the upright nor to move from it, she is said to be in neutral or in- different equilibrium. A well-designed ship floats in stable equi- librium when upright ; but many ships, when floating light, without cargo or ballast, are in neutral or in unstable equilibrium when up- right, and consequently " loll over " to one side or the other when acted upon by very small disturbing forces. Damage to the skin of a ship which was in stable equilibrium when intact, and the entry of water into the hold, may also produce unstable or neutral equilibrium in the upright position. It will be shown hereafter that there is a marked distinction between such instability and the conditions which lead to the capsizing of ships. The statical stability of a ship may be defined as the effort which she makes when held steadily in an inclined position by a mechanical couple to return towards her natural position of equilibrium — the upright — in which she rests when floating freely. This effort, as explained above, is measured by the moment of the couple formed chap, in.] THE STATICAL STABILITY OF SHIPS. 83 by the weight and buoyancy. Hence we may write, for any angle of inclination — Moment of statical stability = D x G-Z. But in doing so, it must be noted that in all ships, angles of inclina- tion may be attained for which the line of action of the buoyancy, instead of falling to the right of Gr (as in section, Fig. 34), and so tending to restore the ship to the upright, will fall to the left and tend to upset her or make her move away from the upright position. Starting from the upright, a ship may be inclined transversely, or longitudinally, or in any " skew " direction lying between the two. It is only necessary, however, to consider transverse and longitudinal inclinations in connection with statical stability; the innumerable possible skew inclinations being easily dealt with when the con- ditions of stability for the two principal inclinations have been ascer- tained. The minimum stability of a ship corresponds to transverse inclinations; the maximum stability, to longitudinal inclinations. It is, therefore, of the greatest importance to thoroughly investigate the changes in the statical stability of ships as they are heeled to greater and great er transverse inclinations, especially for ships which have masts and sails. Longitudinal stability is less important, but claims some notice, especially as regards its influence on changes of trim and pitching motions. FIG. 34 Taking first transverse inclinations, let them be supposed to be small ; it is then easy to estimate the statical stability when the position of the metaeentre is known. For our present purpose the metacentre may be defined, with sufficient exactitude, as the intersection (M in the cross-section, Fig. 34) of the line of action (BM) of the buoyancy when the ship is inclined through a very small angle, with the line of action (B,GM) of the buoyancy when the ship is upright and at 84 NAVAL ARCHITECTURE. [chap. m. rest. In vessels of ordinary forms, no great error is introduced by supposing that, for angles of inclination between the upright and 10 or 15 degrees, all the lines of action of the buoyancy (such as BM) pass through the same point (M) — the-metacentre. For any angle of inclination a within these limits the perpendicular distance (G-Z) of the line of action of the buoyancy from the centre of gravity is determined by — GZ = GM sin a. Hence by what is usually termed the "metacentric method," it follows that — Moment of statical stability = D X GM sin a. As an example, take a ship weighing 6000 tons, for which the distance GM = 3 feet, and suppose her to be steadily heeled under canvas at an angle of 9 degrees. Then — Moment of statical stability = 6000 tons X 3 feet X sin 9° = 18,000 X -1564 = 2815 foot-tons. For most ships the angles of steady heel under canvas lie within the limits for which the metacentric method holds; and consequently this method may be used in estimating the " stiffness of a ship, i.e. her power to resist inclination from the upright by the steady pressure of the wind on her sails. It must be noticed that this term " stiffness " is used by the naval architect in a sense distinct from " steadiness." A stiff ship is one which opposes great resistance to inclination from the upright, when under sail or acted upon by external forces; a crank ship is one very easily inclined; the sea being supposed to be smooth and still. A steady ship, on the contrary, is one which, when exposed to the action of waves in a seaway, keeps nearly upright, her decks not departing far from the horizontal. Hereafter it will be shown that frequently the stiffest ships are the least steady, while crank ships are the steadiest in a seaway. At present we are dealing only with still water, and must limit our remarks to stiffness. From the foregoing remarks it will be evident that, so far as statical stability is concerned, and within the limits to which the metacentric method applies, a ship may be compared to a pendulum, having its point of suspension at the metacentre (M, Fig. 34), and its weight concentrated in a " bob " at the centre of gravity G. Fig. 35 shows such a pendulum, held steadily at an angle a. The weight (D) acting downwards produces a tendency to return to the upright, measured by -the moment D X GM sin a, which is identical with the expression for the righting moment of the ship at the same angle. But this comparison holds only while the ship and the pendulum chap, hi.] THE STATICAL STABILITY OF SHIPS. 85 are at rest ; as soon as motion begins, the comparison ceases to be correct, and the failure to distinguish between the two cases has led some writers into serious error. If the centre of gravity of the ship lies below the metacentre, she tends to return towards the upright when inclined a little from it ; that is, her equilibrium is stable. If the centre of gravity of the ship lies above the metacentre, she tends to move away from the upright when slightly inclined ; that is, her equilibrium is unstable. If the centre of gravity coincides with the metacentre, and the ship is inclined through a small angle, she will have no tendency to move on either side of the inclined posi- tion, and her equilibrium is indifferent. The metacentre, therefore, measures the height to which the centre of gravity may be raised, without rendering the vessel unstable when upright ; and it was this property which led Bouguer, the great French writer to whom we owe the first investigations on this subject, to give the name metacentre to the point. Changes in the height (GM) of the metacentre above the centre of gravity produce corresponding changes in the stiffness of a ship ; in fact, the stiffness may be considered to vary with this height — usually termed the "metacentric height." If it is doubled, the stiffness is doubled ; if halved, the stiffness is reduced by one-half, and so on. Care has, therefore, to be taken by the naval architect, in designing ships, to secure a metacentric height which shall give sufficient stiffness without sacrificing steadiness in a seaway. In adjusting these conflicting claims, experience is the best guide. The vertical position of the centre of gravity of a ship depends upon the distribution of the weights of structure, equipment, and load. Over this distribution the designer has usually but little control. In war-ships, for example, the distribution of weights is governed largely by the freeboard, armament, protection, speed and coal- supply considered suitable in various types. In merchant ships, and especially in cargo-carriers, the case is even more difficult, as the loads vary in amount and character on different voyages ; and the designer can have little or no influence upon the stowage of cargo. The weight of cargo in the majority of merchant ships bears a considerable ratio to the weight of hull, propelling apparatus, and equipment. Passenger-steamers, in which the weight of cargo is relatively less, present a simpler problem than cargo-carriers; but in them also the designer has to work within specified conditions, and has little power to vary the vertical position of the centre of gravity. The vertical position of the metacentre depends upon the form of a ship, especially near the water-line at which she floats, and the extent to which she is immersed. Hence it is possible for the naval 86 NAVAL ARCHITECTURE. [chap. in. architect to exercise considerable control over its position by means of changes in form. For every water-line at which a ship can float, between her fully laden condition and the extreme light condition, the corresponding vertical position of the metacentre can be deter- mined by exact calculations. Other requirements have to be fulfilled, of course, concurrently with the provision of the amount of stiffness considered desirable in a new ship, under certain assigned conditions of lading. Ques- tions of propulsion necessarily exercise great influence upon the selection of forms and dimensions. Limitations of draught have to be accepted ; and frequently limitations of breadth, in view of the dimensions of dock-entrances. In some instances, other considera- tions impose such forms and ratios of draught to breadth, as give to vessels a higher position of the metacentre and greater stiffness than would be preferred for good behaviour. Speaking broadly, however, it is true that the naval architect can and does exercise control over the position of the metacentre by changes in forms and proportions. It has been explained above that when the position of the meta- centre is known, it affords a ready means of determining the line of action of the buoyancy for a moderate inclination of a ship of ordinary form, and of avoiding the necessity for determining the place of the corresponding centre of buoyancy. But in practice the position of the metacentre is fixed with reference to the centre of buoyancy, corresponding to the upright position of the ship. The distance (B,M, Fig. 34) is given by the formula * — -r, M _ moment of inertia of water-line area volume of displacement For transverse inclinations, such as we are now considering, the moment of inertia would be calculated about the middle line of the water-line section ; and this may be expressed in terms of the length (L) and breadth extreme (B) of that section. It may in fact be written — Moment of inertia = K x L x B s , where K is a quantity ascertained by calculation for the particular ship. Since the cube of the breadth appears in the expression for the moment of inertia, and only the first power of the length, any increase in the breadth must be most influential in adding to the * The " moment of inertia " of an from the axisi The proof of the formula area about any axis may be defined as given above involves mathematical the sum of products of each element of treatment which would be out of place that area, by the square of its distance here. chap, hi.] THE STATICAL STABILITY OF SHIPS. &7 value of the height (B X M) of the metacentre above the centre of buoyancy. The drawings of a ship furnish the naval architect with data for exact calculations of the volume of displacement, the position of the centre of buoyancy, and the moment of inertia of the water-line area, corresponding to any assigned draught of water. Details of the method of calculation would be out of place here ; but it may be of interest to state certain approximate rules derived from such calcula- tions, by means of which rough estimates may be made of the vertical positions of the centre of buoyancy and transverse metacentre in ships of ordinary form. I. For the approximate depth of the centre of buoyancy below the water-line from two-fifths to nine-twentieths of the mean draught may be taken. The larger coefficient should be used, for ships of full form. If the draught is increased by an unusually deep keel or false keel, the centre of buoyancy will lie higher than in ships of ordinary form. In yachts, for example, it is sometimes distant from the water- line only from 27 to 30 per cent, of the mean draught. H. For the coefficient K in the formula for the moment of inertia of the water-line area, or plane of flotation, the following approximate values may be taken : — K •04 to -045. Ships with extremely fine forms of load ^ water-lines j Ships with moderately fine forms of ditto *05 to "055. Ships of full forms of ditto . . . -06 to -065. A rectangle -083. In applying these coefficients it must be noted that the length and beam, in the formula for the height of the metacentre above the centre of buoyancy, are to be measured at the load-line ; so that these dimensions may differ from the extreme length and breadth. As an example, take her Majesty's ship Iron Duke, for which length (L) is 280 feet, breadth extreme (B) 54 feet, mean draught 22 feet, displacement 6000 tons. Here K should about equal £fo. Hence — Moment of inertia of water- 1 y ^ x Volume of displacement . = 6000 X 35. Height of metacentre above ) _ 11 x 280 x (54) 3 _ centre of buoyancy (BiM) J ~200 x 6000 x 35 6G ' Also (by Kule I.) approxi- \ mate depth of centre of I f x 2 2 feet = 8-8 feet, buoyancy below water j 5 surface . . . . ) 88 NAVAL ARCHITECTURE. [chap. in. Hence the metacentre should be situated about 2-7 feet above the water surface. Exact calculation showed it to be about 24 feet above the water surface. A still more rapid method of approximating to the height of the metacentre above the centre of buoyancy is based upon a combina- tion of the preceding formula, with the rules for " coefficients of " fineness " given on p. 3. Calling these coefficients C, and using the same notation as before, we have — t> m _ K x L x B 8 ^"CxLxBxD neglecting any small difference there may be between the length between perpendiculars and breadth-extreme of the ship and her greatest dimensions at the load-line. Eeducing this expression, it appears that — „, r K B 2 B a which is an expression of the simplest character, and shows how influential upon the height BjM is the ratio of breadth to mean draught. It will be noted that the coefficient a increases with increase in the value of K, and decreases with increase in C, the coefficient of fineness for displacement. Consequently the values of a may be practically identical in ships of very different degrees of fineness of form. In the extremely fine cruiser Blake, for example, the value of a is -078, and in the Royal Sovereign armoured battle-ship is "08. Taking a large number of examples, the values found for a range from -08 to "1. The latter value applies fairly to the older classes of unarmoured ships in the Eoyal Navy, and to some merchant ships. For the majority of armoured ships, and for many classes of merchant ships, a has the value "09. In vessels, like yachts, with very fine under-water forms or deep keels, a rises to '15. In some vessels of full under-water form, and in others with very fine ends, a has the value -08. Hence it will be evident that, while the foregoing approxi- mate rules are useful in making rough estimates, the naval architect must adhere to exact calculations for fixing the position of the meta- centre in any new design. By means of a series of such calculations, it is possible to con- struct a diagram — termed the " metacentric diagram " — showing the vertical positions of the metacentre and the centre of buoyancy for any mean draught of water between the deep load-line at which the vessel floats when fully laden, and the light-line at which she floats when empty. Such diagrams are very useful, especially for merchant chap, in.] THE STATICAL STABILITY OF SHIPS. 89 ships subjected to great variations of draught. The construction is very simple. Any horizontal line W^ (Fig. 36) is taken to repre- sent the maximum load-line of the ship. Through any point W, on it a vertical line ^d&-\ is drawn: the depth of the centre of buoyancy corresponding to the load-line is then set down below W^ on a certain scale, and this fixes the point B^ The length BjMj represents, on the same scale, the corre- sponding height of the metacentre M u above the centre of buoyancy B t . Through W 1 the straight line WVW2W3 is also drawn, making an angle of 45 degrees with W^. Then, for some other water-line parallel to the load-line WjLj (say WuLa, Fig. 36), a cor- responding construction is performed. The known distance between the two water-lines is set down from W^, and W 2 L 2 is drawn parallel to W^ ; through the point W2, where W 2 L 2 cuts the line WW 2 W 3 , a new vertical B 2 M 2 is drawn. On this vertical are set off, to scale, the calculated depth of the centre of buoyancy (B 2 ) below the line W.L2, and the height (B 2 M 2 ) of the corresponding metacentre above the centre of buoyancy. A similar process is applied to several other parallel water-lines at still lighter draughts : and so finally a series of points, B^Bs..., are determined, through which a curve is drawn, showing the locus of the centre of buoyancy for variations in mean draught from the extreme load condition to the extreme light condition. In a similar manner a curve M^M^M^... is drawn, giving the corresponding locus of the metacentres. Having obtained these curves, it is possible by means of simple measurement to determine the vertical positions of the centre of buoyancy and metacentre corresponding to any water-line parallel to the load-line W.Li and intermediate between it and the light-line. For example, let WL (Fig. 36) represent such a line at a given distance below W^. Where WL cuts W{W^W 3 draw the vertical BWM ; the intersection of this vertical with the metacentric curve gives the position M of the metacentre corresponding to WL ; and its intersection with the curve of centres of buoyancy fixes the position B of the centre of buoyancy. The metacentric locus is the more important, and the other curve is chiefly valuable as the means of constructing that locus. It should be remarked that the meta- centric locus only applies accurately to water-lines drawn parallel to W^j. If, as commonly happens, a ship changes trim considerably as she lightens, then the vertical positions of both centre of buoyancy and metacentre corresponding to the lighter line may not be accurately represented by the points fixed on the metacentric diagram by means 90 NAVAL ARCHITECTURE. [chap. III. FIG. 37. Displacement ■per inch xt.if M£j£ JErpnin/p/ital SB'.9f 8l'.9i Load/ Light % Light c.a of the mean draught, obtained by taking half the sum of the draughts forward and aft. FrOm the preceding explanations, it will be obvious that m different classes of ships the forms of metacentric curves (such as M^Mj, Fig. 36) may vary con- siderably. The only safe course in practice is, therefore, to construct the metacentric diagram for each class. But it may be interesting to give a few typical illustrations of such curves.* Fig. 37 shows a very common case for war-ships of ordi- nary form; the metacentric curve gradually rises from the load to- wards the light draught. On the same diagram is, indicated a con- venient arrangement for the most important data — displacement, and tons per inch — at each draught. Note. — This diagram represents the Another form occurring less fre- HT&L"rt ri th e he St^' ^^y » wai " sM P s T kes ^ condition 430 tons of water-hallast metacentric curve almost horizontal are supposed to he placed in the between the extreme draughts. In om '. vessels with "peg-top" forms of cross-sections — such as the Symondite type of the Eoyal Navy — the . metacentre occupies its highest position in the ship when she is at the load-draught, and falls gradually as the draught lightens (see Fig. 38).- Another variety of metacentric locus ap- pears in Fig. 36, where the metacentre first falls as the draught lightens, then passes through a position of minimum height, and gradually rises again. This frequently occurs in merchant ships of deep draught (in proportion to their beam) when fully laden, and with approximately vertical sides in the region between the load and light lines. The highest position of the metacentre in these ships usually corresponds to the light-line ; and the lowest to a draught intermediate between the load and light lines : very fre* quently the heights at the load and light lines are nearly equal, and (as indicated on Fig. 36) the metacentric locus for all variations in draught occurring on service lies wholly below the load-line. In war-ships, on the contrary, that -locus usually lies wholly above the * For further details on this subject see a paper by the author on " The Geometry of Metacentric Diagrams : " Transactions of the Institution of Naval Architects for 1878. chap, m.] THE STATICAL STABILITY OF SHIPS. 91 FIG load-line, the ratio of breadth to load-draught being greater than the corresponding ratio for merchant ships. The range of draught from the load to the light condition is much less for war-ships than for merchant ships. Metacentric diagrams are chiefly useful as a means of rapidly determining the stiffness of a ship when floating at a certain water- line, and with the centre of gravity in a cer- tain position, which is fixed by an independent investigation. For a certain mean draught and trim, the metacentre remains at a constant height in the ship ; and variations in the stowage of a given amount of dead weight can only affect the stiffness by the changes they produce in the vertical position of the centre of gravity. When that position has been ascertained for any given condition of stowage, it is usually shown on the metacen- tric diagram. For instance, in Fig. 36, when the ship floats at WL with M as the meta- centre, suppose the point G- to represent the ascertained position of the centre of gravity. Then G-M represents (to scale) the " metacentric " height," which measures the stiffness of the ship. For war-ships it is customary to perform this construction for both the load and light conditions, as well as for the condition of the ships when inclined (see p. 103), for the purpose of ascertaining the vertical position of the centre of gravity. For merchant ships the light condition only can be dealt with accurately in the same fashion ; since the stiffness in the load condition varies with changes in stowage. In many cases, however, the volumes and common centre of gravity of the total volume of the spaces assigned to cargo are estimated ; the maximum load-line is fixed; the corresponding dead weight is ascertained, and thence the number of cubic feet of space available fot stowing each ton of dead weight is ascertained. A homogeneous cargo of this density is then supposed to be placed on board, with its centre of gravity at the centre of gravity of the cargo-space. The weight of the ship when floating light, as well as the position of her centre of gravity in that condition, can be readily ascertained by an inclining experiment. Hence, combining the assumed cargo with these experi- mental data, a final result is obtained for the vertical position of the common centre of gravity of the fully-laden ship; and her metacentric height is determined for the assumed conditions of stowage, which are about as little favourable to stiffness as any conditions likely to occur in actual service, and lie outside the range 92 NAVAL ARCHITECTURE. [CHAP. III. of probability in some classes 'of ships. An interesting extension of this method is shown on Fig. 39.* The metacentric locus is drawn from light to load lines in the usual manner. In the light con- dition Mj is the metacentre, and Gc l the centre of gravity of the ship lies above it, so that FIG. 39. 8 OKI the vessel is in unstable equilibrium. It is found that a homogeneous cargo occupying about 58 - 5 cu- bic feet per ton of dead weight would just fill the cargo-spaces and bring the ship to her intended maximum load-line. If ]i .. fully laden in this manner, the homogeneous cargo has its centre of gravity at O2, the common centre of gravity of ship and cargo is at Gr a and the metacentre is at M 2 , about 15 inches above the centre of gravity G 2 . As the ship has taken in cargo, References. — 1, Curve of metacentres ; 2, curve of centre of gravity of homogeneous cargo ; 3, curve of centre of gravity of hull and homo- geneous cargo; 4, curve of capacity for space occupied by cargo; 5, soale of capacity (in units of 1000 cubic feet) ; 6, scale for height of cargo above ceiling ; 7, scale of mean draught gj^ has therefore acquired ofwater - stiffness. So far the dia- gram represents the common practice described above; but it furnishes further information of a valuable character. First, there is a " curve of capacity " giving the volume of the cargo-space corresponding to various heights of cargo in the hold ; second, there is a curve giving the locus of the centre of gravity of the cargo- space as the height of the cargo is increased. The curve of capacity resembles in its construction the curve of displacement described on p. 5 ; and the curve of centres of gravity of cargo-spaces resembles the locus of the centres of buoyancy on metacentric diagrams. Having this data graphically recorded, another step may be taken. Suppose the ship to be taking in cargo of the assumed average specific gravity, and, while her lading is incomplete, to be floating at a given water-line intermediate between the load and light lines. Her displacement at this given line is known ; thence the dead weight on board her is easily estimated, also the volume it occupies ; the height of its surface and that of its centre of gravity can then The author is indebted for this diagram to his friend Mr. John Inglis. chap, ni.] THE STATICAL STABILITY OF SHIPS. 93 be read off on the appropriate curves of capacity and centres of gravity of homogeneous cargo. Finally, the common centre of gravity of hull and homogeneous cargo can be found for the given water-line. A curve passed through the points G 1 && etc., gives the locus of this common centre of gravity of hull and cargo, throughout the period of loading; and the relation of this curve to the metacentric curve shows how the stiffness varies, under the assumed conditions, as the loading goes on. Such a graphic record as that in Fig. 39 can scarcely fail to be of value; although it does not strictly correspond to the con- ditions of ordinary service, it enables any other conditions to be readily estimated for. The greatest interest, of course, attaches to the two extreme draughts ; and of these the fully-laden condition is the more important, as previously indicated. Fig. 40 contains another example of this method applied to a cargo-steamer ; but in this case the curves of capacity and heights of centres of gravity of cargo are omitted. The reference letters»agree with those on Fig. 39. Under the assumed conditions of stowage the vessel is in neutral equilibrium when light, and unstable when fully laden, whereas for a considerable range of draught between these extremes she possesses a positive metacentric height, reaching a maximum value of 1 foot about midway between load and light draught. This vessel represents a class which is success- FIG. 40. fully employed in certain trades, with ' the frequent use of water-ballast when homogeneous cargoes are carried. If the coal in a cargo-steamer is stowed low in the hold, it may happen that, as it is burned and the ship lightens, she will become un- stable unless water-ballast is ad- mitted. This actually occurs in some types of ships, and will be readily understood by reference to Fig. 39. In the case supposed, the metacentre falls as the coal is burnt out; while the removal of the coal from the lower hold causes a sensible rise in the centre of gravity, and may cause it to rise centre of gravity of ship without cargo; Gr 2 , centre of gravity of ship and cargo, supposing the latter to be homogeneous, to fill the holds, and to weigh 2250 tons ; G 1; centre of gravity of ship and cargo, the dead weight being 1430 tons and other conditions as before ; 1, curve of metacentres ; 2, curve of centre of gravity of ship and cargo as the 2250 tons are dis- charged ; 3, curve of centre of gravity of ship and cargo as the 1430 tons are discharged ; 4, scale for mean draughts of water. 94 NAVAL ARCHITECTURE. [chap. III. above the corresponding metacentre. The necessary instructions for the admission of water-ballast and the maintenance of stability are easily prepared, and may be given in a simple form for the guidance of commanding officers.* Summing up the foregoing remarks on the metacentric method of estimating stability, it may again be stated that the metacentre is simply a fixed point through which the buoyancy of a ship may be supposed to act for all angles of inclination up to 10 degrees or 15 degrees in vessels of ordinary form. This is tantamount to saying that the metacentre may be taken as a hypothetical point of suspen- sion for a ship in order to estimate the righting moment when she is steadily heeled to any angle within the limits named, as indicated on Fig. 34, p. 83. For vessels of unusual form — as, for example, the monitor type with extremely low freeboard — the metacentric method cannot be trusted for such considerable inclination as in ordinary types. On the other hand, there are certain forms for which the metacentric method applies to even greater inclinations, or even for all possible inclinations. The well-known cigar-ships exemplify the last-named condition. All transverse sections of these ships are circles. Suppose Fig. 41 to represent the section containing the centre of buoyancy B for the upright position, WL being the water-line. Then obviously for any inclined position (such as is shown in Fig. 42, where the FIG. 42. original water-line is marked W^ and the original centre of buoyancy BJ the new centre of buoyancy B determines the vertical line of action (BM) of the buoyancy, which intersects the original * See a paper by Mr. A. Denny, on "The Practical Application of Stability Calculations : " Transactions of the In- stitution of Naval Architects for 1887. FIG. 43. chap. III.] THE STATICAL STABILITY OF SHIPS. 95 vertical (B X M) in the centre (M) of the cross-section. Hence, if Gi- be the centre of gravity, we shall have for any angle of inclination a, Moment of statical stability =Dx GrM sin a. In other words, the cigar-ship may be regarded as a pendulum turning about the point of suspension M throughout the whole range of its transverse inclinations, instead of limiting that comparison to 15 degrees, as is done for ordinary ships. The conditions of stability of a wholly submerged or submarine vessel are as simple as those of the cigar-ship. In Pig. 43 a cross- section of such a vessel is given ; B is the centre of buoyancy, and for a position of equilibrium B and the centre of gravity Gr must lie in the same vertical line. When this condition is unfulfilled (as in the diagram), the weight and the buoyancy form a mechanical couple, just as in the case of a ship having a part of her volume above water. For the submarine vessel, however, inclination pro- duces no change in either the form of the displacement or the position of the centre of buoyancy ; for all positions the buoyancy acts upwards through the same point B, and the total weight downwards through the centre of gravity Gr. Consequently stable equilibrium is only possible when the centre of gravity lies (as in the diagram) below the centre of buoyancy ; for obviously, if G- were placed vertically above B, and the vessel were inclined ever so little, no position of rest could be reached until Gr was placed vertically below B. For wholly submerged floating vessels, therefore, the centre of buoyancy takes the place of the metacentre in vessels partially immersed, and for all angles of inclination (such as a) — Moment of statical stability = D x GB sin a. It has been remarked above that experience is the best guide for naval architects in selecting the values of " metacentric heights " (GrM, Fig. 34) for various classes of ships, when circumstances permit of such selection. The following information respecting the actual metacentric heights in different classes will be of interest. Taking, first, war-ships, two tables summarize the facts for armoured, protected, and unarmoured vessels respectively ; and for the fully laden con- ditions. When the coals and consumable stores are not on board, 9 6 NA VAL ARCHITECTURE. [chap. hi. the change in metacentric height varies in different classes, being affected both by the character of the metacentric locus and by the manner in which the consumable weights were originally stored. In some cases there is practically no change in " stiffness " with consumption of coals, etc. This is true of armoured vessels like the Inflexible, with large proportions of the coal carried near the height of the load-line. It is also true in most classes of modern swift protected cruisers in the Eoyal Navy, and this practical constancy in stiffness is advantageous. Other classes with lower stowage of coal, etc., lose in stiffness as they lighten to the extent of from 6 inches to 1 foot, or even more. Calculations are always made for the stiffness in the extreme load and light conditions, and often for intermediate conditions of coal expenditure. The tables on p. 97 require few explanatory remarks. Experience has led to the common selection of metacentric heights of from 2£ to 4 feet in vessels of war possessing moderate sail-power as well as steam-power. Such heights gave a fair amount of stiffness under sail, in association with good behaviour in rough water. As the speeds of war-ships have been increased, and sail-power has been either abolished or greatly diminished, the metacentric heights have also been diminished, especially in the cruiser classes. These heights now commonly vary from If to 2£ feet, and this amount of stiffness is found sufficient for all manoeuvring, while it favours steadiness at sea. In certain special classes of armoured ships, with limited lengths of the water-line protected by vertical armour, it has been deemed desirable to accept much larger values of the meta- centric heights, in order to provide against possible losses of stability due to damage in action. These very stiff ships are not as steady gun-platforms as their predecessors with more moderate metacentric heights. The latest types of battle-ships are designed in accordance with the earlier models, and the anticipation that they would be steadier in consequence has been realized on service. Merchant ships, especially cargo-carriers, as above explained, are subjected to considerable variations in the character and stowage of their cargoes, over which the designer has no control. Conse- quently, the stiffness of an individual ship may vary greatly on different voyages; and the stevedores who regulate the stowage, chiefly by practical rules deduced from experience, to a large extent control the stiffness of the laden ship. Under these circumstances it is not possible to give exact particulars of metacentric heights, such as have been given for war-ships. From facts recorded, it appears that in fully laden merchant steamers the metacentric heights sometimes fall as low as 6 or 8 inches ; frequently they lie between 1| and 3 feet, and occasionally have still higher values. chap, in.] THE STATICAL STABILITY OF SHIPS. 97 Armoured ships. Metacentric height (GM). A. Sail-power and steam — 1. Converted frigates (formerly two-deckers): Prince Consort class, Boyal Navy ; Gloire class, French Navy 2. Warrior and Minotaur classes, Royal Navy; Flandre class, French Navy .... 3. Central-battery ships : Bellerophon, Hercules, Alexandra, Royal Navy ; Alma class, French Navy 4. Ocean class, French Navy B. Steam-power only — 5. Seagoing turret-ships, Royal Navy (moderate freeboard) : Devastation, Dreadnought, Tra- falgar 6. Barbette-ships, Royal Navy: Admiral and Im- perieuse classes ...... 7. Barbette-ships, Royal Navy and French Navy: latest types 8. Central citadel turret-ships, Royal Navy : Inflex- ible and Ajax classes 9. Coast-defence ships : Qlatton, Royal Navy ; Belter, French Navy 10. American type of coast-defence monitor Feet. 6to7 4to4£ 2|toi If to! 3£to4£ 4|to6 2|to3| 5£to8£ 6 to 8 About 14 Unarmoured and protected ships. Metacentric height (GM). A. Sail-power and steam (single screws) — 1. Obsolete screw line-of-battle ships 2. Obsolete screw frigates and corvettes . 3. Wood and composite corvettes and sloops (types still on service) 4. Wood and composite gun-vessels and gunboats . 5. Swift frigates and corvettes : Inconstant and Active classes, Royal Navy ; Tourville and Seignelai/ classes, French Navy B. Steam only, or very light rig (twin screws) — 6. Swift despatch-vessels (unprotected) : Iris class . 7. Protected cruisers of recent construction, Royal Navy : Mersey, Medea, and Apollo classes ; and unprotected torpedo cruisers : Archer class 8. Sloops and small protected cruisers, torpedo gun- boats 9. Coast-defence and river-service gunboats (unpro- tected) 10. Troop and store ships 11. Tugs and small vessels not seagoing . 12. Torpedo-boats (1st class), earlier types „ „ later types . 13. „ (2nd class), earlier types „ „ later types . Feet. 4£to6£ 4to5 2f to 4 2|to3 2£to3 2|to3 l|to2£ 2to2£ 7 to 12 2to3 lto2 0-8 to 1£ l|to2 0-4 to 0-8 0-8 to 1-0 98 NAVAL ARCHITECTURE. [chap. in. Not a few instances have occurred where, with heavy dead-weight cargoes improperly stowed, vessels have been made unduly stiff, and heavy rolling at sea has resulted with serious damage in some cases. On the other hand, large ocean-going passenger-steamers with meta- centric heights of from 1 to 2J feet have gained high reputations for steadiness. For cargo-carriers, homogeneous cargoes, such as grain, are usually considered to favour stiffness least with a given dead- weight. Under this condition cargo-steamers have been found to possess metacentric heights of ^ to ^ ff of a foot ; others have had 1J to 2 feet; but some types cannot carry such cargoes without ballast, although they require no ballast in actual service with miscellaneous cargoes. Sailing merchant ships, when laden, must possess sufficient stiffness to stand up under their canvas, and this fact furnishes a valuable practical test of the minimum amount of metacentric height which is permissible. It is stated on good authority that with ordinary stowage these vessels may possess metacentric heights of 3 to 3£ feet. On the other hand, it must be noted that the dead- weight carried by such vessels frequently exceeds two-thirds of their load displacements ; so that differences in stowage may produce very considerable variations in stiffness. As a rule a sailing-ship laden with a homogeneous cargo would not possess a metacentric height exceeding 1 foot or 18 inches ; and would require to carry ballast, or dead-weight serving as ballast, low down in the hold in order to obtain sufficient stiffness. There are, however, exceptions to this rule, in which metacentric heights of 2 to 3 feet can be secured with a homogeneous cargo, and without ballast ; in order to increase the stiffness even in such vessels some dead-weight or ballast would usually be carried, although less in proportion than in ships of ordinary form. The opposite extreme to a homogeneous cargo is, of course, that where the cargo consists of heavy materials, such as pig-iron, rails, etc. ; and if care is not exercised in stowing such cargoes excessive stiffness may be obtained, causing heavy rolling at sea. The comparatively large metacentric heights of the obsolete classes of sailing war-ships doubtless tended to increase their rolling ; but these vessels had to fight under sail, and had large sail-power, so that a considerable degree of stiffness was essential, in order to prevent excessive heeling and consequent inefficiency of the guns fought on the leeward broadside. Only a few experiments were made to determine the actual stiffness of these vessels. The best information available gives them metacentric heights of from 4£ to 6J feet when fully laden, and about 1J to 2 feet less when light. Considerable weights of ballast and water in tanks were carried chap, in.] THE STATICAL STABILITY OF SHIPS. 99 permanently to give this stiffness. As much as one-seventh to one- eighth of the total displacement was often assigned to water and ballast, and sometimes a large proportionate weight of ballast was carried. In sailing-yachts metacentric heights of 3 to 4 feet are common ; there are, however, some classes of broad shallow yachts in which the corresponding heights rise to 8 or 10 feet. Small yachts of from 3 to 5 tons (Thames tonnage) have metacentric heights, in some instances, of from If to 2£ feet. Yachts possessing steam as well as sail power, and having good reputations as sea boats, have been found by experiment to have metacentric heights of 3 to 4 feet. Examples occur where the corresponding heights are only about 2 feet.* The systematic experimental determination of the metacentric heights of war-ships belonging to the Eoyal Navy may be said to date from 1870. Prior to that time many experiments were made on typical ships, but the practice was not general. In private ship- yards similar experiments were but rarely conducted until a much later date. Now many leading firms regularly make inclining experi- ments, and there is reason to hope that the practice will become general. Already a great mass of information has been obtained, and constant additions are being made thereto. Most of this! infor- mation is naturally in the private records of shipowners and ship- builders, although much has been published. From the designer's point of view, interest chiefly centres in the condition of merchant ships when floating light with no weights on board other than those belonging to hull, equipment, or machinery. Having ascertained the vertical position of the centre of gravity for this condition, it is an easy matter to approximate to the change in that position pro- duced by putting any weights on board, and thus to estimate the " metacentric height " for a given stowage of dead-weight. This will appear more clearly from the explanations given on p. 117. Con- fining attention for the present to the light condition of merchant steamers, the following table will be of some interest, containing as it does results deduced from experiments made to determine the actual stiffness of a number of vessels of various classes.! * See \ Mr. Dixon Kemp's " Yacht Denny, of Dumbarton ; Messrs. A. and Architecture " for details of experimental J. Inglis, of Glasgow ; Messrs. R. Napier results. and Sons, of Glasgow. The remaining t For many of the facts in this table examples are taken from the results the author is indebted to gentlemen of inclining experiments made on mer- connected with some of the leading cantile steamers bought into the Royal private shipbuilding firms — including Navy. Messrs. Laird, of Birkenhead; Messrs. roo NAVAL ARCHITECTURE. [CHAP. III. Tabular Statement of the Results of Inclining <2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Length between perpendi- culars. ft. in. 440 350 390 340 320 320 320 313 285 290 290 264 253 234 195 227 210 220 220 200 178 125 60 Breadth, extreme. ft. in. 46 S.g.8. g o"S .8 — 5 44 6 39 46 2 40 40 34 33 6 35 34 32 32 33 2 29 29 2 28 28 27 30 6 26 27 20 12 feet. 36-25 34-5 30-8 34-0 28-5 22-7 26-5 25-5 26-5 25-8 16-6 23-0 26-3 19-6 180 20-6 15-0 22-0 22-5 13-9 20-0 9-5 6-3 Experimental data for ships floating light, with water in boilers, but no cargo or other dead- weight on board. Mean Draught. ft. in. 13 2 18 8 13 6 16 6 9 7 11 5 11 4 11 6 9 10 9 2 10 3 8 11 9 10 10 6 12 11 8 9 9 4 Displace- ment. 8 5J 9 6 4 9 3 11 tons. 4570 4240 3200 3140 2110 1900 1880 1760 1610 1530 1410 1240 1130 1100 1040 860 780 780 750 630 600 180 32 Meta- centric height (GM). feet. -1-0 1-2 - -7 2-3 2-9 5-2 -1-25 •2 2-1 1-5 2-4 1-5 2-0 1-5 1-3 •83 • -3 1-8 1-4 3-2 1-8 o o "3 MO w feet. 22-5 20-5 17-9 20-0 18-0 15-8 17-0 15-4 14-85 14-9 12-7 14-5 14-1 11-2 12-0 11-9 11-5 12-8 12-7 10-4 11-5 7-4 4-3 Ratio, A;D. •62 •594 •58 •588 •63 ■696 •64 •6 •56 •577 •765 •63 •536 •57 •67 •577 •77 •58 •565 •75 •575 •78 •68 It will be remarked from the table that there are very consider- able differences in the stiffness, as well as in the vertical position of the centre of gravity (in relation to the total depth) of different ships. Many of these vessels are sufficiently stiff, when floating chap, hi.] THE STATICAL STABILITY OF SHIPS. IOI Experiments made on Various Types op Merojhant Steamships. REMARKS. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ( Trans- Atlantic mail steamer ; new type ; cellular double bottom ; large \ deck-houses ; light rig. ( Mail steamer (old type) ; good speed ; good sail-spread ; forecastle, poop, \ and deck-houses ; 180 tons of permanent ballast. ( Cargo and passenger steamer ; good speed ; light rig ; deck-houses and \ turtle covers at ends. Same type as (2) ; with 75 tons of permanent ballast ; deck-houses only. {Cargo and passenger steamer ; good speed ; light rig ; poop and forecastle ; continuous double bottom. {Cargo and passenger steamer ; good speed ; light rig ; awning deck ; and heavy deck-houses. ( Cargo steamer ; moderate speed ; light rig ; turtle covers at ends, and \ deck-houses ; water-ballast tank above ordinary floors. Passenger and cargo steamer ; high speed ; light rig ; deck-houses. ( Cargo steamer ; moderate speed ; light rig ; forecastle and deck-houses ; \ continuous double bottom. Ditto ditto ditto. Passenger steamer (paddle-wheel) ; high speed ; light forecastle and full poop. Cargo steamer ; low speed ; light rig ; flush deck. Ditto ditto, f Cargo and passenger steamer ; moderate speed ; light rig ; forecastle, poop, \ and deck-house. j Armed sloop ; composite built ; good speed ; full rig ; light armament ; I 150 tons of permanent ballast. ( Cargo and passenger steamer ; moderate speed ; brig rig ; awning deck \ and deck-houses above. j Cargo and passenger steamer ; moderate speed ; moderate rig ; forecastle, \ poop, and deck-houses. Cargo steamer ; moderate speed ; light rig ; deck-houses. Ditto ditto. ( Cargo and passenger (Channel service) ; good speed ; light rig ; poop, fore- \ castle, and deck-house. Cargo steamer ; low speed ; light rig ; deck-houses ; 80 tons of ballast. Cargo boat ; low speed ; light rig ; forecastle and raised quarter-deck. Steam-launch. light, to permit of their being shifted from berth to berth in port without requiring ballast. Others are so stiff that they might, as far as this quality is concerned, be safely trusted from port to port with little or no ballast. Others, on the contrary, require to be ballasted 102 NAVAL ARCHITECTURE. [chap. hi. in order that they may stand up without cargo ; although when fully laden they may have sufficient metacentric heights without ballast. Some of the steamers in this last category are worked without ballast, coals being shipped as cargo is discharged in order to preserve sufficient stiffness ; while others use water-ballast as the most con- venient method of meeting the requirements of the case, and others of older type require rubble-ballast, or pig-iron, to be put on board as cargo is discharged. The explanatory notes attached to the table will enable the effect of forecastles, poops, and deck-houses upon the vertical position of the centre of gravity to be traced, as well as the influence of differences in the rig or structure of various ships. For purposes of guidance in design fuller details would be required, but for the present purpose the particulars given will suffice. Another table (pp. 104, 105) contains results of experiments made on several classes of sailing-ships, to determine their metacentric heights and the positions of the centres of gravity. For the obsolete classes of war-ships both the load and light conditions are given ; for the merchant ships only the light condition ; and for yachts only the load condition, the weight of consumable stores, etc., carried in them being comparatively small.* Practical Applications of Metacentric Stability. — Attention will next be directed to some of the more important practical applications of the metacentric method of estimating stability for transverse incli- nations. The first to be noticed will be the inclining experiment, by means of which the vertical position of the centre of gravity of a ship is ascertained after her completion. In designing a new ship the naval architect makes an estimate fpr the position of the centre of gravity, and with care can secure a close approximation to accuracy. On the other hand, a lengthy and laborious calculation is required in order to fix the position of the centre of gravity accurately ; and it is now generally agreed that, for purposes of verifying estimates, as well as of obtaining trustworthy data for future designs, inclining experiments are desirable. These experiments are simple as well as Valuable, and it may be of service to indicate the manner in which they are usually conducted in ships of the Eoyal Navy. The ship being practically complete — with spars on end, the bilges dry, the boilers either empty or quite full, no water in the * This table is compiled from infor- Mr. Dixon Kemp's publications. Special mation given in the " Papers on Naval thanks are due to Mr. John Inglis and Architecture " (1827-33) ; " Reports," by the late Mr. Henry Laird for facts re- Messrs. Read, Chatfield, and Creuze specting merchant ships. The particulars (1842-46) ; " Reports on Masting," made for the Sunbeam are published with the to the Committee of Lloyd's Register permission of Lord Brassey. (1877); and (for yachts) chiefly from chap, in.] THE STATICAL STABILITY OF SHIPS. 103 interior free to shift, and all weights on board well secured so that they may not fetch away when she is inclined — is allowed to come to rest in still water. A calm day is desirable, but if there be any wind, the ship should be placed head or stern to it and allowed to swing free, the warps being so led that they may practically have no effect in resisting the inclination of the ship. For the purpose of producing inclination, piles of ballast are usually placed on the deck (see W, W, Fig. 44), being at first equally distributed on either side, but in some cases the guns of a ship have been traversed from side to side instead of using ballast. Two or three long plumb-lines are hung in the hatchways, and by means of these lines the inclinations from the upright are noted. All being ready, and the ship at rest, the positions of the plumb-lines are marked, and the draught of water is taken. The position of the metacentre corresponding to this draught can then be ascertained by calculation from the drawings. Next, a known weight of ballast (W, Fig. 44) is moved across the deck through a known distance. The vessel becomes inclined, and after a short time rests almost steadily in this new position ; in other FIG. 45. words, is once more in equilibrium, as shown in Fig. 45. Conse- quently, for this new position, the metacentre M must be vertically above the new centre of gravity (GJ ; for obviously the shift of ballast has moved the centre of gravity of the whole ship through a certain distance GG : parallel to the deck, and it is this movement of the centre of gravity that produces the inclination. Suppose a to be the angle of inclination noted on the plumb-lines when the ballast W has been moved through the transverse distance d. Then (since GGj is perpendicular to GM) we have — GGc x = GM tan a ; or GM = GGi cot a. And if GG X can be determined, the distance of the centre of gravity below the known position of the metacentre can be found, and the true vertical position of the centre of gravity is ascertained for the experimental condition of the ship. Any subsequent corrections io4 NAVAL ARCHITECTURE. [chap. in. Tabular Statement of the Results or Inclining 12 13 14 15 16 17 18 19 Length between" perpendi- culars. Breadth, extreme. War-ships- feet. 113 100 100 141 131 feet. 35-4 30-9 32-3 38-8 40-6 u ex, w - ~ a. s la* -a a> Q 5Q feet. 19-2 15-4 17-7 27-5 27-5 Mean draught. ft. in. 15 4 13 8 13 9 12 9 16 7 15 17 4 16 Displace- ment. tons. 670 495 475 405 1075 875 1055 890 Meta- centric height. feet. 4-85 4-77 •a 5,-, w feet. 15-4 12-2 12-5 13-5 180 19-9 17-6 19-3 Merchant ships (light condition)- Yachts— 86-0 100-0 90-5 85-75 81-25 79-5 103-0 154-75 18' 16 18' 19 20 17 20-8 27-5 14' 13 14 13 12 13 12 17-3 10 9 9 4 10 1 10 10 9 5 10 6 9 7 13 160 158 155 150 128 115 135 576 3-45 12-4 Ratio, A:D. 6 273 43-1 25-4 9 7 1440 2-7 20-1 7 263 38-3 24-6 9 2 1100 •75 19-5 8 225 37-5 24-6 9 3 1010 -1-5 21-0 9 217 35-5 22-7 8 7 860 •0 18-8 10 215 35-0 22-3 9 810 - -5 18-4 11 148 26-9 15-0 6 5 290 2-0 12-2 •8 •79 •7 •76 •65 •72 •64 •7 •79 •79 •85 •83 •825 •81 •528 •43 •57 •64 •72 •62 •64 •72 * For the vessels named in this table, except the yachts, the depth (D) is The height, h, of the centre of gravity is also estimated above the top of this draught and the least freeboard ; and the height of the centre of gravity is measured mean draught. The lengths and breadths extreme for the yachts are taken at the consequent on the removal of the ballast, addition of water in the boilers, or other alterations in the condition of the ship when fully equipped, can be easily made. The value of GGri can be readily estimated by means of a simple chap, in.] THE STATICAL STABILITY OF SHIPS. I05 Experiments, etc., made on Various Classes of Sailing-Ships.* REMARKS. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 18-gun corvette of 1832 ; load condition. 18-gun sloop of 1830 ; load condition. Brig ; load condition. Brig ; light condition. Frigate ; load condition. Frigate; light condition. Frigate ; load condition. Frigate ; light condition. Full ship rig ; estimate by Lloyd's surveyors ; registered length and breadth. Ditto ditto ditto. Poop, forecastle, and exceptionally heavy rig ; result of inclining experiment. Poop, forecastle, and full ship-rig ; ditto. Forecastle, deck-house, and full ship-rig ; ditto. ( Three-masted schooner ; estimate by Lloyd's surveyors ; registered length \ and breadth. Miranda, schooner ; 78 tons of ballast N pernor, yawl; 79-5 „ „ I The stability of these vessels &a We schooner; 73 „ „ V has been foUy investigated £foWa,yawl; 54 „ „ / by Mr . rfeon Kemp. Rose of Devon, yawl ; 57 Kriemhilda, cutter; 54 Revenue cutter ; 48 . ( Sunbeam, three-masted schooner ; 75 tons of ballast ; Lord Brassey's \ yacht, with good steam-power. reckoned to the top of the projection of keel, false keel, etc., beyond the garboards. projection. For the yachts, the total depth is taken; i.e. the sum of the mean from a line drawn parallel to the load-line, at a distance below it equal to the load-line. calculation, the character of which may be better seen by means of an illustration. A uniform lever (Fig. 46) is loaded with two weights, W, placed at equal distances from the middle ; it will then balance upon a support placed at the middle (G) of the length. !06 NA VAL ARCHITECTURE. [chap. in. Now let one of the weights W be moved to the opposite end (as in Fig. 47) through a distance d. Obviously the point about which w FIG. 46. w * ne l ever w iH balance (that is, J^i c __JML i the centre of gravity of the A Mihh lever and the weights W) will F(G 47 no longer be at the middle, but at some point (G l5 Fig. 47) to the right of the middle. r A ~ 3 \ 5 If D be the total weight of the lever and the weights it carries, by the simplest mechanical principle it follows that — W d T>xGGl = W.d; whence GG t = -=p What is true in this simple case is true also for the ship ; the line GG 15 in Fig. 45, joining the old and new positions of the centre of gravity, must be parallel to the deck-line, across which the weight W is moved, and the above expression for GG X holds. Hence, since — W d GM = GG X . cot a, while GG X = -^j- it follows that — W GM = — . d cot a, an equation fully determining the position of the centre of gravity G in relation to the known vertical position of the metacentre M, ascertained by calculation from the drawings. As an example, suppose a ship for which the displacement (D) is 4000 tons to have 60 tons of ballast placed upon her deck, 30 tons on each side. When the 30 tons (W) on the port side is moved to starboard through a transverse distance of 40 feet (d), the vessel is observed to rest at a steady heel of 7 degrees from her original position of rest. Then, from the above expression — W 30 GM = — . d cot a = — - x 40 X cot 7° D 4000 3 = — X 8-144 = 2-43 feet. In practice it is usual to subdivide the ballast on each side into two equal piles, and to make four observations of the inclinations produced by — (1) Moving one pile of ballast from port to starboard ; (2) Moving second pile of ballast from port to starboard. These two piles having been restored to their original places, the plumb-lines should return to their first positions, unless some chap, in.] THE STATICAL STABILITY OF SHIPS. 107 weights other than the ballast have shifted during the inclinations. Then two other inclinations are produced and noted by — (3) Moving one pile of ballast from starboard to port ; (4) Moving second pile of ballast from starboard to port. The results of observations (1) and (3), (2) and (4) should agree respectively, if the four piles of ballast are of equal weight, and if the distance d is the same for all; the inclinations in (2) and (4) should be about twice those in (1) and (3). The values of GM are deduced from each experiment, and the mean of the values is taken as the true value of the metacentric height at the time of the experiment. Thence it is easy to deduce the metacentric height for the vessel in her fully equipped seagoing condition or in any other assigned condition. The reason for great caution in preventing any motion of weights on board, other than the ballast, during the inclining experiment, will appear from the expression given above for the motion (GG^ of the centre of gravity. The moment due to the motion of the ballast ~Wd is comparatively small ; in the above example, which is a fair one — Wd = 30 tons x 40 feet = 1200 foot-tons, and — GGl = 4000 = AfoOtOnly - Now, if other weights, and particularly free water in the bilges, shift as the ship inclines, their aggregate moments may bear a considerable proportion to W . d, and so the estimated value of GG a may be less than the true one, if no account is taken of the shift of water. For example, 5 tons of water free to shift 30 feet in a transverse direction would have a moment (5 x 30) of 150 foot- tons, or no less than one-eighth that of the ballast, and if its effect were unobserved through carelessness, the motion of the ballast would be credited with producing an inclination about one-eighth greater than it could produce if acting alone. In the foregoing example, if such an error had been made, instead of writing Wd = 1200 foot-tons, it should have been 1200 + 150 = 1350 foot-tons ; so that the metacentric height would have been — 1 R'iO 27 GM = ^ x cot 7° = -^ x 8-14 = 2-75 feet. 4000 80 In performing inclining experiments, too great care cannot, there- fore, be taken to ensure that no other weights shall shift than those made use of to produce the inclinations. Various proposals have been made for enabling the actual metacentric heights of laden merchant ships to be experimentally Io8 NAVAL ARCHITECTURE. [chap; m. determined by commanding officers, in any condition of lading. The principle of all such proposals is that of the inclining experi- ment just described ; and to produce inclinations, instead of shifting ballast, a fixed quantity of water, measured by filling a tank or boat, is used at a given distance from the middle line. The moment producing inclination being thus made a constant, it is necessary, in order to determine the metacentric height, to know the displacement for the water-line at which the ship is floating, and to note the angle of heel produced by filling the boat or tank. By means of tables or diagrams prepared by the shipbuilder and placed in the hands of the captain, the latter is to be freed from the necessity for any calculations. TJp to the present time these plans have not been extensively adopted; they would add much to our information if carried out with sufficient care, but under working conditions there are often considerable difficulties in the way of satisfactory experiments.* A second useful application of the metacentric method is found in a practical rule for estimating the angle of heel produced by moving a weight athwartships in a ship. Referring to the formula — W GM = — d cot a, we may arrange it as follows : — W.d tan a = D.GM and for the case under consideration assume that all the quantities on the right-hand side of the equation are known, the value of tan a being thus determined. As an example, suppose a weight (W) of 5 tons to be moved horizontally a distance (d) of 30 feet athwartships in a ship of 1500 tons displacement (D), having a metacentric height of 3 feet ; then — 5 30 1 tan a = ——— X — = — 1500 3 30 a = 2° (nearly). This rule is of service in approximating to the heel produced by transporting guns or heavy weights from side to side on a deck or platform which is nearly horizontal athwartships. When the vertical positions of weights already on board a ship are changed, the result is simply a change in the position of the * For details see Mr. Taylor's paper tects for 1884; and a paper by Mr. A. on a Stability Indicator in the Transac- Denny in the Transactions for 1887. tions of the Institution of Naval Archi- chap, m.] THE STATICAL STABILITY OF SHIPS. 109 centre of gravity of the ship ; for obviously the displacement and position of the metacentre remain unaltered, since there is no addition or removal of weights. The shift of the centre of gravity can be readily estimated by the rule already given. Suppose the total weight moved to be w, and the distance through which it has been raised or lowered to be h, then, if GG X be the rise or fall in the centre of gravity — where D is the total displacement of the ship. If GM was the original height of the metacentre above the centre of gravity, for an angle a within the limits to which the metacentric method applies — Original moment of statical stability = D x GM x sin o Altered moment of statical stability = D (GM + GG 2 ) sin a. The alteration is an increase when the weights are lowered; a decrease when the weights are raised. As an example, take the case of a ship of 6000 tons displacement, having a metacentric height of 3J feet ; and suppose spars, etc., weighing together 10 tons, to be lowered 70 feet. Then — 10 x 70 7 GG 2 (fall of centre of gravity) = g = — foot. Original moment of statical stability = 19,500 foot-tons x sin a. Altered moment of statical stability = 6000 (3£ + — ) sin a = 20,200 foot-tons x sin a. Another case where weights already on board a ship are shifted, involves a motion of the centre of gravity of the weights moved in both the horizontal and the vertical directions. For example, when coal or grain cargoes are carried, and a vessel is steadily heeled under sail to one side for a considerable period, the cargo may shift to leeward. In such cases, if the inclining forces were removed, the ship would obviously not return to the upright^ but would rest in an inclined position, which can be very simply determined. Let Pig. 48 illustrate this case. WL is the load-line ; M is the metacentre corresponding thereto. Suppose, when the ship is upright in still water, the grain in a partially filled hold has ah for its surface ; and that after she has been steadily heeled for a considerable time that surface changes to cd. Let ah and cd intersect in e. Then, what has happened is this: a wedge-shaped mass of grain originally at aee, of known weight W, and having its centre of gravity at g u has been shifted into the position bed with its centre of gravity at g?.. no NAVAL ARCHITECTURE. [chap. III. Join g t g 2 . Then, as explained above, if G x be the centre of gravity of the ship and cargo before any shift took place, its new position FIG. 48. jtfter cargo d&b i! Vqftm cargo « G 2 will be found on a line G X G 2 drawn parallel to g^ ; and we must have — W GiG 2 = -j- . g x g % Now, if the inclining forces are supposed to be removed, the ship will find her position of equilibrium, when the new position G 2 of the centre of gravity lies vertically below the metacentre M. And since two sides of the triangle GiMG 2 (G X M and GjG 2 ) are given, as well as the angle MGjG^ that triangle is fully known, and the angle GiMGa can be ascertained. This will be the angle of heel required. As an example, take the case of a ship of 3200 tons displacement, which, when fully laden with a cargo of coals, has a metacentric height of 2J feet. Suppose 80 tons to be shifted so that its centre of gravity moves 20 feet transversely, and 4 feet vertically. Then the corre- sponding transfers of the centre of gravity of ship and cargo will be given by the equations — Horizontal motion = — „^„„ = - 5 foot. Vertical rise = 3200 80 x 4 3200 = •1 The angle of heel in this case would be given with quite sufficient accuracy by the equation — horizontal transfer of centre of gravity -5 1 tan a = — — . . . , = — = - original metacentric height 2*5 5 or a = 11£° (nearly). If the vertical rise in the centre of gravity had been greater, the more accurate method of determining the heel would have been chap, in.] THE STATICAL STABILITY OF SHIPS. Ill applied. In practice precautions are taken to limit the possible transverse shift of cargoes. Shifting boards, or longitudinal partitions, are commonly fitted in grain-laden ships ; and instead of being free to move across the full breadth, as assumed in Fig. 48, the upper part of the cargo can move only through the distance between the adjacent partitions and the sides. The movement of the common centre of gravity of ship and cargo and the resultant heel of the ship are thus diminished. Water-ballast is now extensively used, especially in cargo- steamers. Cellular double bottoms or special tanks situated below the turn of the bilge are usually constructed to receive such ballast ; and arrangements are made for readily filling the ballast spaces, or for pumping them out. It is important for purposes of stability that ballast compartments should be completely filled. The weight of water contained in them may then be treated as if it were solid ballast, since it cannot shift as the ship heels. If ballast compart- ments are only partially filled, and the water contained in them can shift transversely, or has a free surface, this transverse shift may, and often does, produce a reduction in stability, or an increase in heel, similar to that above described for shifting cargo. Whereas the surface of cargoes such as grain, coals, etc., will stand at a considerable " slope " to the horizon, water will always rest with its free surface horizontal when a ship has settled to a steady heel. Cases arise in practice where caution has to be exercised during the admission or pumping out of water-ballast, when ships are in a condition of lading which gives them very small metacentric heights ; and this is especially true when external forces, such as wind-pressure or wave-motion, tend to produce transverse inclina- tions. When liquid cargoes, such as oil, are carried, precautions are also necessary under some conditions, and it may be well to illustrate this point briefly. For simplicity take first the case of a prismatic vessel, whose uniform cross-section when upright is illustrated in Fig. 49. In the first diagram the vessel is upright ; W^ is the load-line; wj^ the surface of the contained liquid, which occupies a length of c feet. M is the metacentre corresponding to WiLj, and Gi the common centre of gravity of ship and lading (including the liquid) when the vessel is upright. Suppose the liquid to weigh x tons per cubic foot, and, as a first condition, to be free to shift across the whole breadth of the hold wh when the ship inclines. Let the whole breadth be called 26 ; so that sw 1 or sZ x (the half-breadth) is b feet. Fig. 50 shows the vessel inclined to a small angle a (circular measure used) within the limits to which the metacentric method applies. If D is the weight of ship and lading in tons, and the 112 NAVAL ARCHITECTURE. [chap. III. liquid were solidified in the position shown in Fig. 49, then as above explained — Eighting moment (liquid solidified) = D x GZ = D x GM sin a (foot-tons). When the liquid is free to shift, at the inclination a its surface (w 2 y will be horizontal ; and for small inclinations will intersect the original surface (w^) at or near the middle line (s), as shown in Fig. 50. The transfer due to this shift is represented by the FIG. 49. FIG. 50. FIG. 51. movement of a wedge-shaped mass w x sw 2 into the position l^. Let v = volume of this mass (cubic feet) ; g 1 be the centre of gravity of WiSWa, and g 2 that of l^. Then the transfer involves a movement of the common centre of gravity of ship and lading from G x to G 2 along a line parallel to stability . . . . J = ( 19 > 500 + 10 ° X 16 ) "k « = 21,100 (foot-tons) x sin a. It is unnecessary to give illustrations of the remaining rules for the removal of weights. When "metacentric diagrams," such as those given on p. 90, are available, the foregoing rules cease to be of much value ; because the effect.upon the vertical position of the centre of gravity of the ' addition or removal of any weights, however large, is easily estimated ; the corresponding change in draught can be determined; and the new position of the metacentre corresponding to the altered draught chap, in.] THE STATICAL STABILITY OF SHIPS. 1 19 is indicated on the metacentric diagram. Where no metacentric diagrams are available, the approximate rules given above will be of service to a commanding officer. Estimates for Changes of Trim. — Attention must next be turned to longitudinal inclinations, or changes of trim. The process by which the naval architect estimates changes of trim produced by moving weights already on board a ship is identical in principle with the inclining experiment described above ; only in this case he makes use of a metacentre for longitudinal inclinations (or, as it is usually termed, the " longitudinal metacentre "), instead of the transverse metacentre with which we have hitherto been concerned. The definition of the metacentre already given for transverse inclina- tions is, in fact, quite as applicable to inclinations in any other direction, longitudinal or skew ; but it has already been explained that, as the transverse stability of a ship is her minimum, while the longitudinal stability is her maximum, only these two need be considered. The general expression for the height of the longitudinal meta- centre above the centre of buoyancy resembles in form that given on p. 86, for the transverse metacentre ; but for longitudinal inclina- tions the moment of inertia of the plane of flotation has to be taken about a transverse axis passing through the centre of gravity of that plane. Hence, using the same notation as before, we may write — Moment of inertia of plane of flotation (for \ estimates of height of longitudinal meta- > = K^ x B x L 3 centre) ) Height of longitudinal meta- ] "R" v "R v T 3 centre above centre of / = — 1 „ ... — : buoyancy. . . .) volume of displacement Following out a process of reduction similar to that described for the transverse metacentre, this last formula may be written — K x B x L 3 L 2 Height of longitudinal metacentre = - — ^ — — = b • ^r The values of K and vary considerably in different classes of ships ; and so does the ratio b ; but the following averages obtained for various types may be of some value, although no approximations can be trusted to replace exact calculations from ship-drawings : — Values of 6. Unarmoured war-ships and merchant } . 07 , .qq ships of ordinary proportions . .)' Armoured ships ; merchant ships of ) .™, , ,qq special classes . . . .3 120 NAVAL ARCHITECTURE. [chap. in. The value -075 may be used as a rough, approximation in most cases ; but there are many exceptions to its use. In ships of war the ratio of mean draught to length frequently lies between 1 to 12 and 1 to 14 ; the average of these ratios, 1 to 13, is as nearly as possible the average value of b stated above. Hence, in such vessels, the height of the longitudinal metacentre above the centre of buoyancy usually approximates to equality with the length, in some classes exceeding it by 20 to 25 per cent., and in others falling below it by 10 to 15 per cent. In sea-going merchant ships the ratio of mean draught to length is usually less than in war-ships ; and the height of the longitudinal metacentre above the centre of buoyancy is sometimes 40 per cent, greater than the length. In vessels of extremely shallow draught, such as river steamers having small displacements, but large moments of inertia of the planes of notation, the height of the longitudinal metacentre is exceptionally great in proportion to the length. As ships lighten, the heights of their longitudinal metacentres usually increase con- siderably, and for merchant ships where the variations in draught are considerable, it is often found useful to construct " metacentric diagrams," for the loci of longitudinal metacentres resembling in character those described for transverse metacentres on p. 89. For war-ships the changes from load to light draught are less consider- able, and it is not customary to construct these longitudinal meta- centric diagrams. Damage to the skin of a ship, and the consequent admission of water to the interior, usually affects the longitudinal as well as the transverse stability; and the general remarks made on p. 115 may also be applied here. It is evident, moreover, that the greatest loss of longitudinal stability must result from the flooding of com- partments near the bow and stera, unless the buoyancy of the water-line area at the tops of these compartments is preserved by watertight flats or platforms, as explained on p. 27. The moment of inertia, it will be remembered, consists of the sum of the products of each element of area of the plane of flotation by the square of its distance from the transverse axis passing through the centre of gravity of that plane ; hence the most distant portions of the area contribute the largest part of the moment of inertia, and if their contributions are withdrawn that moment is considerably diminished. As an extreme example, the Inflexible may be again mentioned. When the unarmoured ends are intact, the longitudinal metacentre of that ship is 292 feet above the centre of buoyancy ; but when the ends are "riddled," the corresponding height is reduced to rather less than 33 feet. A comparison of the statements made ;respecting the heights of chap, in.] THE STATICAL STABILITY OF SHIPS. 121 the transverse and longitudinal metacentres, will show how much greater is the longitudinal than the transverse stability of ships. An example may enforce the contrast. The Warrior has a longi- tudinal metacentric height of about 475 feet against a transverse metacentric height of 4 - 7 feet. To incline her 10 degrees longi- tudinally would require a moment one hundred times as great as would produce an equal inclination transversely. Or, to state the contrast differently, the moment which would hold the ship to a steady heel of 10 degrees would only incline her longitudinally about ^ degree, equivalent to a change of trim of 6 or 8 inches on a length of 380 feet. In Tigs. 53, 54, are given illustrations of the change of trim w FIG. 53. 1 J T c C sea*- /Si i ' ? i B 5_ produced by moving weights already on board a ship ; but, before proceeding further, it may be well to repeat the explanation given in an earlier chapter of the term " change of trim." The difference of the draughts of water forward and aft (which commonly takes the form of excess in the draught aft) is termed the trim of the ship. Tor instance, a ship drawing 23 feet forward and 26 feet aft is said to trim 3 feet by the stern. Suppose her trim to be altered, so that she draws 24 feet forward and 25 feet aft, the " change of trim " would be 2 feet, because she would then trim only one foot by the stern. In short, " change of trim " expresses the sum of the increase in draught at one end and decrease in draught at the other ; so that, if the vessel be inclined longitudinally through an angle a, and L be her length — Change of trim = L X tan a. Suppose the height of the longitudinal metacentre above the centre of gravity to be GM, as in Fig. 54, then, when the weight w is shifted longitudinally along the deck from A to C through a distance d, we shall have, by similar reasoning to that given in the case of the inclining experiment, the centre of gravity moving parallel to the deck, and — Shift of centre of gravity (GGJ = -^r- also — w . a t , w GG X = GM tan a = — — ; whence tan a = d D D x GM 122 NAVAL ARCHITECTURE. [chap. hi. and from the above expression — Change of trim = L x tan a = — - — X — 5 D GM Take the case of the Warrior, for which, at a draught of 25J feet, length = L = 380 feet ; metacentric height = GM = 475 feet ; dis- placement = 8625 tons. Suppose a weight (w) of 20 tons to be shifted longitudinally 100 feet — Change of trim = 2Q x 10 ° x — = -186 foot = 2£ inches. 8625 475 It is usual to obtain for a ship the value of the " moment to change " the trim one inch," when floating at the load-draught ; and then for changes of trim up to 2 or 3 feet no great error is involved in assuming that for a change of trim of any number of inches the moment required will equal that number of times the moment which will change the trim one inch. Substituting in the equation — Change of trim = — — x D GM one inch as change of trim (i.e. ^ foot), we have — 1 w . d L , , D GM — = x — : whence w . a = — x — 12 D GM 12 L Here wd = moment to change trim one inch. In war-ships of ordinary proportions, as explained on p. 120, the height, GM, approaches to equality with the length, L, and the following rule holds with a fair degree of approximation : " The moment to change " the trim of a war-ship one inch — that is, the product of the weight " moved by the longitudinal distance it is shifted — will very nearly chap, hi.] THE STATICAL STABILITY OF SHIPS. 1 23 " equal (in foot-tons) one-twelfth of the ship's displacement (in tons)." In long fine vessels like the Warrior, this rule will give results rather below the truth, because GM is greater than L, whereas in short full ships its results will be rather in excess, because GM is less than L. In the Warrior, for example, where the metacentric height is proportionately great, -^ X D = 718 ; whereas, the moment to change trim one inch is about 900 foot-tons. In the Hotspur, on the contrary, ^ xD = 334 ; whereas the moment to change trim is 300 foot-tons, the metacentric height in this case being 211 feet, and the length 235 feet. In sea-going merchant ships the moment to change trim one inch would probably be 30 to 40 per cent, in excess of the approximate rule ; and clearly that rule does not apply to shallow-draught vessels or special types. The conditions are rather more complicated when weights are to be added to a ship, being placed with their centres of gravity in certain known positions, and it is required to determine the resultant draughts of water at the bow and stern. A good approximation may, however, be made as follows, supposing that the weights added are small when compared with the total weight of the ship — a sup- position which will be fair in most cases. First, suppose the weights to be placed on board directly over the centre of gravity of the load-line section of the ship; then the vessel will sink bodily without change of trim, until she reaches a draught giving an addition to the displacement equal to the weights added. This can be estimated by the method of tons per inch immersion previously explained. The centre of gravity of the load-line section, or plane of flotation, usually lies a few feet abaft the middle of the length of the ship at the water-line, say, from one-thirtieth to one- fiftieth of the length abaft the middle. Having supposed the weights concentrated over this point, the next step is to distribute them, moving each to its desired position ; each weight is multiplied by the distance it would have to be moved either forward or aft, and the respective sums of the products forward and aft being obtained, their difference is ascertained, this difference constituting the "moment to change trim." The final step is to estimate the resultant change of trim due to this moment by the metacentric method previously explained. For example, take the Warrior, and suppose the weights in the table on p. 124 to be placed on board. Moment to change trim one inch (say) = 890 foot-tons ; .'. Change of trim = = 2 inches ; 8 890 Increase in mean) _ weights added 250 _ g ^j^g draught . . j ~ tons per inch ~ 41 124 NAVAL ARCHITECTURE. [chap. m. Distance from centre Weight. of gravity of plane of flotation. Products. tons. feet Before. Abaft. 10 140 f 1400 — 30 20 120 40 Before 1 3600 J 800 — 40 sJ I 200 — 60 8j { — 480 50 25 100( Abaft = 3000 2500 15 120 J ( _ 1800 250 6000 7780 Mome 6000 at to change trim (by the stern) . .. 1780 If the original draught of water was 25 feet forward and 26 feet aft, mean 25£ feet, the altered mean draught will be 26 feet, and the corresponding draft forward will be about 25 feet 5 inches, and aft 26 feet 7 inches.* Stability of Ships partially Water-borne. — A vessel partially water- borne and partly aground loses stability as compared with her con- dition when afloat. One of the commonest illustrations of this fact is found in the case of boats run bow-on to a shelving beach ; and instances are on record where vessels in dock have fallen over on their sides in consequence of a similar loss of stability,t when just taking or leaving the blocks, and not supported by side-shores, while the water was being admitted to or pumped out of the docks. For our present purpose it will suffice to indicate in general terms the conditions influencing the loss of stability. When afloat, the ship is wholly supported by the buoyancy due to the water she dis- places ; when her keel touches the blocks or ground, she is partly supported by the upward pressure at that point, the remainder of her weight being supported by the water then displaced, which is by supposition less than the total displacement due to her weight. Having given the height to which the water rises on the ship at * To be exact, the alterations in draught forward and aft should be pro- portioned to the distances of the centre of gravity of the water-line plane from bow and stern. t A well-known case is that of her Majesty's troopship Perseverance, which fell over on her side when being undocked at Woolwich some years ago. The matter was fully investigated at the time by Mr. Barnes, and he has since con- tributed an article on the same subject to No. 4 of the Annual of the Royal School of Naval Architecture. chap, in.] THE STATICAL STABILITY OF SHIPS. 1 25 any instant, it is easy to estimate the corresponding buoyancy ; then the difference between it and the weight of the ship measures the pressure at the point of contact, and corresponds to the buoyancy contributed by the volume of the ship lying between her load-line when afloat and the actual water-line at the time she is partly water- borne. What has really been done, therefore, is to transfer the buoyancy of this zone (acting through the centre of gravity of the zone) down to the point of contact of the keel with the ground. And when the vessel is inclined through a small angle from the upright, this pressure actually tends to upset her, whereas the buoyancy it has replaced would usually tend to right her. Hence the decreased stability. It is possible to obtain a ready rule for estimating the loss. Suppose — P = pressure of end of keel on ground ; h = height of centre of gravity of the aforesaid zone above the point of contact of the keel and ground ; W = total weight of ship. Then a simple mathematical investigation shows that — Loss of metacentric height (G-M) due to partial} _ Ph grounding (approximately) i ~ W Take as an example the case of the Perseverance, for which — P = 51 tons ; W = 1303 tons ; h = 13 feet, 51 x 13 .*. Loss of metacentric height = = 6 inches (about). J.0U0 Vessels having a very considerable normal trim by the stern are most liable to this kind of accident, and the upsetting tendency due to the pressure reaches its maximum when the vessel is about to take the ground along the whole length of the keel. The practical method of guarding against such accidents of course consists in care- fully shoring,-using mast-head tackles, or otherwise supporting the vessel externally, in order to prevent her from upsetting. Transverse Stability at Large Angles of Inclination. — Up to this point attention has been directed exclusively to the stability of ships inclined to angles lying within the limits to which the meta- centric method applies. For longitudinal inclinations, except in very special cases, nothing further is required ; but for transverse inclinations it is necessary to ascertain the statical stability at greater angles, and to determine the inclination at which the ship becomes unstable. The general principles previously laid down for determining the moment of the couple formed by the weight and buoyancy apply to all angles of inclination ; and it is consequently 126 NAVAL ARCHITECTURE. [CHAP. III. only necessary to fix for any angle the vertical line, passing through the centre of buoyancy, along which the resultant upward pressure of the water acts. This is done by calculation from the drawings of a ship, and involves considerable labour ; but the principle upon which it is based may be simply explained. Fig. 55 shows the FIG. 55. cross-section of a ship which, when upright, floated at the water-line WxLj, having the volume of displacement indicated by WjXLj, and the centre of buoyancy B^ When inclined as in the diagram, WL is the water-line, WXL the volume of displacement, and B the corresponding centre of buoyancy. Since the displacement remains constant, the volumes WXL and W^L L are equal, and they have the common part WSI^XW. Deducting this common part, the remainder (WjSW) of the volume WjXIn must equal the remainder (LSL X ) of the volume WXL ; or, as it is usually stated, the wedge of immersion LSL t must equal the wedge of emersion WiSW. In other words, the inclination of the vessel has produced a change in the form of the displacement equivalent to a transfer of the wedge WSWj to the equal, but differently shaped, wedge LSL X . This is obviously a parallel case to that of the lever explained on p. 106. In Fig. 55, let g l be the centre of gravity of the wedge of emersion, g 2 that of the wedge of immersion, and v the volume of either wedge ; then what has been done is equivalent to a transfer of this volume v to the immersed side, into the position having g a for its centre of gravity. The moment due to this shift = v X g^ ] and its consequence is a motion of the centre of gravity of the total chap, hi.] THE STATICAL STABILITY OF SHIPS. 127 volume of displacement V from the original position, B D to the new one, B, the line B X B being parallel to g x g 2 , and the length — BBx = 1 x g,g* It thus becomes obvious that, when the positions of the centres of gravity of the wedges (g ± and g 2 ) for any inclination are known, the new position of the centre of buoyancy (B) can be determined with reference to its known position (B^ when the ship is upright. And this is virtually the process adopted in the calculation.* If BxR be drawn perpendicular to BM, Fig. 55, and gji^ g 2 h 2 perpen- FIG. 56. 60° SO' /OO" ISO" Angles of mclination. ieo° dicular to WL, then, by the same principle as is used above, the length B X B = — x hJh- Also, if the angle of inclination WSWi be called a — GZ = BjE - B X G sin a, and consequently— ., Moment of statical stability = V X GZ = V(B X E - B& sin a) = v x hjt 2 - V x BjGr sin a. This expression for the righting moment (in terms of the volume of displacement) is known as " Atwood's formula," and is commonly employed in constructing " curves of stability." Fig. 56 shows the method of construction for such a curve. On the base-line OPX degrees of inclination are set off on a certain scale, corresponding to the upright ; the ordinate of the curve drawn perpendicular to the base-line at any point measures, on a certain scale, the " arm of the righting couple " (GrZ) for the corre- sponding angle of inclination. Thus, OP represents an inclination * For details of methods of calcula- tion, see a paper contributed by the late Mr. W. John and the author to the Transactions of the Institution of Naval Architects for 1871, and by other writers in the same Transactions for 1882, 1884, etc. I2S NAVAL ARCHITECTURE. [chap. in. of 50 degrees, and the corresponding ordinate PN represents the length of the arm of the couple formed by the weight and buoyancy at that inclination. By calculation, successive values of GZ are found for inclinations differing by an interval of 8 or 10 degrees ; and the curve is drawn through the tops of the ordinates thus found. Measurement of the ordinates renders any calculation unnecessary for inclinations other than those made use of in drawing the curve. It will be observed that, starting from the upright position, the stability gradually increases, reaches a maximum value, and then decreases, finally reaching a zero value (where the curve crosses the base-line) at the inclination where the ship becomes unstable. The preceding! explanation of the causes governing the position of the centre of buoyancy will furnish the reason for this gradual increase and subsequent decrease in the stability. The length (OX), measuring the inclination at which the ship becomes unstable, deter- mines what is known as the range of stability for the ship, and this is an important element of safety. One of the simplest illustrations of a curve of stability is that for the cigar-shaped ship shown in section by Figs. 41, 42, p. 94. In such vessels, as previously explained, for any angle a, GZ = GM sin a, and the curve of stability is constructed by simply setting up, at any point on the base-line, a length representing the sine of the angle of inclination corresponding to that point. Fig. 56 shows this curve. The range is 180 degrees; the maximum stability is reached at 90 degrees, and the curve is symmetrical about its middle ordinate. Variations in the values of the metacentric height (GM) affect all the ordinates of the curve in the same proportion. Ship-shaped forms are less easy to deal with ; but a brief explanation of the causes chiefly influencing the form and range of curves of stability in ships will be of value. These causes may be grouped under the following heads : (1) Freeboard ; (2) beam ; (3) the vertical position of the centre of gravity ; (4) the vertical position of the centre of buoyancy when the ship floats upright Both freeboard and beam are of course relative measures, and should be compared with the draught of water. With freeboard, moreover, must be associated the idea of "reserve of buoyancy" (see p. 8). The vertical position of the centre of gravity must be compared with the total depth of the ship (excluding projecting keel), and so must that of the centre of buoyancy. It is also necessary to note the relation between the mean draught and the depth of the centre of buoyancy below the water-line, as that relation indicates roughly the fulness or fineness of form in the under-water portion of the ship. Before giving any illustrations of curves of stability for actual ships, a few simple examples may be taken from box-shaped chap, in.] THE STATICAL STABILITY OF SHIPS. 129 vessels in order to show the relative influence of the above-mentioned features. The following cross-sections will serve the purpose : — Dimensions. No. 1. No. 2. No. 3. Beam .... Draught .... Freeboard Metacentric height (GM) feet. 50i 21 6* 26 feet. 2? 2*6 feet. ? Taking No. 1 as a standard for comparison, its curve of stability is shown by A in Fig. 57. The effect of adding 7 feet to the freeboard — supposing the centre of gravity to be unchanged in position — is seen by comparing the curve of stability B for No. 2 with the curve A. FIG. 57. 10 20 30 40 50 60 70 80 90 Angles of IneLiita-tion. Similarly, the effect of adding 7 feet to the beam is seen by com- paring the curve of stability C for No. 3 with the other two curves. Only a few further words of explanation will be necessary. At an inclination of 14J degrees, the "deck-edge," or angle, of No. 1 will be immersed ; for No. 2 the corresponding inclination is nearly doubly as great, viz. 27J degrees. Fig. 58 shows No. 2 with its deck-edge "awash." Fig. 59 shows No. 1 at the same inclination, with a considerable portion of its deck immersed. Up to the inclination, when the deck-edge of either vessel is just immersed, the centre of buoyancy B moves steadily outward in relation to the centre of gravity as the inclination increases, in consequence of the gradual increase in the volume of the wedges of immersion and emersion, and in the distance g^g 2 between their centres of gravity. But after the deck goes under water, this out- ward motion of the centre of buoyancy relatively to the centre of 130 NAVAL ARCHITECTURE. [CHAP. III. gravity becomes slower, or is replaced by a motion of return, in consequence of tbe decrease in the distance g^ between the centres FIG. 58. FIG. 59. of gravity and the less rapid growth of the volumes of the wedges. The increase in value of the term B X G sin a in the formula — V x GZ = v x ItJh - V . B t G sin a, also tends to diminish GZ as the inclination increases. The greater the angle of inclination corresponding to the immersion of the deck- edge — in other words, the higher the ratio of freeboard to breadth — the greater in ordinary cases will be the inclination at which the statical stability reaches its maximum value. Up to 14^ degrees, the curves A and B in Fig. 44 are identical ; but then B continues to rise rapidly, not reaching its maximum until 45 degrees, whereas A reaches its maximum at 20 degrees. The low-freeboard box, moreover, has a range of less than 40 degrees, whereas the high- freeboard box (No. 2) has a range of 84 degrees. Turning to No. 3 section, and the curve of stability C, it will be noticed that the increase of 7 feet in beam causes a considerable increase in the metacentric height (GM). For moderate inclinations, GZ = GM sin a, and therefore this increase in GM is accompanied by a corresponding increase in the steepness of the earlier part of the curve of stability C, as compared with the curves A and B in Fig. 57. The deck-edge becomes immersed, however, at 13 degrees, the maximum stability is reached at 20 degrees, and the range of stability is less than 50 degrees as against 84 degrees in curve B for the higher freeboard vessel. The comparison of these curves wiU show how much more influential increase of freeboard is than increase of beam in adding to the amount and range of the statical stability of ships. Lastly, to illustrate the effect of the vertical position of the centre of gravity upon the forms of curves of stability, let it be assumed that the high-freeboard vessel (No. 2 section) has its centre of gravity raised one foot, leaving the value of the metacentric height (GM) 1*6 foot. This will be no unfair assumption, seeing CHAP. III.] THE STATICAL STABILITY OF SHIPS. 13 1 that the increase in freeboard, and consequently in total depth, would in practice be associated with a rise in the centre of gravity. The curve of stability D, Fig. 57, corresponds to this last case. For each inclination the decrease in the arm of the righting couple, as compared with curve B, is given by the expression — Decrease in GZ = GG X x sin a, where GG X (rise in position of centre of gravity) is one foot. Initially the curve D falls within A and B, the vessel being more crank. It has, however, its maximum ordinate at 45 degrees, and a range of 75 degrees, comparing very favourably indeed with the curve C for the low-freeboard vessel with broad beam (No. 3). Turning from these simple prismatic forms to actual ships, it will be interesting to notice how the curves of stability for different classes of ships illustrate the varying influence of beam, freeboard, vertical position of the centre of gravity, etc. The earliest curves of stability on record were constructed at the Admiralty in 1867, prior to which date there appears to have been no exact determi- nation of the stability of ships at large angles of inclination when their upper decks were partially under water, or of their ranges of stability. So long as ships of high freeboard were employed exclu- sively this limitation of inquiry as to variation in statical stability was natural enough ; but when low-freeboard vessels came into use the necessity arose for more extended calculations, in order to determine the angles of inclination at which the vessels became unstable. Since 1870 the practice of constructing curves of stability for each class of vessel in the Boyal Navy has been established; and has been followed in foreign navies. More recently similar curves have been constructed for yachts and for various classes of merchant ships. A large amount of valuable data has thus been accumulated already, and important additions are continually being made thereto. The first set of illustrations of curves of stability, contained in Fig. 60, is limited to representative types of war-steamers, and to their fully laden condition. In all cases the centres of gravity have been ascertained by experiment, and the distribution of the weights is accurately known. Those weights are supposed to be secured in such a manner that no shift takes place even at the most extreme inclinations. This may be considered an improper supposition, espe- cially in cases where stability is maintained beyond the inclination of 90 degrees from the upright ; but it is to be observed that such extreme inclinations are not likely to be reached, whereas for less inclinations the supposition affects all classes similarly. Further, it is assumed in making the calculations that throughout the inclina- 132 NAVAL ARCHITECTURE. [chap. hi. tions no water enters the interior through ports, scuttles, hawse-pipes, and other openings in the sides ; or through hatchways, ladder-ways, and other openings in the decks. This assumption is fair enough as FIG. 60. 30 40 50 60 70 80 Angler of Inclination- 90 100 IIC 1. Juno. 2. Inconstant. 3. Endymion. 4. Serapis. 5. Invincible. 6. Achilles. 7. Miantonomoh. 8. Monarch. 9. Devastation. 10. Captain. 11. Glatton. regards most of the openings, which are furnished with watertight coTers, plugs, etc., and as regards some of the hatchways which are usually kept open even in a seaway, it is only necessary to remark that they might be battened down on an emergency, while their situation near the middle line of the deck prevents the water from reaching them except at very large angles of inclination. It is not usual to include erections above the upper decks of war-ships in making calculations for curves of stability unless they are thoroughly closed in and made watertight. For example, deck-houses, open- ended forecastles and poops, etc., are not included : but closed batteries, breastworks, forecastles, and poops are reckoned in the contributories to stability. Partially watertight erections no doubt aid ships in recovering from extreme lurches, etc., which put them under water only for very short periods, so that their omission from the calculation is on the side of safety. The following table gives the principal dimensions, etc., of these representative war-steam- ships: — chap, in.] THE STA TICAL STABILITY OF SHIPS. 133 Height of npper Name. Class of ship. Length. Breach extreme. Mean draught. deck amidships above -water. Displace- ment. Unarmoured. ft. ft. in. ft. in. ft. in. tons. Endymion Old type steam frigate 240 47 10 20 6 14 8 3300 Juno Covered-deck corvette 200 40 17 4 14 6 2215 Inconstant . Swift cruising frigate 337 50 3£ 23 10J 15 3J 5782 Serapis . Indian troopship . Armoured. 360 49 19 5 15 5976 Glatton . Breastwork monitor 245 54 18 9 3 4912 Miantonomoh American monitor . 250 52 10 14 3 3842 Captain (late) Low-freeboard 1 . .1 320 53 3 25 Oh 6 6 7790 Monarch 330 57 6 24 If 14 8215 Devastation . 285 62 3 26 n 11 3* 9061 Achilles . Early type \ broadside j Later type j ships. \ 380 58 3i 26 5 15 9484 Invincible 280 54 22 6 16 6060 * 0nly.4J feet aft. In Fig. 60 the respective curves of stability for these vessels appear with reference numbers, enabling them to be distinguished ; and they will repay a careful study, as illustrations of the comparative stabilities of high- and low-sided vessels, armoured and unarmoured. It will be remarked that the ordinates of the curves have to be multiplied by the respective displacements of the ships in order to obtain the righting moments. As ships of war lighten by the consumption of coals, provisions, stores, etc., their curves of stability frequently lose in area and range. This is due to the fact that the rise in the vertical position of the centre of gravity as the ships lighten produces a greater effect in reducing the stability than the increase in freeboard produces in the contrary sense. Any such decrease in stability can be prevented in ships fitted to carry water-ballast, as all armoured ships are ; but as a rule there is no necessity to use water-ballast even in the extreme light condition. There are, moreover, exceptions to the rule just stated ; some types having little, if any, less stability in the light condition than they have when fully laden. In many modern cruisers and battle-ships a considerable portion of the coal is stowed above the protective decks ; consequently in the light condition the centre of gravity is not much higher than in the load condition, and this rise is counterbalanced by the increase in freeboard. As an example, reference may be made to the two curves for the Inflexible in Fig. 61. The curve 1 shows the ship fully laden, and the curve 2 indicates her condition when 1500 tons of coals and consumable stores have been removed. This diagram also illustrates the influence which damage to the skin of a ship and the consequent entry of water into *34 NAVAL ARCHITECTURE. [chap. hi. the hold may have upon the form and range of her curve of stability. The curves 3 and -i show the conditions of statical stability of the Inflexible when the unafmoured ends are completely riddled. This 1 r -«f* 8 s ; S^ i N. FIG. 61. ts =-«** 1 — art <* ao lg — Mff * — -<* s m ' so ' 3C 40° SO « " 70° 1. Load condition, ends intact. 2. Light „ „ 3. Load „ ends riddled. 4. Light „ „ „ extensive damage would cause the ship to sink more than 2 feet below her ordinary load-line, reducing her freeboard by an equal amount, and lessening her stability very greatly. The tabular statement appended will supplement the information given in the diagram.* Condition of Inflexible Em s a s OQ *-■ *S5 go 1*8 8,5 ■°4 •so 88* (see Fig. 61). OS (5 a a "SbS a a -< S S-3 as f3 JS a.8 ft. in. tons. feet. feet. 1. Fully laden, ends \ intact . . J 24 7 11,500 14° 31-2° 3-28 74-3° 8-25 2. Light condition, 1 ends intact . 1 21 10 10,000 18° 31-7° 3-98 71-5° 8-5 3. Fully laden, ends \ riddled . . / 26 8} 11,500 11° 13-5° •57 30-0° 2-0 4. Light condition, \ ends riddled . J 23 9 10,000 15° 20-8° •79 36-8° 2-22 This is an extreme illustration of the loss of stability due to damage to the shin of a ship ; but similar considerations hold good in all ships, and the extent to which their stability may be decreased by collision or other accident can be readily estimated when the extent of the damage is known. Without any actual damage to the skin of a ship water may find its way into the interior through open ports or scuttles in the sides, or open hatchways in the decks, the * For a full discussion of the sta- Committee bility of this ship see the Keport of the Paper). of 1878 (Parliamentary chap. HI.] THE STATICAL STABILITY OF SHIPS. 135 result being a more or less serious decrease in stability. Such occurrences are clearly exceptional, but they have happened in ships caught by squalls of wind in comparatively smooth water. The Ewrydice is an example. Fig. 63, p. 138, shows two curves of stability for that ill-fated vessel. The first, marked 3, is the curve for her fully laden condition with all ports closed, and openings in sides and decks made watertight ; the second, marked 4, is the curve corresponding to her condition when she was capsized, the ports having been open, and the water having entered through them. In curve 3, the freeboard (to the upper deck) was between 11 and 12 feet ; whereas in curve 4 the freeboard was virtually reduced to 4 feet. Having regard to the explanations given on p. 130, as to the in- fluence of freeboard on range of stability, the reduction of range and area of the curve of stability from 3 to 4 in Fig. 63 will be readily understood. Turning from war-ships to merchant ships, it is not possible to give similarly full and exact information respecting their curves of stability. The principal reasons for this difference have been stated on p. 85. In Fig. 62 there are given, however, the curves for a FIG. 62. (\JS* « : y^" a — 3F? J 1 Z j __T ^—1FP /, ^a. e ' ^ y 3 z &£ is — —-£— . 10° 30° 50° 70° 80 90° Carves of stability for merchant steamers. Note. — The dimensions, etc., of these vessels appear in the table on p. 136, under the respective reference numbers marked on the curves. considerable number of representative merchant steamships, laden to certain assumed load-lines, which are approximately those at which the ships would be worked. The nature of the stowage assumed in each case is explained in the tabular statement on p. 136, and the principal dimensions, etc., of the vessels are also recorded therein.* * For a few of these examples of curves of stability the author is indebted to Mr. Martell's Paper on "Causes of Unseaworthiness" (Transactions of the Institution of Naval Architects for 1880). The remainder have been obtained by direct calculation for ships bought into the Royal Navy, and by calculations 136 NAVAL ARCHITECTURE. [chap. III. Pabticttlabs of the Vessels whose Cubves of Stability abe given in Fie. 62. £ C Glass of ship. 5 CO o ►4 ft. in. 390 320 264 » 320 I> 312 6 »s 245 285 245 300 § a III a I f o {Long, swift steamer, miscella- \ neons cargo . . . J {Steamer of moderate speed, mis- \ cellaneoas cargo {Steamer of moderate speed, ho mogeneous cargo . {Same vessel, but in light condi Hon .... (Steamer, large carrying power. homogeneous cargo {Same vessel, 300 tons less cargo, \ and 300 tons water-ballast . I Same vessel, light condition ( Passenger-steamer, misoellane- \ \ ons cargo . . . . / {Same vessel, assumed initially) unstable . . . . j Steamer, grain cargo . Steamer, cargo of iron Steamer, grain cargo Despatch vessel (iris) ft. in. 39 34 32 J» 40 »» » 33 4 33 4 35 4 32 4 46 ft. in. 23 18 3 15 9h 8 11 23 6 9 7 16 3 19 18 16 19 9 feet. 2-0 2'0 11 1-5 0-4 1-2 3-0 2-0 0-5 0-7 3-5 0-8 3-7 ft. in. 8 6 8 5 5 2 15 0J 6 U n 21 0J 9 8 tons. 6400 3560 3220 1240 63S0 ! » 2110 2870 4 3600 6 6 ! 3800 8 I 3100 8 7} I 3735 It is interesting to compare the curves of stability for the same vessels in the extreme load and light conditions, or to contrast the curves for a vessel carrying the same total weight differently dis- tributed. Curve 9, Fig. 62, illustrates a hypothetical case, where a fully laden ship is unstable when upright, and yet has a considerable range of stability. Such conditions would not be accepted, in practice, for a ship proceeding to sea, but they are interesting as illustrations of the principles above laid down. When the vessel is upright, the metacentre is "5 feet below the centre of gravity. Initially the curve of stability falls below the base-line, and this is a graphic representation of instability. At an inclination of 20 degrees the curve crosses the load-line, and thence onward, the vessel has a positive righting moment until, at 80 degrees, she once more becomes unstable. The position (20 degrees) at which the curve crosses the base-line, is one of stable equilibrium ; the upright position and that where she is inclined 80 degrees correspond to unstable equilibrium. It is a general law under the conditions assumed in calculating curves of stability that positions of stable and unstable equilibrium occur made by the author's pupils at the Royal Naval College. For fuller details of certain of the last-mentioned calcu- lations see a paper by the author in Transactions of the Institution of Naval Architects for 1881. chap, hi.] THE STATICAL STABILITY OF SHIPS. 137 alternately. The position of 20 degrees is that to which the vessel would " loll " over from the upright in still water ; and if moved slightly from this position, either to greater or less angles of heel, she would return to it as her position of rest. Similar conditions may occur in merchant ships when floating at light draught, without cargo on board ; and they have been noted in special classes of war- ships when light. It will be observed, on comparing Figs. 60 and 62, that many of the fully laden merchant ships have much greater ranges of stability than the armoured war-ships. This is largely due to the very different vertical distribution of the weights. In merchant ships great relative weights of cargo or equipment are usually carried low down in the holds, and the common centres of gravity of ships and cargoes lie low in proportion to the total depth. In war-ships, although the weights of machinery, coals, and ammunition are carried low down in the holds, heavy loads of armour, armament, etc., have to be carried high up on the sides or decks. As a consequence the centre of gravity usually lies higher (in proportion to the total depth) in war-ships, and especially in armoured ships, than it does in merchant ships, and this tends to diminish the range of stability. Further, the deep lading of merchant ships brings the centre of buoyancy for the upright position higher in the ships than is usual in war-ships ; and this diminishes the distance between the centre of buoyancy for the upright position and centre of gravity, consequently tending to lengthen the range of stability. In yachts these two features are still further exaggerated, the distance between the centres of gravity and centres of buoyancy being very small, while the centres of gravity are drawn low down by the heavy weights of ballast fitted on the keels and floors. To the foregoing illustrations of curves of stability for steam- ships may be added a few for sailing ships of various classes. Fig. 63 contains these additional curves, and in the accompanying tabular statement the principal dimensions, etc., of the vessels appear. They include a few examples of the now obsolete sailing ships of the Eoyal Navy, others of existing sailing ships of the mercantile marine, and others of typical yachts.* In nearly all cases the fully laden condition is taken. For the yachts and war- * For the facts as to sailing yachts to whom they were presented by the late the author is indebted to the valuable Mr. W. John. The curves 6 and 7 were researches of Mr. Dixon Kemp ; for calculated by the author's pupils at the those relating to the Sunbeam he has to Royal Naval College for the ship built thank Lord Brassey ; most of those as to by Messrs. A. and J. Inglis, of which the merchant sailing ships are taken from metacentric diagram appears in Fig. 39. the Report of the Atalanta Committee, 138 NAVAL ARCHITECTURE. [chap. hi. ships the stowage is accurately known, so that the curves strictly correspond to the actual condition of the vessels in their seagoing trim. For the merchant ships a stowage has necessarily been »• so" SO' 30' 40' SO' 60° 70' 6 Curves of Stability for Sailing Vessels. Note. — The dimensions, etc., of these vessels appear in the following table, under the respective reference numbers marked on the curves. Particulars op the Vessels whose Cubves op Stability abb given in Fig. 63. s So a > Class of ship. -5 "S ■a ■s £ 1 ■a O is t- m §23 u 1 s3 a a o § a s ■§J3 s III K •a 5 ft. in. ft. in. ft. in. feet. ft. in. tons. 1 Sailing frigate, load condition . 131 40 7 17 4 6-2 10 9 1055 2 Sailing frigate, light condition . V> 16 4-1 12 1 887 3 /Sailing frigate, load condition, \ \ ports shut . . . . / 141 3S 8 16 7 4-5 10 6 1075 4 | Sailing frigate, load condition, \ \ ports open . . . . / J* '' 3) 51 » » Sailing brig, load condition 100 6 32 4 14 0| 5-9 4 3J 483 6 Sailing merchantman 222 35 4 16 9 3 5 3 2030 - /Sailing merchantman, homoge-\ \ neons cargo, and no ballaBt . / 1-3 » »» » ^\ ■ ^^5" 70° of considerable interest. The metacentric heights and dimensions are given in the table below. Large experience has been gained at sea with the English first-class boats, which have given the greatest satisfaction and proved themselves to be safe and sea- worthy when properly handled. It will be seen that the angles of maximum stability on curves 4 and 5 occur at or about 40 degrees O Meta- 63 £ a 3 Description of boat. Length. Displace- ment. centric height Kange of stability. 3 a Szi (GM). First class — feet. tons. feet. degrees. 1 Danish .... 137 110 1-38 over 90 2 French (as first built) 115 53 1-46 59 3 „ (as altered) . 115 53 1-46 77 4 English . 130 93 1-47 77 5 English .... 125 89 •82 86 6 Second class — English 63 14 •66 89 of inclination, and the range of stability is from 80 to 90 degrees. The Danish boat has even greater stability, and is of larger size. For the French boats, curve 2 shows conditions of stability which experience proved to be most unsatisfactory. These boats had con- siderable " tumble-home " of the sides above water, and comparatively large erections at the fore end for the torpedo apparatus. Some of them capsized in rough water, and the remainder were altered considerably in order to improve their stability. Curve 3 shows the HO NAVAL ARCHITECTURE. [chap. hi. result of the changes made, and will be seen to compare well with the curves for the English boats. Curve 6 is for a second-class boat — the type built to be lifted on board and carried by large ships. Although the metacentric height is moderate, the character and range of the curve is very satisfactory, and many of these boats have satisfactorily stood the test of service in rough weather, although not built primarily for sea-work. In connection, with the alterations effected in the French torpedo- boats, some interesting investigations were made by M. Ferrand of the variations which might be caused in the curves of stability by changes of trim in smooth water, or by the changes in level of the water surrounding a boat steaming end on to the waves.* The curve 2 in Fig. 64 corresponds to the normal trim. When the boat was immersed more deeply at the bow and correspondingly lightened aft in still waterj the mean draught remaining as before, the meta- centric height was diminished, and the area and range of the curve of stability were reduced. This resulted from the greater fineness of the fore body as compared with the after body. On the contrary, when the boats were trimmed more by the stern than in their normal condition, the metacentric height remained almost unaltered, while the range and area of the curve of stability were increased. Passing to wave-water, M. Ferrand showed, by calculations which were con- fessedly approximate and useful chiefly in making comparisons, that the instantaneous conditions of stability of the boats must be sensibly affected by the substitution of wave profiles for still water, and by the position of the wave-crest in relation to the centre of the length of the boats. Obviously, if the after-part were almost emerged for a moment, and the fore part deeply buried in a wave- crest as the boat pitched, there would be a very serious decrease in stability. When the contrary condition occurred, the instantaneous conditions of stability would be much more favourable, although inferior to those for still water. Various intermediate positions of the wave-crest and different dimensions of hypothetical waves were made the basis of calculation, with the general result that the unusually fine fore body as compared with the after body, and the great fall home of the top-sides, involved unusual variations in stability under the conditions assumed as compared with torpedo-boats of ordinary form. No doubt the points to which II. Ferrand drew attention exercise influence on the statical stability in all cases, so far as change of trim in still water, or the passage of waves along the sides of ships or boats is concerned. As a rule, however, it has not been found * See vol. 2 (1892) of the Bulletin de L' Association Technique Maritime. chap, in.] THE STATICAL STABILITY OF SHIPS. I4 1 necessary to calculate curves of stability for these conditions. About the year 1871, when the loss of the Captain caused special attention to be given to questions of stability for war-ships, and especially for those of moderate freeboard, the author and the late Mr. John made a number of calculations for different types, assuming them to be trimmed excessively by the bow or stern. The results were very interesting, but showed that under the extreme assumptions made, with the low ends deeply immersed, but the sides and decks assumed to be intact and capable of excluding water, the ships in question retained a large amount of transverse stability. In cases where the sides or decks are broken through near the extremities by collision or other causes, and considerable spaces in the interior are thrown open to the sea, large changes of trim must be produced, and the loss of buoyancy will be accompanied by serious decreases in the moments of inertia of the planes of flotation, for both longitudinal and transverse inclinations. Under any assumed conditions of damage and subdivision for a particular ship, the calculations necessary to determine her position when brought to rest, or whether she will founder, can easily be made. Apart from such calculations, it may be stated that the general case for a vessel in which the damage is not fatal, finds the new position of equili- brium with deeper immersion of the damaged end, a transverse inclination towards the damaged side, and a considerable decrease in the metacentric heights for both longitudinal and transverse inclina- tions. If the damage and access of water are so serious as to cause foundering, then in many cases as the injured extremity becomes more deeply submerged the transverse stability is necessarily so greatly reduced as to result in the vessel being capsized either before or at the instant of foundering. Experience with actual ships and experiments with models have confirmed these deductions from calculations for the stability of ships injured by collision. Stability of Ships when launched. — Ships are usually launched in an incomplete condition, and when afloat have a less mean draught of water than is reached subsequently in actual service. Curves of stability for the launching condition were not constructed prior to 1883, when accidents which occurred at the launch of certain vessels led to more extended investigations, and yielded interesting results to which reference may be made.* Fig. 65 contains a few examples of curves of stability for ships as launched. The curve AAA repre- * See the " Report on the Daphne of the Institution of Engineers and Ship- disaster," by Sir Edward Eeed ; Parlia- builders in Scotland for 1883. The mentary Paper, C 3764—1883; also a curves in Fig. 65 are either taken from paper by Mr. Biles in the Transactions or based upon these publications. 142 NAVAL ARCHITECTURE. [chap. III. sents the condition of the Daphne, which capsized in launching. The metacentric height was estimated for the launching condition at 4 inches. The curve BBB represents the condition of a large steamer which took a very heavy list to starboard after getting afloat ; her metacentric height was estimated at six-tenths of a foot. The curve CCC represents another large vessel having nearly the same meta- centric height in launching as the second example, but a much better curve of stability ; she was safely launched. The curve DDD shows what the curve BBB would become if the total weight remained unaltered, but the centre of gravity were lower.ed four-tenths of afoot, so as to make the metacentric height about 1 foot. The features common to most ships in launching condition are, extremely light draught, great relative height of freeboard, a low position of the centre of buoyancy (consequent on the light draught), a considerable vertical distance between the centre of gravity and the centre of buoyancy, and (commonly) a high position (in the ship) of the metacentre. Shipbuilders have it in their power to vary the vertical position of the centre of gravity and the draught by putting ballast on board ; the other conditions they practically have to accept. Ordinarily they are content to secure such an amount of stiffness as experience indicates to be desirable for vessels of the class and size about to be launched. Having approximated to the launching draught and trim, the corresponding position of the metacentre is known ; that of the centre of gravity is also approximately deter- mined, and then the ship is ballasted if thought necessary. For special or novel types it may be desirable to go further ; and the practice of constructing " cross-curves of stability," described hereafter, enables the stability for the launching draught to be rapidly deter- mined at various angles of inclination. Even in such cases the amount of metacentric height to be secured for safe launching is a CHAP, in.] THE STATICAL STABILITY OF SHIPS. 1 43 governing condition. Taking the curves BBB and DDD, we find an illustration of this statement. Lowering the centre of gravity less than 5 inches adds 50 per cent, to the maximum righting moment (at about 35 degrees inclination) ; and converts a zero of righting moment on the curve BBB at 52 degrees of inclination into a positive righting moment not much less than the maximum righting moment on BBB, while instability is not reached up to 90 degrees. While recognizing the interest of these extended inquiries into the stability of ships at launching draughts, it will be obvious, therefore, that one great practical lesson derivable there- from is the danger of unduly diminishing metacentric heights. If an error is made, it should rather be on the side of greater stiffness than is absolutely necessary ; in other words, rather more ballast should be used than the approximate calculations may show to be desirable. It has been suggested that at least one foot of metacentric height should be obtained for safe launching, and that curves of stability should be ; constructed in special cases. General practice appears to proceed very much on the earlier lines above described. The righting moment of a ship being represented by the pro- duct of her weight into the ordinate of the curve of stability corre- sponding to any angle of inclination, it follows that the smallness of the weights of ships when launched makes them very liable to be inclined by weights on board which can readily shift, or by external forces. Precautions are both usual and necessary in order to prevent the shifting of weights, and many accidents have been due to the neglect of such precautions. The curve BEE, Fig. 65, shows the change from BBB if the metacentric height were 0-8 foot instead of 0-6 foot. It has been drawn to illustrate an interesting case of stability for some ships at very light draught, and it will be seen that the vessel would then be in stable equilibrium when upright, and again at nearly 80 degrees of inclination, while at 60 degrees (where EEE crosses the base-line) she would be in unstable equilibrium. At 90 degrees there is a con- siderable righting moment. This case of variation in stability for .ships at very light draught had not been investigated until the accidents in launching above mentioned took place. It had, however, been fully discussed by Atwood in a paper read before the Boyal Society in 1796, for floating bodies of square section having the centre of gravity in the centre of figure. The contrast between the curve EEE in Fig. 65 for a ship at a very light draught, and the curve 9 in Fig. 62 for a laden ship initially unstable, is worth noting. Cross-cwrves of Stability. — In the preceding illustrations many examples will be found of curves of stability for the same ship in two extreme conditions — "fully laden" and "quite light." For 144 NAVAL ARCHITECTURE. [chap. hi. war-ships these two extremes commonly suffice, the range of draught being moderate, and the conditions of loading fixed. In merchant ships, where Tariations in draught and stowage may be considerable, it has been found desirable to carry the investigations further, and to make calculations by means of which the curve of stability for any draught of water, within working limits, and any position of the centre of gravity of ship and lading, may be readily constructed. A description will now be given of the so-called "cross-curves of ••' stability," which enable this to be done.* Reverting to Atwood's formula on p. 127, it will be seen that if the centre of gravity G, Eig. 55, coincided with the centre of buoyancy B^ each ordinate of the curve of stability would equal (BjR) the horizontal component of the transverse movement of the centre of buoyancy corresponding to any angle of inclination. In actual calculations for curves of stability, the successive values of lyj at certain selected angles of inclination are determined. These values of BjR, being dependent only on the extent of immersion and form of displacement of the ship, are the same for all possible positions of the centre of gravity G corresponding to a particular displacement. The F,G - 66. term B^ sin a in Atwood's formula is, in short, not affected by any other con- siderations than the distance B^, and the value of a. Suppose the cross- section of a ship to be represented by Fig. 66, the ship being inclined at any angle, a. Let wh represent the maxi- mum load-line, for which the volume of displacement is Y t ; when the vessel is steadily heeled to the angle a, the new water-line is Willi, cutting off the same volume V x . When the ship is up- right, the centre of buoyancy corresponding to Wil x is ^ ; at the angle * Details of the methods of cal- culating and constructing cross-curves will be found in vol. 25 of the Trans- actions of the Institution of Naval Archi- tects. An excellent discussion of the whole subject by Mr. Elgar appears in the Proceedings of the Royal Society for 1884. chap, in.] THE STATICAL STABILITY OF SHIPS. 145 a the new position of the centre of buoyancy is B x ; and bjin is the horizontal component of the transverse motion of the centre of buoyancy produced by the inclination. Four other water-lines, wj^, W3Z3, wjf, w 6 l 5 , when the ship is upright, correspond to volumes of displacement V a V 3 , V4, V 5 , and to centres of buoyancy b a b 3 , 64, l s . For the inclination a these respective volumes are cut off by W 2 L 2 , W3L3, W4L4, W 5 L 5 , and the new positions of the centres of buoyancy are B* B 3 , B^ B 3 ; while b^, 6 3 K 3 , i 4 Et, & 6 B 5 represent the horizontal components of the motions. It will be obvious that for the upright positions, " curves of displacement " (such as Fig. 2, p. 5) give the volumes V l5 V^ etc.; and metacentric diagrams (such as Fig. 36, p. 89) give the positions of the corresponding centres of buoyancy. For the inclined water-lines, the positions of B l5 B^ etc., are either found by direct calculation, based on the principles above explained, or else, for any inclined water-line chosen, a calculation is made of the volume that water-line cuts off, and the position of its centre of buoyancy. A " mechanical integrator " of great ingenuity, devised by Dr. Amsler (the inventor of the planimeter), enables these cal- culations to be very rapidly performed ; and the instrument is now largely used by naval architects, as a substitute for laborious arith- metical processes.* Next a diagram is constructed of the character shown in Fig. 67. A FIG. 67. is w. base-line OWW, taken ; corresponds to the point in Fig. 66, and is the zero of draught. The draughts of water corresponding to the upright water-lines WjZj, w 2 li, etc., are next set off (to any selected scale) on the base-line, measuring from ; W b W 2 W 3 , etc., represent these draughts; ordinates are drawn at the points so fixed. The length W^, Fig. 67, represents (to scale) the measurement bjR lt Fig. 66; W 2 d 2 > Fig- 67, represents feJElj, and so on. The length W^ represents to scale the product V x X JiEj ; W-jftj represents the product V 2 X i 2 B 2 , and so on. Through the points c x c 2 e 3 a curve is drawn, and through the points £?! d 2 d 3 another curve. Then for any water-line, such as wl, Fig. 66, W, W Wj YI4 Scale of Draughts. Ordinates of Cjtgtj represent Disptv. iR. d l d 2 d± •3—- bR. * For a description of the instrument and its uses, see vol. 25 of the Trans- actions of the Institution of Naval Archi- tects. L 146 NAVAL ARCHITECTURE. [chap. hi. for which the abcissa measurement is OW in Fig. 67, the measure- ments of ordinates Wd and Wc to the curves give respectively the values of JR and of the product Y X bR. In other words, for the selected angle of inclination a, calculations performed for four or five water-lines, including extreme load and extreme light conditions, enable the quantities mentioned to be determined for any inter- mediate draught by simple measurements. Sometimes the launching condition is taken as the lightest draught to be calculated for, in- stead of the TrnnimnTn draught for actual working conditions. Of the two curves in Fig. 67, c t <% C3 is the more valuable, since it takes account of the varying displacements, as well as the varying values of bR ; and when the righting moment opposed to external forces is in question, this product has to be considered. The construction of curves such as those in Fig. 67 has to be carried out for a number of angles of inclination, usually increasing by intervals of 10 to 15 degrees up to the theoretical " beam-end " position, or 90 degrees of inclination to the vertical. All these curves are usually put upon one diagram, each curve, Cj <% <%, eta, being marked with the angle of inclination to which it corresponds. Having drawn these curves once, they remain available for future use at any draught selected within the working limits. The process of constructing the curve of stability for any assigned draught is very simple. The corresponding abscissa value (say 6W in Fig. 67) is known, and the ordinate is drawn at the point W. Measuring the length of that ordinate (Wd) to any cross-curve (such as d^ d^, etc.) corresponding to a certain angle of inclination (a), the value (bR) of the horizontal transfer of the centre of buoyancy is obtained. The distance (JG) of the centre of buoyancy from the centre of gravity is known ; hence the value JG sin a is ascertainable. This operation is repeated for each cross-curve at the same ordinate (OW), and thus successive values of the righting lever (GZ) are obtained. Having these, the curve of stability is constructed in the manner explained above. Besides the methods which have been mentioned for making estimates of stability at successive angles of inclination, either by direct calculation or by the use of Amsler's integrator, various simple mechanical methods have been devised for approximating rapidly to these results. Some of these are extremely ingenious, but limits of space prevent any further reference to them here. They are chiefly of interest to the naval architect, and rest upon the principles which have been described in the preceding pages.* * See the description of Captain Stability Balances given in vols. 26 and Blom's method given in "Naval 28 of the Transactions of the Institution Science," and of Mr. Heek's ingenious of Naval Architects. ( H7 ) CHAPTEE IV. THE OSCILLATIONS OP SHIPS IN STILL "WATEK. If a ship, floating in still water, has been inclined from a position of stable equilibrium by the action of external forces, and is after- wards allowed to move freely, she will perform a series of oscillations, the range of which gradually decreases, on either side of the position of equilibrium ; and will finally come to rest. For practical purposes attention may be limited to the case of the transverse inclinations and oscillations of ships, reckoning from the upright position where they are in stable equilibrium ; and, unless specially mentioned, it may be assumed that the following remarks deal only with rolling motions in still water, the other principal oscillations — viz. pitching — not taking place to any sensible extent except in a seaway. There is an obvious parallelism between the motion of a ship set rolling in still water and that of a simple pendulum moving in a resisting medium. Apart from the influence of resistance, both ship and pendulum would continue to swing from the initial angle of inclination on one side of the vertical to an equal inclination on the other side ; and the rate of extinction of the oscillations in both depends upon the resistance, the magnitude of which depends upon several causes to be mentioned hereafter. In what follows, the term " oscillation " will be used to signify a single swing of the ship from port to starboard, or vice versa* The " arc of oscillation " will simply mean the sum of the angles on either side of the vertical swept through in a single swing ; for instance, a vessel rolling from 12 degrees inclination to port, and reaching 10 degrees inclination to starboard, would have (10° + 12°) 22 degrees as the arc of oscillation. The period of oscillation means the time occupied (in seconds, say) in performing a single swing. * In the usual mathematical sense the text agrees with the practice of the an oscillation would mean a double Royal Navy in recording rolling motions, swing, say from port to starboard and and is therefore followed, back again to port ; but the definition in 148 NA VAL ARCHITECTURE. [chap. iv. No vessel can roll in still water without experiencing resistance to her motion ; but considerable advantage results from first con- sidering the hypothetical case of unresisted rolling, and afterwards adding the conditions of resistance. Kigorous mathematical reason- ing may be applied to the hypothetical case, but this is not true of an investigation which takes account of the total resistance experienced by a ship when rolling; and it is necessary to adopt a mixed method when dealing with resisted rolling, superposing, as it were, data obtained from experiments made to determine the effects of resistance, upon the mathematical investigations of the hypothetical case. No endeavour will here be made to follow out either part of the inquiry, as such a course involves mathematical treatment lying outside the province of this work ; but it is possible in popular language to explain some of the chief results obtained, and this we propose to do. Supposing the rolling of a ship in still water to be unresisted, it may be asked, What is the length of the simple pendulum with which her oscillations keep time, or synchronize? It has been sometimes assumed that the comparison made in the previous chapter between a ship held in an inclined position and a pendulum of which the length is equal to the distance between the centre of gravity and the metacentre held at an equal inclination, will remain good when the ship and the pendulum are oscillating. In fact, it is supposed that the whole of the weight may be concentrated at the centre of gravity (G, Figs. 34 and 35, p. S3), while the metacentre is the point of suspension for the ship in motion as well as for the ship at rest ; but this is an error. If it were true, the stiffest ships, having the greatest heights of metacentre above the centre of gravity, should be the slowest-moving ships. All experience shows the direct opposite to be true. For example, a converted ironclad of the Prince Consort class, with a metacentric height exceeding 6 feet, will make twelve or thirteen single rolls per minute, and an American monitor, with a metacentric height of 14 feet, will make more than twenty single rolls per minute, while vessels like the Hercules or Sultan, with metacentric heights under 3 feet, will only make seven or eight rolls per minute. What is thus shown to be true by experience had been proved nearly a century and a half ago, by the great French writer Bouguer, in his Traite dv, Navire. The necessity for carefully distinguishing between the cases of rest and motion in a ship may be simply illustrated by means of a bar pendulum (such as AB, Fig. 68) of uniform section, having its centre of gravity at the middle point, G. To hold the pendulum at any steady inclination to the vertical must require a force exactly equal to that required to hold at the same inclination a simple chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. 1 49 FIG. 68. pendulum of length AG, and of equal weight to the bar pendulum. But if this simple pendulum were constructed, and set moving, it would be found to move much faster than the bar pendulum. The simple pendulum keeping time with the bar, instead of having a length AG equal to one-half of AB, will have a length AK equal to two- thirds of AB ; and it is important to notice the causes producing this result.* Suppose the pendulum to have reached one extremity of its swing, and to be on the point of returning : at that instant it will be at rest. As it moves back towards the upright, its velo- city continually increases, reaching a maximum as the pendulum passes through the upright position, and afterwards decreasing until at the other extremity of the swing it will once more be instantaneously at rest. These changes of velocity, accelerations or retardations, from in- stant to instant can only be produced by the action of certain forces ; and according to the first principles of dynamics, these changes of velocity really measure the intensity of the forces. For instance, a body falling freely from a position of rest acquires in one second a velocity of rather more than 32 feet per second ; at the end of two seconds it has twice as great a velocity ; and so on. This " rate of change of velocity " — some 32 feet per second — is regarded as a measure of the uniform accelerating force of gravity. For any other accelerating force the corresponding measure is expressed by the ratio which the rate of change of velocity produced by gravity bears to the change of velocity which would be produced by that accelerating force, if its action continued uniform for one second. For accelerating forces which are not uniform this mode of measure- ment gives a varying rate of change from instant to instant. In the case of the simple pendulum, the bob moves in a circular arc, having a radius equal to the length of the pendulum ; hence the Imea/r velocity of the bob in feet per second may be expressed in terms of the product of this radius into the cmgulwr velocity.! Similarly, the * A simple pendulum, as previously explained, is one having all its weight concentrated at one point (the "bob"), and supposed to be hung from the centre of suspension (A, Fig. 68) by a weightless rod. The point K in Fig. 68 is termed the "centre of oscillation," and the bar pendulum will oscillate in the same time, whether it is hung at A or at K. ■j- The angular velocity may be de- fined as the angle swept through per second if the motion is uniform, or that which would be swept through per second if the rate of motion existing at any in- stant were continued for a second. These angles are usually stated in circular measure. 15° NAVAL ARCHITECTURE. [chap. iv. changes in velocity, measuring the accelerating forces, may be expressed in terms of the product of the radius into the changes of angular Telocity. These accelerating forces at any instant act at right angles to the corresponding position of the pendulum rod ; and so finally we obtain for the simple pendulum : — Moment of accelerating | = Cx weight of the bob X (radius) 8 forces about centre of f X rate of change of angular suspension .... J Telocity ; where C is a constant quantity (viz. ^, nearly — the reciprocal of the velocity per second due to gravity). Hence follows this important principle : for any heary particle oscillating about a fixed axis the moment' of the accelerating forces at eTery instant involves the product of the weight of the particle by the square of its distance from the axis of rotation. Turning from the simple pendulum to the bar pendulum (Fig. 68), we may consider the latter as made up of a number of heavy particles, and take each separately. For example, take a particle of weight ic at a distance aj from the axis of rotation (A) ; the moment of the accelerating force upon it, about the point A, is given by the expression — Moment = C X w x as 2 X rate of change of angular velocity. At any instant the change of angular velocity is the same for all particles in the bar-pendrdum, whatever may be their distance from A; whence it follows that for the whole of the particles in the bar-pendiUnm — Moment of accelerating i = Cx weight of bar X it 2 X rate forces at any instant ) of change of angular velocity. To determine k 2 , we have only to sum up all such products as w x a;* for every particle in the bar, and divide the sum by the total weight of the bar. Or, using S as the sign of summation — p = S(tw>») weight of bar Turning to the case of a rigid body like a ship, oscillating about a longitudinal axis which may be assumed to pass through the centre of gravity, it is necessary to proceed similarly. Take the weight of each elementary part, multiply it by the square of its distance from the axis of rotation, obtain the sum of the products (which sum is termed the "moment of inertia"), and divide it by the total weight of the ship; the quotient (#") will be the square of the " radius of gyration " for the ship when turning about the assumed axis. If the whole weight were concentrated at the distance k from chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. I5 1 the axis of rotation, the moment of the accelerating forces and the moment of inertia would then be the same as the aggregate moment of the accelerating forces acting upon each particle of lading and structure in its proper place. It will be obvious from this popular explanation of established dynamical principles why we cannot assume that a ship in motum resembles a simple pendulum suspended by the metacentre, and having all the accelerating forces acting through the centre of gravity. These accelerating forces developed during motion constitute, in fact, a new feature in the problem, not requiring consideration when there is no motion. For a position of rest, it is only necessary to determine the sum of the statical moments of the weight of each element about the centre of suspension, and this sum equals the moment of the total weight concentrated at the centre of gravity. But for motion, there is the further necessity of considering the moment of inertia, as well as the statical moment. A ship rolling in still water does not oscillate about a fixed axis, corresponding to the centre of suspension (A) of the pendulum in Fig. 68 ; but still her motions are similar to those of the pendulum. At the extremity of a roll, when her inclination to the upright is a maximum , the moment of statical stability is usually greater than that for any other angle within the arc of oscillation, and this is an unbalanced force, tending to restore the vessel to the upright. She therefore begins to move back, and at each instant during her progress towards the upright is subject to the action of a moment of statical stability tending to make her move in the same direction, and consequently quickening her speed. But the moment of stability gradually decreases in amount, and at the upright is zero ; the velocity reaching its maximum at that position. On the other side of the upright the statical stability opposes further inclination, and at every instant grows in magnitude ; the result is a retardation of speed, and finally a termination of the motion of the ship at the other end of the roll at an inclination to the vertical equal to that from which she started. All this, be it observed, is on the hypothesis of unresisted rolling. As a matter of fact, with resistance in opera- tion, it always acts as a retarding force, tending to extinguish the oscillations. The position of the instantaneous axis about which a ship is turning at any moment, supposing her motion to be unresisted, and the displacement to remain constant during the motion, may be determined by means of a geometrical construction due to the late Canon Moseley. It may be most simply explained by reference to a cylindrical vessel with circular cross-section such as is shown in Fig. 69. If a circle F-jFFa be described concentric with the circular 152 NAVAL ARCHITECTURE. [chap. IV. section, and touching the water surface at F, this circle will touch the water-line corresponding to any other inclined position ; for all the tangents to this circle cut off from the circular section a segment equal in area to ~WTL. The circle I^F^ is termed the " curve of flotation," and a right cylinder described upon it as base would haTe this pro- perty : if the water surface is supposed to become rigid and perfectly smooth, and the cylinder of which F 3 FiF is a section, is supposed also to have a perfectly smooth surface, and to project before and abaft the ship, carrying her with it while the projecting ends roll upon the water surface, the conditions for unresisted rolling will be fulfilled. To determine the instantaneous centre, it is then only necessary to consider the simultaneous motions of the point of support, or " centre of flotation," F, and the centre of gravity G. The point F has its instantaneous motion in a horizontal line ; consequently it must be turning about some point in the ver- tical line FM. As to the motion of the centre of gravity, it must be noticed that, resistance being supposed non-existent, the only forces impressed upon the floating body are the weight and buoyancy, both of which act vertically ; therefore the motion of translation of the centre of gravity must be vertical, and instantaneously G must be turning about some point in the horizontal line GZ. The point Z, where the two lines GZ and FM intersect, will, therefore, be the instantaneous centre about which the vessel turns. This simple form of vessel always has the centre of buoyancy B, the centre of flotation F, and the metacentre M in the same vertical line, for any position it can occupy. An ordinary ship presents different conditions, as shown in Fig. 70, where the centre of flotation F does not lie on the vertical line BjZK^ Here, however, the same principles apply : G moves about some centre in the line GZO ; F about some centre in the vertical line FO ; the point oi intersection of these two lines fixes the instantaneous axis for the whole ship. In war-ships the centre of gravity G ordinarily lies near to the water-line (WJi,, Fig. 70) for the upright position ; while for oscil- lations of 12 or 15 degrees on either side of the vertical, the centre of flotation F does not move far away from the middle line A of the load-line section WjLj. In other words, the common case for war- chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. 153 vessels of ordinary form is that where the instantaneous axis passes through or very near to the centre of gravity. Although the position of the instantaneous axis changes from instant to instant (as its name implies), it is not productive of any serious error in FIG. 70. most cases to regard the ship as rolling about a fixed axis passing through the centre of gravity. In theoretical investigations no such assumption is necessary, because the principle known in dynamics as the " conservation of the motions of translation and rotation " then becomes applicable. The motion of translation of the centre of gravity is considered separately from any motion of rotation ; this latter motion being then supposed to take place about an axis passing through the centre of gravity. By this means the " period " of an oscillation in still water can be very closely approxi- mated to, although there is no fixed axis of rotation. It may be interesting to show how the metacentre moves during unresisted roll- ing, instead of being fixed in space, as is often supposed. Taking once more the cylin- drical vessel of circular cross- section, we have a case where the metacentre is fixed in the vessel, but moves in space as the vessel rolls. In Fig. 71 the darker circle represents the vessel in her upright position ; the lighter one shows 154 NAVAL ARCHITECTURE. [chap. iv. her position at the extremity of the roll. The centre of gravity G mores vertically, as explained above, and during the roll rises from Gr to G 1; the corresponding position of the metacentre being M P As the ship rolls, therefore, the metacentre sways to and fro horizontally ; but in less simple forms it would neither be fixed in the vessel nor have so simple a motion. Summing up the preceding remarks on unresisted rolling, it appears that the active agent in producing the motion, after the vessel has once been inclined and then set free, is the moment of statical stability ; and that the moment of inertia about a longi- tudinal axis passing through the centre of gravity is also of great importance. Mathematical investigation leads to the following expression for the period of oscillation of a ship : — Let h = her radius of gyration (in feet). m = metacentric height (GM) (in feet). T = period in seconds for a single roll. Then T = *■*/— = 3-1416 */-£- V gm V gm where g (measuring force of gravity) = 32J feet (nearly) per second. This may be written — T = -554 A /^ m A fair approximation to the still-water, or " natural " period of oscillation for a new ship can be made by means of this equation. The metacentric height is determined for a war-ship as one of the particulars of the design; and the distribution of the weights is known, so that the moment of inertia can be calculated about the assumed axis of rotation passing through the centre of gravity. This latter calculation is laborious, the weight of each part of the structure and lading having to be multiplied" by the square of its distance from the axis; but with care it can be performed with a close approach to accuracy. Calculations of this kind are rarely made, except in connection with novel types of ships, for which thorough investigations are needed in order to be assured of their safety and seaworthiness. As examples of close estimates of natural periods we may refer to the Devastation and a monitor of the American type, which were under the consideration of the Admiralty committee on designs for war-ships in 1871. It was estimated that the Devastation would have a period of about 7 seconds ; the actual period obtained by experiment was 6f seconds. The estimated period for the American monitor was 2£ seconds ; the actual period, 2 T ^ seconds. The formula given for the period supposes the rolling to be unresisted ; but the influence of resistance is much more chap, rv.] OSCILLATIONS OF SHIPS IN STILL WATER. 155 marked in the extinction of oscillations than it is in affecting the period of oscillation, and this accounts for the close agreement of estimates made from the formula with the results of experiments. This statement may be illustrated by reference to experiments made both in this country and in France. Mr. Froude discovered that the period of the Greyhound remained practically the same after exceedingly deep bilge-keels had been fitted, as it was without such keels. Similar results were obtained with a model of the Devastation (see p. 177). MM. Eisbec and De Benaze, of the French Navy, ascertained that the tug Morn, which had a period of 2-18 seconds without bilge-keels, had, that period increased only to 2-25 seconds by the addition of those keels. And yet in all these cases the effect of the keels in extinguishing the oscillations was most marked. The Elorn was not merely set rolling in still water, but was also rolled (on specially contrived supports) in dry dock ; when her natural period for unresisted rolling was found to be 2 - 03 seconds. This last experiment furthermore confirmed the practical accuracy of the calculation that had been made beforehand of the moment of inertia, and the natural period of this vessel.* The preceding formula for the still-water period enables one to ascertain approximately the effect produced upon the period by changes in the distribution of the weights on board a ship. Such changes usually affect both the metacentric height and the moment of inertia, and their effects may be summarized as follows : — Period is increased by — (1) Increase in the radius of gyration ; (2) Decrease in the metacentric height. Period is decreased by — (1) Decrease in the radius of gyration ; (2) Increase in the metacentric height. " Winging " weights — that is, moving them out from the middle line towards the sides — increases the moment of inertia and tends to lengthen the period. The converse is true when weights — such as guns — are run back from the sides towards the middle line. Eaising weights also tends to decrease the moment of inertia, if the weights moved are kept below the centre of gravity ; whereas if they are above that point, the corresponding change tends to increase the moment of inertia. But all such vertical motions of weights have an effect upon the position of the centre of gravity, altering the metacentric height, and affecting the moment of inertia by the * For particulars of these valuable Academy of Sciences in 1873; this is experiments see the Memoir e presented reprinted in Naval Science for 1874 and by Messrs. Eisbec and De Benaze" to the 1875. 156 NAVAL ARCHITECTURE. [chap. iv. change in the position of the axis about which it is estimated. It is therefore necessary to consider both these changes before deciding what may be their ultimate effect upon the period of rolling. The principles stated above will enable the reader to follow out for himself the effect of any supposed changes in the distribution of the weights. One or two examples may be given. A ship of 6000 tons weight has a metacentric height of 3 feet and a period of 7 seconds ; a weight of 100 tons is raised from 15 feet below the centre of gravity to 15 feet above. In consequence of the transfer of the weight, the centre of gravity will be raised, and we have — „. , , 100 tons X 30 feet Eise of centre of gravity = 6000 tons = £ foot - New value of GM = 3 - \ = 2£ feet. Originally, according to the formula for the period — 7 = -554^1 i = : 55lV / 3 = 22 (nearly). The rise in the centre of gravity slightly alters the position of the axis about which the ship is considered to revolve, and this pro- duces a change in the moment of inertia ; but the change is so small that it may be neglected. Then, after the weights are moved, the period T will be given by the equation — T = -554x7*! V 2} . T /3 ,, ■■rv^ =H .*. T = 7 X 1-1 = 7-7 seconds (nearly). The decrease of 6 inches in the metacentric height thus lengthens the period about 10 per cent. As a second case, suppose weights amounting in the aggregate to 100 tons, placed at the height of the centre of gravity to be " winged " 15 feet from the middle line ; their motion, being hori- zontal, does not affect the position of the centre of gravity.* Then we have — * The expressions for changes in the necessary to determine for each position moment of inertia produced by winging the actual distances of the weights from weights not originally at the middle line, the axis passing through the centre of nor placed at the height of the centre of gravity, gravity, can be easily formed ; it is only chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. 157 Original moment of inertia = 6000 X ¥ Additional moment of inertia = 100 X 15 2 = 22,500 •\ New moment of inertia = 6000 x ¥ + 22,500 6000 x¥ + 22,500 (New radius of gyration) 2 = 6000 -*» + « / K Originally, 7 seconds = -554 \/ -^ (1) Now T = -554 / — g — (2) Therefore T = 7 V 1 +— . a i so #» = 475 ■•■ T - 7 ^ /T7 iSo- 7 x 1 ' 004 = 7-028 seconds. This alteration in period is very slight, as compared with that produced by the supposed transfer of weight in a vertical sense, and furnishes an illustration of the much greater changes rendered possible by alterations of metacentric heights than by changes in the moments of inertia. It is important to remark that in the mathematical investigation upon which the formula for the period of oscillation is based, it is assumed that there is no sensible difference between the time occupied by the ship in swinging through large or small arcs. Within a range of, say, 12 or 15 degrees on either side of the vertical in high-sided ships — for which range the metacentric method of estimating the stability gives fairly accurate results — this condition has been proved by direct experiment to be fulfilled very nearly in vessels of ordinary form. For example, the Sultan was rolled in still water until an extreme inclination of nearly 15 degrees on either side of the upright was reached, and then allowed to come to rest, the observations being continued until the extreme inclination attained was only 2 degrees ; but the period of rolling through the arc of 30 degrees was practically identical with that for the very small arc of 4 degrees. This note- worthy fact is usually expressed by the statement that the rolling of ordinary ships is isochronous within the limits named above. For larger angles of oscillation such ships would probably have a somewhat longer period than for the small oscillations, and it is possible to approximate to this increase. But as yet direct experi- ment has not been applied to determine the actual periods when 158 NAVAL ARCHITECTURE. [chap. iv. high-sided ships swing to 20 or 30 degrees on either side of the vertical ; and the case is one which can be best dealt with by means of model experiments in the manner described on p. 167. Vessels of low freeboard or exceptional form may not be isochronous through arcs of oscillation so large as those named for ordinary vessels ; and the reasons for this difference will be understood from the remarks made hereafter. For unresisted rolling the theoretical condition for isochronism may be very simply stated : — Within the limits of incli- nation to the vertical, for which the statical righting moment varies directly as the angle of inclination, the rolling of a vessel will be isochronous. In other words, if the curve of stability is practically a straight line for a certain distance out from the upright, the rolling will be isochronous within the limits of inclination fixed by that distance. Dynamical Stability. — Before concluding these remarks on the hypothesis of unresisted rolling, a brief exposition of the principles of dynamical stability must be attempted. On the assumption that no account shall be taken of the effect of fluid resistance, dynamical stability may be defined as the " work " done in heeling the ship from her upright position to any angle of inclination ; the amount of work done, of course, varying with the inclination. Work, it need hardly be said, is here used in its mechanical sense of a pressure overcome through a distance ; for example, a ton raised one foot may be taken as our unit of work, and then to raise 100 tons through a foot, or a ton through 100 feet, will require 100 units of work, or " foot-tons." It has been shown how to estimate the moment of the couple for statical stability at a given angle ; and if the vessel is gradually inclined beyond that angle, the forces inclining her must do work depending upon the righting couples corresponding to the successive instantaneous inclinations, as well as to the ultimate angle attained. In short, it is easy to determine the dynamical stability, when the variations in statical stability ' 2 * are known, and the curve of stability has been constructed. A simple illustration may make this clearly understood. A man is pushing at the end of a capstan bar (Z, in Fig. 72) with a force P, the centre of the capstan (G) is distant I feet from Z. Then the statical mo- ment of the pressure P about G will equal P x Z, and this exactly corresponds to the expression for the moment of statical stability (D x GrZ) obtained in the previous chapter. Now suppose the man to push the bar on through an angle A (circular measure) ; then — chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. 159 Distance the man walks = I X A ; Work he does = pressure x distance through which it acts = P x I X A = statical moment x A. Next suppose that, as the man pushes the bar round, he moves inwards or outwards along it, varying the value of Z'from instant to instant ; then we shall have a parallel case to that of the ship where the arm of the righting couple varies from angle to angle of incli- nation. The man walks for a very small distance from the first position (GZ, Fig. 72), pushing as before ; then for that very small angle a, GZ will have practically the constant value I, and (as above) — Work = statical moment (for position GZ) x a. By the time he has completed the angle A, he has moved in on the bar to the position Z r ; let GZ X = Z : . Then, as he pushes with a constant force P, we must have for a very small angle a from the position GZj — Work = statical moment (for position GZ L ) x a. Similarly, for any other position, the work for a very small angle beyond may be expressed in terms of the corresponding statical moment. And what is thus true of the capstan is equally true of a ship ; the work for any small inclination a from a given position is given by — Work = statical moment of stability for that position x a = displacement X GZ (for that position) x a. Turning next to any curve of stability (say, to Pig. 56, p. 127), we have a graphic delineation of the values of GZ for every inclina- tion until the vessel becomes unstable. Supposing OP is taken to represent any assigned angle of inclination, and %>n drawn very close to PN (the distance Py corresponding to the very small angle a), the area of this little strip (PNnp) will graphically represent the product GZ x a. Consequently it follows that on the curve of stability for a ship, reckoning from the upright (0) to any angle of inclination (such as OP), the dynamical stability corresponding to that inclination is represented by the area (OPN) cut off by the ordinate corresponding to that inclination. The total area of the curve of stability therefore represents the total work to be done (excluding fluid resistance) in upsetting a ship. Bearing this fact in mind, fresh force will be given to the remarks made in the previous chapter as to the comparative influence of beam and freeboard upon the form and range of curves of stability ; and the contrasts exhibited between the curves of stability for various classes of ships given in that chapter, become still greater when the 160 NAVAL ARCHITECTURE. [chap, i v. consideration of their relative total areas is added to that of their range. These are matters upon which any one so desiring may proceed to independent investigation with the materials afforded: and no more will here be said respecting them. We owe the term, and the first investigation for dynamical stability, to the late Canon Moseley. and his formula differs somewhat in appearance, though not in fact, from that given above. It may be well, therefore, to briefly indicate the chief steps in Canon Moseley's investigation. Starting from the principle that, apart from resistance, the only external forces impressed upon a ship rolling freely would be her weight and buoyancy, he remarked that the work done upon her in producing any inclination might be expressed in terms of the rise in space of the centre of gravity, where the weight might be supposed concentrated, and the fall of the centre of buoyancy, where the buoyancy might be supposed to be centred. Turning to Fig. 55, p. 126, it will be seen that, when the ship is upright, B X G is the vertical distance between these two centres, whereas in the inclined position their vertical distance becomes equal to BZ. In forming an estimate of the work done in producing an inclination, we are only concerned with the changes in the relative vertical positions of these two points ; hence we may write, if V = volume of displacement (in cubic feet) — Work done in producing an inclination a \ _ V ,^y. _ B G1 • (dynamical stability in foot-tons) . . • ) ~ 35 also — BZ = EZ + BR = B X G cos a + BR; and by the principle of the motion of the centre of buoyancy previously explained (see p. 127) — BR= y^A + S'A)- Substituting these values in the foregoing expression — Dynamical stability = — J— ( = -gr |«(yA + for their different displacements. It will be assumed that they have equal sail-spread and moments of sail, so that one wind-curve will serve for both ships. The force of wind is supposed sufficient to hold the Captain at a steady heel of nearly 10 degrees, and the Monarch at a slightly greater heel. No matter how far the vessels become inclined, if the wind continues to act upon them, the part of the areas of the curves lying between the wind-curve and the base- line will be absorbed in counterbalancing the steady pressure of the wind. Hence only the areas lying above the wind-curve are avail- able to resist gusts or squalls ; and these areas are therefore termed the " reserve dynamical stability." Supposing the reserve to be large, the ship is much safer than if it be small, and on reference to the diagram (Fig. 76) it will be seen how Aery small was the reserve in the Captain, when compared with the Monarch. Lowness of free- board associated with a moderate metacentric height contributed to give the ill-fated Captain a curve of stability of quite a different character from that of any other ship of war carrying masts and sails. Prior to her loss information respecting the curves of stability for various classes of ships was very meagre ; but now that numerous and laborious investigations have been made, the very exceptional character of the Captain stands out clearly, as may be seen by reference to Figs. 60 and 63. In comparing her with the Monarch, as in Fig. 76, we have taken a rigged ironclad below the average as to the range of her stability, but even then the contrast chap, iv.] OSCILLATIONS OF SHIPS IN STILL WATER. I8 7 is most remarkable. This will appear from the following statement, published, by authority, soon after the loss of the Captain, when many persons expressed fears, which were groundless, that a similar catastrophe might happen to the Monarch : — Monarch. Captain. Angle at which the edge of the deck is immersed Amount of righting force in the above position \ (in foot-tons of moment) . . . . J Angle of maximum stability .... Maximum righting force (in foot-tons of moment) Angle at -which the righting force becomes zero ■> Eeserve of dynamical stability at an angle of "l heel of 14 degrees (in foot-tons of work) . . / 28° 12,542 40° 15,615; 69i° 6,500 14° 5,600 21° 7,100 64*° 410 The last comparison is the most important as regards safety, and from it one sees how small was the margin of safety of the Captain when sailing, as she is reported to have done on the day prior to her loss, at an angle of heel of 14 degrees. Adding to the wind-pres- sure, the heave of the sea, and rolling oscillations, the reasons of the disaster are obvious. Fig. 76 also furnishes an illustration of the method by which an approximation can be made to the maximum heel to which a ship is driven by a squall of wind having a certain force if her motion is unresisted. Let WW be the wind-curve as before; the point C, where WW intersects the curve of stability (1) for the Captain, determines the steady heel corresponding to the assumed force of wind. The ship is upright and at rest when struck, and between the upright and the angle of steady heel the moment of sails con- tinuously exceeds the statical righting moment ; hence there is an unbalanced force throughout this part of the motion, storing up work (represented by the area OWC) which is afterwards expended in carrying on the ship until an inclination (EF) is reached (about 20 degrees in this case) making the area (OEF) above the wind- curve equal to the area WOC. The Monarch would be driven over to nearly an equal angle by the same squall ; GH marks the inclina- tion, the area GKH being equal to the area WOK A still more critical case is that where the ship has just com- pleted a roll to windward when the squall strikes her. Accumula- tion of work then becomes far more serious ; the righting moment and the moment of the sails act together as an unbalanced moment all the time that the vessel is moving back to the upright, the con- dition of things on the leeward side of the upright being similar to that already described. Fig. 77 illustrates this case for the Captain. 1 88 NAVAL ARCHITECTURE. [chap. IV. The extreme angle of roll to windward, before the squall strikes the ship, is indicated by the ordinate GHK (8 degrees) ; the ordinate L3I marks the inclination (40 degrees) she must reach to leeward Y FIG. 77. before the reserve of dynamical stability measured by the area CELMC can furnish the requisite amount of work to destroy the motion due to the accumvdated work of roll and wind measured by the equal area GKOCWG.* This case shows that even in a calm sea a rigged ship of low freeboard or limited range of stability may run great risk of being capsized if struck by a squall, and illustrates the great advantages possessed by vessels having a large reserve of dynamical stability. Ships of the mastless type are less affected by the action of these suddenly applied squalls and gtists. Their broadsides do not offer sufficient surface to produce any sensible inclination in storms of ordinary severity. For instance, in the Devastation it is estimated that, with a storm of wind exerting a pressure of 100 lbs. per square foot, an inclination of only 5 degrees would be produced ; but this pressure is about twice as great as that of a hurricane having a speed of 100 knots per hour. Hence a far more moderate range and area of the curves of stability is admissible for such vessels than is proper in rigged ships, and the Admiralty Committee on designs recommended a range of 50 degrees as sufficient for such vessels, regarding them as safe even with a less range of stability. It is necessary to remark that in the preceding estimate for the heeling effect of squalls no account has been taken of fluid resistance, . which would assist in checking the motion, and bring a ship up at * The wind-curve is the same as in Fig. 76, the corresponding angle of steady heel being nearly 10 degrees ; this curve will obviously be symmetrical about the upright position indicated by OY. On the windward side (to the left) of OY it will be noticed that the curve of stability is drawn below the base-line OX ; the reason for so doing is that on the right-hand side (to leeward) ordinates measured above the axis tend to make the vessel move back to windward, so • that it is convenient to indicate the con- trary tendency existing on the windward side (i.e. a tendency to drive the vessel back to leeward) by drawing the ordi- nates below the axis. No other feature in the diagram appears to require further explanation. chap. IV.] OSCILLATIONS OF SHIPS IN STILL WATER. 1 89 a less inclination than has been indicated. When the curve of extinction for a ship is known, and her " coefficients of resistance " have been deduced therefrom, it is possible to make the necessary corrections in the estimates for heeling ; but this is not commonly done. The method to be followed will be understood from the explanations given (on p. 171) of the manner in which the " work " done by the resistance during a single swing can be measured from the curve of extinction. Moreover, it must be noted that when a ship is struck by a squall and moves away to leeward, her motion affects both the relative velocity and pressure of the wind on her sails, as well as the height of the centre of pressure. This matter has been mentioned above, and was fully discussed by the author in a paper read before the Institution of Naval Architects in 1881 ; but the treatment is of too mathematical a character to be reproduced here. It may be interesting, however, to quote from that paper a few figures illustrating the very great influence which the action of fluid resistance, and the diminu- tion in the moment of wind-pressure produced by the angular motion of the sails, may have upon the angle to which a ship lurches when struck by a squall. Taking the unarmoured wood frigate Eiidymion of the Boyal Navy, she is supposed to have reached an extreme inclination of 20 degrees to the windward side of the vertical and to be instantaneously at rest when a squall strikes her ; then, by the method explained in Fig. 77, she would be driven over to 39 degrees on the leeward side of the vertical. All other conditions remaining xmaltered, except that the effect of the fluid resistance is included, the extreme roll to leeward is found to be reduced from 39 degrees to 31 degrees. And, taking one step further, if allowance is made for the reduction in the effective pressure of the wind on the sails during the roll to leeward, the extreme inclination reached is 22 degrees, or 2 degrees only beyond the initial inclination to windward. The process of " graphic integration " by which these results are obtained is briefly explained on p. 249, and it would enable the problem to be solved completely, were it not for the fact that so little is known of the laws governing the pressure of wind on sails. But enough has been done to show how large is the margin of safety which is provided by the method described in Fig. 77. Unfortunately, illustrations are not wanting of the possibility of sailing vessels being capsized in smooth water by the action of squalls. Two well-known cases are those of the American yacht Mohawk and H.M.S. Eurydice.* The Mohawk was at anchor off * See reports of evidence given Kemp's valuable work on " Yacht and before the Eurydice Court Martial; Boat-sailing." also, as to Mohawk, see Mr. Dixon 190 XAVAL ARCHITECTURE. [chap. iv. Staten Island in 1876, with sail set, when the squall struck her. Being unprepared for bad weather, the heavy furniture and ballast shifted as the yacht heeled over ; and, soon after her deck was immersed, the water poured into the cabin and cock-pit, so that all chance of righting was lost. It has been estimated that if the curve of stability of the Mohawk were calculated in the usual manner, on the assumption that no weights shifted and no water entered the hold, the angle of maximum stability would have been reached at 30 degrees, and the range would have been about 80 degrees. Under the circumstances described such a curve obviously did not represent the actual conditions of stability of the vessel. In the case of the Eurydice also the actual curve of stability at the time the vessel was struck by the squall differed greatly from that made on the ordinary assumptions; and the ports being open virtually reduced the vessel to the condition of a low freeboard rigged ship. The Court Martial recognized these facts in their report; and recorded their opinion that some of the lee-ports being open "materially conduced to the catastrophe." In their judgment, also, these ports "having been open was justifiable and usual •• under the state of the wind and weather up to the time of -the " actual occurrence of the storm." ( I9i ) CHAPTER V. DEEP-SEA WAVES. Many attempts have been made to construct a mathematical theory of wave-motion, and thence to deduce the probable behaviour of ships at sea. The diversity of these theories affords ample evidence, if evidence were needed, of the difficulties of the subject. To an ordinary observer perhaps no phenomena appear less susceptible of mathematical treatment than the rapid and constant changes witnessed in a seaway; but it is now generally agreed that the modern or trochoidal theory of wave motion fairly represents the phenomena, while preceding theories do not. "Without attempting any account of the earlier theories, it is proposed in the present chapter to explain, in a simple manner, the main features of the trochoidal theory for deep-sea waves. Let it be supposed that, after a storm has subsided, a voyager in mid-ocean meets with a series of waves all of which are approxi- mately of the same form and dimensions ; these would constitute a single, or independent, series such as the trochoidal theory con- templates. According to this theory the series of waves is regarded as traversing an ocean of unlimited extent, where the depth, in pro- portion to the wave dimensions, is so great as to be virtually unlimited also. The bottom is supposed to be so deep down that no dis- turbance produced by the passage of waves can reach it ; and the regular succession of the waves requires the absence of boundaries to the space traversed. It is not supposed, however, that an ordinary seaway consists of such a regular single series of waves. On the contrary, more frequently than otherwise two or more series of waves exist simultaneously, over-riding one another, perhaps moving in different directions, and causing a " confused sea," successive waves being of unequal size and varying form. Sometimes the condi- tions assumed are fulfilled — a well-defined regular series of waves is met with ; and from the investigation of their motions it is possible, as we shall see hereafter, to pass to the case of a confused sea. Nor is it supposed that only deep-sea waves are worthy of investigation ; 192 NAVAL ARCHITECTURE. [chap. v. those occurring in shallower water also present notable features, but for our present purpose they are not nearly so important as ocean waves, since these latter so largely influence the behaviour of ships. It will be understood, then, that in what follows, unless the contrary is stated, we are dealing with a single series of regular deep-sea waves. Any one observing such waves cannot fail to be struck with their apparently rapid advance, even when their dimensions are moderate. A wave 200 feet in length, from hollow to hollow, has a velocity of 19 knots per hour — nearly as fast as the fastest steamships — and such waves are of common occurrence. A wave 400 feet in length has a velocity of 27 knots per hour ; and an Atlantic storm wave, 600 feet long, such as Dr. Scoresby observed, moves onward at the speed of 32 knots per hour. But it is most important to note that in all wave motion it is the wave form which travels at these high speeds, and not the particles of water. This assertion is borne out by careful observation and common experience. If a log of wood is dropped overboard from a ship past which waves are racing at great speed, it is well known that it is not swept away, as it must be if the particles of water had a rapid motion of advance, and as it would be on a tideway where the particles of water move onwards; but it simply sways backward and forward as successive waves pass. Before explaining this distinction between the motions of the particles in the wave and the motion of the wave form, it will be well to illustrate the mode in which, according to the modern theory, the wave form or profile may be constructed. Fig. 78 will serve this 0X2 FIG. 78 3 4 5 6 7/ / \ K 3 w / i >\ ^rh : 1 1 R t I 1 /[ iii/! 1 ! ' / ! 1 * d\ 1 \ --'"' ' X /k s. J a 1 ^^^ IP V R. 1$-' __ — - purpose, r Suppose QK to be a straight line, under which the large circle whose radius is OQ is made to roll. The length QR being- made equal to the semi-circumference, the rolling circle will have chap, v.] DEEP-SEA WAVES. 193 completed half a revolution during its motion from Q to E. If this length QE and the semi-circumference QE X are each divided into the same number of equal parts (numbered correspondingly 1, 2, 3, etc., in the diagram), then obviously, as the circle rolls, the points with corresponding numbers on the straight line and circle will come into contact successively, each with each. Next suppose a point P to be taken on the radius OE x of the rolling circle ; this will be termed the " tracing point," and as the circle rolls, the point P will trace a curve (a trochoid, marked P, c&j, foj, c 2 . . . A 2 in the diagram) which is the theoretical wave profile from hollow to crest, P marking the hollow and h 2 the crest. The trochoid may, therefore, be popularly described as the curve traced on a vertical wall by a marking-point fixed in one of the spokes of a wheel, when the wheel is made to run along a level piece of ground at the foot of the wall; but when thus described, it would be inverted from the position shown in Fig. 78. To determine a point on the trochoid is very simple. "With O as centre and OP as radius describe the circle "Seh. As the rolling circle advances, a point on its circumference (say 3) comes into contact with the corresponding point of the directrix-line QE ; the centre of the circles must at that instant be (S) vertically below the point of contact (3), and the angle through which the circular disc and the tracing arm OP have both turned is given by Q03. The angle POc, on the original position of the circles, equals Q03 ; through S draw Se 2 parallel to Oc, and make $c 2 equal to Oc ; then c 2 is a point on the trochoid. Or the same result may be reached by drawing ce 3 horizontal, finding its intersection (e 3 ) with the vertical line S3, and then making c 2 e 3 equal to &> x . In algebraical language, this may be simply expressed. Take Q as the origin of co-ordinates, QE for axis of abscissae (x). Let radius OQ = a, „ OP = I, angle Q03 = 0, and x,y = co-ordinates of point c 2 on trochoid. Then x = C& = c x e z + c 2 c 3 = aO + b sin 6 ; y = Cl Q = OQ + Cl = a + b cos 6. The tracing arm (OP) may, for wave motion, have any value not greater than the radius of the rolling circle (OQ). If OP equals OQ, and the tracing point lies on the circumference of the rolling circle, the curve traced is termed a cycloid ; such a wave is on the point of breaking. The curve ExTE, in Fig. 78, shows a cycloid, o 194 NAVAL ARCHITECTURE. [chap. v. and it will be noticed that the crest is a sharp ridge or line (at JR), while the hollow is a very flat curve. A few definitions must now be given of terms that will be frequently used. The length of a wave is its measurement (in feet usually) from crest to crest, or hollow to hollow — QR in Fig. 78 would be the half-length. The height of a wave is reckoned (in feet usually) from hollow to crest ; thus in Fig. 78, for the trochoidal wave, the height would be P7i ; or twice the tracing arm. The period of a wave is the time (usually in seconds) its crest or hollow occupies in traversing a distance equal to its own length. The velocity (in feet per second) will, of course, be obtained by finding the quotient of the length divided by the period, and would commonly be determined by noting the speed of advance of the wave crest. Accepting the condition, that the profile of an ocean wave is a trochoid, the motion of the particles of water in [the wave requires to be noticed, and it is here the explanation is found of the rapid advance of the wave form, while individual particles have little or no advance. The trochoidal theory teaches that every particle revolves with uniform speed in a circular orbit (situated in a vertical plane which is perpendicular to the wave ridge), and completes a revolution during the period in which the wave advances through its own length. In Fig. 79, suppose P, P, P, etc., to be particles on the FIG. 79. Direction of uidvaiuse upper surface, their orbits being the equal circles shown ; then, for this position of the wave, the radii of the orbits are indicated by OP, OP, etc. The arrow below the wave profile indicates that it is advancing from right to left ; the short arrows on the circular orbits show that at the wave crest the particle is moving in the same direction as the wave is advancing in, while at the hollow the particle is moving in the opposite direction. For these surface particles the diameter of the orbit equals the height of the wave. Now suppose all the tracing arms OP, OP, etc., to turn through the equal angles POp, POp, etc. ; then the points p, p, p, etc., must be corresponding positions of particles on the surface formerly situated at P, P, etc. The curve drawn through p,p, p, etc., will be a trochoid CHAP, v.] DEEP-SEA WAVES. 1 95 identical in form with P, P, P, etc., only it will have its crest and hollow further to the left ; and this is a motion of advance in the wave form produced by simple revolution of the tracing arms and particles (P).* The motion of the particles in the direction of advance is limited by the diameter of their orbits, and they sway to and fro about the centres of the orbits. Hence it becomes obvious why a log dropped overboard, as described above, does not travel away on the wave upon which it falls, but simply sways backward and forward. One other point respecting the orbital motion of the particles is noteworthy. This motion may be regarded at every instant as the resultant of two motions — one vertical, the other horizontal — except in four positions, viz. : (1) when the particle is on the wave crest ; (2) when it is in the wave hollow ; (3) when it is at mid-height on one side of its orbit ; (4) when it is at the corresponding position on the other side. On the crest or hollow the particle instantaneously moves horizontally, and has no vertical motion. At mid-height it moves vertically, and has no horizontal motion. Its maximum horizontal velocity will be at the crest or hollow; its maximum vertical velocity at mid-height. Hence uniform motion along the circular orbit is accompanied by accelera- tions and retardations of the component velocities in the horizontal and vertical directions. The particles which lie upon the trochoidal upper surface of the wave are situated in the level surface of the water when at rest. The disturbance caused by the passage of the wave must extend far below the surface, affecting a great mass of water. But at some depth, supposing the depth of the sea to be very great, the dis- turbance will have practically ceased ; that is to say, still, undis- turbed water may be conceived as underlying the water forming the wave. Beckoning downwards from the surface, the extent of dis- turbance must decrease according to some law. The trochoidal theory expresses the law of decrease, and enables the whole of the internal structure of a wave to be illustrated in the manner shown in Fig. 80. f On the right-hand side of the line AD the horizontal lines marked 0, 1, 2, 3, etc., show the positions in still water of a series of particles which during the wave transit assume the trochoidal forms numbered respectively 0, 1, 2, 3, etc., to the left of AD. For * It is possible to construct a very f This diagram we borrow from Mr. simple apparatus by which the simul- Froude's paper on " Wave Motion " in taneous revolution of a series of par- the Transactions of the Institution of tides will produce the apparent motion Naval Architects for 1862; it was one of advance ; and, in lectures delivered of the first constructed, and is therefore at the Koyal Naval College such an reproduced, apparatus was used by the author. ig6 NAVAL ARCHITECTURE. [chap. v. still water every unit of area in the same horizontal plane has to sustain the same pressure: hence a horizontal plane is termed a surface or subsurface of " equal pressure " when the water is at rest. FIG. 80. 1 1 1 1 1 • / I 1 * Mr i 3 F C V \ \ \ \ a b c d £ f 4 1 1 E s \ I 1 -**jl_\- JLi i_ \ , , f / -o*^ 1 ; ; / a - — s- -~h> ^7 -j-~ 1 \ ■* C^V" |~>" -J— - 2 \ 1 1' ■ i "" ~ U-^*^- -£. -M^^l /"" iz ""/ v £p — B-. — ~~ J. 4 sX 3 4 5' • --W- • . v 7"\ • a '1 ^. m 9 8 9 .J 10 ID & u 18 ___ _ - n As the wave passes, the trochoidal surface corresponding to that horizontal plane will continue to be a subsurface of equal pressure ; and the particles lying between any two planes (say 6 and 7) in still water will, in the wave, be found lying between the corresponding trochoidal surfaces (6 and 7). In Fig. 80, it will be noticed that the level of the still-water surface (0) is supposed changed to a cycloidal wave (0), the con- struction of which has already been explained ; this is the limiting height the wave could reach without breaking. The half-length of chap, v.] DEEP-SEA WAVES. 197 the wave (AB) being called L, the Radius (CD) of the orbits of the surface particles will be given by the equation — OD = E=- = — L (nearly). All the trochoidal subsurfaces have the same length as the cycloidal surface, and they are generated by the motion of a rolling circle of radius E ; but their tracing arms — measuring half the heights from hollow to crest — rapidly decrease with the depth (as shown by the dotted circles), the trochoids becoming flatter and flatter in con- sequence. The crests and hollows of all the subsurfaces are vertically below the crest and hollow of the upper wave profile. The heights of these subsurfaces diminish in a geometrical pro- gression, as the depth increases in arithmetical progression ; and the following approximate rule is very nearly correct. The orbits and velocities of the particles of water are diminished by one-half, for each additional depth below the mid-height of the surface wave equal to one-ninth of a wave length.* For example — Depths in fractions of a wave length below the ) ft x z s ± P +« mid-height of the surface wave . . . j ' 9 ' 9 ' f ' f ' Proportionate velocities and diameters . 1, \, \, \, ^ s , etc. Take an ocean storm-wave 600 feet long and 40 feet high from hollow to crest: at a depth of 200 feet below the surface (| of length), the subsurface trochoid would have a height of about 5 feet ; at a depth of 400 feet (§ of length) the height of the trochoid— measuring the diameter of the orbits of the particles there — would be about 7 or 8 inches only ; and the curvature would be practically insensible on the length of 600 feet. This rule is sufficient for practical purposes, and we need not give the exact exponential formula expressing the variation in the radii of the orbits with the depths. It will be noticed also in Fig. 80 that the centres of the tracing circles corresponding to any trochoidal surface lie above the still- water level of the corresponding horizontal plane. Take the hori- zontal plane (1), for instance. The height of the centre of the tracing circle for the corresponding trochoid (1) is marked E, EF being the radius ; and the point E is some distance above the level of the horizontal line (1). Suppose r to be the radius of the orbits for the trochoid under consideration, and E the radius of the rolling circle : then the centre (E) of the tracing circle (i.e. the mid-height of the trochoid) will be above the level line (1) by a distance equal * See p. 70 of Shipbuilding, Tkeo- Mr. Froude, did much to develop the retical and Practical, edited by the late trochoidal theory, originally propounded Professor Kankine ; who, with the late byGerstner. 198 NAVAL ARCHITECTURE. [chap. v. to r 2 — 2R. Now E is known when the length of the wave is known : also r is given for any depth by the above approximate rule. Consequently, the reader has in his hands the means of drawing the series of trochoidal subsurfaces for any wave that may be chosen. Columns of particles which are vertical in still water become curved during the wave passage. In Fig. 80, a series of such vertical lines is drawn (see the fine lines a, b, c, d, etc.) ; during the wave transit these lines assume the positions shown by the strong lines (a, b, c, d, etc.) curving towards the wave crest at their upper ends, but still continuing to enclose between any two the same particles as were enclosed by the two corresponding lines in still water. The rectangular spaces enclosed by these vertical lines (a, I, e, d, etc.) and the level lines (0, 1, 2, etc.) produced are changed during the motion into rhomboidal-shaped figures, but remain unchanged in area. The motions of these originally vertical columns of particles have been compared to those occurring in a corn-field, where the stalks sway to and fro, and a wave form travels across the top of the growing corn. But while there are points of resemblance between the two cases, there is also this important difference — the corn-stalks are of constant length, whereas the originally vertical columns become elongated in the neighbourhood of the wave crests, and shortened near the wave hollows. These are the chief features in the internal structure of a tro- choidal wave, and in the following chapter they will be again referred to in order to explain the action of waves upon ships. It is necessary, however, at once to draw attention to the fact that the condition and direction of fluid pressure in a wave must differ greatly from those for still water. Each particle in the FIG. 81. wave, moving at uniform speed in a circular orbit, will be subjected to the action of centrifugal force as well as the force of gravity ; and the resultant of these two forces must be found in order to deter- mine the direction and magnitude of the pressure on that particle. This may be simply done as shown in Fig. 81 for a surface particle in a wave. Let BED be the orbit of the particle ; A its centre ; and B the position of the particle in its orbit at any time. Join the centre of the orbit A with B ; then the centrifugal force acts along the radius AB, and the length AB may be supposed to represent it. Through A draw AC vertically, and make it equal to the radius (B.) of the rolling circle ; then it is known that AC will represent the force of gravity on the same scale as AB represents centrifugal force. Join BC, and it will CHAP. V.] DEEP-SEA WAVES. 199 represent in magnitude and direction the resultant of the two forces acting on the particle. Now, it is an established property of a fluid that its free surface will place itself at right angles to the resultant force impressed upon it. For instance, take the simple case of a rectangular box (shown in Fig. 82) containing water, which is made to move along a smooth horizontal plane by the continued applica- FIG. 82. (nearly). tion of the force F ; then we shall have uniformly accelerated motion, equal increments of velocity being added in successive units of time. In order to compare this force with that of gravity, if / is the velocity added per second of time, and W is the weight of the box and water, we should have — W g 32i Now, it is well known that under the assumed circumstances of motion the surface of the water in the box will no longer remain level, but will attain some definite slope such as AB in Fig. 82 ; and it is easy to ascertain the angle of slope. Through any point G draw GH vertical to represent the weight W, and GK horizontal to represent the force F ; join HK, and it will represent the resultant of the two forces, the water surface AB placing itself perpendicular to the line, on the principle mentioned above. The tangent of the angle which the surface AB makes with the horizon will equal the ratio of F toW. Eeverting to Fig. 81, the resultant pressure shown by BO must be normal to that part of the trochoidal Surface PQ where the particle B is situated. Similarly, for the position B^ OB! will represent the resultant force ; T?^ drawn perpendicularly to OB l5 being a tangent to the trochoid at B^ Conversely, for any point on any trochoidal surface in a wave, the direction of the fluid pressure must lie along the normal to that surface. Hence it follows that wave motion involves constant changes in the magnitude and direction of the fluid pressure for any trochoidal surface ; these changes of direction partaking of the character of a regular oscillation keeping time with the wave motion. At the wave hollow the fluid pressure acts along 200 NAVAL ARCHITECTURE. [chap. v. a vertical line ; as its point of application proceeds along the curve, its direction becomes more and more inclined to the vertical, until it reaches a maximum inclination at the point of inflection of the trochoid ; thence onwards towards the crest the inclination of the normal pressure is constantly decreasing until at the crest it is once more vertical. If a small raft floats on the wave (as shown in Fig. 83), it will at every instant place its mast in the direction of FIG. 83. afSainhhr the resultant fluid pressure, and in the diagram several positions of the raft are indicated to the left of the wave crest. These motions of the direction of the normal to the trochoid may be compared with those of a pendulum, performing an oscillation from an angle equal to the maximum inclination of the normal on one side of the vertical to an equal angle on the other side, and completing a single swing during a period equal to half the wave period. The maximum slope of the wave to the horizon occurs at a point somewhat nearer the crest than the hollow, but no great error is assumed in supposing it to be at mid-height in ocean waves of common occurrence where the radius of the tracing arm (or half- height of the wave) is about one-twentieth of the length. For this maximum slope, we have — Sine of angle = radius of tracing circle radius of rolling circle _1 half-height of wa ve length of wave -H 6-2832 _ 3.1416 x k ei g ht of wave length of wave For waves of ordinary steepness all practical purposes are served by writing the circular measure of the angle instead of the sine ; hence ordinarily we may say — Approximate maximum wave slope ) _ , Rno (in degrees) . . . . J — height of wave length of wave CHAP, v.] DEEP-SEA WAVES. 201 Take, as an example, a wave for which the dimensions were actually determined in the Pacific, 180 feet long and 7 feet high — Maximum slope = 180° x — =7° (nearly). 180 The variation in the direction of the normal was in this case similar to an oscillation of a pendulum swinging 7 degrees on either side of the vertical once in every half-period of the wave — some 3 seconds. These constant and rapid variations in the direction of the fluid pressure in wave water constitute the chief distinction between it and still water, where the resultant pressure on any floating body always acts in one direction, viz. the vertical. But it is also necessary to notice that in wave water the intensity as well as the direction of the fluid pressure varies from point to point. Eeverting to Fig. 81, and remembering that lines such as BC represent the pressure in magnitude as well as direction, we can at once compare the extremes of the variation in intensity. In the upper half of the orbit of a particle, centrifugal force acts against gravity, and reduces the weight of the particle ; this reduction reaches a maximum at the wave crest, when the resultant is repre- sented by OE = (E — r). In the lower half of the orbit, gravity and centrifugal force act together, producing a virtual increase in the weight of each particle ; the maximum increase being at the wave hollow, where the resultant is represented by CD = (B + r). If a little float accompanies the wave motion, it may be treated as if it were a particle in the wave, and its apparent weight will undergo similar variations. In a ship, heaving up and down on waves very large as compared with herself, the same kind of variations will occur, though perhaps not to the same extent as in the little float. Actual obser- vation shows this to be true. Captain Mottez, of the French navy, reports that on long waves, about 26 feet high, the apparent weights of a frigate at hollow and crest had the ratio of 12 to 8. According to the preceding rules, we must then have — B - r ^_8_ B + r 12 2E-.20 2r ~ 4 E = 5r = 5 X 13 = 65 feet. Length of waves (by theory) = 2irE = 6-28 X 65 = 408 feet. This, in proportion to the height recorded, is not an unreasonable length ; but, unfortunately, Captain Mottez does not appear to have completed the information required, by measuring the actual length of the waves. The important fact he proved, however, is one that 202 NAVAL ARCHITECTURE. [chap. v. theory had predicted, viz. that the heaving motion of the waves may produce a virtual variation in the weight of a ship equivalent to an increase or decrease of one-fourth or one-fifth, when the proportions of the height and length of the waves are those common at sea.* Instead of the raft in Fig. 83, if the motions of a loaded pole or plank on end (such as SSj), be traced, it will be found that it tends to follow the originally vertical lines, and to roll always toward the crest as they do. Here again the motion partakes of the nature of an oscillation of fixed range performed in half the wave period, the pole being upright at the hollow and crest. A ship differs from both the raft and the pole; for she has lateral and vertical extension into the subsurfaces of the wave, and cannot be considered to follow either the motion of the surface particles like the raft or of an originally vertical line of particles like the pole. This case will be discussed in the next chapter. The trochoidal theory connects the periods and speeds of waves with their lengths alone, and fixes the limiting ratio of height to length in a cycloidal wave. The principal formulae for lengths, speeds, and periods for trochoidal waves are as follows : — I. Length of wave (in feet) = 5'123 x square of period (in seconds) = 5J x square of period (nearly). II. Speed of wave (in feet) ^ x iod = V 5 . 123 x t th per second) . . . j ° = 2^,/length (nearly). III. Speed of wave (in I g x iod ( hl } . knots per hour) . j IV. Period (in seconds) = \/ e f% =»Vlength (nearly). V. Orbital velocity of ) (speed of particles on surface } \ wave 3-1416 x height of wave length of wave height of wave , , . = 7 i x ,\ o v =Knearly). a ^/length of wave v JJ To illustrate these formulae, we will take the case of a wave 400 feet long and 15 feet high. For it we obtain — 4 Period = -^400 = 8| seconds. 9 Speed = -V400 = 45 feet per second. = 3 x 8§ = 26 § knots per hour. * See also an article by Lieutenant les Na-vires a la Mer," Revue Maritime, Gruyon, " De la Pesanteur Apparente sur 1885. CHAP. V.] DEEP-SEA WAVES. 203 = 7ix 15 \ X .-r^r = 5£ feet per second. Orbital velocity of sur- 1 face particles It will be remarked that the orbital velocity of the particles is very small when compared with the speed of advance ; and this is always the case. In formula V., if we substitute, as an average ratio for ocean waves of large size, Height = ^(j x length, the expression becomes — Orbital velocity of surface particles = 7^ X 3 V X length ^/length = 0-355 ^length. Comparing this with Formula II. for speed of advance, it will be seen that the latter will be between six and seven times the orbital velocity. The periods of waves are most easily observed, and the following table will be useful as giving the lengths and speeds of trochoidal waves for which the periods are known : — Period. Length. Speed of advance. seconds. feet. feet per second. knots per hour. 1 5-12 5-12 3-03 2 20-49 10-24 6-07 3 46-11 15-37 9-1 4 81-97 20-49 12-14 5 128-08 25-62 15-17 6 184-44 30-74 18-21 7 251-04 35-86 21-24 8 327-89 40-99 24-28 9 414-99 46-11 27-31 10 512-33 51-23 30-35 11 619-92 56-36 33-38 12 737-76 61-48 36-42 13 865-84 66-6 39-45 14 1004-17 71-73 42-49 15 1152-74 76-85 45-52 16 1311-56 81-97 48-56 As a mathematical theory, that for trochoidal waves is complete and satisfactory, under the conditions upon which it is based. Sea- water is not a perfect fluid such as the theory contemplates ; in it there exists a certain amount of viscosity, and the particles must experience resistance in changing their relative positions. There is every reason to believe that the theory closely approximates to the phenomena of deep-sea waves, but it is very desirable that extensive and accurate observations of the dimensions and speeds 204 NAVAL ARCHITECTURE. [chap. v. of actual waves should be made, iu order to test the theory, and determine the closeness of its approximation to truth. The recorded observations on waves are not so complete or numerous as to furnish the test required ; and, by adding to them during their service at sea, naval officers will do much to advance one important branch of the science of naval architecture. Systematic observations of ocean waves scarcely appear to have been attempted until within the last half-century. Amongst the earliest workers in this field were Dr. Scoresby, Mr. Walker, and Commodore "Wilkes (United States navy) ; and of these the first named is justly the best known.* In 1847, Dr. Scoresby made a series of valuable observations on Atlantic storm-waves ; and in 1856 he made a still more extensive series of observations during a voyage to Australia via the Cape of Good Hope, and a return voyage to England via Cape Horn. The records of wave-phenomena, published by Dr. Scoresby, constituted, until recently, the most valuable information on the subject ; but in recent years very numerous and trustworthy observations have been made by officers of the Eoyal Navy, and by officers of the French navy. Of the French observers the most laborious and distinguished was the late Lieutenant Paris, who, during a voyage of more than two years 1867-70), observed and recorded several times each day the state of the sea and the force of the wind. He has been followed by other officers, whose labours have resulted in the accumulation of a mass of facts respecting the lengths, periods, speeds, and heights of ocean waves. Much of this information has been published, and will repay careful study .f No similar publication has appeared of the results of observations of waves made by officers of the Eoyal Navy during the period above-named ; but the regulations issued by the Lords Commissioners of the Admiralty provide for the fre- quent conduct of such observations, and an analysis of the records- ought eventually to yield valuable information. * For the data obtained by Dr. in vol. xxxi. of the Revue Maritime, and Scoresby see the Report of the British in a posthumous Memoir : Paris, 1885. Association for 1850, and his Journal The most oompleto summary of the of a Voyage to Australia. The results French observations with whioh we are of Mr. Walker's observations will be acquainted is M. Antoino's Des Lames found in the Report of the British As- de Haute Mer (Paris, 1879). Muolr Bociation for 1842 ; these observations interesting information and valuable' were made at Plymouth. Commodore suggestion is to be found iu M. Bertin's Willies' " Narrative of the United essay on the " Experimental Study of States Exploring Expedition " (1838- Waves," published in the Transactions. 42) oontains the details of his observa- of the Institution of Naval Arohiteots tions made to the south of Cape Horn. for 1873. t Lieutenant Paris' work is recorded CHAP. V.] DEEP-SEA WAVES. 205 From a scientific point of view, and as a test of the trochoidal theory, the observations made when a ship falls in with a single series of approximately regular waves are most valuable. More frequently observations have to be conducted in a confused sea, successive waves differing from one another in lengths, heights, and periods; and occasional waves occurring of exceptional size as compared with their neighbours. Careful notation of such phenomena would throw light upon the question of the super- position of series of waves, and explain many apparent discrepancies met with in simultaneous observations of waves made by ships sailing in company. It is, however, obviously essential to the value of all these observations that they should be conducted on correct methods, and be accompanied by full records of the attendant circumstances. Supposing a single series of waves to be encountered, the lengths and periods of successive waves can be easily determined, if the speed of the ship and her course relatively to the line of advance of the waves are known. The method adopted by Dr. Scoresby and other early observers is still in use, and may be briefly described.* Two observers (A and B, Fig. 84) are stationed as far apart as FIG. 84. References. 1. Initial position of stern of ship. 2. Position of stern of ship at time t from beginning of observations. 3. Position of stern of ship at time t r from beginning of observations. possible, and at a known longitudinal distance from one another. At each station a pair of battens is erected so as to define, when used as sights, a pair of parallel lines at right angles to the ship's * We here follow very closely the Memorandum prepared by the late Mr. Froude, and approved by the Admiralty for use in the Koyal Navy. 206 NAVAL ARCHITECTURE. [chap. v. keel. The observer at the foremost station notes the instant of time when a wave crest crosses his line of sight ; he also notes how long an interval elapses before the next wave crest passes that line. The second observer makes two similar notations for the respective crests. Comparing their records, the observers determine (1) the time (say t seconds) occupied by the wave crest in passing over the length (L feet) between their stations; (2) the time (say t t seconds) elapsing between the passage of the first and second crest across either line of sights: this time is termed the "apparent period "• of the waves. Suppose the ship to be advancing at a speed of V feet per second towards the waves, her course making an angle of a degrees with that course which would place her end-on to the waves. Then, expressing the facts algebraically — Apparent speed of wave (feet per second) = — Keal speed of wave „ ,. = V! = ( V) Eeal length of wave (feet) = (V x + V cos a)^ = L cos a . h. cos a. Period of wave = L cos a 1 1 _ L . £j If the ship is supposed to be steaming away from the waves on the same course at the same speed, all that is necessary is to correct the sign of V in the foregoing equations. As an example, take the following observations made by Dr. Scoresby during his voyage to Australia, in 1856. The Boyai Cliarter was scudding directly before wind and sea, at a speed of 12 knots. An interval of 18 seconds elapsed between the passage of two successive wave crests across the observer's line of sight ; and any single wave crest took 9 seconds to traverse a length of 320 feet. Here we have — a = ; L = 320 feet ; i x = 18 seconds ; t = 9 seconds ; V = 20-25 feet per second. Substituting in the foregoing equations — Eeal speed of waves = V t =( — + 20-25^ = 55-8 ft. per sec 18 Eeal length of waves = 320 x — = 640 feet. y Eeal period of waves = ■?=- = 11£ seconds (nearly). chap, v.] DEEP-SEA WAVES. 207 From the foregoing remarks it will be obvious that the simplest method of observing the lengths and periods of waves can be applied when a ship is placed end-on to the waves and is stationary. The true period and true speed of the waves can then be obtained by direct observation, and the lengths estimated. When ships are sailing in company, a good estimate of the lengths of waves may be made by comparing the length of a ship with the distance from crest to crest of successive waves. Care must be taken, of course, to note the angle which the keel of the ship used as a measure of length makes with the line of advance of the waves; otherwise the 'apparent length of the wave may considerably exceed the true length. Another method of measuring wave lengths consists in towing a log-line astern of a ship, and noting the length of line when a buoy attached to the after end floats on the wave crest next abaft that on which the stern of the ship momentarily floats. This was the method used by Commodore Wilkes of the United States navy in the observations of waves made by him south of Cape Horn in 1839 ; it has also been used in the Eoyal Navy. For its successful application a ship should be placed end-on to the waves, or allowance must be made for the departure of the log-line from that end-on position. Wave heights are, in most cases, readily measured by the following simple method. When the ship is in the trough of the sea, and for an instant upright, the observer takes up a position such that the successive average wave ridges, as viewed by him from the trough, just reach the line of the horizon without obscuring it. The height of his eye above the water-level correctly measures the height of the wave. In making such observations it is desirable to select a position nearly amidships, so that the influence of pitching and 'scending may be diminished as much as possible. If it becomes necessary to take stations near the bow or stern, allowance must be made, in estimating the height of the eye above water, for the deeper immersion which may be caused at the instant by pitching or 'scending. Due allowance must also be made for changes of level occasioned by rolling or heeling, as well as for the fact that when a ship end-on to the waves is in the middle of the trough the curvature of the wave hollow gives extra immersion to her ends, while the water surface amidships is somewhat below her natural water-line. This method of estimating wave heights was used by Scoresby, and has been adopted by most of his successors. To measure very high waves the observer may have to ascend the rigging ; while for waves of less height a station on one of the decks may suffice, or 208 NAVAL ARCHITECTURE. [chap. v. some temporary expedient devised for placing an observer near the water-level. Other methods of measuring wave heights have been proposed, based upon the fact that at a considerable depth below the sur- face of a disturbed sea, practically still water may be found. Mr. Froude devised one of the best methods of this kind, the apparatus required being very simple and easily managed. It consisted of a light tapered spar of comparatively small diameter, graduated and marked in such a manner as enabled an observer to note with ease the rise and fall of the waves upon it. When in use this pole was " anchored " to the undisturbed water by means of a deep-sea line, to the lower end of which a light frame (see Fig. 85) fig 85 was ^t 8 *^ 16 ^' th^ frame carrying a certain amount of ballast. The pole thus weighted stood upright, and performed extremely small vertical oscillations as the waves passed ; consequently an observer on board a ship near the pole could note the heights and periods of waves with a close approach to accu- racy. This method was applied by Mr. Froude in connection with his experiments with the model of the Devastation at Spithead. It is particularly ap- plicable to cases where waves of small height are to be measured, and where horizon observations are not easily made. For general use at sea it is scarcely likely to find favour ; nor was it expected to do so by Mr. Froude. Any apparatus of this kind requires that the ship using it must be practically " hove-to " during the time occupied in putting the apparatus over- board, testing its adjustments, making the observations, and after- wards recovering it. On the other hand, horizon observations, when practicable, can be made without interference with the progress of the ship. Similar objections apply to the automatic "wave-tracer" con- structed in 1866 by the late Admiral Paris of the French navy, and tried at Brest with considerable success. The design of this instru- ment was very simple. A light pole was prepared (similar to that used by Mr. Froude) upon which to measure the rise and fall of the waves. This pole was of considerable length as compared with the heights of the waves to be measured, its cross-section was of small area. It was ballasted with sheet lead in order that it might float upright, with a considerable portion of its length projecting above the surface of still water. No attempt was made to " anchor " the pole to the subjacent undisturbed water, and it consequently per- formed sensible, but small, vertical oscillations as the waves rose and chap, v.] DEEP-SEA WAVES. 209 fell upon it. On its upper end a float was fitted, this float rising and falling- with the waves and sliding up and down the pole. By means of simple mechanism the motions of the float were automati- cally recorded on a revolving cylinder, and the wave profiles were thus traced.* Waves up to 10 feet in height were thus recorded, and Lieutenant Paris claimed for the instrument a full realization of the hopes of its inventor. He frankly confessed, however, that " a ship not especially detached for the purpose could hardly be expected to arrest her progress several times a day " in order to make use of the wave-tracer. Furthermore, it is evident that in waves of con- siderable height the instrument could not be used successfully, unless anchored to the undisturbed water lying far below the surface. The automatic instruments devised by Mr. Froude and M. Bertin for ; recording the rolling of ships in a seaway, furnish also a means of obtaining valuable information respecting the waves amongst which the ships carrying such instruments may be situated. This will appear from the description given in Chapter VII. Having briefly described the principal methods of conducting observations on ocean waves, it may be well to summarize the dimensions of the largest waves of which we have any trustworthy accounts. The longest wave observed was measured by Captain Mottez, of the French Navy, in the North Atlantic, and had a length of 2750 feet — half a mile — from crest to crest; its period was 23 seconds. Dr. Seoresby speaks of waves he observed in the Southern Indian Ocean spreading out to " a quarter if not half a mile " in one undulation and crest. In the South Atlantic, Sir James Boss observed a wave 1920 feet long. The largest waves observed in European waters are said to have had a period of 19| seconds, corresponding to a theoretical length of some 2000 feet ; in the Bay of Biscay waves have been noted having a length of 1320 feet. These monster waves are not, however, commonly encountered, and waves having a length, of. 600 to 700 feet would ordinarily be regarded as large waves. Dr. Scoresby's largest Atlantic storm waves had lengths of about 500 to 600 feet, and periods from 10 to 11 seconds. According to the best authorities, ocean waves of 24 seconds' period, and some 3000 feet in length, may be taken as the extreme limit of size yet proved to exist ; waves of 18 seconds' period, and about 1650 feet in length, constitute the upper limit in all except extraordinary cases ; and what may be called common large storm waves have periods varying from 6 to 9 seconds, the corre- sponding lengths varying, from 200 to 400 feet. * See the Revue Maritime, vol. xx., and Transactions of the Institution of Naval Architects for 1867. P 2IO NAVAL ARCHITECTURE. [chap. v. Turning next to measurements of heights in a single series of waves, it appears that waves having a greater height than 30 feet from hollow to crest are not commonly encountered. There are, however, numerous records of heights exceeding 30 feet. Scoresby and others have measured heights of 40 to 45 feet, and there are trustworthy observations of heights of 44 to 48 feet. Com- mander Kiddle, E.N., claims to have observed waves 1180 feet long and 70 feet high in latitude 48° ST., longitude 40° W., during a passage made in January, 1875, from Queenstown to New York, when a heavy and prolonged gale was encountered. From the account given of his method of estimating heights, it appears there were several possible sources of error.* It has been stated also that, during a voyage round Cape Horn waves have been measured having heights of 58 to 65 feet, and lengths varying from 750 to 800 feet. This ratio of height to length would seem to indicate that the waves observed were not a single series, but formed by the superposition of two or more series. Under these conditions, or when a great local rise is produced by waves driving against a shore or passing over isolated rocks, heights and steepness may be Teached not met with in a single series of waves traversing deep water. An explanation of the causes of unintentional exaggeration in the estimate of wave heights will at once suggest itself when the variation in the direction of the normal to the wave slope (previously explained) is taken into account. To an observer standing on the deck of a ship, which is rolling amongst waves, nothing is more difficult than to determine the true vertical direction, along which PI G 86 the height of the wave must be measured. If he stands on the raft shown in Fig. 8b', he will, like it, be affected by the wave motion ; and the apparent vertical at any instant will be coincident with the mast of the raft and normal to the wave slope. He will, therefore suppose himself to be looking horizontally when he is really looking along a line parallel to the tangent to the wave slope at that point, which may be considerably inclined to the horizon. Suppose TT, Fig. 86, to represent this line for any position : then the apparent height of the waves to an observer will be HT, which is much greater than the true height. If the observer stands on the deck of a ship, * For Commander Kiddle's own noted off Cape Horn, an .account of account see the Nautical Magazine for which appeared in the Liverpool Mercury August, 1878. We have to thank him • during 1888, , , also for drawing attention to the waves ' : chap, v.] DEEP-SEA WAVES. '2 1 1 the conditions will be similar ; the normal to what is termed the " effective wave slope " (see p. 227) determines the apparent vertical at any instant ; and the only easy way of determining the true horizontal direction is by making an observation of the horizon as described above. The extent of the possible error thus introduced will be seen from an example. Take a wave* 250 feet long and 13 feet high ;, its maximum slbpe to the horizontal is about 9 degrees. Suppoise a shipi to be at; the mid^height between hollow and crest, and the observer to be watching the crest of the next wave ; standing about the watetf level, the wave height will seem to be about 1 30 feet instead of 13 fqet. The! steeper the slope of the waves;, the j greater liability is th4re to serious errors in estimates of heightsj unless proper means are taken to determine the true horizontal and 'vertical directions. In' some cases the apparent height would be about three times the real height. Next as to the ratio of the heights to the lengths observed in deep- sea waves. All authorities agree that, as the lengths increase, this ratio diminishes, and the wave slope becomes less steep. The shortest waves are the steepest ; and the greatest recorded inclinations are for very short waves where the ratio of height to length was about 1 to 6. For a cycloidal wave it will be remembered that the ratio is about 1 to 3 - 14 ; so that in the steepest deep-sea waves observed this ratio is only about one-half that of the theoretical limiting case. For waves from 300 to 350 feet in length, the ratio of 1 to 8 has been observed, but these were probably exceptionally steep waves ; for waves of 500 to 600 feet in length, it falls to about 1 to 20' ; and for the longest waves, of uncommon occurrence, it is said to fall so" low •as 1 to 50. But it is obvious that all measurements of such gigantic waves must be attended with great difficulties, so that the results, even when the greatest care is ' taken, are only receivable as fair approximations. It. seems probable that, in waves of the largest size commonly met, the height does not exceed one"twentieth of the length ; and the higher limit of steepness in ocean waves,- which 1 are large enough to considerably influence the behaviour of ships, does not give a ratio of height to length exceeding 1 to 10. Long series ,of observations made in ships of the French .Navy show that a common value of the height is about one twenty-fifth— fiom- one- twentieth to oneTthirtieth of the length. Waves from 400 to 900 feet in length are sometimes encountered, having heights' of from 4 to 10 feet only, and the small ratio of height to length of 1 to 50 has been repeatedly observed in waves from 100: to 400 feet long. Excluding these exceptionally low ratios of height to length, and taking account of observations where the ratio • did not fall below 1 to 40, the following approximate insults have been obtained 'from 212 NAVAL ARCHITECTURE. [chap. v. an analysis of the published French observations of waves, made in all parts of the world : — Lengths of wares. Number of obser- vations. Length -=- height. Average. Maximum. Minimum. 100 feet and under 100 to 200 feet . 200 to 300 „ 300 to 400 „ 400 to 500 „ 500 to 650 „ 11 55 44 36 17 16 17 20 25 27 24 23 30 40 40 40 40 40 5 9 10 17 15 17 179 This table is worthy of study ; although the figures it contains are not exact, and exception may reasonably be taken to the method of averages as applied to these observations. It suggests much as to the comparative frequency with which waves of certain lengths occur, and confirms the opinion that waves become less steep as they increase in length. The comparison of the relation between the periods and speeds of ocean waves, with the relation which should hold in accordance with the trochoidal theory, has shown a very fair agreement between theory and observation. In not a few cases there are wide divergencies from such agreement ; but it is extremely probable that the observations showing these divergencies were made under the conditions of a confused sea, not embraced by the trochoidal formulae. It is to be observed that in the cases where a single and approximately regular series of waves has been encountered, observa- tion and theory agree most closely. For example, Commodore Wilkes observed to the south of Cape Horn waves having a length of 380 feet, and a period of nearly 8*5 seconds; according to the trochoidal theory, the period should have been about 8-6 seconds. Again, Dr. Scoresby observed Atlantic storm waves having lengths of 560 to 600 feet, and periods of about llf seconds ; the period, according to the trochoidal theory, for a wave 580 feet long, would be about 10 - 6 seconds. On his voyage to Australia, Scoresby noted waves 640 feet long and 11^ seconds period; the theoretical period for waves of this length would be a little over 11 seconds. Lieu- tenant Paris, also, in the Southern Indian Ocean measured waves from 300 to 400 metres long, and having a speed of 19 metres per second ; their period, according to this data, must have been about CHAP. V.] DEEP-SEA WAVES. 21 18 seconds, and, according to theory, it would have been about 15 seconds. On another occasion the same observer noted waves 180 metres long, and 10£ seconds period ; according to theory; the period would, have been about lOf -seconds. A few observations of wave|s made hi the Pacific on board one of her Majesty's ships gave periods for waves from 180 to 320 feet long agreeing almost exactly with the! theoretical periods. During the voyage of the Cliallenger the dimensions of waves werel observed at times. On one occasion she was running before a north-west gale fairly steady in strength, the wind having a speed of 30 miles an hour. The waves were found to have lengths ai 420 to 480 feet, heights of 18 to 22 feet, and speeds of about 29"5 knots per hour, or 50 feet per second. Taking 450 feet as the mean length of the waves, their average period was 9 seconds; the theoretical period for that length being about 9-36 seconds, which indicates a very close approximation between observation and theory.* Passing from these special test cases to the ordinary cases where waves are less regular and uniform in character, it may be well to give a few examples of the comparison between observed and theoretical lengths of waves. The first table is based upon the results of French observations, exceeding 200 in number, made by different observers on various stations. Lengths of Ocean Waves (in Metres). Observed. Calculated. Observed. Calculated. Observed. Calculated. 30 30 80 85 143 131 30 42 80 95 148 161 35 42 85 60 150 134 42 42 90 100 153 175 , 50 60 95 95 160 156 56 60 • 100 67 165 161 60 52 100 108 170 171 60 67 105 .116 170 144 65 52 114 124 172 175 65 73 120 112 180 108 70 67 120 120 180 147 70 74 130 164 180 185 • ■ ,75 60 135 134 190 < 200 79 80 Note. — A metre is 3-281 feet. The second table is based upon observations made on board some of her Majesty's ships. * See p. 330, vol. i., of " Voyage of the Challenger " for details of methods of observation. 214 XA VAL ARCHITECTURE. [CHAP. v. Lengths of Ocean Waves (in Feet). \ Observed. Calculated. Observed. Calculated. Observed. Calculated. 80 > 82 220 184 375 330 160 128 245 250 400 370 160 184 250 250 420 510 180 185 300 250 500 420 •300 184 300 328 530 440 ■200 250 350 328 630 520 On a review of a large number of observations it appears that the observed lengths are, on an average, rather less than the theoretical lengths; but it must be admitted that here also the method of averages is not trustworthy, especially when it is known that in some instances errors of considerable proportionate magnitude exist in the individual observations. These errors arise from various causes, one pf ; the most common being the failure to distinguish correctly the difference between the real and the apparent speeds and dimen- sions of waves. In addition there are the special difficulties frequently encountered when the waves to be measured are the result of the superposition of two or more series of waves, each moving at its own speed, and possibly in different directions. In such a confused sea there is an entire want of regularity or uniformity in successive waves which pass an observer on board a ship, and the best course he can pursue is to note the particulars for a considerable number of waves in order that something like mean results may be obtained. For example, in making a set of observations on board one ofj her Majesty's : ships, when the , sea was formed by two sferies of Waves running' at different speeds in nearly the same direction, the following results were noted. First, l the intervals which ten successive wave crests occupied in passing over a certain length wej-e respectively fi, 7, 4, '6, 6, 3, 6, 5, 7, and 6£ seponds ; the mean being' abou^i 5*6 seconds. Second, the apparent lengths varied from 250 t;o 420 i feet. These apparent variations admit! of easy explanation, and forj this purpose we will take the simple 1 case illustrated by Figs. 87-92. Fig, 87 shows a wave 400 feet long and 20 feet high, having a speed of about 45 feet per second ; Fig, 88, a wave 200 feet long and 12. feet' high, having a speed of about 32 feet per second. The straight lines in both figures indicate the level of still water. In Fig. 89 the shorter wave is superposed upon the longer, the latter being shown by a dotted line ; the two crests coincide, and the resultant wave has a height from hollow to crest of about 26 feet, while the length from hoUpw to hollow is about 300 feet. The longwave form gains about 13 feet per second on the shorter wave. In 2k seconds the profile CHAP/ V.] DEEP-SEA WAVES. 215 of the' combined wave will have changed from the condition of Fig. 89 to that of Fig. 90 ; the heights of successive crests being about 30 feet and 5 feet, and the length between these crests being about 200 feet. In less than 4 seconds the further change shown , in Fig. FIG. 88. FIG. 89 91 will have occurred, and in less, than 8 seconds the condition shown in Fig. 92 will have been reached, a wave hollow appearing where the erest of the 400*feet wave is placed. In this last condition the. height from this hollow to the adjacent crests is only about 3 feet, and';- the .^crests' are 160 feet apart In fact there- occurs a long 216 NAVAL ARCHITECTURE. [CtfAP. v. " smooth " in the series, but the next wave series would have heights of about 25 feet. This illustration shows how difficult the task of making observations of waves may become in a confused seaway formed by the superposition of several series of waves moving in different directions. Here too we find a satisfactory explanation of the differences sometimes noted in the simultaneous observations of waves by ships sailing in company. For example, one ship of a squadron reported the waves to be 450 feet long, whereas a second ship put the length at 150 feet. The observer may, it is true, some- times succeed in distinguishing the principal members of the waves in one or more of the superposed series ; but this involves a long continuance of the observations, and is rarely to be accomplished with certainty. In making such observations in a confused sea the fullest particulars should be recorded, for without a knowledge of the attendant circumstances no possible use can be made of the results. For this reason, also, it is very desirable that any com- parisons between the results of theory and observation should be made by the observers at, or soon after, the time the observations are in progress, since no other person can have an equally good knowledge of the particular circumstances of each case. No theory has yet been accepted which fully accounts for the genesis of waves; the trochoidal theory merely deals with waves already created, and maintaining unaltered forms and velocities. There can, of course, be no question but that waves result from the action of the wind on the sea, and that there must be some connection between the character and the force of the wind and the dimensions and periods of the waves. But as yet we have not sufficient knowledge to determine either the mode of action of the wind or the law connecting its force with the dimensions of waves. Here again is a field where careful and extensive observations can alone be relied upon ; pure theory would be useless. In the preceding pages it has been shown that, with care, the lengths, heights, and periods of waves may be determined very closely when the sea is not confused ; and it is also possible, with care, to ascertain simultaneously the force or speed of the wind. But it is to be noted that the rapidity with which waves travel, and the fact that they maintain their lengths and speeds almost unchanged even when the force of the wind decreases and the wave height becomes less, make it necessary to exercise great caution in associating any observed force of wind with the lengths and periods of waves observed simultaneously. The importance of this matter justifies further illustration. If the wind is at first supposed to act on a smooth sea, and then chap, v.] DEEP-SEA WAVES. 2I 7 to continue to blow with steady force and in one direction, it will ereate waves which finally will attain certain definite dimensions.: The phases of change from the smooth sea to the fully formed waves cannot be distinctly traced. It is, however, probable that changes of level, elevations and depressions, resulting from the impact of the wind on the surface of the sea, and the frictional resistance of the wind on the water are the chief causes of the growth of waves. An elevation and its corresponding depression once formed offer direct resistance to the action of the wind, and its unbalanced pressure producing motion in the heaped-up water would ultimately lead to the creation of larger and larger waves. This is probably the chief cause of wave-growth, frictional resistance playing a very subordinate part as compared with it. So long as the speed of the wind relatively to that of the wave water is capable of accelerating its motion, so long may we expect the speed of the wave to increase, and with the speed the length, and also the height. Finally, the waves reach such a speed that the wind force produces no further acceleration, and only just maintains the form unchanged, then we have the fully grown waves. If the wind were now suddenly withdrawn, the waves would gradually decrease in magnitude and finally die out. This degra- dation results from the resistance due to the molecular forces in the wave — viscosity of the water, etc. — and when the waves are fully grown, the wind must at every instant balance the molecular forces. If the water were a perfect fluid (the particles moving freely past one another), and if there were no resistance to motion on the part of the air, the waves once formed would travel onwards without degradation. But in sea-water the degradation takes place at a rate dependent upon the ratio of the resistance of the molecular forces to the " energy " of the wave.* At each instant the resistance abstracts a certain amount from the energy of the wave, and consequently the height decreases. The period and length of the wave might remain almost unchanged, •and, it would seem from observation, really do so for a considerable time, while the height decreases ; just as it has been shown that in a ship oscillating in still water the resistance gradually diminishes the range of oscillation without decreasing the period sensibly. As examples of this maintenance of length while height is degraded, reference may be made to a long swell observed by the Channel Squadron in 1893, after severe storms in the North-Western Atlantic. * In wave motion the "energy " is the work done in raising the centre of half "actual" and half "potential." gravity of its mass a certain distance By "actual" energy is meant that due above the position which it would occupy to the motions of the particles in a in still water. See remarks as -to this wave ; by "potential " energy is meant rise on p. 197. 2lS NAVAL ARCHITECTURE. [chap. v. Careful • measurements showed lengths of 450 to 520 feet to be associated with heights of 10 to 12 feet, the corresponding heights for fully grown waves of this length and period being about 20 to 25 feet, . Between this condition of fully grown waves and the case of waves gradually dying out in a dead calm lies that which com- monly ocoUrs where the waves are gradually dying out, but the wind still has a certain force and speed. Then an observer, noting the dimensions of the waves and force of the wind simultaneously, might record lengths and periods corresponding, not to the observed force of wind,' but to the force which existed when the waves were of their Ml size. On the other hand, there would, in all probability, be a correspbndence between the observed force of wind and the observed heights, and an analysis of the recorded observations made by officers of the French Navy confirms this view. Nothing but the closest attention on the part of an observer can enable him to make his records a trustworthy basis for theory ; for it is in his power alone, , having regard to all the circumstances of the observations, to say whether, when observed, the waves are fully grown, and correspond to the observed force of wind, or whether they are in process of growth or of degradation. A series of observations might settle this matter, if made in a careful and intelligent manner^ the growth or degradation being indicated by the altera- tions in heights of waves noted after certain intervals from the first observations. Perhaps the most favourable time for observations to be begun would be that when on a nearly calm sea a storm breaks, forming waves of which the dimensions gradually increase, but the oppor- tunities are not likely to be numerous where the waves so formed constitute an independent regular series. Usually the observer would probably find himself in face of a confused sea, when the wave genesis is in its earlier stages ; but if he could note the times occu- pied by waves in attaining their full growth under the action of winds of various speeds, he would do good service. Any pre-existing swell, niust be allowed for in making these observations ; otherwise the assumption that the waves are formed from smooth water would be departed from. In concluding these remarks on wave genesis, M. Bertin's essay on the subject may be quoted. He says : " The study of the time " necessary for each swell to retain its fixed and permanent condition " under the action of the wind which produces it is very interesting. " If the' time be so long as in general to exceed that during which "the wind can remain pretty nearly constant, both in intensity and '• direction, all interest in the connection between the wind and the chap, v.] DEEP-SEA WAVES. 219 " swell would disappear. The length of waves and their inclination "for a given length would he just as irregular as meteorological " variations. If, on the contrary, the waves soon reach their regular " condition— a fact which seems to be pretty well established, inas- "much as those seas which are exposed to the action of constant " winds present no extraordinary agitation — one is necessarily "driven to adopt the law that for each length of waves . there is "a certain height that is most commonly met with, and that cannot be exceeded," Passing from these general! considerations, it may be interesting to refer to the attempts made by French investigators to formulate expressions connecting the dimensions of waves with the force or speed of winds. Admiral Coupvent Desbois laid down a provisional theory, based upon ten thousand actual observations, that the cube of the height of the waves is proportional to the square of the speed of the wind.* Lieutenant Paris suggested, from an analysis of his own observations, that the speed of waves is proportional to the square root of the speed of the wind ; but he was of opinion that much more extensive observations were needed before any law could be accepted. Lieutenant Paris' formula may be expressed as follows, reckoning speeds in metres per second : — Speed of wind = -073 (speed of wave) 2 . Converting this into English measures, and reckoning speeds in feet per second, we have- Speed of wind = -022 (speed of wave) 2 . Whence, making use of the formula connecting the speeds and lengths of waves, it follows that— . Speed of wind = - 115 length of wave. When the sea was heavy Lieutenant Paris always found the speed of the wind exceed that of the wave form ; but in moderate seas having a speed of '36 feet per second, or less, he frequently recorded speeds of wind which were less than the speeds of the waves formed by the action of that force of wind. The following table contains a few illustrations 1 of this noteworthy feature in these admirable records : — * See the Corrvptes-rendus de V Academic des Sciences of 1866. 2 20 NAVAL ARCHITECTURE. [CHAP. Locality. Mean heights of wares. Mean speeds.* Wind. Ware. Atlantic (region of trade winds) South Atlantic .... Indian Ocean (south of) . Indian Ocean (region of trade winds) Seas of China and Japan metres. 1-9 4-3 5-3 2-8 3-2 3-1 4-8 13-5 17-4 0-5 14-6 8-5 11-2 14-0 150 12-6 11-4 12-4 In the present state of knowledge, we are not able to say that there is anything impossible in the observation of waves moving faster than the winds, which have a force corresponding, to their full growth, although this condition would scarcely be anticipated. Ee- membering what was said above as to the difference between the rates of the actual orbital motions of particles in their circular paths and the apparent speed of advance of the wave form, it will be clear that, even when the wave form advances faster than the wind travels, the wind may be moving much faster than the particles in the wave. Take, for example, the waves of the Southern Indian Ocean. M. Paris gives them a mean height of 5 - 3 metres, and a mean period of 7 - 6 seconds. Diameter of orbits of surface particles = 5 - 3 metres. Circumference of orbits of surface particles = 16'6 metres. Orbital velocity of particles = . = 2£ metres per second. 7 - 6 Velocity of wind observed = 17 - 4 metres per second. "Whether the relative velocity of the wind and the wave form should be taken as the measure of the full effect of the wind, or whether, the relative velocity of the wind and the particles of water in the wave does not also exercise considerable influence, must for the present, &i least, be considered a matter open to debate. In the maintenance of the wave speed as the wind speed slackens, we have a possible explanation of the apparent anomaly in the above table ; and, further, it is difficult for an observer on board a ship in motion to measure the speed of the wind accurately. But actual observations, such as have been recommended in this chapter, will settle this and many other doubtful points. M. Antoine, of the French Navy, has also endeavoured to frame formulse connecting the dimensions and speeds of ocean waves with In metres per second; a metre is 3 "281 feet. CHAP. V.] DEEP-SEA WAVES. 221 the speeds of wind ; and for this purpose has made a very lengthy analysis of the returns furnished by French war-ships.* Taking 130 observations made in vessels of the French Navy, M. Antoine classified them as follows in his Memoir of 1876 : — Speed of ^ind. Number of observations per series. Waves. Mean lengths. Mean heights. Calculated by Calculated by Observed. approximate formula. Observed. approximate formula. Metres per metres. metres. metres. metres. 1-5 12 54-6 36-0 1-7 1-0 4-0 16 63-7 60-0 2-4 1-9 7-0 18 87-9 79-5 3-2 2-7 11-0 29 79-7 99-6 4-0 3-7 16-0 22 100-0 120-0 5-4 4-8 22-0 19 90-0 141-0 5-1 5-9 29-0 11 131-0 161-0 7-7 7-1 37-0 3 180-0 182-0 8-5 8-3 It will be observed that the calculated heights agree very closely with the observed heights ; whereas there are very considerable dif- ferences between the calculated and the observed lengths. This is a suggestive contrast, as will appear more clearly in reference to the remarks made above. In obtaining the approximate formulas for lengths and heights of waves, M. Antoine used the following notation : — . Let V = speed of waves (in metres per second). v= „ wind „ „ 2L = length of waves (in metres). 2T — period „ (in seconds). 2H = height „ (in metres). Then, assuming Admiral Coupvent Desbois' law to hold, the follow- ing are considered to be good approximations : — . . . (1) • • • (2) • • • (3) 2H = 0-75 x V 3 2L = 30v* . 2T = 44»* . V = 6-9** (4) * See Notes complementaires sur les Lames de haute mer, 1876 ; also Des Lames de haute mer (Paris, 1879). 222 NA VAL ARCHITECTURE. [chap. v. The " constants " in equations (1) and (4), 31. Antoine derives from an analysis of numerous observations; those in equations (2) and (3) are derived from (4) by means of the theoretical formula given on p. 202. In his later publication, M. Antoine somewhat varied his pro- cedure, and attempted to investigate whether " in the deformation of •' a wave the product of the length by the height would not remain •• practically constant for waves created by the action of a wind of a •■ given force, the value of this product being termed the modulus of " (lie wave." He retained the fundamental formulae given above, and as the result of his analysis of over 200 observations formed the following: table : — MoDrxi of Waves (Product of Height bt Length). Speed of wind. Moduli. Metres per second. Calculated. Obserred. to 2 to 51 so 3 to 5 78 to 148 170 6 to 8 184 to 255 362 9 to 13 297 to 443 379 14 to 18 493 to 648 595 19 to 25 685 to 960 650 26 to 32 1010 to 1283 1070 33 to 42 1332 to 1765 1516 31. Antoine added, " According to the preceding formulae, the ■• modulus of a wave should be proportional to the expression — (Speed of wind) & ; •• I reserve to myself the investigation, when more numerous observa- •■ tions have been made, of the problem whether one might not sup- ■■' pose the modulus to be proportional simply to the speed of the wind, •• which would make the length of a regular wave proportional to the " square root of the height." Attention has. been drawn to the preceding attempts to connect wave phenomena and wind forces with the hope that the subject will be treated also by English observers with the consideration it un- doubtedly deserves. The problem still awaits solution, for the formulae given above are based upon reasoning to which grave objections may be taken, althoiigh they cannot be stated here. Lieutenant Paris attempted to ascertain what were the prevalent waves most likely to be encountered in particular localities. The following table prepared by him, gives the result of observations extending over more than two years. It is a notable effort to describe the mean condition of the sea, and well worthy of the;attention of CHAP. V.] DEEP-SEA WAVES. 223 naval officers, who would render good service to science by en- deavouring to extend the investigation. Locality. Mean period. South Atlantic (region of the westerly winds) Indian Ocean, South (region of the easterly winds) seconds. 5-8 9-5 7-6 7-6 6-9 8-2 In concluding this chapter, brief reference must be made 'to the attempts to obtain motive power for propulsion or other purposes from the motions impressed upon a ship by the wave motion. Mr. Spencer Deverell, of Victoria, was the first to draw attention to the subject ; and his brother conducted a series of observations in 1873 during a voyage from Melbourne to London, for the purpose of proving that during an ocean voyage a ship will be continually oscillating — rolling, pitching, and heaving — even when there 1 is a dead calm. Limits of space prevent any extracts being given from the interesting records of these observations, which will well repay perusal ; nor can any account be given of the apparatus proposed for the purpose of obtaining motive power from the wave^motion.* The principle of all the proposals may be simply explained. In a seaway the heaving and other motions impressed upon a ship cause variations in her virtual weight (as explained at p. 201). If a Weight iuboard is suspended by a spring balance, the latter will indicate less than the true weight on the wave crest, and more than the true weight in the wave hollow. The extensions of the spring will vary according to the virtual weight, being greatest at the wave hollow, and least at the crest. By some appropriate mechanism these varying extensions of the spring are made to produce rotary or other motions. Numerous experiments have been made with models, but hitherto no practical use seems to have been made of the principle. * See papers on "Ocean Wave Power and its Utilization," in the Transactions of 'the Koyal Society of Victoria for 1873 ; and " The Continuous Oscillation of a Ship during an Ocean Voyage," in the Transactions of the Institution of Naval Architects for 1874,, ; by Mr. Spencer Deverell; also .a; paper by Mr. Tower in the Transactions of 'the Institu- tion of Naval Architects for 1,875; 224 NAVAL ARCHITECTURE. [chap. vi. CHAPTEE VI. THE OSCILLATIONS OF SHIPS AMONG WAVES. In the two preceding chapters we have discussed the condition of a ship oscillating in still water, and the phenomena of wave motion in the deep sea, subjects which have an interest in themselves, but derive their greatest importance from their connection with the subject now claiming attention. The motions of a ship in a seaway are influenced by her stability, her inertia, by the variations in direc- tion and magnitude of the fluid pressure incidental to wave motion, and by the fluid resistance ; so that, without clear and correct con- ceptions of each of these features in the problem, it would be impossible to deal with their combined effect. The oscillations of a ship in a seaway, like those in still water, may be considered as resolvable into two principal sets : first, the transverse oscillations of rolling ; second, the longitudinal oscilla- tions of pitching and 'scending. Transverse oscillations, having by far the most important bearing upon the safety and good behaviour of ships, will receive the greatest attention. Pitching and 'scending may become violent and objectionable in some ships, but this is not commonly the case, nor is it so difficult of correction as heavy rolling. Only a brief discussion of these longitudinal oscillations will therefore be necessary, and it will follow the remarks on rolling. Very various causes have been assigned for the rolling motion of a ship at sea. Some of the earlier writers, impressed by the great speed of advance of waves, attributed rolling to the shocks of waves against the sides of ships. Others considered motion as originated by the slope of the wave surface ; observing that, if a ship remained upright on the wave slope, her displacement would change its form from that in still water, the centre of buoyancy moving out from below the centre of gravity towards the wave crest, and the moment of stability thus produced tending to make the vessel heel away from the wave crest. There were obvious objections to both these theories. It is a matter of common experience that vessels often roll very heavily in a long smooth swell, where the slope is so small that the chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 225 departure from the horizontal is scarcely perceptible, and where no sensible shock is delivered against the sides of the ships. The best of the earlier theories, put forward by Daniel Bernoulli about a century ago, departed from the preceding theories, and was content to speak of the oscillations of a ship as comparable to those of a penclulum, subjected to the action of " impulses " from the waves, no analysis being attempted of the character or causes of these impulses. Some of the conclusions which Bernoulli reached even now command respect ; but he, in common with his contemporaries, failed to realize or to express the fundamental condition wherein wave water differs from still water, viz. that the direction and intensity of the fluid pressure are continually varying instead of being constant, as in still water. For nearly a century the subject remained very nearly in the condition in which Bernoulli, Euler, and other writers of that period had left it, until the late Mr. W. Froude introduced the now accepted theory of rolling. This theory rests upon the fundamental doctrine, explained in the previous chapter, that in wave water the direction of the pressure at any point is a normal to the trochoidal surface of equal pressure passing through that point ; and in that particular the modern theory differs from all that preceded it. It is not put forward as a perfect theory, fully expressing all the conditions of the problem; but it far more completely represents those conditions than any theory which preceded it, and has exercised a great and beneficial effect upon ship designs. Moreover, in its main features, it has secured the adhesion of the greatest authorities on the science of naval architecture, both English and foreign, some of whom have very considerably helped its extension. An attempt to describe in popular language the main features of the theory cannot, therefore, be devoid of interest, even though the avoidance of mathematical language may render the description which follows incomplete. At the outset it may be well to state that the modern theory of rolling finds the governing conditions of the behaviour of a ship among waves to be twofold : — (1) The ratio which the period of still-water oscillations of the ship (or " natural period ") bears to the period of the waves amongst which she is rolling. (2) The magnitude of the effect of fluid resistance. Both the natural period and the means of estimating the magni- tude of the fluid resistance for any ship may be obtained from experiments made in still water, as previously explained. It will be convenient to deal separately with these conditions, first illustrating the causes which make the ratio of the periods so important, and in doing So leaving resistance out of account ; after- wards illustrating the effect of resistance in limiting the range of Q 226 NAVAL ARCHITECTURE. [chap. vi. oscillation. In practice the two conditions, of course, act con- currently ; but the hypothetical separation here made will probably enable each to be better understood. EeTerting to the case illustrated by Fig. 82, p. 199, where a small raft floats upon the inclined surface (AB) of the water in a vessel which is moving horizontally, it will be noticed that the raft is acted upon by the following fluid pressures : P, acting downwards on the upper side ; an equal pressure, P, acting upwards on the lower side ; and the buoyancy b acting normally to the surface AB through the centre of buoyancy of the raft. Let to be the weight of the raft acting vertically downwards through the centre of gravity when in still water. When the vessel containing the water is in motion, this weight w must be combined with the horizontal accelerating force due to the motion, in the manner explained on p. 199. Using the same notation as before, we have — Resultant of weight and horizontal accelerating force = w sec a. This resultant will act perpendicularly to the inclined water surface, just as the buoyancy b does ; and for equilibrium we must have — b = w sec a, and the line of action of b must pass through the centre of gravity of the raft. Hence it follows that the normal to the free water surface indicates the direction towards which the raft will tend to return if her mast is inclined from it ; just as in still water the upright is her position of equilibrium. The normal to the water surface may therefore be termed the " virtual upright " for the raft when it and the water are subjected to horizontal acceleration ; since the normal fixes the position of equilibrium. Next suppose this very small raft to float on the surface of a wave, as in Fig. 83, p. 200. Here reasoning similar to the foregoing applies, if the raft be considered so small in relation to the wave that it may be treated as if it replaced a particle, and moved just as the particle would have done. In the preceding chapter it has been shown that at any point in a trochoidal wave the normal represents the direction of fluid pressure at that point, and it has also been stated that this direction changes from point to point along the wave surface, the variations in inclination resembling the oscillation of a pendulum having a period for a single swing equal to half the wave period. The cases of Figs. 82 and 83 therefore differ in this : in the former, where the water surface has a constant inclination, the " virtual upright " also has a constant direction ; whereas on the wave the " virtual upright," or position of equilibrium, in which the masts of the raft will lie, varies in direction from instant to instant, the varia- chap, vl] oscillations of ships among waves. 227 tions being dependent upon the wave slope and wave period. On the wave the raft is also subjected to vertical as well as horizontal accelerations, affecting both the value of the fluid pressure upon its bottom and its own apparent weight, but affecting both equally, and therefore not changing the volume of displacement of the raft from that in still water. The law of this variation in the pressure and apparent weight has been given in the preceding chapter, and illus- trated by Fig. 81, but for our present purpose the variation in the direction of the pressure is of greater importance. A ship differs from this hypothetical raft, having lateral and vertical extension in the wave, as shown by ADC in Fig. 83. Even though she may be small when compared with the wave, it is obvious that she cannot be treated as a single particle replacing a particle in the wave. At any moment she displaces a number of particles which, were she absent, would be moving in orbits of different radii, and at different speeds. Her presence must therefore introduce a disturb- ance of the internal motions in the wave, and this disturbance must in some manner react upon the ship and somewhat influence her behaviour. Our present knowledge of the conditions governing the internal molecular forces in the waves of the sea is not sufficient to enable exact mathematical treatment to be applied in estimating the effect of this disturbance, and determining at each instant the position of the " virtual upright " for the ship. If the positions of the virtual upright were known, each of them would be a normal to a surface termed "the effective wave slope." Conversely, the effective wave slope may be defined as the surface, the normal to which at any point represents the instantaneous position of equilibrium for the masts of the ship. Although our knowledge of the subject does not enable the form of the effective wave slope to be accurately determined, certain considerations of a general character must influence that form. For example, the size of the ship relatively to the waves, the form of her immersed part, its lateral extension along, and vertical exten- sion into, the waves, as. well as the vertical position of her centre of gravity, are all known to affect the effective wave slope. Moreover, that slope may differ considerably from the upper surface of the waves. Large ships, for instance, when floating among very small waves, even with their broadsides to the line of the wave advance, may be supported simultaneously by the slopes of successive waves, and these slopes being inclined in opposite directions, the effective slope may be practically horizontal. Again, ships of very great breadth, such as the IAvadia, or the circular ironclads, when floating broadside on to the waves, occupy so great an extent of the slope of one_ of the largest _ocean waves, that the, effective sjope can only 228 NAVAL ARCHITECTURE. [chap. vi. hare a very moderate amount of steepness as compared with the maximum slope of the waTe surface. In the extreme case of a ship of narrow beam but great draught of water, the effective slope obviously would have its steepness decreased in virtue of the fact that trochoidal subsurfaces in a wave are flatter than the upper surface. All these illustrations serve to show that the determination of the effective wave slope for a particular case can only be made approxi- mately. For the purpose of mathematical investigation of the hypothetical case of unresisted rolling it is, however, usual to assume that a ship falls in with waves so large relatively to her own dimen- sions that she accompanies their motion. Starting with this assump- tion of the relative smallness of a ship, it has sometimes been assumed that the effective slope will nearly coincide with the trochoidal subsurface passing through the centre of buoyancy of the ship. In Fig. 83, let B represent the centre of buoyancy of the ship shown in section by ACD ; then TT D the subsurface of equal pressure passing through B, would be termed the effective wave slope, and the normal to it, NN U would be taken as determining the instan- taneous position of equilibrium for the ship. In the diagram the ship is shown purposely with her middle line (G-M) not coincident with the normal NN\ ; M, the point of intersection of these lines, may be regarded as the metacentre for small transverse inclinations of the ship from the virtual upright ; the angle BMNi measures the inclination of the ship from the instantaneous position of equilibrium. Through the centre of gravity G, GZ is drawn perpendicularly to Mj ; then instantaneously the effort of stability, or righting moment, with which the ship tends to move towards the position NNu is measured by the expression — Bighting moment = apparent weight X GZ. In estimating the apparent weight of the ship, which is practically equal to, and has a line of action parallel to, the fluid pressure acting along NN it is of course necessary to take account of the radii of the particles situated in the subsurface TT^ Very often the actual weight may be substituted for the apparent weight without any great error ; but this is a matter easily investigated, in accordance with the principles previously explained. This method of approximating to the effective slope, although widely adopted, is not universally accepted, nor does it profess to be more than an average or approximation under the assumption of the relative smallness of a ship as compared with the waves. In some cases the effective slope lies nearer the upper surface than TT! would be situated. Cases may be conceived also where the effective slope chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 229 is steeper than the upper surface. Amongst relatively large waves the effective slope is usually less steep than the upper surface — a fact which is confirmed by the careful and extensive observations made by Mr. Froude on board the Devastation. In practice, there- fore, it is an error on the side of safety to assume, as is not unfre- quently done, that the variations in inclination and magnitude of the fluid pressure and the apparent weight of the ship, may be determined from the upper surface of the wave. This was the plan adopted by Mr. Froude in his earliest investigations, as well as that followed by the Admiralty Committee of 1871 on Designs for Ships of War, in their estimate of the probable limits of rolling of the Devastation class. It will be seen that this substitution of the upper surface for the less steep effective surface in no way affects the period occupied by the wave normal in performing the set of motions from upright at the hollow onward to upright at the crest of a wave. The difference is solely one of the maximum inclina- tion to the vertical reached by the wave normal, and taking the upper surface usually somewhat increases this beyond the true maximum in the critical cases with which the mathematical theory deals. Suppose a ship lying broadside-on to the waves to be upright and at rest when the first wave hollow reaches her ; at that instant the normal to the surface coincides with the vertical, and there is no tendency to disturb the ship. But a moment later, as the wave form passes on and brings the slope under the ship, the virtual upright towards which she tends to move, becomes inclined to the vertical. This inclination at once develops a righting moment tend- ing to bring the masts of the ship into coincidence with the instan- taneous position of the normal to the wave. Hence rolling motion begins, and the ship moves initially at a rate dependent upon her still-water period of oscillation. Simultaneously with her motion, the wave normal is shifting its direction at every instant, becoming more and more inclined to the vertical, until near the mid-height of the wave it reaches its maximum inclination, after which it gradually returns towards the upright ; the rate of this motion is dependent upon the period of the wave. Whether the vessel will move quickly enough to overtake the normal or not, depends upon the ratio of her still-water period to the interval occupied by the normal in reaching its maximum inclination and returning to the upright again, which it accomplishes at the wave crest ; this interval equals one-half the period of the wave. Hence it appears that the ratio of the period of the ship (for a single roll) to the half-period of the wave must influence her rolling very considerably, even during the passage of a single wave, and still more is this true when a long series of waves 230 NAVAL ARCHITECTURE. [CHAP. VI. move past the ship, as "will be shown hereafter.* It will also be obvious that the chief cause of the rolling of ships amongst waves is to be found in the constant changes in the direction of the fluid- pressure accompanying wave motion. As simple illustrations of the foregoing remarks, two extreme cases may be taken. The first is that of a little raft, like that in Fig. 83, having a natural period indefinitely small as compared with the half-period of the wave. Her motions will consequently be so quick as compared with those of the wave normal, that she will be able continuously to keep her mast almost coincident with the normal and her deck parallel to the wave slope. Being upright at the wave hollow, she will have attained one extreme of roll about the mid-height of the wave, and be again upright at the crest. The period of this single roll will be half the wave period. As successive waves in the series pass under the raft, she will acquire no greater motion, but continue oscillating through a fixed arc and with unaltered period. The arc of oscillation will be double the maximum angle of wave slope. The other extreme case is that of a very small vessel having a natural period of oscillation, which is very long when compared with the wave period. For instance, a small cylinder like that in Fig. 69, p. 152, may be so weighted that the centre of gravity may approach closely to the height of the axis, but remain below it; then, as explained previously, there will be stable equilibrium, and a very long period of oscillation may be secured by disposing the weights towards the circumference of the circular cross-sections. If such a vessel were upright and at rest in the wave hollow, she would be subjected to rolling tendencies similar to those of the raft, owing to the successive inclinations of the wave normal — her instantaneous virtual upright. But her long period would make her motion so slow as compared with that of the wave normal that, instead of keeping pace with the latter, the ship would be left far behind. In fact, the half-wave period during which the normal completes an oscillation would be so short relatively to the period of the ship that, before she could have moved far, the wave normal would have passed through the maximum inclination it attains near the mid- height of the wave, and rather more than halfway between * It has already been explained that to a double roll, and the term " period " we follow the Admiralty method in term- to the time occupied in performing the ing a single roll "an oscillation," and the double roll. We again refer to the time occupied in its performance the matter, as in many published papers " period of oscillation." Mathematicians the mathematical terms are employed, commonly apply the term " oscillation " chap, vi.] OSCILLA TIONS OF SHIPS AMONG WA VES. 2 3 1 hollow and crest. From that point onwards to the crest it would be moving back towards the upright ; and the effort of the ship to move towards it, and further away from the upright, would in con- sequence be diminished continuously. At the crest the normal is upright, and the vessel but little inclined — inclined, it will be observed, in such a sense that the variations in direction of the normal, on the second or back slope of the wave, will tend to restore her to the upright. Hence it follows that the passage of a wave under such a ship disturbs her but little, her deck remains nearly horizontal, and she is a much steadier gun-platform than the raft-like vessel. No ship actually fulfils the conditions of either of these extreme ■cases, nor can her rolling be unresisted as is here assumed. Expe- rience proves, however, that vessels having very short periods of oscillation in still water tend to acquire a fixed range of oscillation when they encounter large ocean waves, keeping their decks approxi- mately parallel to the effective wave slopes. Actual observations also show that vessels having the longest periods of oscillation in still water are, as a rule, the steadiest amongst waves, keeping their decks approximately horizontal, and rolling through small arcs. Hereafter, the details of some of these observations of the behaviour of actual ships will be given ; but attention must be confined, at present, to the general hypothesis of unresisted rolling among waves. Having cleared the way by the foregoing illustrations, we shall now attempt a general sketch of the modern method of investigation. The following assumptions are made in order to bring the problem of the motion of a ship in a seaway within the scope of exact mathematical treatment : — (1) The ship is regarded as lying broadside-on to the waves with no sail set, and without any motion of progression in the direction of the wave advance ; in other words, she is supposed to be rolling passively in the trough of the sea. (2) The waves to which she is exposed are supposed to form a regular independent series, successive waves having the same dimensions and periods. (3) The waves are supposed to be large as compared with the ship, so that at any instant she would rest in equilibrium with her masts coincident with the corresponding normal to the " effective slope," which is commonly assumed to coincide with the upper surface of the wave. (4) The righting moment of the ship at any instant is assumed to be proportional to the angle of inclination of her masts to the corre- sponding normal to the effective wave slope — the virtual upright. 232 NAVAL ARCHITECTURE. [chap. vi. (5) The Tariations of the apparent weight are supposed to be so small, when compared with the actual weight, that they may be neglected, except in very special cases. (6) The effects of fluid resistance are considered separately, and in the mathematical investigation the motion is supposed to be unresisted and isochronous (see p. 157). Objections may be raised, with justice, against most of these assumptions ; and it was never intended that they should be regarded as including all the varying circumstances which may influence the rolling of a ship among waves. The results of experience and obser- vation, however, confirm the general accuracy of the deductions drawn from mathematical investigations based upon these assump- tions ; and this is one great recommendation in their favour. Another fact worthy of notice is that no better and more complete assumptions have been proposed on which to base a rigorous mathe- matical investigation of the rolling of ships among waves. Many attempts have been made in this direction, but the conclusion reached up to the present time is that the problem lies beyond the reach of purely mathematical treatment, and can only be successfully attacked by the process of " graphic integration," to be described hereafter. Two principal objections to the foregoing assumptions may be mentioned in passing. It may be thought that since ships much more frequently encounter a " confused sea " than a single regular series of waves, the latter condition should not be supposed to exist. In reply it may be stated that extensive observations of the behaviour of ships seem to show that the irregvdarities of a confused sea often tend to check the accumulation of rolling, the heaviest rolling being produced by waves which are approximately regular. No doubt there are exceptions to this rule ; but, unfortunately, the attempt to express the conditions of a confused sea in the mathe- matical investigation renders the latter unmanageable. Objection may be taken also to the assumption that the ships shall be regarded as small in comparison with the waves. This is not always true ; yet it must be noted that — excluding the special case of synchronous oscillations — the heaviest rolling is usually produced by the largest waves, while the supposition of relative smallness is favoured by the smallest dimension of the ship — her beam — being presented to the length of the wave. Upon the basis of the foregoing assumptions, dynamical equations are formed representing the unresisted rolling of the ships. The following are the principal steps. Some fixed epoch is chosen wherefrom to reckon the time at which the ship occupies a certain position on the wave slope, and has an inclination (0) to the vertical. chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 233 The inclination (0 X ) to the vertical of the wave normal for that position can then be expressed in terms of the steepness of the wave and the wave period; both ascertainable quantities. Next the angle (6 — 0i) between this normal and the masts can be deduced from the preceding expressions ; and the righting moment corre- sponding to that angle can be estimated. This moment constitutes the active agency controlling the motion of the ship at that instant, and it must be balanced by the moment of the accelerating forces, which can be expressed in terms of the inertia of the ship and the angular acceleration.* Finally, an equation is obtained involving the following terms : The angular acceleration at that instant ; the inclination of the masts of the ship to the vertical at that instant ; and the effort of stability at that instant. The solution of this equation furnishes an expression for the angle of inclination (0) of the ship to the vertical at any instant, in terms of her own natural period, the wave period, the ratio of the height to the length of the wave, and certain other known quantities. Assuming certain ratios of the period of the ship to the wave period, it is possible from the solution to deduce their comparative effect upon the rolling of the ship ; or, assuming certain values for the steepness of the waves, to deduce the consequent rolling as time elapses and a continuous series of waves passes the ship. In fact, the general solution gives the means of tracing out the unresisted rolling of a ship for an unlimited time, under chosen conditions of wave form and period. A few of the more important cases may now be briefly mentioned. One critical case is that in which the natural period of the ship for a single roll equals the half-period of the wave. This had been foreseen by several of the earlier writers, including Daniel Bernoulli, apart from mathematical investigation, from the analogy between the motions of a ship and a pendulum. It is a matter of common experience that, if a pendulum receive successive impulses, keeping time with (or " synchronizing " with) its period, even if these impulses have individually a very small effect, they will eventually impress a very considerable oscillation upon the pendulum. A . common swing receiving a push at the end of each oscillation is a case in point. When a similar synchronism occurs between the wave impulse and the period of the ship, the passage of each wave tends to add to the range of her oscillation, and were it not for the deterrent action of the fluid resistance, she would finally capsize. Such, in general terms, was the opinion of the earlier writers, which recent and more exact investigations have fully confirmed. Apart from the action of resistance, it has been shown that the passage of * See the explanations of these terms given at p. 149. -34 XAVAL ARCHITECTURE. [chap. VI. a single wave would increase the range of oscillation of the ship by an angle equal to about three times the maximum slope of the wave. For instance, in an Atlantic storm wave series, each wave being 250 feet long and 13 feet high, and having a maximum slope of some 9 degrees, the passage of each wave would, if there were no resistance, add no less than 27 degrees to the oscillation of the ship ; so that a very few waves passing her would overturn her. Here, however, the fluid resistance comes in, and puts a practical limit to the range of oscillation in a manner that will be explained hereafter. It may be well to examine a little more closely into the character of the wave impulse which creates accumulated rolling in this case. Suppose a vessel to be broadside-on in the wave hollow when the extremity of her roll is reached, say to starboard, the waves advanc- ing from starboard to port. Then the natural tendency of the ship, apart from any wave impulse, will be to return to the upright in an interval equal to one-half her period, which by hypothesis will be equal to the time occupied by the passage of one-fourth the wave- length. In other words, the ship would be upright midway between hollow and; crest of the wave near which its maximum slope occurs. Xow, at each instant of this return roll towards the upright the inclination of the wave normal, fixing the direction of the resultant fluid pressure, is such as to make the angle of inclination of the masts to it greater than their inclination to the true vertical ; that is to say, the inclination of the wave normal at each instant virtually causes an increase of the righting moment. Consequently, when the vessel reaches the upright position at the mid-height of the wave, she has by the action of the wave acquired a greater velocity than she would have had if oscillating from the same initial inclination in still water. She therefore tends to reach a greater inclination to port than that from which she started to starboard ; and this tendency is increased by the variation in direction of the wave normal between the mid-height and the crest — that part of the wave which is passing the ship during the period occupied by the second half of her roll. On reference to Fig. 83 — where the directions of the wave normal are indicated by the masts of the rafts— it will be seen that, when the ship during the second half of the roll inclines her masts away from the wave crest, the angle between the masts and the wave normal is constantly less than the angle they make with the vertical. The effect of this is to make the righting moment less at every instant during the second half of the roll on the wave than it would have been in still water. For unresisted rolling, it is the work done in overcoming the resistance of the righting couple which ex- tinguishes the motion away from the vertical. On the wave, therefore, the vessel will go further to the other side of the vertical chap, vi.] OSCILLATIONS OF SHIPS AMONG WA VES. 235 from that on which she starts than she would do in still water, for two reasons : (1) she will acquire a greater velocity before she reaches the upright ; (2) she will experience a less check from the righting couple after passing the upright. From the above state- ments, it will be evident that there must be a direct connection between the maximum slope of the wave and the successive increments of her oscillations. More or less close approximation to this critical condition will give rise to more or less heavy rolling ; but it is a noteworthy fact that, even where the natural period of the ship for small oscillations •equals the half-period of the wave, and may thus induce heavy rolling, the synchronism will almost always be disturbed as the magnitude of the oscillations increases ; the period of the ship will be somewhat lengthened, and thus the further increments of oscilla- tion may be made to fall within certain limits, lying within the range of stability of the ship. It will be understood that this •departure from isochronism in no way invalidates what was said in Chapter IV. as to the isochronism Of ships of ordinary form when oscillating 10 or 15 degrees on either side of the vertical. The character of the change can best be illustrated by reference to a common simple pendulum. Such a pendulum swinging through very small angles on either side of the vertical has, say, a period of -one second ; if it swings through larger angles, its period becomes somewhat lengthened, and the following table expresses the •change : — Angles of swing. Period. seconds. Very small .... 10 30° ... 1-017 60° 1-073 90° 1-183 120° 1-373 150° 1-762 - For ships the angles. of swing are rarely so large as to make the increase of period great proportionally, but yet, as above remarked, the increase may be sufficient to add sensibly to the safety of a ship exposed to the action of waves having a period double of her own ^period for small oscillations ; although it is by the action of fluid resistance that the overturning of a ship so circumstanced is chiefly prevented. * See Report of Committee on De- signs (1871), where Professor Rankine applied similar reasoning to the dis- cussion of the probable safety of the Devastation class. 236 NAVAL ARCHITECTURE. [chap. vi. A second interesting deduction from the solution of the general equation for unresisted rolling is found in the '• permanent oscilla- tions of ships." If a Tessel has been for a long while exposed to the action of a single series of waves, she may acquire a certain maximum range of oscillation, and perform her oscillations, not in her own natural period, but in the possibly different wave period. This case differs from the preceding one in that the period of the ship for still- water oscillations does not agree with the half-period of the ware ; but, notwithstanding, the oscillations among waves keep pace with the wave, their period being '■' forced " into coincidence with the half-period of the waTe. At the wave hollow and crest a ship so circumstanced is upright ; she will reach her maximum inclination to the vertical when the maximum slope of the wave is passing under her (about the mid-height of the wave) ; and the passage of a long series of waves will not increase the range of her oscillations, which are " permanent " in both range and period — hence their name. The maximum inclination then attained depends, according to theory, upon two conditions : (1) the maximum slope of the wave ; (2) the ratio of the natural period of oscillation of the ship to one- half the wave period. Let a = maximum angle made with the horizon by the wave profile; 6 = maximum angle made with the vertical by the masts of the ship; T = natural period of still-water oscillations of the ship ; 2T t = period of wave. If fluid resistance is neglected, and the conditions above stated are fulfilled, mathematical investigation for this extreme case leads to the following equation : — 9 = a L— ° >< W j _ T^ T^-T 2 T, 3 Three cases may be taken in order to illustrate the application of this equation. I. Suppose T = T l5 then becomes infinity; that is to say, we have once more the critical case of synchronism previously discussed,, respecting which nothing need be added. II. Suppose T less than T D so that ^ is a proper fraction less than unity : then and a always have the same sign, which indicates that the masts of the ship lean away from the wave crest at all positions, except when the vessel is upright at hollow and crest. The closer the approach to equality between T x and T, the greater chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 237 the value of 6 ; which is equivalent to an enforcement of the statement previously made, that approximate synchronism of periods leads to heavy rolling. The smaller T becomes relatively to Tj, the smaller does become, its minimum value being a when T is indefinitely small relatively to T x . This is the case of the raft in Fig. 83, which keeps its masts parallel to the wave normal. III. Suppose T greater than T 1 : then and a are always of opposite signs, and, except at hollow and crest, the masts of the ship always lean towards the wave crest. The nearer to unity is the ratio of T to T l5 the greater is ; illustrating as before the accumulation of motion when there is approximate synchronism. The greater T becomes relatively to T u the less does 6 become ; in other words, as explained above, a ship of very long period keeps virtually upright as the wave passes. As an example of the use of the formula, take the following figures drawn from the report on the behaviour of the Devastation during a passage to the Mediterranean : — a = maximum wave slope = 1J degrees ; T = natural period of ship for single roll . = 6 - 8 seconds ; T x = half (apparent) wave period . . . . = 6 „ If the conditions of permanent rolling had been fulfilled, the formula would give — Maximum inclination of ship, sup- )_ ,, 1 posing motion unresisted . . 5 i /'6'8 '' - (V7 = U X = H degrees (nearly). The observed oscillation of the ship, from out to out, at this time was about 7 degrees, and the less magnitude of this oscillation, as compared with that given by the formula, must be accounted for chiefly by the want of absolute uniformity in a sufficiently long series of waves to make the rolling permanent, as well as by the steadying effect of the resistance. The example has, however, been given merely as an illustration of the use of the formula, not as a proof of its accuracy ; in practice all deductions from the theory of unresisted rolling, as to the extent of oscillation, require to be modified to allow for the effect of fluid resistance. An inspection of the records of rolling of a large number of ships, under various conditions of sea, leads to the conclusion that the periods are rarely " forced " into coincidence with the wave-period. It is possible, by means of very simple experiments, to illustrate the influence which changes in the relative periods of ships and 238 NAVAL ARCHITECTURE. [CHAP. vi. waves may have upon the rolling.* Let AB, Fig. 93, represent a pendulum with a very heavy bob, having a period equal to the half period of the wave. To its lower end let a second simple pendulum, BC, be suspended, its weight being inconsiderable as compared with the wave pendulnni AB; then, if AB is set in motion, its inertia will be so great that, notwith- standing the suspension of BO, it will go on oscil- *\\ lating very nearly at a constant range — say, equal to the maximum slope of the wave — on each side of y the vertical. First suppose BC to be equal in length A and period to AB : then, if the compound pendulum \\ is set in motion, and AB moves through a small (J. range, it will be found that BC, by the property of ^\ synchronizing impulses, is made to oscillate through \Vv very large angles. Second, if BC is made very long, \ X^- and of long period, as compared with AB, it will be ^ found that BC continues to hang nearly vertical while AB swings, just as the ship of comparatively long period remains upright, or nearly so, on the wave. Third, if BC is made very short and of small period when AB is set moving, BC will always form almost a continuation of AB, just as the quick- moving ship keeps her masts almost parallel to the wave normal. A third notable deduction from the solution of the equation for unresisted rolling is that, except when the conditions of synchronism or permanent oscillation are obtained, the rolling of a ship will pass through phases. At regular stated intervals equal inclinations to the vertical will recur, and the range of the oscillations included in any series will gradually grow from the minimum to the maximum, after attaining which it will once more decrease. The time occupied in the completion of a phase depends upon the ratio of the natural period of the ship to the wave period. If T = ship's period for a single roll, T x = half-period of wave, and the ratio of T to % be expressed in the form P> where both numerator (p) and denominator (q) are the lowest wlwle numbers that will express the ratio : then — Time occupied in the completion of a phase = 2q . T seconds. For example, let it be assumed that waves having a period of 9 seconds act on a ship having a period (for single roll) of 7^ seconds. ™ T 7* 15 _ 5 _ p Then T^ § " F " » " i Tune. for completion of phase = 3 x 2 x 7£ = 45 seconds. * Such experiments were made some, and by the author in connection with years ago by the late Professor EankineJ' bis lectures at the Eoyal Naval College. ' chap. VI.] OSCILLA TIONS OF SHIPS AMONG WA VES. 239 Although the mathematical conditions for these " phases " of oscillation are not fulfilled in practice, the causes actually operating on the ship — such as the differences in form of successive waves, and the influence of fluid resistance — commonly produce great differences in the successive arcs of oscillation. It is important, therefore, in making observations of rolling, to continue each set over a con- siderable period. In the Eoyal Navy each set of observations extends over ten minutes, and the minimum inclinations reached are always found to differ considerably from the maximum inclinations. The mean oscillation for any set is frequently only a little more than half the maximum inclination, and the following examples are fairly representative in this respect. Detached Squadron (1874). Ships, ' Mean arcs of oscillation. ^Maximum arcs of oscillation. Newcastle .... Topaze Immortalite .... Narcissus .... Doris Raleigh ..... degrees. 29-6 22-6 20-0 19-6 18-7 5-8 degrees. 58 50 39 36 48 15 Channel Sqtjadeon (1873). Ships. Mean arcs of Maxim am arcs oscillation. of oscillation. degrees. degrees. Bellerophon .... 16-9 25 Minotaur .... 22-3 46 Agincourt ... 16-4 37 Hercules 8-1 14 Sultan 6-6 12 In comparing the rolling of ships, it is usual to take the mean arcs of oscillation (i.e. the mean of the sums of successive inclinations on either side of the vertical), and on the whole this appears the fairest course. But in analyzing rolling returns, it is always desirable to look further, and to note the maximum and minimum oscillations, as well as the rate of growth of the range. AH these particulars are readily ascertainable from the forms upon which the records of rolling are kept .in the Eoyal Navy. For considerations of safety, the maximum angle of inclination reached is obviously of the greatest importance ;- but vessels do not usually roll so heavily as 240 NAVAL ARCHITECTURE. [chap. vi. to be liable to capsize, and, apart from this danger, the mean oscilla- tions afford the best means of comparing the behaviour of ships. In concluding these remarks on the hypothetical case of unresisted rolling among waves, it may be well to summarize the conclusions which have the greatest practical interest, and to compare them with the residts of experience. It need scarcely be remarked again that the actual behaviour of ships at sea is greatly influenced by fluid resistance. First. Heavy rolling is likely to result from equality or approxi- mate equality of the period of a ship and the half-period of waves, even when the waves are very long in proportion to their height. Manv facts might be cited in support of this statement, but a few must suffice. Admiral Sir Cooper Key observed that the vessels of the Prinze Consort class were made to roll very heavily by an almost imperceptible swell, the period of which was just double that of the ships. Admiral Sir E. Yesey Hamilton noted that, on one occasion, the Adiilles. a vessel having a great reputation for steadiness, rolled more heavily off Portland in an almost dead calm than she did off the coast of Ireland in very heavy weather. Mr. Froude reported a very similar circumstance as having occurred during trials with the Active. And, lastly, during the cruise of the combined squadrons in 1S71, when the Monarch far surpassed most of the ships present in steadiness in heavy weather, there was one occasion when, through the action of approximately synchronizing periods, she rolled more heavily in a long swell than did the notoriously heavy rollers of the Prince Consort class. The effect of approximate synchronism of periods may be tested by changing the course of a ship relatively to the advance of the waves, and this was done most satisfactorily during the trials of the Devastation, the ship remaining in the same condition, and the waves, of course, remaining unchanged, while the apparent period of the waves was altered by change of course and speed.* Lying passively broadside-on to waves having a period of about 11 seconds, the Devastation was observed to roll through the maximum angles of 6£ degrees to windward, and 7J degrees to leeward, making the total arc 14 degrees. She was then put under way, and steamed away from the waves at a speed of 7£ knots, having the wind and sea on her quarter, when her maximum roll to windward became 13 degrees, and to leeward 14J degrees, making the total arc 27£ degrees. The difference between the two cases is easily explained, in view of the foregoing considerations. When rolling passively in the trough of the sea, the apparent period of the waves was their real period ; and For an explanation of the term " apparent period," see p. 206. chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. ' 24 1 this was less than the double period for the Devastation (13£ seconds). When she steamed away obliquely to the line of advance of the waves, their apparent period became increased, and the diagrams of the ship's performance then taken showed that the speed and course of the ship had the effect of making the apparent period of the waves just equal to the period of a double roll for the Devastation — in fact, established that synchronism of ship and wave which is most con- ducive to the accumulation of motion. This case also furnishes an example of what to every sailor is a truism, viz. that the behaviour of a ship is greatly influenced by her course and speed relatively to the waves. Theory, as we have shown, takes account of the case which is probably the worst for most vessels — the condition of a ship which has become unmanageable, and rolls passively in the trough of the sea. But so long as a ship is manage- able, the officer in command can largely influence her behaviour by the selection of the course and speed, which make the ratio of the periods of ship and wave most conducive to good performance. In the case of the Devastation just cited, had she steamed obliquely, as before, but head to sea, the apparent period of the waves would have been decreased, and the rolling would probably have been less than it was in either case recorded. Of course, synchronism in some cases may be produced by steaming towards, instead of from, the waves. For instance, if a ship having a period of 4 to 5 seconds had been amongst the waves which the Devastation encountered, when broad- side-on, her period would have been less than half that of the waves ; but if she had steamed obliquely towards the waves, their apparent period might have been lessened,, and made about 8 to 10 seconds. However obtained, such synchronism will probably lead to the heaviest rolling the vessel is likely to perform, and the steeper the waves the heavier is the rolling likely to be. Second. It follows from the investigation for unresisted rolling that the best possible means, apart from increase in the fluid resist- ance, of securing steadiness in a seaway, is to give to a ship the longest possible natural period for her still-water oscillations. This deduction it is which has been kept in view in the design of most recent war-ships, both English and foreign, and its correctness has been fully established by numerous observations. It would be easy to multiply illustrations from the published record of rolling of the ships of the Eoyal Navy, as well as from those of the French Navy ; but we can only give a few, referring the reader to the original documents for more.* During the cruise * See Parliamentary Papers, " Re- on Designs for Ships of War of 1871 ; and ports on Channel Squadrons," 1863-68 ; various reports on the behaviour of ships the Report' of the Admiralty Committee, in. the French Navy. E 242 NAVAL ARCHITECTURE. [chap. VI. of the Combined Squadron in 1871, some of the " converted " iron- clads of the Prince Consort class, and other of the earlier ironclads having short periods, were in company with armoured ships of more recent design, having longer periods. The following table of observations refers to a time when the weather was reported to be exceptionally heavy, bnt unfortunately no particulars were noted of the dimensions and periods of the waves. Ships. Approximate natural periods. Arcs of oscillation. Lord Warden Caledonia .... Prince Consort Defence .... Minotaur Northumberland seconds. 1 5to5£ | 7 to 7£ 8 degrees. r 62 57 46 49 f 35 t 38 25 It may be interesting to note that the period of the Prince Consort class, from 5 to 5£ seconds, would just synchronize with the half- period of waves from 500 to 600 feet long. It has been stated in the preceding chapter that these are almost identically the dimensions which careful and extensive observations have led us to accept as belonging to large Atlantic storm-waves. Hence it is easy to explain the relatively bad behaviour of these converted ironclads with their quick motion and short period. Another illustration of the superior steadiness of ships of long period may be drawn from the observed performances of the representative ships in the Channel Squadron of 1873, as under : — Ships. Approximate natural periods. Mean arcs of oscillation. Belhrophon .... Minotaur Agincourt Hercules seconds. 6$ to 7 } 7 to7£ 8:0 8-9 degrees. 16-9 f 22-3 \ 16-4 8-1 6-6 This, it should be understood, is a fairly representative case, and by no means an exceptional one. In the French Navy similar results have been obtained. Almost at the outset of the ironclad reconstruction, the returns from the French experimental squadron of 1863 furnished evidence of the same kind, as the following table chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 24c shows. The observations were made when the vessels were running broadside-on to a heavy sea. Ships. Approximate natural periods. Mean arcs of oscillation. Normandie .... Invincible Oouronne Magenta Solferino .... seconds. } 5 to 5J- 6 } 7 to 7£ degrees. / 43-6 \ 41-4 37-7 / 36-0 \ 35-0 The Magenta and Solferino were making only ten oscillations per minute, whereas the other ships were making twelve. Another striking contrast is to be found in the behaviour of the French ironclad Ocean and other vessels of her class, having periods of about 10 seconds for a single roll, as compared with the behaviour of the armoured corvettes of the Alma class having periods varying from 5£ to 5 - 7 seconds for a single roll. It is recorded that in the first cruise of the Ocean she never rolled more than 2 to 3 degrees on each side of the vertical, while three of the corvettes were rolling 34, 35, and 36 degrees from the vertical. The maximum inclination to the vertical reached by the Ocean under any circumstances during this cruise never exceeded 7 degrees. Experience with the ships of the Invincible class in the Eoyal Navy has given no less satisfactory results. The commanding officer of one of these ships has stated " that they may go through "a commission and never heel or roll more than one or two degrees." Eecords of rolling have been mostly limited to the behaviour of armoured ships, the apprehensions entertained in some quarters as to the unseaworthiness of these vessels having caused greater attention to be bestowed upon them than upon unarmoured vessels. But now that rolling returns have been ordered to be made in all her Majesty's ships, a large mass of facts relating to unarmoured as well as armoured ships has been collected, and is continually being increased. The Detached Squadron has in this way enabled a good comparison to be made between the behaviour of early types of screw-frigates, forming the main strength of the squadron, and that of the swift cruisers which have been in company — particularly the Inconstant and the Baleigh, both ships of long period. The following table is taken from the observations of rolling made in the heaviest weather experienced by the squadron in the spring of 1875, and, like the other examples given, is only a specimen of many similar cases : — 244 NAVAL ARCHITECTURE. [chap. VI. Ships. Approximate natural periods. Mean arcs of oscillation. Newcastle .... Topaze . Immortal it e . Narcissus .... Doris . . . . Raleigh . seconds. 1 • J 8 i degrees. r29-6 22-6 •20-0 19-I5 U8-7 5-8 In passing, it may be well to illustrate the importance of the slower motion being associated with the smaller arc of oscillation in ships rolling at sea. In the table on p. 242, compare the behaviour of the Lord Warden with that of the Hercules : the former rolling through an arc of 62 degrees about eleTen or twelve times each minute, while the latter rolled through 25 degrees only about seven or eight times each minute. A man aloft, say, at a height of 100 feet, in the Lord Warden would be swept through the air at a mean rate of some 1200 feet per minute, having the direction of his motion reversed about every 5 seconds ; whereas a man placed as high in the Hercules would only be moving at a mean rate of some 350 feet per minute, and be subjected to a reversal of the direction only about once every 8 seconds. The maximum rates in passing through the vertical would of course be greater than these mean rates. Here- after it will be shown how great are the strains brought upon the structure, masts, and rigging of ships which roll violently and rapidly. The remarks on wave genesis made in the previous chapter will assist the explanation of the undoubtedly greater average steadiness of vessels of long natural periods. What may be termed ordinary storm winds may by their continued action produce waves having lengths of 600 feet or under, with periods of 10 to 11 seconds or less ; and these waves would have half-periods about equal to the still-water periods of the wooden screw-frigates of the older type and the converted ironclads. Extraordinary conditions would, on the Other hand, be required to produce waves having periods double the still-water periods now commonly given to the largest war-ships armoured and unarmoured ; for these waves would be from 1200 to 1500 feet in length— sizes that have been noted, but are not often encountered. Before such waves could have reached these enormous dimensions, they would probably have passed through a condition resembling that of the ordinary storm wave; and although, in becoming degraded, they may lose in their lengths much more slowly than they do in their heights, yet they may once more, before chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 245 dying out, approach the lengths and periods of the ordinary storm wave, being less steep than that wave when fully grown. It appears probable, therefore, that the ship of long period (say 7 to 9 seconds) will much less frequently fall in with waves synchronizing with her own natural period than will the vessel of shorter period (say 4 to 6 seconds) ; and when these large waves are encountered, their chance of continuance is much less than that of smaller waves ; so that on both sides the slower-moving ship gains, when rolling passively in the trough of the sea. Changes of course and speed of the ship relatively to the waves, • as before explained, affect the relation between the periods, and may either destroy or produce the critical condition of synchronism. But this is equally true of both classes of ship, and as long as they remain under control, all ships may have their behaviour largely influenced by such changes, whether their period be long or short. When synchronism is the result of obliquity of course relatively to the waves, it implies the retention of control over the vessel by her commander ; for when she becomes unmanageable, a vessel falls off into the trough of the sea. Hence such synchronism in the case of vessels of naturally long period may be easily avoided by change of course ; for them rolling passively broadside-on to the longest, waves of ordinary occurrence is not the worst condition (see previous case of the Devastation). On the contrary, the vessels of shorter, period would occupy their worst position relatively to such waves when rolling passively in the trough of the sea. In short, syn- chronism of periods usually results only from obliquity of course in. the vessels of long period; it can only be avoided in storms of average severity by obliquity of course in the quicker-moving; ships. One other important point of difference between very long waves and ordinary large storm waves is the much less comparative steep- ness of the former. The fact was illustrated in the previous chapter ; its bearing upon the behaviour of ships will be obvious if the previous remarks on the influence of the maximum wave slope are recalled to mind. It has been shown that the upper limit attained during rolling motion is very largely governed by that slope, as well as by the ratio of the periods. Hence, for a certain fixed ratio of periods, that ship will fare best which encounters the flattest and longest waves. Probably few waves having the large periods of 13 to 16 seconds have slopes exceeding 4 or 5 degrees ; whereas waves having periods of 8 or 10 seconds have been observed to slope 9 or 10 degrees to the horizon. Moreover, when the condition of syn- chronism of periods results from the oblique motion of a ship relatively to waves, that obliquity produces a virtual reduction of -4 6 NAVAL ARCHITECTURE. [chap. vi. the wave slope, and thus favours ships of long period when rolling among ordinary storm waves. Third. It appears from the investigation of unresisted rolling that vessels having very quick periods, say 3 seconds or less for a single roll, fare better among ordinary large storm waves than vessels having periods of 4 to 6 seconds. The tendency in these very quick-moving vessels is to acquire a fixed range of oscillation, keeping their decks approximately parallel to the effective wave slope, as described for the little raft in p. 200. As examples, the deep-sea fishing-boats used off the Dutch coast at Scheveningen may be named ; and amongst war-ships, the American monitor type. It is reported of the Miantonomoh, which crossed the Atlantic in 1866, with a height of upper deck above water of only 3 feet, that she rolled but moderately in heavy weather, and shipped very little water on her low deck, even when broadside-on to large waves, the water which did come on the deck on the weather side usually passing off again on the same side as that it broke over. This is very good evidence that the motions of the monitor were so quick relatively to the wave motion that her deck was kept approximatelv parallel to the surface. Obviously such a vessel would not be a steady gun-platform, as the range of her oscillation might be con- siderable, being governed by the wave slope. For instance, if the Miantonomoh were placed broadside-on to Atlantic storm waves, 600 feet long and 30 feet high, the maximum slope of the wave would be about 9 degrees, and its period about 11 seconds. Once in every 5£ seconds (the half-wave period), therefore, if the ship kept pace with the wave, she would really swing through a total arc of 18 degrees — 9 degrees on either side of the vertical, although to an observer on board, owing to causes explained in the preceding chapter, she might seem to continue nearly upright. The wave period is about twice the natural period for a double roll of the monitor. In other words, while the wave normal or virtual upright in 5£ seconds completed a single set of motions between the hollow and the crest, the monitor could move twice as quickly, and might therefore keep her deck nearly parallel to the surface. When this quickness of motion is obtained by the adoption of great beam a vessel has the further advantage (explained above) of a very flat effective wave-slope, so that her range of oscillation may be very limited even among large waves. The Kussian circular ironclads and the Livadia are examples of this class. They are reported to be wonderfully steady; and in exceedingly heavy weather in the Bay of Biscay, the maximum roll of the Livadia is stated to have been only 4 degrees. Somewhat different conditions hold in the cases of small sea- chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 247 going vessels, for which the still-water periods are made short by the smallness of their moment of inertia, and the necessity for retain- ing a sufficient amount of stiffness. For such vessels the effective slope is very nearly the upper surface of the waves, and their range of oscillation among large waves is practically determined by the wave-slope. Amongst smaller waves, approaching the condition of synchronous periods, these small vessels are worse off than very broad vessels of identical period, because the effective slope for the broad vessels is so much flatter. In fact, a small vessel of 3 seconds' period among waves of about 180 feet in length, might accumulate motion and roll heavily, much as larger vessels of from 4 to 6 seconds' period have been shown to do among ordinary large Atlantic waves. The Livadia, on the contrary, with her beam of 150 feet, might remain almost free from rolling, even when her period was nearly identical with that of the waves. On the other hand it must be noted, and will be more fully illustrated hereafter, . that in these small vessels the accumulation of rolling motion may be checked by the use of bilge-keels to an extent not possible in larger vessels. Resisted Boiling among Waves.— Only a passing notice has been bestowed hitherto upon the very important effects of fluid resistance in modifying the rolling of ships among waves. This branch of the subject is, however, of great interest, and has attracted the attention of several able investigators. Although they are not agreed in all points, there are many general considerations which command universal support ; to some of these brief reference will now be made. The deductions from the hypothetical case of isochronous unre- sisted rolling, to which attention has been drawn, can be regarded only as of a qualitative and not of a quantitative character. For example, one of these deductions is that a ship rolling isochronously and unresistedly among waves having a period double her own natural period will accumulate great rolling motion, and infallibly upset. As a matter of fact, we know that, while the assumed ratio of periods leads to the production of heavy rolling, ships do not commonly, nor in any but exceptional cases, upset under the con- dition of synchronism. Although the character of the motion is well described by the deduction from the hypothetical case, its extent is not thus to be measured. Similarly, in other cases, the effect of resistance and change of period with increased arcs pf oscillation must be considered when exact measures of the range of oscillation are required, as they may be in discussing the safety of ships. The problem, therefore, resolves itself into one of correcting the deductions from the hypothetical case of isochronous unresisted 248 NAVAL ARCHITECTURE. [chap. vi. rolling, by allowing for departures from isochronism as rolling becomes heavier, and bj- the consideration of the effect of fluid resistance. In accordance with the principles explained in Chapter IV., it is possible by means of still-water rolling experiments to ascertain the amount of resistance of a snip corresponding to any assigned arc of oscillation. If the ship herself has not been rolled for that purpose, but a model or a sister ship or similar vessel has been so rolled, her coefficients of resistance may be estimated with close approximation, and the retarding effects of resistance may be deter- mined. This is true within the limits of oscillation reached by the still-water experiments, say 10 or 15 degrees on each side of the vertical, and in high-sided ships of ordinary form the limits may probably be extended. In fact, it may be assumed that the coefficients of resistance for most ships are, or may be ascertained by rolling experiments, for inclinations as great as are likely to be reached by the same ships when rolling in a seaway, in all but exceptional circumstances. If a vessel rolls through a certain arc amongst waves, it appears reasonable to suppose that the effect of resistance will be practically the same as that experienced by the ship when rolling through an equal arc in still water. The intrusion of the vessel into the wave, as already remarked, must somewhat modify the internal molecular forces, and she must sustain certain reactions, but for practical purposes these may be disregarded. Resistance is always a retarding force ; in still water it tends to extinguish oscillation ; amongst waves it tends to limit the maximum range attained by the oscillating ship. This may be well seen in the critical case of synchronism; where a ship rolling unresistedly would have a definite addition made to her oscillation by the passage of each wave. The wave impulse may be measured by the added oscillation ; the dynamical stability corresponding to the increased range expressing the " energy " of the wave impulse. At first the oscillations are of such moderate extent that the angular velocity is small, and the wave impulse more than overcomes the effect of the resistance ; the rolling becoming heavier. As it becomes heavier, so does the angular velocity increase, and with it the resistance. At length, therefore, the resistance will have increased so much as to balance the increase of dynamical stability corresponding to the wave impulse — then the growth of oscillation ceases. As successive waves pass the ship after this result is attained, they each deliver their impulse as before, but their action is absorbed in counteracting the tendency of the resistance to retard and degrade the oscillations. When a ship is rolling "permanently" amongst waves, her chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 249 oscillations having a fixed range and period, a similar balance will probably have been established between the wave impulse and the resistance ; and here also the actual limit of range will fall below the theoretical limit given by the formula for unresisted permanent rolling on p. 236. The influence of resistance may, in this case, be viewed as similar to that of a reduction in the steepness of the waves ; this diminished slope taking the place of what has been termed the " effective slope " for unresisted rolling. Assuming that the coefficients of resistance for a ship have been determined experimentally, and that the curve of stability has been constructed, it is possible to trace her behaviour among waves of any selected form by means of the process of "graphic integration," introduced by the late Mr. Froude. This process must be regarded as the most valuable means yet suggested for approximating to the maximum rolling to which a ship is likely to be subjected in a seaway, and for pronouncing upon her safety against or liability to capsizing. It has already been applied in certain critical cases, and its accuracy has been confirmed by comparisons of the results obtained by its use with the actual behaviour of ships.* No detailed descrip- tion of the process can be given here, but it may be interesting to .give an illustration of its application. Fig. 94 contains the result FIG. 94. •of an investigation made for H.M.S. Endymion when rolling, with no sail set, among waves 512 feet long and 22 feet high. On the base-line AB, abscissae measurements correspond to time reckoned from some selected epoch. Any ordinate of the curve of "wave slope" shows the slope of the effective wave surface to the horizon at the Instant fixed by the corresponding abscissa. Similarly any ordinate •of the curve of " inclination of ship " shows the angle which her masts * For an example of these com- parisons see the appendix to the Eeport of the Inflexible Committee {Parlia- mentary Paper C-1917 of 1878) ; and for a detailed account of the process of graphic integration, see the Transactions of the Institution of Naval Architects for 1875 and 1881. 250 NAVAL ARCHITECTURE. [chap. VI. make with the vertical at the corresponding time. Hence it follows that the intercepts, or lengths of ordinate, between the curves of inclination and wave slope show for each instant the angle of inclina- tion of the masts of the ship relatively to the normal to the wave slope, which angle, as previously explained, governs the virtual righting moment, and enables an opinion to be formed as to the stability or instability of a ship. The " curve of force " in Fig. 94 has ordinates representing successive values of the moment of the impressed forces acting on the ship. For example, in the case under consideration, the moment of the impressed forces at any time includes the instantaneous righting moment and the instantaneous moment of resistance. During certain parts of the motion of the vessel the instantaneous risrhtinsr moment tends to add to her angular velocity, while the moment of resistance tends to diminish it ; the corresponding ordinates of the force curve then represent the differences between the moments. During other parts of the motion the righting moment, as well as the moment of resistance, tends to retard the angular velocity ; and the corresponding ordinates of the force curve represents the sums of the moments. In building up the force curve it is necessary to know, therefore, instant by instant the inclination of the masts of the ship to the wave-normal and her angular velocity, because the instantaneous righting moment depends upon that inclination, while the moment of resistance is governed by the angular velocity. The process is really one of " trial and error," but each step admits of a complete check and verification in con- sequence of the inter-dependency of the curve of inclinations and the force curve. In practice, the work of graphic integration can be rapidly performed, and after certain preliminaries have been arranged in any particular case, the remaining steps are very simple. It will be understood that the process of graphic integration is based on strict mathematical reasoning ; but it surpasses any purely mathematical investigation in its inclusion of the effect of fluid resistance, and in its scope of application. By means of this process the rolling of a ship in the most confused seaway can be approxi- mated to, the appropriate curve of wave-slope being supposed to be known. The behaviour of the same ship under different conditions of sea can be compared ; the probable effects of changes in bilge- keels, etc., can be investigated ; and the probable rolling of different types under identical conditions of sea can be contrasted. It is greatly to be desired that comparisons might be multiplied between the observed behaviour of ships and their probable behaviour deduced by means of graphic integration. Such comparisons would doubtless have the effect of still further establishing the great practical utility of the process ; and they would probably throw much light upon chap, vi.] OSCILLA TIONS OF SHIPS AMONG WA VES. 25 1 certain obscure questions, particularly upon those relating to the effective wave slope. Another method of investigation for the maximum rolling of ships among waves, including the effect of fluid resistance, has been proposed by M. Bertin, and deserves mention, although it does not compare, in our judgment, with the process of graphic integration. Starting from the fundamental conception that the heaviest rolling will take place when a ship is exposed to the action of waves whose period equals the still-water period of the ship for a double roll, M. Bertin considers that, apart from the action of resistance, the passage of each half-wave would add to the amplitude of the oscillation of the ship an angle equal to the maximum slope of the effective wave surface." This estimate, it may be observed, differs somewhat from that mentioned on p. 234. Even when resistance is operating the wave form tends to add to the amplitude of successive rolls, and will do so until a range of oscillation is reached, for which the work done in overcoming the moment of resistance balances the work (or dynamical stability) corresponding to the increase of amplitude which the passage of the wave tends to create. Using M. Bertin's notation : — 9 = the maximum slope of the effective wave surface ; = the maximum amplitude of rolling ; N = coefficient of resistance deduced from still-water rolling experiments. Then, as explained on p. 173, M. Bertin would write — Aip = loss of range due to resistance = N<£ 2 ; and on the foregoing assumptrons he would also write — Af = 9; so that — ]Sty 2 = 9. " Supposing that the quantities neglected in the calculation affect the values of $ in very nearly the same manner for all ships," M. Bertin finally proposes to introduce a constant into this last equa- tion, writing it — IV = ¥ . 9. In his examples this constant is usually omitted. For instance, La Galissoniere has a value of N = - 0075, and when among syn- chronizing waves, for which 9 = 9°, her maximum roll is given by the equation — V — =34-7°. N The reciprocal of \/N M. Bertin terms the coefficient d'ecclisite. 252 NAVAL ARCHITECTURE. [chap. vr. la the examples given by him it varies from S or 9 in the smaller classes of nnarmoured war-ships, up to 11 to 15 in armoured ships. Roughly speaking, if 9 degrees is a fair average slope for ocean waves of large dimensions, the maximum roll obtained from the above formula would be three times the coefficient d'ecelisitS. From this brief description it will be observed that M. Bertin here confines attention to the critical case of synchronism, and does not attempt the discussion of the limits of rolling likely to be reached by a ship among waves of other periods. He is careful to note the fact that this critical case is less likely to occur as the still-water periods of ships are lengthened; and that for certain classes of war-ships the periods are so long that they are never likely to encounter synchronizing waves. In order to meet such cases of departure from synchronism M. Bertin has proposed an empirical formula, which need not be reproduced.* The broad practical deduction from all these investigations is that increase in the fluid resistance to the rolling of a ship tends to limit her maximum oscillations among waves. It has already been explained (see Chapter IT.) that in the use of bilge-keels is found one of the most convenient and effective methods of influencing the resistance to rolling, and that their employment is most effective in small ships of short period. Formerly some high authorities in the science of naval architecture opposed the use of bilge-keels ; but extended experience has placed the matter beyond doubt, and it may be well to quote a few facts in support of this opinion. The Admiralty Committee on Designs took evidence in 1871 as to the advantages or otherwise of bilge-keels; this evidence was not unanimously favourable to the use of such keels, but its general tenour was so. Some of the Indian troopships had been fitted with deep bilge-keels at that time, and the reports of their effect on the behaviour of the ships were most definite. The captain of the Serapis reported that the bilge-keels, having been tried under all conditions of wind and sea, had proved a perfect success, and added, " I can confidently say her rolling has been lessened 10 degrees each way." As regarded the Crocodile, no similarly severe tests had at that time been made, but the opinion was expressed that " the rolling had been much checked by the bilge-pieces," the ship having often rolled heavily before they were fitted, and being considered "re- markably steady " afterwards. Mr. Froude also came forward with the reports of his experiments on models, and strongly recommended the use of deep bilge-keels— a recommendation which was endorsed * For full details of these investigations, see " Les Vasnies et le Eoulis." Paris : 1877. chap, vr.] OSCILLATIONS OF SHIPS AMONG WAVES. 253 by the committee in their report. These experiments were made at Spithead with the same model of the Devastation as had previously been used to determine the effects of different depths of bilge-keels upon still-water oscillations.* At the time considerable doubt was entertained in some quarters as to the safety of the Devastation ; and it was intended to try the model amongst waves having approxi- mately the same period as its own for a double roll, in order to obtain a verification of the theoretical investigations of the probable behaviour of the ship when similarly circumstanced. Waves were found having the desired period, but they proved to be propor- tionately much steeper than any waves would be that would synchronize with the double period of the ship. Hence the trials became simply a test of the relative merits of the different bilge- keels, and in no sense a representation of the probable behaviour of the ship. The results were found to be as follows : — Condition of model. Maximum angle attained. With 6 feet bilge-keel on each side . ,, teet „ ,, ... 5 degrees. 13* „ Model upset. The deeper bilge-keels, therefore, proved very influential in limiting the range of oscillation, the waves remaining of the same character, and the variations in the depths of the keels being the only changes made during the trials. The most complete evidence of the usefulness of bilge-keels in limiting the rolling of ships in a seaway is that afforded by the experiments made off Plymouth in 1872. Two sloops, the Greyhound and Perseus, had been placed by the Admiralty at the disposal of Mr. Froude for this purpose; the Greyhound was fitted with temporary bilge-keels about 3£ feet deep, which were not applied to the Perseus. So far as external form and dimensions were con- cerned, the two vessels were very similar ; and by means of ballast they were made to have practically the same draught of water and still-water period ; the latter being about 4 seconds for a single roll. With the one exception of the bilge-keels, the conditions influencing the behaviour of the two ships were thus made as nearly as possible identical; and their comparative rolling, when exposed simul- taneously to the same series of waves, necessarily afforded a measure of the effect of the bilge-keels. When the trials were made, the See the accounts of these experiments at p. 176. 254 NAVAL ARCHITECTURE. [chap. vi. waxes were of moderate length, and from 4 to 5 seconds' period ; tie two vessels were towed out and placed broadside-on to the waves, in immediate neighbourhood, but not so close to one another as to favour one by any shelter from the other. Their simultaneous rolling was then observed, and the Perseus was found to reach a maximum roll about twice as great as that for the Greyhound ; the proportions for the mean oscillations of the two ships being much the same as those of the maximum. Thus, taking twenty successive rolls, the mean for the Greyhound was less than 6 degrees, whereas that for the Perseus was 11 degrees ; the maximum inclination of the Greyhound during this period was about 7 degrees, that for the Perseus about 16 degrees. Comment upon these facts is needless. The accidental loss of a portion of one of the temporary bilge- keels attached to the Greyhound at the end of these trials furnished an unlooked-for illustration of their beneficial effect. Such a loss would not be probable in a vessel with permanent bilge-keels, but the deep bilge-keels in the Greyhound, being fitted for experimental purposes only, were not very strongly secured to the hull, and a portion of one gave way. Its loss was not known until afterwards, but it was noticed that the behaviour of the ship had sustained a sudden change, the rolling being more heavy than before ; and the cause could not be detected until the detached portion of the bilge- keel was seen floating alongside. This careful and conclusive series of experiments does not, of course, fairly represent the ordinary conditions of bilge-keel resistance, the depth of the keels fitted to the Greyhound being proportionately very great indeed. But it exemplifies what may be accomplished in this direction, and the facts obtained are very valuable for the future guidance of naval architects. Circumstances may and do arise in the designing of war-ships which make it difficult, if not impossible, to associate requisite qualities with the long still-water period which theory and observation show to be favourable to steadiness. In such cases the use of bilge-keels is generally advantageous, and in ships of small size their effect may be most marked in limiting rolling. Merchant ships with periods varying greatly according to the nature and stowage of their cargoes may also derive benefit in all conditions from bilge-keels. In making these lengthy references to bilge-keel resistance, it is not intended to pass by the fact that the form of the immersed part of a ship and the condition of her bottom very considerably affect the aggregate resistance. But all these conditions are included in the determination of the coefficients of resistance to rolling ; and, moreover, the form of a ship is determined by the naval architect mainly with reference to its stability, carrying power, and propulsion, chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 255 not with reference to the increase of the resistance to rolling. The latter is a subordinate feature of the design, and is best effected by leaving the under-water form of the ship herself unaltered, and simply adding bilge-keels in cases where the size and inertia of the ship are such as to make them useful, and when the conditions of service of the ship, the sizes of the docks she has to enter, or other special circumstances permit their use. Certain classes of ships present singular features considerably affecting their behaviour at sea. Vessels with projecting armour, like the American monitors, or the Glatton in the Royal Navy, or the Devastation class as they were originally designed, really possess in these projections virtual side-keels of great efficiency in adding to the resistance to rolling. The records of the behaviour of American monitors prove that the projections had a steadying effect. There was, however, the drawback that the alternate emersion and im- mersion of the armour shelf brought considerable shocks or blows upon the under side of the projecting armour, tending to shake and distress the fastenings of these singularly constructed vessels. Similar shocks were experienced in the Devastation when rolling in a seaway, although the vastly different construction of the armoured side prevented any injurious effects similar to those said to have been experienced in the American monitors. After several trials it was decided to " fill-in " the projection of the armour shelf in the Devastation in order to avoid the shocks ; the reduction of the resistance being accepted when it had been ascertained beyond question that the vessel was steady and well behaved. Low freeboard also, as previously explained, develops deck resistance by the immersion and emersion of the one or other side that accompanies moderate angles of rolling ; and observations of the behaviour of monitors amongst waves have clearly shown that conditions similar to those of still-water obtain also for rolling amongst waves. In vessels of ordinary forms and good freeboard nothing similar to this deck resistance exists ; and therefore in monitors the use of bilge-keels is not so necessary as it is in ordinary vessels. The extinctive effect of free water contained in specially con- structed chambers has been discussed on p. 180, when dealing with rolling in still water. Observations made at sea in the Inflexible and Colossus show that such water-chambers, even of moderate size, have a sensible steadying effect. In 1882, observations were made of the behaviour of the Inflexible off Alexandria when rolling in the trough of the sea, first with the water-chamber empty, and afterwards with different weights of water, varying from 40 tons to 120 tons. From an analysis of the records, it has been estimated that when the water- 256 NAVAL ARCHITECTURE. [CHAP. vi. chamber was about half full, the mean angle of roll was reduced by 20 to 25 per cent., as compared with the mean angle when the chamber was empty.* In 1886, a series of observations was made in the Colossus under various conditions of sea. It was found on one occasion that, with the water-chamber empty, the ship made 121 rolls in 10 minutes; the mean angle of oscillation was 117 degrees, the maximum o-± - 5 degrees, and the mininrum 1"5 degrees. With 100 tons of water in the chamber, 125 rolls were made in 10 minutes ; the mean angle rolled through was 10 - 4 degrees, the maximum was 25'5 degrees, and the •mi-nim iTm 1 degree. The general conclusion reached was that free water, properly adjusted in depth, had a con- siderable effect on the rolling, particularly during the heavier rolls, and that the rolling was a little quickened. Heavy shocks were delivered on the deck forming the top of the water-chamber, and also on the sides. No injury was done to the structure, but the shocks were disagreeable to those on board. Experience has shown also that in these broad, stiff ships the rolling is never excessive, although it is very common. For example, the Inflexible, on her passage across the Bay of Biscay in 1881, encountered heavy weather, including waves from 20 to 25 feet high, and nearly co-periodic with her rolling, yet she never rolled more than 10 or 11 degrees to the vertical. In view of this and similar experience in other vessels, the use of water-chambers has practically ceased in the Royal Navy. Allusion has already been made (on p. 182) to the ingenious apparatus devised by Mr. Thornycroft for steadying ships in a sea- way by means of a movable weight, and to the results obtained with a yacht in rough water. It may be added that a pendulum of very short period practically determines the instantaneous direction of the normal to the effective wave slope, or virtual upright, when placed in a suitable position on the vessel. The motions of this pendulum, by means of most ingenious electrical arrangements, control the move- ments of the valves of a hydraulic ram, and secure the prompt and accurate movements of the weight in a manner that checks the tendency to roll due to the variations in the wave slope. Boiling of Sailing Ships. — Up to this point attention has been confined to the rolling of ships among waves when no sail is set ; it is now proposed to attempt an explanation of the still more difficult case where a ship under sail is exposed to the action of the wind and waves. This explanation must necessarily be brief, and the avoidance of mathematical language must make it even more imperfect than it would otherwise have been. The reader desirous of following out * See Mr.Watts's paper in the Transactions of the Institution of Naval Architects for 1883. chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 257 the subject may refer to a paper contributed by the author to the Transactions of the Institution of Naval Architects for 1881, which is as full as the present state of our knowledge seems to permit, and which summarizes both what is known and what yet requires to be determined. When a ship with sail set is rolling amongst waves, the forces operating upon her at each instant include all those which would be in operation if there were no sail set ; and, in addition, the moment of the wind pressure on the sails, as well as the moment of the resistance of the air to the oscillatory motions of the sails. Our knowledge of the laws which govern the pressure of the wind on the sails is very imperfect ; a brief resume of that knowledge will be found in Chapter XII. Exact estimates cannot be made, therefore, for the moment of the wind pressure at any instant, even when the inclination of the masts to the vertical, the instantaneous angular velocity of the sails, and the direction and velocity of the wind are known. But, while this is true, certain general principles may be established. For example, as a ship rolls to windward the angular velocity of the sails increases the relative velocity of the wind past the sails, and this increase is greatest on the sail-area which is highest above water. Consequently, during this roll to windward, the moment of the pressure of the wind on the sails is increased, not merely by .the greater relative velocity of the wind on the sails, but by the higher position of the centre of pressure. Conversely, during the roll to leeward at any instant the inclining moment of the wind pressure is decreased, and may be very largely decreased, by the angular velocity of the sails. Any attempt at exact investigation must take account, therefore, of these variations in the moment of the wind pressure. Account must also be taken of the effect which the heaving motion produces upon the instantaneous righting moment which the ship can oppose to the inclining moment of the wind pressure. It has been shown (on p. 201) that a ship accompanying the motion of the waves, and heaving up and down as they pass under her, is sub- jected to accelerating forces which alternately tend to increase and decrease her " virtual weight." Now, the " instantaneous righting moment " is equal to the product of that virtual weight into the ordinate of the curve of stability corresponding to the instantaneous inclination of the masts to the normal to the effective wave slope. An illustration of this statement is given in Fig. 95. NNx shows the instantaneous direction of the normal (that is, the " virtual upright ")• The masts are inclined to the normal at an angle of 37 degrees. The instantaneous righting moment equals the product of the " virtual weight " (allowing for heaving) into the arm of the righting lever 258 NAVAL ARCHITECTURE. [chap. vi. measured on the curve of stability for 37 degrees inclination. When the ship floats on the upper half of the waves her virtual weight is less than the true weight, and may be as much as 20 per cent. less. Consequently her instantaneous righting moment on the upper half of the waves is correspondingly decreased. And since the force of the wind is not similarly affected by the wave motion, it must during this time have a greater inclining effect upon the vessel than the same force of the wind would have in still water. It is a matter of common observation, which the foregoing remarks may help to explain, that boats and small craft are most frequently capsized when floating on wave crests. Of course, on the lower half of the waves, from mid-height to hollow, the virtual weights and instan- taneous righting moments are greater than the corresponding values in still water. Fig. 95 also serves to illustrate another point of importance, viz. that on the supposition that the wind acts horizontally, the moment of the wind pressure must be estimated in terms of the inclination of the masts to the vertical at each instant. Whereas, in consequence „ of the variations in the «7 J\ direction of fluid pressure, **> — *■ J A J the stability or instability ^z^jbLd of the ship must be esti- nf/y/ I FIG- 95- mated by the inclination =2fc4-*/ °f *he ma sts to the y '"virtual upright" NN\. / In Fig. 95 NY is the ver- gflfllflfffiBISlflt^ tical; the masts are in- gggg^^^^^^^^^^g^^^^^^^P clined 27 degrees to it, ^ ~~ but the wave slope adds 10 degrees to this inclina- tion, and makes the angle by which safety or danger of capsizing is to be reckoned 37 degrees. Remembering what has been said in Chapter V. of the slopes of waves, it is desirable, when considering the sufficiency of the range of the curve of stability for any vessel, to regard it as abridged by 8 or 10 degrees in order to allow for the influence of wave slope upon the virtual inclination to the position of instantaneous equilibriuni. A ship with sail power, besides having provision made for resist- ing the heave of the sea, like a mastless ship, must be capable of resisting the heeling action of a steady force of wind continually applied, as well as the impulsive action of gusts and squalls. For all these reasons a rigged ship requires a greater range of stability than a vessel of the mastless type, and a glance at the curves of the typical ships in Fig. 60 will show that in all the types of rigged chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 259 war-ships therein represented, except the ill-fated Captain, this condition was complied with. In her case, however, the range of stability was very moderate : her initial stability not great, and her sail-spread large for an ironclad, all of which causes contributed to her capsizing. Without discussing the circumstances further, it may be interesting to make use of the ship for purposes of illustra- tion, since we have very full published accounts of her qualities. Suppose the Captain, with no sail set, to have floated on a wave 400 feet long and 22 feet high, having a maximum surface slope of about 10 degrees. The total range of stability for the ship (see curve 10 in Fig. 60) being 54 degrees, if the allowance of 10 degrees be made for wave slope, there will remain 44 degrees, measuring the inclination to the vertical, which the ship would have to reach before she became unstable. Under the assumed conditions with sails furled, there would have been little or no risk of her reaching such an inclination, the Captain having proved herself to be a well- behaved ship in a seaway. Next, take the case where sail is set, and the ship is acted upon by a steady pressure of wind which in still water would keep her at a steady angle of heel, say, of 10 degrees ; this is within the truth, as it appears from the official reports that, on the day before she was lost, the Captain heeled from 10 to 14 degrees under canvas. We have already discussed the case where the Captain is sailing at a steady heel of 10 degrees in still water, and Fig. 76, p. 186, illus- trates it. CD is the " wind curve," indicating the inclining effect of the wind on the sails for different angles of heel ; and if by any means the vessel, which has been sailing at a heel of 10 degrees, is carried over to a greater inclination, the wind will follow, and always absorb that part of the area OCDDiO of the curve of stability lying between the line CD and the axis of abscissas (or " base-line ") ODj. It will be observed that the wind curve cuts the curve of stability at an inclination of 47 degrees, marked by the ordinate DDj ; so that the same force of wind that will steadily heel the ship 10 degrees will also hold her at 47 degrees, where she will be on the verge of capsizing. The effective range of the curve of stability, excluding the part absorbed by the steady force of wind, is therefore about 37 degrees only, that being the limit of inclination to the vertical which the ship can reach without being blown over when floating at mid-height on the wave. The decrease of 17 degrees from the total range, thus shown to be requisite to provide for the steady action of the wind, is a very serious matter. Apart from gusts and squalls, there would still be a good "provision for safety, taking into account the steadiness of the ship; but even ships reputed steady occa- sionally roll as much as this, and if the Captain had reached a 260 NAVAL ARCHITECTURE. [chap. VI. position 10 degrees beyond that indicated in Fig. 95, she would have been on the point of capsizing. With steeper wares having a greater slope, the capsizing point would be sooner reached. In Mr. Childers' minute on the loss of the Captain (pp. 56 and 57) will be found similar illustrations to the foregoing, only on waves of very exceptional steepness, 200 feet long, 23 feet high, and having a maximum slope of 20 degrees ; then, supposing the Captain to be subjected to a steady wind capable of inclining her 8 degrees in still water, it is estimated that only 21 degrees inclination to the vertical would suffice to bring her to the verge of capsizing. Reverting to Fig. 76, and taking the case of the Monarch exposed to a force of ■wind equal to that assumed to act on the Captain, it will be seen that, after providing for the steady action of the wind, there remains an available range (KW) of over 55 degrees, instead of 37 degrees, as in the Captain under identical circumstances. From these two cases it will be evident that good range in the curve of stability is of the highest importance in rigged ships. The greatest danger of capsizing results, not from the action of a steady force of wind, but from that of gusts and squalls which may strike the sails of a ship, upon which considerable rolling motion has been impressed previously by the action of the wind or waves. In Chapter IV. we have discussed the action of such gusts of wind upon sailing ships rolling in still water ; similar but much more complicated conditions hold when a ship rolling among waves is caught by a squall at the extreme of a roll to windward. Various attempts have been made to deal with this difficult problem, and to enable the naval architect to form an opinion as to the ranges of stability sufficient in various classes of rigged ships. None of these attempts can be regarded as entirely successful, nor does the nature of the case permit of its solution by exact scientific investigation. Before such an investigation can be begun certain preliminary assumptions must be made : as to the sail-spread that shall be associated with a certain force of wind, the character of the waves amongst which the ship is placed, the inclination of the masts and their angular velocity at some instant, and the force of the squall as well as the position of the ship when struck. In short, some combination of circumstances has to be assumed as the worst likely to occur, in order that an opinion may be formed as to the probability of the ship capsizing or not. From this brief statement of the case, and bearing in mind what was said above as to the imperfect knowledge we possess of the laws governing wind pressure, it will be obvious that science has not yet enabled us to discuss with certainty the behaviour of sailing ships when rolling in a seaway. The naval architect has, therefore, to resort to experience in order to appreciate fairly the influence chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 26 1 of seamanship and the relative manageability of ships and sails of different sizes. Having before him the curves of stability of sail- ing ships of various classes, and the records of their performances at sea, the designer can proceed with greater assurance in the deter- mination of the stability and sail-spread which shall be deemed sufficient in a new ship. A good range and large area of the curve of stability undoubtedly denote conditions which are very favourable to the safety of a ship against capsizing. But, in practice, such favourable conditions cannot always be secured in association with other important qualities, and a comparatively moderate range and area of curves of stability have to be considered when the question arises whether or not sufficient stability has been provided. Under these circumstances experience, and the analysis of the qualities of ships which have proved successful and safe, are of the greatest value. Sailing ships of the mercantile marine and yachts usually have great range of stability when fully laden, for the reasons given in Chapter III. Eigged war-ships, on the other hand, frequently have moderate range of stability. So far as experience enables an opinion to be formed, it appears that in the smaller classes of seagoing war- ships with steam as well as sail power, a range of 60 to 70 degrees in the curve of stability suffices for safety ; in the larger classes, above corvettes, the corresponding range is about 70 to 80 degrees. It will be understood that these values are based upon experience, and they probably provide a reasonable margin of safety. The provision of a large range of stability cannot be regarded, however, as a guarantee against accident apart from proper management and good seamanship. Examples are not wanting of the truth of this state- ment, and one of the most forcible is that of the merchant sailing ship Stuart Hahnemann. Her curve of stability is marked 8 in Fig. 63, p. 138 ; the angle of maximum stability exceeded 40 degrees, and the range exceeded 80 degrees. This vessel was thrown on her beam ends and sank ; the court of inquiry found that she was well built and perfectly equipped, her loss being attributed to the too long continued use of a heavy press of sail, so that when the wind increased the sail could not be taken in. Although it is impossible in the present state of knowledge to predict the worst possible combination of circumstances to which a sailing ship may be liable, it is possible to trace her behaviour, with fair approximation to accuracy, when a certain set of conditions has been selected. This can be done by means of an adaptation of the process of graphic integration to which reference was previously made. An example of the results obtained in this manner is given in Fig. 96. The general construction resembles that described for 262 XAVAL ARCHITECTURE. [chap. VI. Fig. 94. Measurements along the base-line represent time. Ordinates of the curve of " wave slope " represent the slope of the effective wave surface to the horizon at the corresponding time. At the instant from which time is counted, the ship is assumed to have her masts inclined 20 degrees to the windward side of the vertical, to float at the mid-height of waves having a niaxi- FIG. 96. mum slope of 9 degrees, and to have no angular motion. Her in- stantaneous inclination to the wave normal is therefore 29 degrees. It is then supposed that she is struck by a squall of wind, having such a force as would hold her at a steady heel of 10 degrees in still water. This suddenly applied wind pressure follows her up as she rolls away to leeward, and at any instant the process of graphic integration takes accoimt of the following forces as acting upon her : (1) The moment of wind pressure on the sails, corrected for the angular velocity (as described on p. 257) ; (2) the moment of the resistance offered by the water to the motion of the ship; (3) the instantaneous righting moment, corrected for heaving. The resultant of these three moments at any instant appears as the ordinate of the " curve of force " in Fig. 96 ; and the ordinate for the same instant of the curve of inclination shows the inclination of the masts to the vertical. Under these assumptions the vessel, which started from 20 degrees to windward, is driven over by the squall to 24 degrees to the leeward side of the vertical. If allowance were not made for the reduction in moment of wind pressure due to the motion of the sails away from the wind, then, starting from the same inclination to windward, the squall would drive the vessel over to 34 degrees to leeward. Further, were the effect of the fluid re- sistance neglected, the angle reached to leeward of the vertical would be 45 degrees. These figures are suggestive if not strictly accurate. They show how impossible it is to pronounce upon the maximum rolling of a ship without taking account of all the circumstances which may influence that behaviour. Finally, on this part of the subject, reference must be made to the steadying effect which sail exercises upon a ship. This effect is a matter of common observation, and may be very simply explained. If a ship with sail set were rolling in a calm, the air would oppose great resistance to the oscillatory movement of the sails, and the rolling would be rapidly extinguished ; this case is parallel to that described for water resistance in Chapter IV. When a ship is set chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 263 rolling by the action of the sea, while the wind blows uniformly, it is difficult to estimate separately the effects of wind pressure and the air resistance to rolling. But when squalls or gusts of wind act intermittently on a vessel, the influence of air resistance may become most important. Suppose, for example, the wind to lull when a ship has reached her extreme roll to leeward; then, on the return roll to windward, both air resistance and water resistance are tending to check the motion and lessen the extreme angle of roll to wind- ward. So that if the squall strikes her again when the ship is at the extreme of the roll to windward, it finds the ship much less inclined to the vertical than she would be if air resistance were not operative. The following lurch to leeward would consequently be much less heavy. Pitching and 'Scendmg. — The longitudinal oscillations of pitching and 'scending experienced by ships among waves must be briefly considered before concluding ^this chapter. In still water these longitudinal oscillations do not occur under the conditions of actual service ; and it is difficult, even for experimental purposes, to establish such oscillations, because of the great longitudinal stability of ships. On this account we have little definite information respecting still- water periods for pitching, or the "coefficients of resistance" for longitudinal oscillations. One or two small ships of shallow draught and full form have been experimented with, the period of longitudinal oscillation having been found to have been about three-fourths the period of transverse oscillation. Other observations made at sea indicate that in many cases the period of pitching oscillations lies between one-half and two-thirds the period for rolling. In some cases it may fall as low as one-third the period for rolling, and in the Russian circular ships the two periods must be nearly equal. The formula for the period of unresisted pitching may be expressed in the same form as that given on p. 154 for the period of unresisted rolling. Only the height m must be made equal to the height of the longitudinal metacentre above the centre of gravity ; and the radius of gyration h must be estimated by multiplying each element of weight by the square of its distance from the transverse axis pass- ing through the centre of gravity. It may be taken for granted that, as a rule, the effect upon the period of the great height of the longitudinal metacentre above the centre of gravity of a ship more than counterbalances the effect of the increased moment of inertia for longitudinal oscillations ; whence it follows that the period for pitching is usually considerably less than that for rolling. Calcula- tions for the period of unresisted pitching have been made in a few instances, but they have little practical importance. The existence of waves supplies a disturbing force capable of 264 NAVAL ARCHITECTURE. [chap. VI. setting up longitudinal oscillations ; this is a matter of fact, and it is easily accounted for. Suppose a snip to be placed bow-on to an advancing wave ; its slope will at the outset rise upon the foremost part of the ship above the water-level in still water; and perhaps simultaneously at the after part of the ship the wave profile may fall below the still-water level. The obvious tendency of the bow will be to rise under the action of the surplus buoyancy at that part, the stern falling relatively ; that is to say, a 'scending motion will be established, and its initial rate will depend upon the still-water period for longitudinal oscillations. After the wave-crest has passed the bow of the ship, supposing for the instant that the wave is long as com- pared with the length of the ship, there will probably be a reversal of the conditions. The wave profile on the back slope of the wave would probably fall below the still-water load-line at the bow, and this excess of weight over buoyancy would tend to check 'scending and cause pitching to begin. The motion thus created by the passage of the first wave would of course be modified by the passage of suc- ceeding waves in the series ; and in the end there would probably be established a certain phase of pitching and 'scending oscillations, corresponding in character to the phases of rolling described above, and largely influenced by the ratio of the apparent wave period to the natural period for still-water longitudinal oscillations. This is the simplest case that can be chosen. It by no means represents all the conditions of the problem ; but it shows how the existence of waves and their passage past a ship lead to disturbances of the conditions of equilibrium existing in still water, and to the creation of accelerating forces due to the excess or defect of buoyancy. No account has here been taken of the variations in the direction and magnitude of the fluid pressure at different parts of the wave ; although these variations would undoubtedly produce some modification in the behaviour of the ship, the modification would not be likely to change the character of the motion, with which alone we are at present concerned. This illustration also shows that the following are the chief causes influencing the pitching and 'scending of ships: (1) the relative lengths of the waves and the ships ; (2) the relation between the natural period (for longitudinal oscillations) of the ship and the apparent period of the waves, this apparent period being influenced by the course and speed of the ship in the manner previously ex- plained ; (3) the form of the wave profile, i.e. its steepness ; (4) the form of the ship, especially near the bow and stern, in the neigh- bourhood of the still-water load-line, this form being influential in determining the amounts of the excesses or defects of buoyancy cor- responding to the departure of the wave profile from coincidence chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 265 with that line ; (5) the longitudinal distribution of the weights, determining the moment of inertia. In addition, fluid resistance exercises a most important influence in limiting the range of the oscillations. This resistance is governed by the form of the ship, and particularly by that of the extremities, where parts lying above the still-water load-line are immersed more or less as the ship pitches and 'scends, and therefore contribute to the resistance. This summary requires but few comments. It is obvious that, when the length of a ship is great as compared with the wave length, there is no probability of extensive pitching motions being produced. The Great Eastern, for example, with her length of 680 feet, could span from crest to crest even on the very large Atlantic storm waves observed by Dr. Scoresby ; and on storm waves of common occurrence she might be floated simultaneously on three of them. Even less imposing structures, such as the largest ships of the Eoyal Navy, with lengths of 300 to 400 feet, are long as compared with ordinary storm waves, and therefore are not likely, as a rule, to accumulate large angles of pitching — a conclusion borne out by experience. Small vessels may, of course, fall in with waves which are long relatively to their own lengths ; but in such cases it is a common observation that the vessels " float like ducks on the water " — that is to say, their natural periods for longitudinal oscillations are so small as compared with the wave period that they can very closely accompany the motions of those parts of the wave slope upon which they float. In fact, their condition furnishes a parallel to the case of the little raft in Fig. 83, except that the raft follows the upper surface of the wave, whereas the ship, stretching over a considerable length on the wave, and penetrating to some depth in it, does not follow the upper surface, but, as it were, averages the slope of a portion of a subsurface corresponding to her own length. According to theory, the case of pitching is best dealt with in a manner similar to that adopted for rolling motions. The ship is supposed at every instant to have a tendency to move towards an instantaneous position of equilibrium which is a normal to her " effec- tive wave slope ; " but in the determination of this effective slope for longitudinal oscillations still greater difficulties are encountered than in the similar problem for rolling. One thing, however, is evident, even in the case where the length of the wave is great as compared with that of the ship, viz. that the steepness of the effective slope will be much less than the maximum slope of the upper surface, both because of the length along the wave which the ship occupies and of the depth to which she is immersed in it. Supposing her to be in the worst position, with the middle of her length at the steepest inclination of the wave, the slope of the surface to the horizon, at 266 XAVAL ARCHITECTURE. [chap. vi. the places occupied by the bow and stem, will be much less than the maximum slope ; and, further, as remarked previously, all subsurface trochoids in the wave are less steep than the upper surface. The effective slope has to be the resultant of these varying condi- tions, and must therefore be much less steep than the maximum surface slope. But even accepting this conclusion, and assuming an effective slope, no practical deductions of importance have yet been drawn from this method of viewing the question, beyond those obtained from general considerations, and stated in the preceding summary. It has been asserted that in large ships extreme pitching is not likely to occur ; but it must be noted that even moderate angles of pitching lead to very considerable linear motions at the extremities of a long ship. For example, in the trials off Berehaven with the Devastation, Agincourt, and Sultan, it is reported that the Sultan on one occasion pitched so that the bow appeared buried very deeply in the wave, and observers on the deck of the Devastation could not determine whether the sea broke over the forecastle, which is some 30 feet above water when the ship is at rest in still water. Very similar remarks were made on another occasion respecting the Agin- court. For each degree of inclination from the upright, however, a point on the bow of the Agincourt would move vertically nearly 4 feet, and one on the bow of the Sultan about 3 feet ; so that very moderate angles of inclination in still water wordd suffice to bring the forecastle deck close to the water-level. Amongst waves, with their varying slopes into which the bow of a ship plunges, still more moderate inclinations might produce the same apparent effect. For example, the Devastation and Agincourt were tried steaming: head-on to waves from 400 to 650 feet long and from 20 to 26 feet high, the speed of the ships being about 7 knots per hour. The periods of these waves varied from 9 to 11 seconds ; their maximum slopes, from 7£ to 9 degrees. Allowing for the speed of the ships, the apparent periods of the waves varied from 7 to 9 seconds, giving apparent half- periods which probably approximated to equality with the natural period (for a single oscillation longitudinally) of the ships. It was a case, therefore, where the conditions were conducive to heavy pitching, and the results of the observations are interesting. The total arcs of oscillation for the Devastation were, on an average, 8 degrees only, that is, about 4 degrees on either side of the upright, or about one-half the maximum slope of the surface of the waves ; the maximum arc of oscillation was rather less than 12 degrees, about 6 degrees on either side of the upright, about three-fourths the maximum slope of the surface. The Agincourt pitched through rather smaller arcs than the Devastation, but, supposing her motion chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 267 to have reached the same maximum, the how would have heen im- mersed in still water ahout 20 feet helow its normal draught ; yet we are assured that a sea broke over the forecastle, which is some 10 feet higher above still water, a circumstance which is attributable to the bow having been plunged into an advancing wave-slope. These facts are mentioned in order to enforce the desirability of taking all possible precautions in estimating the extent of pitching ; so many of the attendant circumstances tending to exaggerate the apparent motion, and to deceive the observer unless he has recourse to actual measurement of the angular motion. From the foregoing remarks it will be evident that further pro- gress in knowledge of the laws which govern pitching and 'scending must be largely dependent upon actual observations made at sea in a trustworthy manner. The Admiralty instructions provide for such observations when favourable opportunities present themselves ; and this branch of the subject is one to which naval officers might devote attention with great advantage. As yet comparatively little in- formation has been recorded; and of the published observations those made by M. Bertin are the most valuable.* With the aid of «n ingeniously contrived instrument (described in Chapter VII.) M. Bertin obtained simultaneous automatic records of (1) the instan- taneous inclination of the ship to the vertical as she pitched ; and (2) the instantaneous position of the normal to the effective wave slope. His conclusions from a careful analysis of these observations may be briefly stated. With a ship head to wind and sea, among waves of sufficient length relatively to the ship to produce sensible pitching motion, and within certain limits of the ratio of speed of ship to speed of wave, all the ships for which observations were made followed the effective wave slope, just as the little raft in Fig. 83 ' follows the wave motion. Under these circumstances, as the speed was increased, but still fell within the assigned limit, the period for pitching was decreased, because this increase in speed shortened the apparent wave period ; but the angle of pitching remained nearly constant. After this limit of speed had been surpassed the ships ceased to ; follow the effective wave slope, their pitching motions falling behind instead of keeping pace with the effective slope. At certain speeds the motion of the ship dropped one-fourth of the period behind that of the effective slope ; and then the pitching was found to have the same amplitude as in the case first described. Further increase in speed and still further decrease in the apparent wave period, was found to produce much heavier pitching, and at * They are to be found in " Observa- V oscillographs double a lord de divers tions de roulis et de tangage faites avec bailments : " Cherbourg, 1878. 268 NAVAL ARCHITECTURE. [chap. vi. length led to the bows of the ships being buried so deeply in the wave slopes that the experiments were stopped. When the ships were running before the sea, and by their motion lengthening the apparent period of the waves, the case was found to be much simpler, the ships practically following the effective wave slopes. Hence, from a review of the whole of his observations, 31. Bertin concluded that the best means of reducing pitching, in the critical case where a ship is driven head to sea, is to make her natural period of pitching as short as possible, by concentrating weights amidships, and reducing the moment of inertia. This conclusion agrees with the recommendations made by experienced seamen. A commanding officer can obviously exercise considerable control over the pitching and 'scending motions of a ship by means of variations in speed and course relatively to the waves. The actual period observed for pitching motions will vary considerably for the same ship under different circumstances, and usually differ considerably from the still-water period for longitudinal oscillations. Most commonly, so far as can be seen at present, the observed periods of pitching closely agree with the apparent periods of the waves which are large enough to produce considerable pitching motions. The longitudinal distribution of the weights in a war-ship has to be regulated by other considerations than those mentioned above- It often happens that, to increase the offensive powers, heavy weights of guns, or armoured batteries, have to be carried near the extremities, thus adding to the moment of inertia, slowing the period of pitching, and rendering it probable that pitching oscillations will be more sustained, even if they are not made more extensive. All that can be done, in most cases, is to minimize the stowage of weights at the extremities as far as possible. Guns, anchors, or other relatively small weights may be transported from the extremities to some position more nearly amidships, when the vessel is making a voyage : these temporary changes are, of-course, the work of the commanding officer, and not of the designer. In merchant ships much more may be done towards securing a longitudinal distribution of the cargo- which favours moderate pitching, if proper care is taken in its stowage. Heavy weights, as a matter of common experience, should be kept out of the extremities ; and where this simple rule is ignored extensive pitching and unnecessarily severe longitudinal straining have to be expected. Fluid resistance is known to play an important part, as already stated, in limiting the range of pitching oscillations ; but the naval architect has not the same control over this feature as he possesses in connection with rolling motions. It would be difficult to fit any chap, vj.] OSCILLATIONS OF SHIPS AMONG WAVES. 269 appendages equivalent to bilge-keels in order to increase the resist- ance to longitudinal oscillations, although something may be done in this direction ; and the under-water forms of ships are settled mainly with reference to their efficient propulsion, the effects of form on pitching usually occupying a subordinate place. Attempts have been made, however, to improve the forms of the bows of ships in order to lessen pitching; and very diverse opinions have been expressed as to the best form that can be adopted. 'Many persons are in favour of V-shaped or "flaring" cross-sections; the out-of-water parts having a large volume as compared with ..the immersed part lying beneath them. Others have strongly objected to flaring bows, and have introduced U-shaped cross-sections, with the view of reducing pitching, as well as of reducing the excess of weight over buoyancy at the bow. The advocates of the U-shaped sections consider that " the bluff vertical sections encounter greater " upward resistance than the V-shaped sections, when the ship tends " to plunge down through the water, and receive a greater lifting "effect when the sea tends to rise up under the ship."* The adoption of pronounced U-shaped sections for the bow has not become general, nor does it appear likely to do so, other considera- tions leading most naval architects to prefer finer under-water forms ; but the use of strongly flaring sections above water is now less common than it was formerly, and naval architects agree that they are undesirable except in special cases. Vessels of low freeboard are subjected to deck resistance when pitching among waves ; and the Devastation furnishes an excellent example of this action. When on trial off the Irish coast, and steaming head to sea at moderate speeds, waves broke over the fore part of the deck, as it was anticipated they would do under these circumstances, the fittings on this deck having been designed to exclude from the interior water lodging upon it. An eye-witness, describing her motion, says, "It invariably happened that the " seas broke upon her during the upward journey of the bow ; and "there is no doubt that to this fact her moderate pitching was " mainly due, as the weight of water on the forecastle deck, during "the short time it remained there, acted as a retarding force, "preventing the bow from lifting as high as it otherwise would, " and this, of course, limited the succeeding pitch, and so on." In American monitors, with their exceptionally small freeboard, this kind of action would be even more effective, were it not for the * Naval Science, vol. iv. p. 55. " On the Bows of the Helicon and Sala- The reader may also consult on this mis," in vol. vii. of the Transactions of subject a paper, by the late Dr. Woolley, the Institution of Naval Architects. 270 NAVAL ARCHITECTURE. [chap. vi. fact, that their natural periods for pitching oscillations are probably so small as to make them capable of accompanying very closely the motions of such waves as would otherwise produce consider- able pitching. Mr. Fox (assistant secretary of the United States navy), reporting on the behaviour of the Miantonomoh, head to sea in a heavy Atlantic storm, said, " She takes over about 4 feet of '•' solid water, which is broken up as it sweeps along the deck, and " after reaching the turret is too much spent to prevent firing the " guos directly ahead." This co nfirms the opinion that these vessels move so quickly as to very nearly accompany the wave slope ; their actual arcs of oscillation in pitching being considerable. But these are cases of comparatively unfrequent occurrence, and are interesting chiefly as instances of the effect of fluid resistance in limiting the pitching motions of ships which immerse or emerge their decks. In ordinary ships the decks are much higher, and the longitudinal oscillations rarely acquire such a magnitude as to immerse the decks considerably. Various proposals have been made for the purpose of increasing resistance to pitching. For instance, it has been suggested to fit horizontal side-keels near the extremities, or to broaden out the keel proper at those parts. At the bows of many armoured ships external supports are fitted to the projecting ram-bows ; and these supports act as side-keels, which give increased resistance to pitching. The spur-bows themselves, prolonged under water as they are, also tend to reduce pitching by increasing resistance ; and in the French navy, where this form of bow has been largely adopted for unarmoured as well as for armoured ships, it is said that a sensible reduction in pitching has resulted. French naval architects, while favouring a form of bow which reaches forward for a considerable distance under water, have often preferred to make the stem fall aft considerably above water ; their intention in the latter particular being to reduce the weight above water at the extremity at the same time that they either increased the buoyancy by the spur-bow or " fined " the under- water form to facilitate propulsion. In recent French practice this form of bow has been abandoned, in consequence of its unsuitability for high speeds under steam. In ships of ordinary form the maximum amplitude of rolling largely exceeds the corresponding maximum for pitching. M. Bertin considers that a fair ratio for these maxima is one (pitching) to six (rolling). We are not in possession of sufficient data to verify this estimate; but of the fact just stated there can be no doubt. Exceptions to this rule are to be found in the Kussian circular ironclads and the Livadia. As the result of observations made on the latter in the Bay of Biscay, it appears that when placed chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 271 head to sea she pitched through somewhat larger arcs than those she rolled through when broadside on to the waves. This departure from ordinary conditions is noteworthy. Heaving Oscillations. — In addition to the transverse and longi- tudinal oscillations above described, a ship floating amongst waves has impressed upon her more or less considerable vertical oscillations, " heaving " up and down as waves pass her. Taking the extreme case of the small raft in Fig. 83, p. 200, it will be seen that her centre of gravity performs vertical oscillations of which the amplitude equals the wave height, and the period is the wave period. This is termed " passive heaving." A ship of large dimensions relatively to the waves obviously would not perform such large vertical oscillations. The extent of these vertical movements would depend upon her position relatively to the waves, her course and speed as affecting the apparent period of the waves, her natural period for " dipping " oscillations (see p. 162), the form of the effective wave slope, and the under-water form of the ship as influencing the fluid resistance to dipping. From the remarks made above, it will be seen that the vertical and horizontal extension of the ship in the wave structure have much influence upon the effective wave slope, whatever may be her position relatively to the waves. It has been suggested that the movement of the centre of gravity of the ship in passive heaving may be considered as similar to that of a particle in the wave lying on the trochoidal surface passing through her centre of buoyancy, when the ship is broadside on to waves. For the other extreme position, end-on to the waves, it has been proposed to take the mean of the vertical motions in the effective wave slope which she covers as an approximate measure. But it has been remarked, when dealing with longitudinal oscilla- tions, that this latter assumption has little practical value. Speaking generally, it may be said that the vertical oscillations of a ship result from the operation of excesses or defects of buoyancy due primarily to the passage of the waves and their trochoidal forms, but accentuated in many cases by the transverse and longitudinal oscillations of the ship, and by the dipping oscillations accompanying these oscillations. Heaving motions are favourable to safety and sea-worthiness, since they make it less probable that waves will break on board. A ship so small as to practically accompany the vertical component of the wave-motion — riding " like a duck " — r makes good weather. When ships are beam-on to the sea and roll but little, heaving motions of considerable extent may take place, and amongst large waves these motions may be nearly as great as those of surface particles. When ships are end-on to waves, although passive heaving may 272 NAVAL ARCHITECTURE. [chap. vi. hare a small amplitude, the effect of dipping oscillations may be considerable wben the natural period for dipping approximates to the apparent period of the waves. Pitching and 'scending oscilla- tions may accompany the vertical movement of the centre of gravity of the ship. As this case has an important bearing on the longi- tudinal bending moments experienced by ships among waves, it may be desirable to examine it briefly.* Suppose a ship to be end-on to waves having a length equal to her own, and for simplicity assume her to be "box-shaped" — that is, a rectangular parallelopipedon. Then one complete wave- profile would always be traced on the side of the vessel, the displace- ment would remain constant, and, although pitching and 'scending motions might be established by the passage of waves, the centre of gravity would have no vertical motion impressed upon it, if the longitudinal, oscillations are considered to be unresisted. A ship of ordinary form with fine ends would be differently circumstanced. If she is astride a wave hollow (as in Fig. 114, p. 311), owing to the fineness of the ends, she will sink more deeply into the wave than when balanced on a wave crest (as in Fig. 113). Hence there will be reciprocating forces set up tending to produce vertical oscilla- tions, which would naturally be performed in the natural period of dipping. If the reciprocating forces have a period synchronizing with the period of dipping, as may happen owing to certain relations of speed of waves and speed of ship, then the vertical oscillations will go on increasing in amplitude until the action of the fluid resistance puts a limit upon their extent. When there is not such synchronism, the amplitude of the vertical oscillations is not nearly so great. The case is parallel to that described for rolling on p. 233. Attempts have been made to deal with this matter quantitatively, on the basis of certain assumptions for the laws of fluid resistance, for the periods of dipping oscillations, and for the variations of pressure at different depths in the wave structure. The results are necessarily open to correction by means of experiments on resistance and dipping, but they are of great interest. They indicate that in ships of large dimensions- the effect of a succession of synchronizing impulses may produce considerable vertical oscillations of the centre of gravity. The alterations in the immersion or emersion of the ship from the positions corresponding to statical equilibrium may amount to 7 or 8 feet. The critical cases are obviously those where * See on this subject a valuable and Naval Architects for 1890 ; and the re- origiual investigation by Mr. T. C. Read marks on longitudinal bending on p. 317. in the Transactions of the Institution of chap, vi.] OSCILLATIONS OF SHIPS AMONG WAVES. 273 the vessel is at its extreme of emersion on a wave crest and its extreme of immersion on a wave hollow. In conclusion, it may be remarked that in the actual behaviour of ships at sea all these kinds of oscillation may be occurring simultaneously, and may mutually influence one another. Careful observations alone can decide upon their absolute values, and ordinarily rolling motions alone are considered worthy of obser- vation. 274 NAVAL ARCHITECTURE. [chap. vii. CHAPTEK YII. METHODS OF OBSEBVTNG THE EOLLING AND PITCHING MOTIONS OF SHIPS. Enough has been said in previous pages to show how variable, and how liable to mislead an observer, are the conditions surrounding the behaviour of a ship at sea. The ship, herself in motion, is surrounded by water also in motion ; and it is extremely difficult, by means of unaided personal observation, to determine even so apparently simple a matter as the position of the true vertical at any instant. To estimate correctly the angles through which a ship may be rolling or pitching, it is therefore necessary to bring apparatus of some kind into action ; and in the use of such apparatus there are many sources of possible error which must be prevented from coming into operation. Upon the correctness of these observa- tions we are greatly dependent, since deductions from theory are thus checked, and the extent to which they can be made a safe guide for the naval architect in designing new ships is ascertained. Numerous examples illustrating the substantial agreement of obser- vation with the chief deductions from theory have been given in the previous chapter ; but up to the present time the comparison has been mainly of a qualitative character, and before more exact results are obtained, it will be necessary to have compiled and collated much more exact and extensive records than are at present accessible. The chief problem to be solved is this. What are the conditions of wave motion that will produce the maximvun oscillation in a ship, of which the still-water period of oscillation as well as the coefficients of resistance are known ; and what will be the ranee of that maximum oscillation? Or, it may be desirable to ascertain generally what extent of motion will be impressed upon a ship by a series of waves of certain assumed dimensions. Pure theory will not be likely to supply correct answers to these questions ; but there is reason to believe that they may be dealt with satisfactorily by a combination chap, vii.] OBSERVATIONS OF ROLLING. ^75 of the experimental and mathematical modes of investigation, such as the process of " graphic integration " described at p. 249. The development of that process and its establishment in general use as a means of predicting the behaviour of ships, demand an extensive compai'ison of the results obtained by its application with the recorded observations of the behaviour of ships. Such a comparison can obviously be of use only when the individual observations are free from errors and accompanied by full particulars of the conditions of wind and sea. Methods of observing correctly the lengths, heights, and periods of waves have been described in detail in Chapter V. ; and it is now proposed to sketch the methods which have been adopted at various times for observing the rolling and pitching oscillations of ships. Of these methods, the folio whig are the most important : — (1) The use of pendulums, with various forms of clinometers ; these pendulums having periods of oscillation which are very short as compared with the periods of ships. (2) The use of gyroscopic apparatus. (3) The use of " batten " instruments, or alternatives. (4) The use of automatic apparatus. Taking these in the order they have been named, it may be well to glance at their chief features, and to indicate the probable correct- ness or otherwise of their records. Pendulums, or clinometers, are the simplest instruments, but they are not trustworthy indicators of the angles of inclination attained by a ship when rolling in still water, and much less of those moved through by a ship rolling or pitching at sea. When a ship is held at a steady angle of heel (as shown by Fig. 34, p. 83), a pendulum suspended in her will hang vertically, no matter where its point of suspension may be placed, and will indicate the angle of heel correctly. The only force then acting upon the pendulum is its weight, i.e. the directive force of gravity, the line of action being vertical. But when, instead of being steadily inclined, the ship is made to oscillate in still water, she will turn about an axis, passing through or very near to the centre of gravity ; hence every point not lying in the axis of rotation will be subjected to angular accelerations, similar to those which were described in Chapter IV. for a simple pendulum. Supposing the point of suspension of the clinometer to be either above or below the axis of rotation, it will be subjected to these accelerating forces, as well as to the directive force of gravity, and at each instant, instead of placing itself vertically, the clinometer, or pendulum, will tend to assume a position determined by the resultant of gravity and the accelerating force. If the period of the pendulum used is short as compared with the 276 NAVAL ARCHITECTURE. [chap. vir. period of the ship, the position towards which it tends to more will probably be reached very nearly at each instant. The case is, in fact, similar to that represented in Fig. 93, p. 238. If the length of the upper pendulum (AB) is supposed to represent the distance from the axis of rotation of the ship to the point of suspension of the pendulum which is intended to denote her inclinations, the clinometer pendulum may be represented by BC. As AB sways from side to side the point B is subjected to angular accelerations, and these must be compounded with gravity in order to determine the position which BC will assume ; for obviously BC will no longer hang vertically. The angular accelerating force reaches its maximum when the extremity of an oscillation is reached, consequently it is at that position that the clinometer will depart furthest from the vertical position. In Fig. 93, suppose YAB to mark the extreme angle of inclination reached by the ship, and let AB be produced to D : then, to an observer on board, the angle CBD will represent the excess of the apparent inclination of the ship to the vertical above the true inclination. It will be seen that the linear acceleration of the point of suspension B depends upon its distance from the axis of rotation A in Fig. 93. If B coincides with the axis of rotation, it is subjected to no accelerating forces, and a quick-moving pendulum hung very near to the height of the centre of gravity of a ship rolling in still water will, therefore, hang vertically, or nearly so, during the motion, indicating with very close approximation the true angles of inclina- tion. Hence this valuable practical rule : when a ship is rolling in still water, if a pendulum is used to note the angles of inclination, it should be hung at or near to the height of the centre of gravity of the ship ; for if hung above that position it will indicate greater angles, and if hung below will indicate less angles, than are really rolled through; the error of the indications increasing with the distance of the point of suspension from the axis of rotation and the rapidity of the rolling motion of the ship. The errors of pendtdum indications for still-water oscillations may be approximately estimated from the following forhuda, proposed by the late Mr. Froude : — Let a = true angle of inclination reached by the ship ; j3 = apparent angle of inclination indicated by the pendulum ; T = period of oscillation (in seconds) for the ship ; h = the distance (in feet) of the point of suspension of the pendulum above the centre of gravity of the ship — Then a = 3 ' 27T2 x /3. 3-27T 2 + h ' CHAP, vii.] OBSERVATIONS OF ROLLING. %77 If, instead of 3*27, we write 3£, this takes the approximate form — 10T 2 ~ 10T 2 + 3/& H which will be sufficiently near for practical purposes. In the case where the point of suspension is at a distance h below the centre of gravity, the corresponding approximate formula is — 10 T 3 10T 2 - 3h X j3. Take one or two illustrative examples. For the Prince Consort T = 5J- seconds ; and h may be taken as 20 feet, if the pendulum were placed on the bridge — ™ a 10T 2 300 5 Then - = = = lOT' + Sh 300 + 60 6 5/a or a = - p ; 6^ and the pendulum indicates an excess above the true angle of heel of 20 per cent. In the Devastation a pendulum placed on the flying deck is about 25 feet above water ; also T = 6 J seconds. Then a _ 10 x (6f) 2 450 450 6. /3 10 X (6|) 2 + 3 x 25 ~ 450 + 75 525 7' 7 Here the pendulum indications exaggerate the true angles of inclination by about 16 per cent. ; notwithstanding the greater height of the point of suspension above the centre of gravity, the slower motion of the Devastation makes the error smaller than in the Prince Consort. So much for the simple case of still-water oscillations. In the more complicated case of a ship oscillating amongst waves, the errors of pendulum observations are frequently still more exaggerated. The centre of gravity of the ship is then, as explained in the preceding chapter, subjected to the action of horizontal and vertical accelerating forces. If the pendulum were hung at the centre of gravity (G-) of the ship, shown on a wave in Fig. 83, p. 200, it would, therefore, no longer maintain a truly vertical position during the oscillations, but would assume at each instant a position determined by the resultant of the accelerating forces impressed upon it and of gravity. The direction of this resultant has been shown to coincide with that of the corresponding normal to the effective wave slope. Hence follows another useful practical rule. When a ship is rolling amongst waves, 278 NAVAL ARCHITECTURE. [chap, vn. a quick-moving pendulum suspended at or near to the height of the centre of gravity will place itself normal to the effective wave slope, and its indications will mark the successive inclinations of the masts of the ship to that normal, not their inclinations to the true vertical. This distinction is a very important one. For example, in an American monitor, supposing her to keep her deck very nearly parallel to the wave slope as she might do, if a pendulum were hung close to the height of the centre of gravity, it would indicate little or no rolling motion ; whereas the monitor would really be reaching inclinations equal to the maximum wave slope on each side of the vertical. On the other hand, if a steady ship, such as the Inconstant. were amongst the same waves, a pendulum hung at the centre of gravity would indicate extreme angles of inclination far in excess of the true rolling ; for if the ship remained practically upright during FIG 97 *^ e P 8888 ^ °f th e ™ves, the pendulum would indicate . angles of inclination nearly equal to the effective wave i slope. ~jp* When hung at any other height than at that of the centre of gravity of a ship rolling amongst waves, the indications of a pendulum are still less to be B trusted. Eeferring to Fig. 97, three pendulums are \ shown combined, viz. AB, to which hangs BC, and V from this is suspended a third, CD. Supposing AB j$P made to swing through a fixed range, it will represent 'Q^ the wave oscillation ; then the motion of BC will represent the oscillations of a ship amongst the waves ; and finally CD will represent the clinometer pendulum suspended at some point other than at the height of the centre of gravity of the ship. In view of what has been said above, it will be obvious that the motions of the pendulum BC will not be indicated correctly by the pendulum CD ; yet this is a parallel case to that when a pendulum or clinometer is trusted to indicate the angles of inclination to the vertical of a ship rolling amongst waves. For a ship rolling among waves there is clearly no fixed axis of rotation, and the problem to be solved in discussing the possible errors of indication in a quick-moving pendulum hung at various heights in a ship is one of great difficulty. It would be out of place to introduce this discussion here ; but reference may be made to some interesting observations with pendulums made by officers of the French Navy. Admiral Bourgois made simultaneous observations of the rolling of the ironclad ship Magenta, in 1863, by correct batten observations of the horizon (such as are described hereafter) and by quick-moving pendulums hung in different vertical positions. In that ship he discovered that a quick-moving pendulum hung CHAP. VII.] OBSERVATIONS OF ROLLING. 279 nearly at the height of the centre of buoyancy indicated practically correct angles of inclination to the vertical when the ship reached her extreme roll. Captain Mottez also made some similiar experi- ments in the frigate Sybille in 1865, when rolling heavily, and reached the following conclusions : that no possible point of suspen- sion could be found where the indications of a pendulum were not influenced by the accelerating forces resulting from the rolling and heaving of the ship ; but that the errors of indication were least when the pendulum was hung at about mid-draught. These results may not hold good in all cases, but they are of considerable practical interest, and may lead other observers to make similar experiments. It must always be an advantage to know where a pendulum may be placed in a ship so as to indicate with approximate correctness her angles of rolling, as circumstances may arise when only pendulum observations are possible. Pendulums are commonly hung above water in ships, and under these circumstances their indications usually err in excess, and in some cases the error is proportionately very great, as the following examples will show. The figures are taken from published returns of rolling for her Majesty's ships : — Ships. Pendulum indications. Correct angles. Lord Warden Minotaur „ .... Bellerophon .... degrees. 11-4 6-1 8-2 8-2 degrees. 9-1 3-8 4-3 3-0 Many similar examples could be given, but they appear un- necessary ; the correct angles stated in the table were observed in all cases with the accurate batten instruments which are now the service fitting. The misleading character of pendulum observations has been for many years acknowledged ; and they are no longer made in ships of the Eoyal Navy, except in special cases. When the horizon is obscured, or at night, batten observations cannot be made, while pendulum observations can ; and it is ordered that under these cir- cumstances the rolling indicated by the pendulums shall be noted. To enable the results so obtained to be afterwards corrected, simul- taneous observations are made, when circumstances permit, of the indications of these same pendulums hung in the same positions, and of the indications of batten instruments. Any other devices, such as spirit-levels or mercurial clinometers, 28 XAVAL ARCHITECTURE. [chap. vii. depending for their action on the directive force of gravity or statical conditions, are affected by the motion of a ship much as the pendu- lum has been shown to be affected. Suppose a spirit-level to be placed in a ship, at the height of the centre of gravity ; in accord- ance with the principles previously explained, when its indications would lead an observer to think it exactly horizontal, it would really be parallel to the effective wave slope. Many persons who admit the faultiness of the pendulum are disposed to cling to the use of the level ; but on reflection it will be seen that both instruments are open to similar objections. Moreover, the extreme sensitiveness aud rapid motions of the spirit-level make it ill adapted for any observa- tions in a seaway. Many proposals have been made for mercurial clinometers, in the form of bent tubes, the mercury in both arms standing level when a ship is upright and at rest, while the difference in the heights of the column in the two arms indicates any angle of steady heel. It is supposed by the inventors that the corresponding difference in height in the two arms will also indicate, at any instant, the angle of inclination to the vertical of a ship rolling at sea. From the foregoing explanations it will be obvious that this is not true ; but as so many persons have fallen into the same error, it may be well to confirm this statement by the result of actual observations. One of the best mercurial clinometers devised was tested in her Majesty's ships during 1886, by simultaneous observations of clinometers and batten instruments — the latter being accurate. In one ship it was found that when the true angle of roll was 16 degrees the clinometer showed 11 degrees ; whereas in another observation in the same ship, made only a few minutes after the first, the clinometer indicated 16 degrees when the true inclination was 13 degrees. Taking the whole observations, 470 in number made in a period of 10 minutes, the mean angle of roll by clinometer was 9'8 degrees, and by batten 10-2 degrees. There was, therefore, a close, but accidental, agree- ment in the mean angle of roll measured by the clinometer and by battens. The clinometer varied widely from the truth, and had no constant rate of error, its indications being sometimes considerably above, and at others considerably below the true angle of roll. Corresponding observations made in another ship gave the follow- ing results among others : — Clinometer indications. Correct angles. degrees. degrees. 2£ 7 4 7 8 2£ 8 4 10 13 12 12 CHAP. VII.] OBSERVATIONS OF ROLLING. 28l Mercurial clinometers are not so sensitive as spirit-levels, and are, in some respects, more convenient than pendulums; but they are not more trustworthy. Several kinds of gyroscopic instruments have been devised for the purpose of measuring rolling and pitching motions, all of them being based upon the well-known principle — exemplified in the toy gyro- scope — that a delicately balanced heavy-rimmed wheel spinning rapidly will maintain the plane of rotation in which it is set spinning, until its speed of rotation is considerably diminished. One of the earliest instruments of the kind is illustrated by Fig. 98. It was FIG. 98. devised and tried at sea about thirty years ago by Professor Piazzi Smyth, and could be used to measure " yawing " motions as well as rolling and pitching.* It consists of a fly-wheel A, the axis of which forms a diameter of the gymbal-ring B ; this is carried by a second gymbal-ring, C, the pivots of which rest on the frame F ; and the * See the description given by the inventor in vol. iv. of the Transactions of the Institution of Naval Architects, from which the drawing is taken. 282 XAVAL ARCHITECTURE. [chap. vii. whole is mounted in an outer frame, enabling it to be easily carried or placed in position. Suppose the pivots of the ring C to be placed athwartships in a ship, the instrument standing on the deck or on the table : then for transverse oscillations the line-of-centres of the pivots will remain parallel to the deck — that is to say, so far as rolling is concerned the ring C must move with the ship. But it is free to oscillate about its pivots as the ship pitches. When the fly-wheel A is spinning rapidly and maintaining its plane of rotation, it is practically uninfluenced by the motions of the ship which so largely affect the pendulum ; and as its axis is carried by the ring B, that ring also must maintain its position. This maintenance of position by B further involves the non-perform- ance of any oscillations by C except in the transverse sense. In other words, neither A nor B changes the direction of its plane, while the ship rolls and pitches, so long as A spins rapidly ; while C can accompany the rolling motion, but not the pitching motion. Hence the graduated semicircle E, shown fixed upon and across C, moves relatively to B as the ship rolls ; and the pointer attached to the upper edge of B sweeps over an arc on the semicircle equal to the arc through which the ship is oscillating. On the left-hand side of the diagram there is shown a graduated circle Gr, which has its centre coincident with one of the pivots of C, and is fixed to the frame F. As the ship pitches, therefore, the frame F moves with her, and oscillates about the ring C, which is prevented from accompanying the pitching in the manner described. Pointers are attached to the under side of 0, and the arcs they sweep over upon the graduated circle Gr indicate the arcs through which the ship pitches. By this ingenious arrangement the simultaneous rolling and pitching motions can be read off by observers with the greatest ease. One point of disadvantage attaching to this as well as to all other gyroscopic instruments should be noted; viz. that there is no separate indication of the angles of inclination attained on either side of the vertical. When the wheel A is set spinning, if it were truly horizontal, then B would be vertical, and this disadvantage would disappear. But a ship in a seaway changes its position rapidly, and it is practically impossible to secure this condition of initial horizontality ; hence the observer must be content to note the total arcs of oscillation. No doubt, in most cases, the rolling of a ship not under sail approaches equal inclinations on either side of the vertical, the roll to leeward being somewhat in excess of that to windward ; but in a ship under sail the rolling takes place about an inclined position, and in any case it is a great advantage to be able to ascertain the extreme inclination on either side of the vertical. Professor Smyth fully appreciated this defect of all gyroscopic chap, vii.] ; OBSERVATIONS OF ROLLING. 2^3 instruments, observing that they had "no power of determining " absolute inclination, or angular position with reference to horizon " or meridian ; " but he was unacquainted with any other instru- ment which did not have its records affected by the accelerating forces due to the motion of the ship, and so preferred the gyroscopic clinometer. Now we have other means of measurement free from the objections belonging to pendulums or spirit-levels, and can therefore afford to dispense with the gyroscope. It has been mentioned that the maintenance of the plane of rotation by a fly-wheel depends upon the maintenance of its speed ; this is well illustrated in the common top, which droops as the speed decreases. The practical difficulties attending the use of these instruments arise, therefore, from the extreme care required in suspending the fly-wheels in order that friction or other causes may have the least effect in hindering free rotation, and in the difficulty of maintaining continuous rotation. The instrument shown in Fig. 98 is said to have been so well designed that, when once care- fully adjusted, it did not require readjustment for some time ; but from the few records of its use that have been published, it would appear that any single series of observations was limited to a very brief period. When a considerable time is occupied in making the observations, there is a danger of the gyroscopic action being some- what interfered with by the loss of speed of rotation.* On this point some interesting facts have been stated by the late Admiral Paris, of the French Navy, who produced a gyroscopic clinometer some years ago, which automatically recorded the rolling of a ship. The gyroscopic wheel in this instrument formed the body of a top, the lower end of the axis about which it spun being wrought to a sharp point, and resting on an agate bearing in order to dimmish friction. To spin this top, a string was wound round the upper part of the axis, and drawn off gradually, giving a gradually accelerated motion of rotation. It was found that this top would revolve steadily on a support for about half an hour; nine minutes sufficed to degrade its revolutions from 23 per second to 12 per second ; but this lower speed sufficed to make the top steady enough to be used for recording the motion of a ship in a seaway. The observations were usually extended over about ten minutes. The automatic recording apparatus was extremely simple. As the ship rolled, the gyroscopic top maintained its axis in the same * When the instrument illustrated in its side instead of its bottom, and the Fig. 98 was used to measure " yawing," wheel B being horizontal. The angles of it was placed with the pivots of the ring " yawing " could then be read off on the C in a. vertical line ; the frame lying on graduated circle G. 284 NAVAL ARCHITECTURE. [chap. vn. direction as that in which it was set spinning, and upon the upper end of the axis a camel-hair pencil saturated with ink was fixed. A sheet of paper was made, by means of clockwork, to travel longitudinally over the pencil point, being curved in the transverse sense, so that the point shovdd just touch the paper as it swayed to and fro. The paper, with the arrangements by which it was made to travel, being attached to the ship, rolled with her, wliile the axis of the top maintained its original direction ; hence the pencil-point traced out on the paper a curve showing the inclinations of the ship at any instant on either side of the initial position of the pencil. The rate at which the clockwork propelled the sheet of paper was constant ; consequently the period of oscillation of the ship, as well as the arc of oscillation, could be read off from the diagram traced. Admiral Paris appears to have endeavoured to set the axis of his top truly vertical before commencing to record the motion, in order that the diagram might show inclinations to the vertical as well as arcs of oscillation ; but in doing this, he must have encountered consider- able difficulties. We cannot further describe his ingenious arrange- ments, which are given in vol. viii. of the Transactions of the Institution of Naval Architects. M. Normand has proposed an instrument for measuring rolling differing from the gyroscope in principle, but intended to effect a similar object, viz. the maintenance of an invariable plane, to which the motions of the ship coidd be referred. A spherical vessel is entirely filled with petroleum, and hung on double gymbal-rings like a compass. It contains a very light pendulum, situated at the centre of the sphere, and formed as a flat disc, carrying a pointer which stands at right angles to the disc. The inventor supposes that the fluid in the central parts of the sphere would have no angular motion set up in it by the reciprocating oscillations of the ship or the small oscillations of the sphere on its gymbal-rings, and that the pendulum would remain practically horizontal while the vessel rolled, its indicator being vertical. Much would obviously depend upon the position in the ship at which this instrument was placed. Supposing it to be at the centre of gravity, M. Normand's supposition might be nearly fulfilled, and the sphere with its contents would act like a common pendulum, its motions being governed by those of the effective wave slope, and keeping time with the wave period. Under these circumstances it is conceivable that the motions of the disc-penduluni might be small, and the motions of the ship might be fairly well indicated. But the use of any such instrument has never found general favour; in practice simpler methods suffice, and for more scientific research it appears preferable to have recourse to a different principle, hereafter to chap, vii.] OBSERVATIONS OF ROLLING. 285 be described, in order to secure an invariable vertical line of reference.* Batten instruments afford the simplest correct means of observing the oscillations of ships ; they can be employed whenever the horizon can be sighted. The line of sight from the eye of an observer standing on the deck of a ship to the distant horizon remains practically horizontal during the motion of the ship. Consequently, if a certain position be chosen at which the eye of the observer will always be placed, and when the ship is upright and at rest, the horizontal line passing through that point is determined and marked in some way ; this horizontal line can be used as a line of reference when the ship is rolling or pitching, and the angle it makes at any instant with the line of sight will indicate the inclination of her masts to the vertical. This principle may be applied in different ways ; one of the most common, generally adopted in ships of the Eoyal Navy, is illustrated in Fig. 99. The point E on the middle line of the cross-section marks the position of the eye of the observer ; and at equal distances athwartships, two battens CC and GG are fixed perpendicularly to the deck, so that, when the ship is upright and at rest, these battens are vertical, and at that time the line FEF will be horizontal. This line may be termed the " zero-line ; " and the points FF would be marked upon the battens, being at a height above the deck, exceeding that of the point E by an amount determined by the transverse curvature or " round " of the deck. Suppose the diagram to represent the case of a ship rolling among waves ; when she has reached the extreme of an oscillation to starboard, EG- marks the line of sight to the horizon, and the angle G-EF measures the angle of inclination of the masts to the vertical. If the battens are placed longitudinally, instead of transversely, the angular extent of pitching may be similarly measured. The angles are usually read off on that side of the point of observation E towards which the vessel is inclined; rolls to starboard being measured, for example, on the starboard battens, rolls to port on the port battens. Sometimes the inclina- * Drawings and descriptions of this the Transactions of the Institution of instrument will be found in vol. vii. of Naval Architects. 286 NAVAL ARCHITECTURE. [CHAP. VII. tions to both port and starboard are read off on one batten, above and below the zero. It is a great practical convenience to have the vertical battens graduated so that an observer can at once read off and note down the angles of inclination in degrees. This graduation is very simply effected when the positions of the battens relatively to E have been fixed, and the zero-line FEF determined. Once graduated, the battens can, of course, be removed when the observations are not in progress, and replaced in the same positions when required. The zero-line on the battens having been fixed in the manner previously explained, the horizontal distance from the position where the eye of the observer will be placed to the vertical batten is measured ; suppose this to be d feet, it will be indicated by EF in Figs. 99 and 100. Then, for any angle a, we have — Vertical height (FGr) to be set off above ) _ , zero-line on batten . . . .J The value of tan a being taken from a table, the product d tan o can be found. For instance, suppose d = 20 feet, and a = 15 degrees : tan a = 0-268, and vertical distance (FG-) to be set above zero-line will be. (20 X 0-268) = 5-36 feet. Another form of the bat- ten instrument is shown in Fig. 101. AB is a straight- edged batten pivoted at C, and carried by a frame having attached to it a semicircular graduated arc. Suppose that, when the ship is upright and at rest, the base of the instrument is so fixed that the pivoted bar, occupying the position AB, FIG. 101. is horizontal. Then the line ACB marks the zero-line to which angles of inclination may be re- ferred. The instrument may, if desired, be set transversely when roll- ing motions are being- observed; the observer looking along the edge of the pivoted batten will always keep it pointed to the horizon, and its motions can be observed on the graduated arc. For example, suppose the position FE to have been chap, vii.] OBSERVATIONS OF ROLLING. 287 reached, then the angle ECB (a little over 20 degrees) will indicate the inclination of the masts of the ship to the vertical at that instant.* Instead of looking lengthwise, and athwartships, along the edge of the batten when the instrument is set transversely, the observer may, if he prefers, stand before or abaft the instrument, and move the pivoted bar so as to keep its edge always parallel to the horizon ; the angular motion of the bar indicated on the graduated arc will measure the inclination as before. To measure pitching, the instru- ment should be set longitudinally in the ship, the zero-line being adjusted as explained for rolling ; and the observer will either look longitudinally along the edge of the batten, in order to keep it pointed to the horizon, or will stand and look athwartships, keeping the edge parallel to the horizon. In either case the angles of pitching may be read off from the graduated arc. It will at once occur to the reader that the angular motions of such a pivoted bar might be readily made, by means of suitable mechanism attached to some point on the bar, to furnish an automatic record on a travelling sheet of paper moved at a uniform speed by clockwork. This has actually been done in some 'cases, a diagram being automatically traced, showing the inclinations of the ship throughout the period of observation. The proper conduct of observations with common batten instru- ments requires at least two observers : one to note the extreme angles of inclination attained by the ship, a second to note the periods of successive rolls. In the Eoyal Navy a single series of observations would last ten minutes, and during that time one observer would have to note the extreme inclinations for from seventy to, perhaps, one hundred and fifty or two hundred single rolls, according to the class of ship and character of the waves. The other observer would, meanwhile, note the times of performing successive rolls, and the total number of rolls during the ten minutes. To facilitate the entry of the particulars, printed forms are issued to the ships of the Eoyal Navy. The dimensions and periods of the waves ought also to be observed simultaneously with the rolling or pitching ; and this requires the attention of an independent set of observers, whose work should be conducted somewhat in the manner indicated in Chapter V. In large war-vessels with numerous complements it is easy to carry on such observations ; in small vessels it is not always easy to provide for the working of the ship and to detail officers for observations of rolling and pitching. The most important observa- tions, are, however, those made in large ships of new types. * It will be evident that this instrument could also be used at night, when stars of known altitude were visible. 288 NAVAL ARCHITECTURE. [chap, vil A Terr ingenious process for automatically making and recording horizon observations of rolling, by means of photography, has been devised by M. Huet of the French Navy, and successfully applied in several vessels. The apparatus consists of a camera fixed in the ship so that its axis is horizontal when the ship is upright. The field of the object lens is narrowed to a vertical slit, and a sheet of sensitive paper is made to travel parallel to the lens, by means of clockwork, at a uniform rate. On this sensitive paper a line is traced which would be in the same horizontal plane with the axis of the camera when the ship was upright, and this is taken as a line of reference. As the ship rolls the sensitive paper receives at each instant an impression of the sea and sky on the horizon ; the colours being quite distinct ; and their junction defining the instantaneous inclination of the ship to the vertical. Let d = the vertical distance of the junction of sea and sky shown on the paper at any instant, measured above or below the line of reference above named. Then, if / is the horizontal distance from the lens of the camera to the sensitive paper, and 9 the angle of inclination of the ship to the vertical — tan0= - / is an equation determining the value of at every instant. The motion of the ship is, therefore, continuously recorded, and her inclinations at anv time as well as her extreme angles of exclusion can be ascertained. As an economizer of labour on the part of observers and an extension of the method of batten observations, this method is valuable. From specimens of the diagrams obtained on the sensitive paper which M. Huet has been good enough to furnish to the author, it also appears that the photographic records obtained are precise and easily interpreted. Independent observations of the wave phenomena accompanying rolling are necessary with this method, as well as with batten observations. For all ordinary purposes batten observations of rolling and pitching, such as are made in the Koyal Navy, suffice. They depend for their accuracy upon the care exercised by observers, and furnish the extreme inclinations attained by the ship, and the period of her oscillation. Although these may be associated with simultaneous observations of the waves, there is no continuous record of the ratio of the angle of inclination of the ship to the angle of wave slope. More complete information, such as is most valuable for scientific purposes, requires the use of automatic instruments, the records of which may be made continuously during prolonged periods. Such instruments require care both in their construc- tion and management; but if they are based upon correct prin- chap, vii.] OBSERVATIONS OF ROLLING. 289 ciples, they can be, and have been, made capable of far surpassing the results obtained by the most careful personal observation. Both in France and in this country such instruments have been made and used. M. Bertin, of Cherbourg, and the late Mr. W. Froude independently constructed instruments for this purpose, based upon very similar principles. That of Mr. Froude has been used on board the Greyhound, Perseus, Devastation, and Inflexible with great success, and a description of its leading features will be given.* Fig. 102 contains a general view of the instrument, mounted on a rocking platform, AAA, the motions of which represent those of the deck of a ship rolling in a seaway. The surface of the rocking platform to which the instrument is secured is shown at a considerable inclination, and the fixed frame upon which it rocks will be readily distinguished. Two fundamental principles, already explained, may be again mentioned in order to facilitate explanation : (1) if a pendulum of very short period is hung at the height of the centre of gravity of a ship rolling among waves, it will at each instant stand practically normal to the effective wave slope ; (2) if a pendulum of very long period is hung in the ship, it will remain practically vertical while she rolls. In the instrument there are two such pendulums ; when the ship is upright: and at rest, they both occupy a vertical position which is marked on some part of the apparatus that accompanies the motion of the ship. When the ship rolls, the oscillations of the quick-moving pendulum indicate the angles of inclination, at every instant, of the masts of the ship to the normal to the effective wave slope; while the oscillations of the very slow-moving pendulum indicate the simultaneous inclination of the masts to the vertical. From these two records the angles of the effective wave slope at various times can be deduced, being the algebraical difference of the pendulum inclinations; and the profile of the effective wave surface can be constructed. In short, every important feature in the behaviour of the ship is brought within the scope of analysis, by means of the diagrams automatically traced by the instrument. The quick-moving pendulum is shown in Fig. 102 by r (on the right side of the drawing, and about mid-height on it). It consists of a horizontal brass tube, filled with lead so as to form a heavy bar-pendulum ; this is suspended at each end on knife-edges, situated near the upper part of the circumference of the bar. The bar is only 2 \ inches in diameter, and about 20 inches long ; so that * For further details see vol. xiv. of particulars given in the text and the Transactions of the Institution of Naval drawing of the instrument are taken. Architects; from- which most of the 290 NAVAL ARCHITECTURE. [CHAP. VII. the arrangement really produces a powerful and sensitive pendulum, of less than 2 inches in length, and consequently having a period of about two-tenths of a second only. It carries an arrangement of light arms (p), at the end of which is a pen, s; and as the bar- pendulum swings to and fro, the pen s registers the motion upon a sheet of paper carried by the cylinder Jc, which is driven by FIG. 102 clockwork. The pen s traces on the paper a continuous line, and as the cylinder k revolves, another piece of clockwork I marks upon the paper a " scale of time ; " so that the diagram produced shows not merely the successive inclinations of the ship to the effective surface, but also indicates the times at which those inclinations are attained. The interval of time marked by this scale, between two consecutive extremes of inclination, will show the " period " of the corresponding oscillation. Considerable practical difficulties had to be overcome in con- chap, vii.] OBSERVATIONS OF ROLLING. 2 9' structing tlie second pendulum, which has a very long period. It consists of. a heavy -rimmed wheel {a, in Fig 102), 3 feet in diameter, weighing 200 lbs. ; this is carried on an axis of steel, 1 inch in diameter, the centre of gravity of the whole being only six-thousandths (0"006) of an inch away from the centre of the axle. Here we see an arrangement identical in character with a ship having very little initial stability, but great inertia, the two contributing to produce a very long period. The observed time for a single swing of this wheel-pendulum, as it may be termed, has been found to be about 34 seconds ; the magnitude of this period becomes evident when it is remembered that the slowest-moving ships have periods for a single roll of about 8 to 10 seconds, and that the half-period of the largest waves commonly met with are still less. Friction rollers (c, e) support the steel axle ; and the extreme delicacy of the suspension of this, heavy wheel is attested " by the fact, that, when " at rest, a breath on the circumference (of the wheel) will move it " perceptibly." This wheel-pendulum continues almost unmoved as the ship rolls. The effects of any very small motion which the wheel may acquire are easily eliminated, and it practically indicates at every instant the true vertical direction, as well as the inclination thereto of the masts. This wheel is also made to record its motions on the revolving cylinder k. A wooden semicircle g is carried on the axis, and by means of the light rods h, h — which are carefully counterbalanced — the relative angular motions of the ship and the steady wheel are made to move a pen, m, which draws a curve on the paper stretched upon the cylinder k. The character of this curve is similar to that traced by the pen s, moved by the pendulum r ; and both these curves are indicated by the curved lines shown on the cylinder k, the rotary motion of the cylinder and the motion of the pens parallel to its axis combining to produce this result. The time scale is the same for both curves ; and on that traced by the pen m the time interval between any two consecutive extremes of inclination measures the corresponding period of oscillation of the ship. When the observations are over, the paper can be removed from the cylinder k, and the diagrams drawn by the automatic apparatus can be analyzed. They furnish the following information : — (1) The relative inclination of the ship and the effective wave slope at any instant. (2) The inclination of the ship to the vertical at any instant. (3) The period of oscillation of the ship at any time — that is, the number of seconds occupied in completing the roll from port to starboard, or vice versa. From 1 and 2 may also be deduced : — 292 NAVAL ARCHITECTURE. [chap. vn. (4) The angle of slope of the effective wave surface at any instant. (5) The period of this effective wave, which will agree with the apparent period of the surface waves when the ship is floating among relatively large waves. If, therefore, careful observations are made, while the instrument is at work, of the dimensions and periods of waves, the comparison between the observed slope of the surface wave and the deduced slope of the effective wave furnishes a test of the correctness of the ordinary assumptions as to the effective wave slope. It also enables estimates of the probable ro llin g of future ships to be made more precise by thus determining the character of the effective wave surface.* In the instrument constructed by M. Bertin the heavy wheel- pendulum has a period, for a single swing, of 40 seconds ; and the quick-moving pendulum a corresponding period of - 2 second. Each pendulum automatically records its indications. M. Bertin has made several series of observations with this instrument, including pitching as well as rolling observations in his work, and the results obtained, as well as their analysis, constitute one of the most valuable additions made in recent years to the experimental study of the oscillations of ships, f It will be obvious that the wheel-pendulum of either of these automatic instruments, stripped of its appliances for recording its indications, would constitute a very trustworthy substitute for the ordinary pendulums whose errors have been described above. Some simpler instrument embodying the same principles will probably yet come into general use as a substitute for the pendulum. Another most ingenious instrument for determining the true vertical in a ship rolling and pitching at sea has been devised by Mr. B. Tower, in connection with his apparatus for providing a steady platform for guns, search-bights, etc. J The essential features of the apparatus include the following : (1) A heavy cast-iron disc wheel mounted on a cup-bearing, and made to revolve in a horizontal plane on a spherical journal resting in the cup, by means of water * Independently of the use of this the simultaneity of the records of bat- instrument, naval officers might do tens and pendulums if this plan were much to add to existing knowledge on adopted. this point if they associated ordinary f Observations de roulis et de ton- batten observations with simultaneous gage faites avec I'oscilbgraphe double, observations of the angles indicated by par M. Bertin. short pendulums hung at the height of J See the full description and draw- the centre of gravity of the ship, ings published in the Transactions of the Great care would be required to ensure Institution of Naval Architects for 1889. chap, vii.] OBSERVATIONS OF ROLLING. 293 supplied from a pump at a pressure of about 100 lbs. per square inch. The water passes through the bearing into the central cavity of the wheel, and thence through radial passages to two small tangential jets at the rim of the wheel. The reaction of the issuing jets causes the wheel to make about 1000 revolutions in a minute. (2) The wheel has its centre of gravity a very small distance below the centre of suspension, and is therefore, when revolving, a conical pendulum of very long period. The complete period of its conical oscillation round the true vertical is 90 seconds. (3) The wheel has most of its weight carried on the water pressure on the cup- bearing; friction is thus lessened, and the wheel is free not merely to revolve, but also to perform its conical oscillations (or " wobbling ") in relation to the cup-bearing and the frame carrying it. Both the bearing and the frame are rigidly connected with the vessel, and move with her. Supposing the vessel to be rolling before the high-pressure water is admitted to the disc wheel ; it rests in its bearing and moves with the ship. Directly the water is admitted and the wheel made to revolve rapidly, it ceases to move with the ship, but becomes a very slow-moving conical pendulum, and very soon settles down to a truly horizontal plane. In other words, the ship virtually rolls about it just as it would about the heavy-rimmed wheel-pendulum in Mr. Froude's apparatus. A pointer fixed at right angles to the disc wheel, therefore, indicates the true vertical, and by simple apparatus the arcs of oscillation on either side of the vertical could be automatically recorded. No matter what may be the position of the wheel when its rotation begins, in a very short time it assumes the horizontal position, and for all practical purposes maintains it. This has been demonstrated both by observations made on a vessel rolling through considerable angles in a seaway, and by rolling experiments in still water. It should be understood that this invention is primarily designed to secure a steady platform, and not to measure rolling or pitching. The arrangements by which this is secured cannot be fully described here, but they are so novel and beautiful in their character as to deserve careful study. From the cavity in the body of the disc wheel an axial pipe is led upwards, ending in a jet co-axial with the wheel. The high-pressure water issuing from this jet acts upon a system of four pipes with their ends brought close together, each leading to one of four cylinders, in which rams work up and down. These rams are made to carry, on a frame and gymbals, the platform which is to be steady. The effect of the axial jet is to cause the rams on the cylinders to move so as to bring the centre of the jet exactly opposite the centre of the ends of the four pipes. Con- 294 NAVAL ARCHITECTURE. [chap. vn. sequently the platform is always maintained practically parallel to the horizontal plane of rotation of the disc wheel. If moved away from this parallelism, the platform speedily returns to it ; and no reaction is possible on the wheel, since the water-jet alone transmits the force which steadies the platform. No doubt con- siderable use will be made of this principle in future. Before concluding this chapter, it may be well to repeat that, whatever method of observing the rolling or pitching may be adopted, the observations made cannot have their full value unless the attendant circumstances are fully recorded. For example, the actual condition of the ship at the time should be noted ; whether she is under sail or steam ; what portions of her consumable stores remain on board ; whether the boilers are full or empty ; whether there is anything unusual in her stowage; whether there is any water in the bilges; and any other features that would affect the still-water period of oscillation. Her course and speed should also be stated, the former being given relatively to the line of the wave- advance, and the angle between the two being stated in degrees where possible. The dimensions and periods of the waves, both real and apparent, should also be carefully determined, as explained in Chapter V. No change should be made affecting the behaviour of a ship for some time before the observations are commenced, nor during their progress ; a change of course, an alteration in the sail spread, a change of speed, or any other changes, made immediately before the observations began, might seriously influence the behaviour during the comparatively short time over which a series of observations extends ; and it is needless to point out the necessity for avoiding any changes during that short time. The Admiralty instructions enforce these conditions, providing that no change of course or speed, or spread of sail, etc., shall be made for at least ten minutes before the observations are commenced. One of the most perfect sets of observations of the behaviour of a ship yet made were those conducted by the late Mr. Froude, on behalf of the Admiralty, on board the Devastation. But unfortu- nately for the scientific interest of the case, the weather encountered during the passage of that ship to the Mediterranean in 1875 was so moderate as neither to severely test her qualities nor to afford good opportunities for showing the Ml capabilities of the automatic instrument. Every naval officer proposing to enter upon similar work may read with advantage the brief report drawn up by Mr. Froude on the observations made during the passage.* Ordinary observers have not similar advantages, but with the aid * Published as Parliamentary Paper No. 104 of 1876. chap, vii.] OBSERVATIONS OF ROLLING. 2 95 of the appliances in common use much valuable information has already been furnished, and it is to observations of a similar character we must look chiefly for still further facts bearing on the behaviour of ships at sea. An intelligent acquaintance with the main deduc- tions from modern theory, as well as with the moot points of the subject, will enable the observer to supply much more valuable information, seeing that he will be capable of distinguishing the more important from the- less important conditions, and of giving a practical direction to his inquiries. 296 NAVAL ARCHITECTURE. [chap. viii. CHAPTER Yin. THE STRAINS EXPEBIENCED BY SHIPS. The structure of a ship floating at rest in still water is usually subjected to various straining forces tending to produce changes of form. When she is rolling and pitching in a seaway, or pro- pelled by sails or steam-power, these straining forces become greater, while others are developed. In order to provide the necessary structural strength, the naval architect has to make choice of the materials best adapted for shipbuilding, and further to distribute and combine these materials so as most efficiently to resist changes of form or rupture of any part. By these means he seeks to secure the association of lightness with strength to the fullest possible extent. Before this intention can be accomplished satisfactorily, the designer of a ship must have an intelligent appreciation of the causes and character of the strains to be provided against ; other- wise materials may be concentrated where strength is not chiefly required, or vice versa. The importance of such knowledge has been recognized from the time when the construction of ships began to receive scientific treatment, but in this, as in most other branches of the subject, the greatest progress has been made within comparatively recent times. We now propose attempting a brief popular sketch of the chief straining actions to which ships are subjected, and in a subsequent chapter will discuss the principles of the structural strength of ships. The magnitude of the forces acting upon the structures of ships obviously cannot be measured by the observed effects. When the strength and rigidity of a structure are ample in relation to the forces acting upon it, there will be no visible change of form; whereas forces of equal magnitude acting on a weaker structure may produce deformation, and thus illustrate the tendency of the forces in question. Wood ships, for example, actually bend longi- tudinally under the action of forces which would produce no similar bending in well-built iron or steel ships, because they are stronger. In many cases wood ships alter form transversely, "working" at chap, viii.] THE STRAINS EXPERIENCED BY SHIPS. 297 the junctions of the decks and sides, or at the bilges, when rolling in a seaway. Forces of equal intensity acting upon stronger iron or steel ships may give no external evidence of their existence. In both cases the tendency to produce change of form is the same ; and the maintenance of form, is no evidence of the absence of straining forces, or of their small amount. The chief strains to which ships are subjected may be classified as follows : — 1. Strains tending to produce longitudinal bending — " hogging " or " sagging " — in the structure considered as a whole. 2. Strains tending to alter the transverse form ; i.e. to change the shape of athwartship sections of a ship. 3. Strains incidental to propulsion by steam or sails. 4. Strains affecting particular parts of a ship — " local strains " — tending to produce local damage or change of form, independently of changes in the structure considered as a whole. Besides these there are other strains, of less practical importance, which are interesting from a scientific point of view, but need not now be discussed, as there is ample strength in the structure of all ships to resist them, and there is no necessity in arranging the various parts to make special provision against them. Vertical shearing forces, for example, are in action in all ships ; they tend to shear off the part of a ship lying before any cross-section from that abaft it ; but no such separation of parts has been known to take place, nor is it likely to be accomplished in ordinary ships. The order indicated in this classification is that which will be followed in our description, being the order of relative importance of the straining actions. All of them require consideration, but, while it is not difficult to provide against the last two classes, it is important to bestow careful attention on the prevention of changes of transverse form, and it is still more difficult to prevent longitudinal bending. Longitudinal Bending Moments in Still Water. — The case to be first considered is that of a ship floating at rest in still water. It has already been shown that there are two essential conditions of equi- librium : the ship must displace a quantity of water having a weight equal to her own weight, and her centre of gravity must be in the same vertical line with the centre of buoyancy. These two con- ditions may be fulfilled, however, and yet the weight and buoyancy may be very unequally distributed; the result being the production of longitudinal bending moments. As a very simple illustration, take Fig. 103, representing a ship floating at rest in still water. Supposing her to be divided by a number of transverse vertical planes (ab, ah, etc.), let each piece of the ship between two con- 298 NAVAL ARCHITECTURE. [chap. vm. secutive planes of division be considered separately. At the bow there will probably be portions for which the weight exceeds the bnoyancy ; these excesses of weight are indicated by W x and W a . Amidships the fuller form of the ship gives greater buoyancy to FIG. 103. & * * I ■ir W, W, L •% "{ FIG. 104. * "£ * those subdivisions, and it is very common to find the buoyancy exceeding the weight, as indicated by B^ Bj, B3, in the diagram At the stem also the weight is likely to be in excess, as shown by W 3 and TV 4 . The sum of these excesses of buoyancy will evidently balance the sum of the excesses of weight at the extremities ; and the second hydrostatical condition of equilibrium requires that the resultant moment of these two sets of forces about any point shall be zero. It will be seen that a ship thus circumstanced is in a condi- tion similar to that of the beam in Fig. 104, which is supported at the middle, and loaded at each end. Such a beam tends to become curved, the ends dropping relatively to the middle, and the ends of the ship tend to drop similarly, the change of form being termed "hogging." Hogging strains are very commonly experienced at every part of the length of ships floating in still water. If the conditions of Fig. 103 were reversed, the excesses of buoyancy occurring at the extremities, and those of weight amid- ships, the ship would resemble a beam supported at the ends and loaded at the middle of the length. The middle would then tend to drop relatively to the ends, a change of form sometimes occurring in ships, and known as " sagging." In all, or nearly all, ships, when floating in still water, the fine form of the extremities under water makes the buoyancy of those parts less than the corresponding weights ; so that sagging strains are rarely experienced throughout the whole length of a ship in still water. Among waves, as will be seen hereafter, the conditions may be changed so as to produce sagging strains at every part of the length of a ship. The opinion is sometimes expressed that, whenever there is an excess of weight amidships in a ship, sagging strains will be de- chap, viii.] THE STRAINS EXPERIENCED BY SHIPS. 299 veloped ; but this is not a necessity. Suppose, for example, that Fig. 105 represents a vessel having an excess of weight (W 2 ) amid- FIG. 105. f*-_ £ $. %- a T a FIG. 106. W 21V, WC 3 t 8^T» ships as well as at the extremities, and excesses of buoyancy at the intermediate portions. This is the condition of very many ships, such as paddle-steamers with their machinery concentrated in a comparatively small length amidships, or ironclads with central armoured breastworks or batteries overlying the spaces occupied by the machinery. Such a vessel may be compared to the beam in Fig. 106, supported at two points, and laden at the middle and ends. According to the view mentioned "^=^^^^^^=^ = " _ above, sagging strains should then be produced under the middle load; but it is easy to show that this may or may not be the case. For this purpose a short explana- tion is needed of a few simple principles, the application of which is general to ships as well as to beams. Suppose it is desired to obtain the " bending moment " at any section — say ah — of the beam in Fig. 106. Conceive the beam to be rigidly held at that section, and reckoning from either end of the beam up to ah, let an account be taken of every force acting upon it, load and support, as well as of the distance of the line of action of each force from the selected section ah. Multiply each force by the corresponding distance, add up separately the moments of the loads and supporting forces, and the differences of the two sums will be the bending moment required. It is immaterial which end is reckoned from in estimating the bending moment. As a very simple case, suppose it to be desired to find the bending moment of the forces acting upon the middle section of the beam in Fig. 106. Let the weight of the beam be neglected, and the supports be midway between the middle of the length and either end. Suppose the following values to be known : — 4? = distance between the loads on ends of beam ; Wx = load on either end ; 2W 2 = load in middle. 3°° NAVAL ARCHITECTURE. [chap. vhi. Then each support will sustain a pressure (B) equal to "Wj + Wj. For the bending moment at the middle of the beam, we must have — Bending moment = W x X 21 - (W 1 + W 3 )Z = (W x - W 2 )Z. Hence it will be seen that the following conditions hold : — (o) If "Wj is greater than Wa, there will be a hogging moment at the middle of the beam, and no section will be subjected to sagging moment, notwithstanding that the middle load 2W 8 is carried. (b) If W x is less than Wa, there will be a sagging moment at the middle of the beam. (c) Even in this second case the sections of the beam situated between the ends and the supports will be subjected to hogging moments, and so also will some part of the beam lying between the supports and the middle. The case of the ship is similar, but more complex, the estimate of the bending moment experienced by the midship section involving the consideration of many vertical forces, some acting upwards and others downwards. But the foregoing is an illustration of the general mode of procedure ; and the conditions of the existence or non-existence of sagging strains amidships stated for the beam are paralleled by somewhat similar conditions for the ship. Beckoning from the bow or stern of a ship to the midship section, or to any other cross-section, it is easy to estimate the bending moment when the relative distribution of the weight and buoyancy has been deter- mined. This is a laborious rather than a difficult operation, and may be briefly described. The longitudinal distribution of the buoyancy in a ship floating at rest in still water may be readily determined from the calculations made for her displacement up to any assigned water-line, and can be graphically represented in a simple fashion. Fig. 107 illustrates this. The base-line AB represents the length of the ship. At equi-distant intervals ordinates are drawn at right angles to the base ; these may be assumed to correspond to hypothetical planes of division, such as ah, ab in Fig. 105. For each such plane of division the area of the immersed portion of the corresponding cross-section of the ship is deter- mined, and on the corresponding ordinate in Fig. 107 this area is set off to scale. A series of points is thus determined, through which the "curve of cross-sectional areas" BBB is drawn. This curve clearly represents the longitudinal distribution of the buoyancy of the ship up to the assigned water-line, and is therefore commonly styled the " curve of buoyancy." Its area represents the total buoyancy or displacement to the assigned load-line. If, midway between any two of the ordinates, a line is drawn perpendicular to chap, viii.] THE STRAINS EXPERIENCED BY SHIPS. SOI AB, the length of this line will represent (to scale) the buoyancy (say in tons) of the portion of the ship lying between the planes of division corresponding to those ordinates. So long as the same draught and trim are maintained the curve of buoyancy obviously remains unaltered, although great changes may be made in the longitudinal distribution of the weights on board a ship. The determination of the longitudinal distribution of the weight of a ship is less simple, and a large amount of work is involved. Ordinarily separate estimates are made of the longitudinal distribu- tion of the fixed weights — such as the structure and equipment of the ship, the engines and boilers — and of the longitudinal distribu- tion of varying or consumable weights — such as coals, cargo, or other lading. For each portion of the length of a ship situated between two planes of division, the weights are separately estimated for the hull and lading. Then on a line drawn perpendicular to the base- line AB, and midway between the ordinates corresponding to the two planes of division, a length is set off representing the weight of that portion of the ship, on the same scale as was used for the curve of buoyancy. A series of points is thus determined, through which is drawn what is termed the " curve of weight," WWW, Fig. 107. Sometimes two such curves are drawn, one representing the fixed weights of hull, machinery, etc. ; and a second, superposed upon it, representing the variable or consumable weights: The area enclosed by the curve WWW represents the total weight of ship and lading. It will be understood that such a curve as WWW does not exactly represent the distribution of weight ; the true graphical representation would not be a curve, but an irregular and discontinuous outline. In fact, it is not unusual to construct the graphical representation of the longitudinal distribution of the weight in this fashion, instead of averaging its irregularities in the form of a curve like WWW. Either process may be used with close approximation to accuracy, when estimating the longitudinal bending moments. The conditions of equilibrium for a ship floating at rest in still water require that: (1) the total area enclosed by the curve of 302 NAVAL ARCHITECTURE. [chap. viii. weight shall equal the total area enclosed by the curve of buoyancy ; (2) that the centres of gravity of the two areas shall be on the same ordinate. Taking any ordinate (say PQ in Fig. 107), the intercept (QR) between the two curves represents the excess (or defect) of buoyancy at that place. Where the curve of buoyancy lies outside the curve of weight (reckoning from the base-line AB), buoyancy is in excess ; where the curve of weight lies outside, the weight is in excess ; at the sections where the curves cross, the weight and buoyancy are equal, and these are termed " water-borne " sections. A more con- venient mode of representing these excesses or defects of buoyancy is furnished in Fig. 108. Here the base-line and the dotted ordinates FIG. 108. correspond to those in Fig. 107 ; and on any ordinate of those curves the intercept (say QR) is measured and transferred to the correspond- ing ordinate QR in Fig. 108, being set above the base-line AB when the buoyancy is in excess, and below when the weight is in excess. The curve LLL drawn through the points thus determined is termed the " curve of loads," and indicates at a glance the unequal distribu- tion of weight and buoyancy. The total area enclosed by the parts of this curve lying above the base-line must equal that of the parts lying below that line. Having constructed the curve of loads for any ship floating at a certain water-line and laden in a specified manner, it is easy to obtain the value of the longitudinal bending moment at any cross-section. This may be done either by direct calculation in the manner explained above, or by simple processes of "graphic integration" from the curve of loads. A first integration of that curve gives the " curve of shearing forces ; " which, being itself integrated, gives ordinates of the " curve of bending moments " (such as MMM in Fig. 108). Any ordinate of the latter curve represents, to scale, the bending moment (usually expressed in foot-tons) at the corresponding cross- CHAP, viii.] THE STRAINS EXPERIENCED BY SHIPS. 303 section of the ship. Ordinates set off above the base-line indicate "hogging" moments, while "sagging moments" are indicated by ordinates set off below the base-line. From the preceding remarks, it will be obvious that a necessary- preliminary to calculations for longitudinal bending moments is the knowledge of the distribution of the weights carried by a ship. For all ships it is possible to deal with the " extreme light condition " when they are cleared of cargo and lading. The draught and trim corresponding to that condition can be ascertained, and the distribu- tion of their " fixed " weights can be estimated as explained above ; so that curves of loads and bending moments can be constructed. Very often the magnitude of the straining forces corresponding to this extreme light condition, which can only be reached in harbour or dock, exceeds the corresponding still-water strains for laden ships. Formerly the case had considerable practical importance, as many wood-built sailing ships, when laid up in ordinary with weights usually stowed amidships removed, "hogged" to a very sensible extent. Under existing circumstances, with iron or steel ships, the extreme light condition usually has only a theoretical interest; although, as above stated, the curve of weight corresponding to that condition is commonly determined, as a basis on which to superpose any known or assumed distribution of weights carried by a laden ship. War-ships are designed to carry known weights of armament and equipment in definite positions. It is easy, therefore, to pass from the extreme light condition to the fully laden condition of such ships ; or to their condition when specified consumable weights of coal, ammunition, or stores have been removed. In most cases only the extreme light and the fully laden conditions are investigated. Merchant ships are necessarily subject to greater variations, and this is particularly true of cargo-carriers, since the character, weight, and disposition of their lading vary from voyage to voyage. The only fixed condition for merchant ships is consequently the extreme light condition, and for the laden condition either assumptions must be made of the character and stowage of the cargo, or those particulars must be obtained from actual observation. The former is more commonly done, and certain typical cargoes taken for purposes of calculation. Frequently, for purposes of comparison, a homogeneous cargo, practically filling the internal spaces, is assumed ; and for this case the calculations are simple. For cargo-steamers it is also common to assume, for purposes of calculation, that exceptionally heavy cargoes, such as railway bars or iron ore, are put on board in positions such as experience shows to be suitable. 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I T3 2*3 » ~ Q, tO __ ■3es> %g « ^ Z* § s s Ort-M B Q.S.S t. b^ (0«* ETC*© gS".ts frSoS •A a co to 00 CO "So F^J4 3 2-m 'O'O'O pa's A> s v a | u CO Q »h iao *j ->± > © S tTco a> ^gj ftft 1 iee |g» s ai? fr t|E?S8 : to « a « » S'7'V B B B a£hH S g>S =5 &! g-53 ■ -g « a a §a ■S3 ig, 3, a & «B X? g to H fP . . , : 4 4 .. 1 ■■& •f |SSS 5 » " 1 9 E h a > „ to tO-S <« .S 2 o o a o a a o l o o e e o o o 1 ^ o o o oooooiooo o e oo on 5- o 1 o a a o o o \ o oio a a o a to j *, b|o o e O O slo o | o O e o a < S j 7 1 ■ ^ f ' i ' "S ii55dmco5BroB505taaa^ in the unbutted planks, to secure them to the ribs of the ship ; and the holes cut for these fastenings at any cross-section may be taken as equivalent to a further loss of about one-eighth of the total sectional area. Putting together the allowances for butts and fastenings, it appears therefore that the effective sectional area of planking thus arranged is about five-eighths of the total sectional area when resist- ance to tensile strains is being considered. When compressive strains have to be resisted, the conditions are different. If the butts are properly fitted and caulked, the butted strakes are nearly, if not quite, as efficient as the unbutted strakes ; and if the bolts and treenails properly fit their holes, no deduction need be made for these holes. Hence, against compressive strains, the effective area practically equals the total sectional area. Similarly, in iron ships, the holes for the rivets securing the outer plating to the ribs cut away about one-seventh or one-eighth of the total sectional area, and this deduction must be made from the total area in order to find the area effective against tensile strains; whereas against compressive strains.no such deduction is needed. In many other instances 34^ KA VAL ARCHITECTURE. [chap. ix. similar allowances are required, and can be readily made when the details of the construction of a ship are known. Some shipbuilders prefer to dispense with this determination of effective sectional areas, and use total sectional areas in constructing the equivalent girder ; which is therefore the same both for hogging and for sagging strains. This procedure is not so accurate as that described above, and the resulting economy in labour is not great. It has been chiefly employed in calculations for merchant ships where the severest strains experienced are usually hogging strains bringing the decks and upper works into tension. So long as the departure from accuracy is borne in mind the process is unobjection- able. But in computing the stresses corresponding to a given bending moment, the employment of the total instead of the effective sectional areas, obviously leads to results which fall below the truth. Another important matter is the determination of the relative values of wood and iron, or wood and steel, when they act together in resisting longitudinal bending. So long as the stresses put upon the materials do not surpass the "limits of elasticity" of the wood, it is a fact, ascertained by experiment, that the wood will act with the metals and lend them valuable assistance. This is very advantageous to the structural strength of ships of all classes, in which plates (stringers or ties) are used on the decks and else- where, with wood planking over them. In composite ships also, with a wood skin worked on iron or steel ribs, and in sheathed ships, wherein wood planks are worked outside the skin plating in order to receive zinc or copper sheathing, this combined action of wood and metals is of great value. The late Professor! Eankine suggested some years ago that a fair allowance, averaging the various strengths of the timbers used in shipbuilding, would be to consider wood equivalent to one-sixteenth of its sectional area of iron ; and this is the allowance usually made in determining the effective sectional areas for the portions of the deck-flanges (A, B, C, in Tig. 124), representing the wood planking, or for other parts where plating and wood act together. When the equivalent girder has been drawn, the next step is to estimate the strength of the midship section thereby represented. This is done exactly in the same manner as if the girder were the cross-section of a long beam, subjected to the same bending strains as those to which the ship is subject. The comparison of a ship tending to hog or sag to a beam is a very old one, having been made by some of the earliest writers on the theory of naval archi- tecture. Like many other suggestions, this was not made use of to any great extent until the introduction of iron shipbuilding. The chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 349 late Sir "William Fairbairn did much towards establishing the practice of treating a ship as a hollow girder, so far as longitudinal bending is concerned. Eeaders familiar with mathematical investi- gations of the strength of beams will not require any further explanation respecting the use made of the equivalent girder ; but, in order to assist those not acquainted with these investigations, a brief explanation will be given of the principal steps by which the strength of a beam may be calculated. Fig. 126 shows the side view and section of a flanged beam, which is bent by the action of the downward pressures P, P, and the upward pressure Q. When it is thus bent, the convex upper side AB must have become elongated, as compared with its length when the beam was straight ; whereas the concave under side CD must have been shortened. Hence at some intermediate part — suppose at BF — there will be found a surface which is neither stretched nor compressed, but maintains the same length which it had when the beam was straight. The surface EF is termed the " neutral surface ; " all parts of the beam lying above it are subject to tensile strain, FIG. 126. all parts below are subject to compressive strain. In the sectional drawing of the beam, ef corresponds to EF, and is termed the / neutral axis of the cross-section. On the neutral surface EF, let any two points ab be taken. When the beam is bent, the corre- sponding length on the upper surface is shown by cd, and that on the lower surface by gh; the figure eghd therefore represents the shape into which the bending of the beam distorts that part which was of the uniform breadth ab throughout the depth of the beam, before it was bent. For any layer in the beam the elongation or compression produced by the bending varies directly as the distance of that layer from the neutral surface. Within the limits of elasticity of the material the elongation or compression also varies directly as the strain applied ; that is to say, a bar of the material will stretch twice as much with a given weight suspended to it as it does with half that weight suspended ; and so on. Hence it will be seen that in a bent beam the stress on each unit of sectional area in a cross-section such as that in Fig. 126, or any other form of 35° NAVAL ARCHITECTURE. [chap. ix. section, varies directly with the distance of that unit from the nentral axis ef. At the upper surface AB the stress will be twice as severe as it is midway between AB and EF, and the tensile strain at AB bears to the compressive strain at CD the same ratio as the distance of AB from EF bears to the distance of CD from that surface. The question thus arises, What governs the position of the neutral axis ? The answer is very simple. It is coincident with the centre of gravity of the cross-section of the beam, supposing (as may fairly be done) that the external forces P, P, Q act per- pendicularly to the surface EF. This follows directly from the consideration that the sum of all the tensile forces developed on any cross-section of the beam must equal the sum of the compressive forces. The neutral surface of the beam contains the centres of gravity of all the cross-sections ; and this condition holds for all forms of cross-section, and all variations in form at different parts of the length ; the preceding remarks containing no assumption that the beam is of uniform cross-section throughout its length. When the form of the cross-section of any beam is given, the above stated property enables the position of the neutral axis to be determined. One further step remains to be explained. At any cross-section of the beam in Fig. 126 (say, at the middle of the length) the ex- ternal forces (P and Q) give rise to a bending moment the value of which is easily ascertained. The effect of this moment is seen in the curvature of the beam ; but it may be asked by what moment is the moment of the external forces balanced. Obviously it must be balanced by the moment of the internal forces* (stresses, as they have been termed) developed by the elongations and compressions. Each of these stresses may be considered as a force acting perpen- dicularly to the plane of the cross-section, and having for its fulcrum the neutral axis ; and in this resistance to the external forces the internal forces all co-operate, from top to bottom of the beam. The total moment of these internal forces, about the neutral axis for any cross-section, is easily determined. It has been remarked that the stress on each unit of sectional area varies directly as its distance from the neutral axis. Let it be assumed, therefore, that under the * In mathematical investigations it deformation resulting from the action of is usual to use the term "stress" as external forces. This course has been denned above, and to restrict the term frequently followed in the text for the " strain " to deformations produced by greater convenience of professional the action of any force or forces. Ship- readers, and no confusion need result, as builders and naval officers use the latter the sense in which the terms " strain " and term more freely; in the sense both of " straining force " are used will always be the internal forces (or stresses) developed, apparent from the context, and the deformation or tendency to chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 35 1 action of certain external forces, a stress of s lbs. is experienced by a square ineh of sectional area at one inch distance from the neutral axis. Then the corresponding stress on a square inch of sectional area at a distance y inches from the neutral axis will be expressed by the equation — Stress = s . y lbs. The moment of this stress about the neutral axis equals the product of its amount by the distance y. That is — Moment of stress = s . y 2 (inch-pounds). This last expression holds good for each square inch of sectional area. Hence for any cross-section of the beam — Moment of resistance = sum of moments of the stresses on each unit of sectional area = S(sy a . 8A) = s . S(y 2 - SA) = s . I where §A is an element of the sectional area at a distance y from the neutral axis ; and 2 is the sign of summation for all such elements making up the total cross-sectional area A. The sum of all these products (y* . §A) is termed the " moment of inertia " (say I) of the cross-section, about the neutral axis; and hence it follows that the moment of resistance may be succinctly expressed as the product of the stress on a unit of sectional area at a unit of distance from the neutral axis into the moment of inertia. This moment of inertia depends upon the size and form of the cross-section ; the stress (s) at distance unity from the neutral axis depends, for a given cross-section, upon the magnitude of the moment of the external forces producing bending in the beam. Finally it should be noted that the foregoing equations hold good only when the maximum stress experienced by the material in the cross-section does not exceed the " elastic limit." The upper and lower surfaces of any cross-section of the beam are those which are subjected to the greatest stresses, being most distant from the neutral axis. If h^ and h 2 are the respective distances of these surfaces from the neutral axis, and p x and p 2 the corresponding stresses per unit of area (say per square inch) ; then from the foregoing expressions we have for any cross-section — p L p 2 moment of resistance ~ h x ~ h 2 ~ moment of inertia (I) But this moment of resistance to bending must balance the bending moment produced by the external forces, such as P and Q in Fig. 126. Hence finally if M = bending moment of the external forces, about any cross-section of a beam — 35 2 NAVAL ARCHITECTURE. [chap. IX. — Pl—P* — — are equations determining the maximum stresses y, aud ^j, when the other quantities are known. The moment of inertia I is proportional to the product of the area of the cross-section into the square of the depth of the beam ; whereas the distances h L and h 2 are proportional to the depth. Hence the ratio of the products of the sectional areas by the depths of two beams of the same material and similar cross- section, is a measure of their relative strengths to resist bendinsr moments. From the foregoing general expressions a few deductions may be made. With a given sectional area, and a certain material, changes in the forms of cross-sections of beams may largely influence the moment of inertia, and therefore influence the resistance to bending. The flanged form of beam shown in Fig. 12(3 is thus seen to have great advantages, as regards the association of strength with Hght- ness; for the material thrown into the flanges is at a considerable distance from the neutral axis, and the moment of inertia is conse- quently increased. The vertical web must possess sufficient strength to keep the flanges at their proper distance apart and to efficiently connect them. When this has been done, all the rest of the available material should be thrown into flanges, and in lattice girder beams and bridges the principle receives its fullest development. Reverting to the equivalent girder for a ship (Fig. 124), it is possible to make use of the foregoing general principles in order to compare the relative importance of different parts of the structure, as measured by their resistance to longitudinal bending. The most important parts are the upper flange A and the lower D ; the flange C, corresponding to the lower deck, lies so close to the neutral axis (mn) as to be of little assistance. The flange B is of much more service, but cannot compare in importance with A. The web EE, formed by the side plating or planking, is mainly useful, when the vessel is upright, in forming a rigid connection between the flanges and enabling them to act together. On account of their distance from the neutral axis, the parts of EE lying nearest to A and D offer considerable resistance to bending. When the vessel is inclined, the conditions are somewhat changed ; she then resembles a hollow girder set angle-wise. The parts contributing most to the longi- tudinal strength will then be the upper deck, the sheer-strakes and side plating adjacent to that deck, and the bottom in the region of the bilges ; but the arrangements which are efficient when the vessel is upright will also contribute greatly to the efficiency when she is heeled over to the most considerable angles likely to be reached in chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 353 rolling. There is good reason to believe that a ship which is strong enough to resist longitudinal bending moments when she is upright will be sufficiently strong in every other position. By general consent, therefore, the upright position is assumed in the construction of the equivalent girder, and most care is bestowed to meet the bending strains incidental to that position. Calculation op Moment op Inertia op Section when the Ship is undeb a Hogging Strain. feet. Total depth of girder = 37-5 Neutral axis below top = ft, = 19*3 Neutral axis above bottom = ft, = 18' 2 Parts of structure. Effective sectional areas = A. Distance of centre of gravity from neutral axis = h. Squares of distances Products Depths of webs in girder = d. Squares of depths = d'. Products ^XAxd 2 . Upper deck flange Main deck flange . Lower deck flange Wing passage bulkhead \ (part) . . ./ Coal bunker bulkhead) (part) . . ./ Shelf plate . Skin' plating . Bottom plating above\ neutral axis . ./ Coal -bunker bulkhead! (lower part) . ./ sq. in. 155-1 654-1 117-2 51-0 feet. 19-2 10-6 3-6 5-5 368-6 112-4 13-0 30-2 57,170 73,521 1,524 1,540 feet. 9-0 81-0 344 14-0 1-4 2-0 28 2-8 7-8 9 24-7 685-1 19 ; 37-8 •85 10-1 •4 3-2 •7 102-0 •2 10-2 17 69,880 4 386 18-4 •8 6-3 338-6 •6 39-7 19,331 1 125 Wing passage bulkhead) (lower part) . ./ Bottom plating above\ bilge . . ./ Bottom flange 63-4 401-0 4-6 7-5 21-2 56-3 1,344 22,576 9-3 12-7 86-5 161-3 457 5,390 889-0 15-8 249-6 221,894 5-5 30-2 2,237 • 449,884 27,894 27,894 I = moment of inertia = When the ship is on a wave crest — = 477,778 M = bending moment at section just outs ide battery = 28,000 foot-tons. foot-tons, fe St. Maximum tensile stress on upper \ 28,000 x IS part of section . . . . f ~ 477,778 •3 — =1-13 tons per square inch. Maximum compressive stress on 1 28,000 x 15 lower part of section . . / — 477,778 •2 — =1-07 tons per square inch. Hogging, it will be remembered, is the change of form produced by the ends of a ship dropping relatively to the middle, the keel 2 a 54 NAVAL ARCHITECTURE. [chap. IX. becoming arched upwards. The conditions are then similar to those in the beam, Fig. 126; the upper parts of the structure being subjected to tensile strains, the lower to compressive strains, and the Calculation of Moment op Inertia op Section when the Ship is tjndeb a Sagging Strain. feet. Total depth of girder = 37*5 Neutral axis below top = &i = 15-9 Neutral axis above bottom = 6, = 21*6 Distance Puts of structure. Effective sectional areas of centre of gravity Squares of distances Products A XV. Depths of webs in girder Squares of depths = *". Products AxAXeP. = A. neutral axis =/t. = *=. = d. sq. in. feet. feet. ! Upper deck flange 202-9 15-8 249-6 50,644 — — — Main deck flange 777-8 7-1 50-4 39,201 — — — Lower deck flange 148-6 •2 •04 6 — — — Skin plating (part) 681-5 7-9 62-4 42,526 15-8 249-6 14,175 Armour and backing . 1657-5 3-2 10-2 16,906 6-5 42-3 5,843 Wing passage bulkhead / 43-8 \ 65-0 3-2 6-6 10-2 43-6 447 2,834 6-5 11-9 42-2 141-6 154 767 ! Goal bunker bulkhead . 46-3 5-2 27-0 1,250 9-2 84-6 326 Shelf plate . 24-7 2-6 6-8 168 — — — Skin plating (part) 92-4 1-3 1-7 157 2-6 «-8 52 Bottom plating above) bilge . . . ./ Bottom flange 3601 11-0 121-0 43,572 13-6 185-0 5,552 767-2 19-2 368-6 282,790 5-6 31-4 2,007 480.501 28£76 I = moment of inertia = 28,876 = 509,377 When the ship is ast ride the wave hollow — M = bending m Dment at section just out' foot-tons. ide batter; eet f = 47, 120 foot-' tons. Maximum tensile stress part of section . on lower "1 47,120 x 2 • J ~ 509,377 L - 6 -*to, is per s quarein ah. Maximum compressive f upper part of section itress on \ ±7,120 X 1. • J 509,377 '• 9 _l-47 tons p sr square inch. division between the two being marked by a neutral surface. Sagging is the converse case where the middle drops relatively to the ends ; the keel becoming arched downwards, the upper parts of the structure being subjected to compressive strains, and the lower to tensile strains, the change of strain being marked by a neutral surface, not agreeing in position with that for hogging. It will indeed be evident, from what has already been said respecting the difference between the total and effective sectional areas of parts of the chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 355 structure, that, strictly speaking, the equivalent girder for hogging strains must be different from that for sagging strains ; although, as stated above, the two are sometimes treated as identical. While the sectional areas of the upper and lower flanges A and D of the equivalent girder in Fig. 124 change both their absolute and relative values, according as hogging or sagging strains have to be resisted, it is still true, for both hogging and sagging, that these are the two parts of the structure which are of the greatest assist- ance in resisting change of form. Their joint action is secured by means of the web formed by the vertical or nearly vertical portions of the skin. FIG. 127. Girder £tn Girder &r Sagging Neutral Battery Deck Main Deck ^SeuiraVAaBlS Axis Ln-wer Deck S s An example, taken from an actual ship, may be of service both as an illustration of the foregoing remarks respecting the relative importance of the several parts of the structure, and as an indication of the simplicity of the calculations for the equivalent girders of ships. That selected is for a broadside ironclad frigate resembling the Invincible class in the Eoyal Navy. Fig. 127 represents the equivalent girders for this ship when subjected to hogging and , sagging strains. The armour is supposed to be efficient only against compressive strains, which is an assumption on the side of safety. In estimating the effective sectional areas of other parts of the 35 6 NAVAL ARCHITECTURE. [chap. ix. structure the rules explained above have been followed. The bending moments (il) for the extreme positions of support, on wave- crest and astride wave-hollow, were estimated in the manner explained in Chapter Y1LL., and are introduced in the calculations for the purpose of deterrnining the corresponding maximum stress on the top and bottom respectivelv. From the preceding explanations and illustrations it will be obvious that the ratio of the depth of a ship to her length should exercise great influence upon the provision of longitudinal strength. The moment of resistance of an equivalent girder section like that in Fig. 124 has been shown to be very largely influenced by the depth ; while the maximum longitudinal bending moment for a ship is expressed in terms of the product of her weight into the length. Broadly speaking, the shallower a ship is in proportion to her length the greater should be the amount of material contributing to the longitudinal strength ; and not unfrequently when the hull-proper is extremely shallow recourse is had to some device for virtually increasing the depth, as is described on p. 375. War-ships of nearly all classes are of greater depth in relation to their length than merchant ships ; and this fact, taken in connection with their structural arrangements and distribution of weight and buoyancy, explains the smaller stresses to which the material in war-ships is usually subjected. It must not be supposed, however, that increase in depth per se necessarily leads to a diminution in stress ; on the contrary, cases may occur where an increase in depth obtained bv building a light continuous superstructure, upon a comparatively strong hull, actually leads to an increase in the maximum stress brought upon the material most distant from the neutral axis.* The reasons for this are obvious enough, on consideration of the funda- mental equations for the strength of beams, given above; but the following example may assist some readers. A belted ironclad having a depth of 42 feet from the flat keel to the spar-deck amid- ships, had a strongly plated protective deck, 16 feet below the spar- deck; and calculations were made for the purpose of ascertaining the maximum stresses likely to be brought (1) upon the material in the spar-deck when the sides were intact, and (2) upon the material in the protective deck when the sides above that deck were shot away in action, so that the protective deck became the top of the girder. Under hogging strains the following were the results : — * Readers desirous of Mowing out actions of the Institution of Naval this subject may turn with advantage Architects for 1878. to a paper by Mr. Purvis in the Trans- chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 357 I. With sides and spar-deck intact — Total depth of girder = 42 feet Neutral axis below top = 23J „ Moment of inertia of ) r,r,o aqa equivalent girder 5 Using the same notation as before, for a given bending moment (M). Maximum stress on material) _ w x — = M x ^ in spar-deck . . . . ) 1 1 376,000 = M x (nearly). 16,100 v yj II. With sides and spar-deck damaged — Total depth of girder = 26 feet Neutral axis below top =11 „ Moment of inertia of } _ n-. q qqq equivalent girder . 5 Maximum stress on material ~) _ -** 11 in protective deck . . .} 210,000 = M X 19^00 (nearly) - Hence it is seen that the diminution in the depth produced by breaking the continuity of the lightly constructed top sides, upper deck, and spar-deck actually resulted in a diminution of tensile stress in the ratio of 191 to 161. This diminution in tensile stress was accompanied in this case by an increase in the compressive stress on the bottom plating, the value of which may be easily ascertained, if desired, from the foregoing data. Although our illustration has been taken from war-ships, the point raised is chiefly important in merchant-ship construction, especially in connection with vessels having continuous spar-decks or awning-decks, in which types the bottoms are usually stronger than the upper decks, under the principal hogging moments experienced. The ratio of length to breadth must be considered also in adjusting the amount of longitudinal strength to be given to a ship. For the upright position the breadth influences the effective sectional areas of the decks, bottom plating or planking, etc., included in the equivalent girder. For the extreme "beam-ends" position the breadth becomes the depth. Ships rarely, if ever, are thrown ab- solutely upon their beam ends, and only reach greatly inclined positions when rolling heavily. For such inclined positions the breadth affects the depths and strengths of the corresponding equivalent girder sections. 35 S NAVAL ARCHITECTURE. [chap. ix. Equivalent-girder calculations are usually made for cross-sections at or near the middle of the lengths of ships ; because the severest hogging and sagging moments, corresponding to exceptional positions of support for ships afloat or ashore, are usually experienced by these cross-sections. Similar calculations may, however, be made for other cross-sections lying towards the bow or stem, the moment of resistance of the equivalent girder for any section being compared with the bending moment experienced by that cross-section, which bending moment is ascertained from the corresponding ordinate of curves such as MMM in Fig. 110, p. 306. Cases occur where the presence of large hatchways or openings in the deck, or peculiarities in the structural arrangements — such as the discontinuance of protective plating at some cross-section in a central citadel or battery ship — lead to greater tensile and compressive stresses being brought upon the material at cross-sections considerably distant from the middle of the length, than are experienced by the material at the midship section. No general law holds good in these matters, but each case must be separately investigated. Broadly speaking, the diminution of the bending moments from the middle of a ship towards her ends, renders possible some diminution in the strength of corresponding cross-sections as compared with the strength of the midship section. Local strains and other considerations interfere with the application of any general rule, but the fullest association of lightness with strength requires that the shipbuilder shall bestow attention upon the longitudinal distribution of the material in a ship. In deciding upon what reductions of scantlings or thicknesses are possible in the parts lying towards the ends of a ship, the builder has to note two important facts. First, the gradual narrowing of the ship towards the extremities is in itself a cause of decrease iu the strength of cross-sections ; it lessens the sectional areas of the plank- ing or plating on decks, sides, and bottoms ; and not unfrequently, owing to the reduction in girths, there are fewer longitudinal stiffeners at the ends than amidships. Second, when a ship is con- siderably inclined, the narrowing of the decks produces a virtual decrease in the depth of the equivalent girder sections ; this may be regarded as the source of a still further loss of strength to the cross- sections lying towards the extremities, which is not in operation when the ship is upright. For the upright position the depth of the equivalent girders in most ships remains practically constant for all cross-sections throughout the length. These facts, taken in connection with local requirements, have led shipbuilders to make only a small decrease in the thicknesses of the planking, plating, etc., forward and aft as compared with the thicknesses used amidships. In wood ships the thickest outer plank- chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 359 ing, the wales, is reduced in thickness towards the bow and stern. In iron and steel ships of the mercantile marine it is customary to maintain the midship thicknesses throughout one-half the length. At the extremities of iron ships it is usual to reduce the thickness, of the outer skin by about ^ inch to -fe inch, according to the size of the vessel. For steel ships the corresponding reductions are from £o to ^5 inch. Stringers on the decks are also often narrowed or decreased in thickness towards the ends. Vessels framed on the longitudinal system have, in addition, the depths of their longi- tudinal frames decreased towards the extremities, and as the girths of the sections become less, the practice is to stop short one or more of the longitudinals. These are the main changes that need be mentioned ; they do not effect any considerable difference in the scantlings at the extremities as compared with those amidships, and although some writers have recommended much more marked differences between the central part of a ship and her ends, the general feeling and experience of shipbuilders have not gone in this direction. Local requirements, as remarked above, exercise a very great influence on the longitudinal distribution of the material, often in a direction exactly opposite to that in which the consideration of the strength of the ship as a hollow girder would lead. Many examples of this will occur to the reader who has an acquaintance with the details of shipbuilding ; only two or three can now be mentioned. The plating near the stern in a single screw-steamer, from the girder aspect of the case, might be made as thin as any plating on the ship, but as a matter of fact it is as thick as any, the reason being that the local strains due to screw propulsion require strong plating to be fitted between the stern-post and the stuffing-box bulkhead next before it. Passing to the other extremity of an armoured ship, another instance is found. In order to meet the local strains pro- duced by the chafing of the cables, and rubs or blows of the anchors on the bows, it is usual in ships of the Eoyal Navy to double the plating for some distance. This additional thickness, of course, adds much to the strength of a ram-bow ; but here again, reasoning from the girder, a minimum thickness of plating should suffice. Very similar remarks may be made respecting the vertical dis- tribution of the material in the cross-sections of ships. Seasoning exclusively from the analogy of the equivalent girder, it would be advantageous to decrease the amount of the material near the neutral axis, which could be best done by thinning the skin-plating or planking at that part. Some slight reductions in thickness have been made in many cases, but there are other considerations which require to be taken into account before proceeding far in this direc- 3 6 NAVAL ARCHITECTURE. [chap. ix. tion. Ships frequently occupy inclined positions, and then side plating or planking which is included in the " web " of the equivalent girder for the upright position, may be so placed as to be capable of yielding the greatest assistance to the structure. In iron and steel ships the common practice is to keep the greater part of the skin-plating of uniform thickness, fitting a few thicker strakes on the bottom below the bilges where the severe local strains due to grounding are principally felt, and thickening or doubling the sheer- strakes. "Wood ships usually have their thickest planking (the " wales ") in the neighbourhood of the middle of the depth, where it can be least effective against longitudinal bending strains when the ship is upright. These wales were probably the outgrowth of the rubbing strakes formerly fitted near the main breadth, and they also formed strong ties above and below the lines of ports in many classes of wooden war-ships, thus restoring, to some extent, the loss of strength due to the want of continuous longitudinal planking in wake of the ports. Modern war-ships have their structural arrangements very much controlled by the necessity for protecting certain parts by armour. The general considerations based upon the comparison of a ship to a girder are, therefore, to a large extent, overruled, material being massed in flanges formed by decks near the middle of the depth, or thrown into the centre of the web of the girder for the upright position, instead of being added to the upper part or to the upper deck. For instance, to increase the resisting power of the target formed by the armoured side, the skin-plating behind the armour is often made about twice as thick as the bottom plating, although its situation is frequently not very favourable to its efficient contribution of longitudinal strength. The strongly plated decks, fitted a few feet above water (as in the belted ships) or at a moderate distance below water (as in the central-citadel type), do not contribute to the longitudinal strength to the same extent as the same weight of material differently distributed might do. The armour plating itself also, even when arranged and fastened with the utmost care, must be regarded rather as a load carried by the structure than as adding much to the longitudinal strength. From the preceding remarks it will appear that, although the comparison of a ship to a girder in her resistance to longitudinal bending is of great service to the shipbuilder, it only holds good within certain limits. Keeping this in view, we now propose to sketch the character of the principal structural arrangements, which supply longitudinal strength to different classes of ships, and to contrast the relative efficiency of those arrangements. Wood ships, iron and steel ships, and composite ships will come under review, as chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 361 well as armoured ships. It must be understood that no endeavour will be made to describe the structural details of any class ; for these the reader must turn to works on shipbuilding. To illustrate the contrast between these classes, and to assist our explanations, Figs. 128-131 have been prepared. The former shows, in cross- section and inside elevation, the construction of a wooden ship according to the former practice of the Koyal Dockyards. Fig. 129, p. 362, shows, in cross-section, the construction of an iron or steel merchant ship with a single bottom. Fig. 130, p. 367, shows, in FIG. 128 Inside Yiew ■cross-section, the construction of an ironclad ship of the " central- battery " broadside type. Fig. 131, p. 370, shows, in cross-section, the construction of an iron or steel merchant ship, with cellular double bottom. Eepeated references will be made to these figures, •and their principal features will be noted in connection with the contribution of individual parts to the general structural strength. First, as to the upper flange in the equivalent girder for ships. The parts ordinarily included for wood ships are as follows : the •deck-planking, allowing for its effective area in the manner explained 362 NAVAL ARCHITECTURE. [chap. IX. above ; the " shelf-piece " under and the thick " water-way " upon the beam ends. Such a flange is much less strong against the tensile strains brought upon it by hogging than it is against the compressive strains due to sagging, the effective area against tensile strains being less than three-quarters of that against compressive strains. It is a matter of common experience that, under severe hogging strains, signs of working and weakness displayed themselves in the upper works of large wood ships. In order to add strength to the upper FIG. 129. deck, iron stringers and plating were worked under the wood plank- ing in many of the later wood-built ships of the Eoyal Navy. In iron, steel, or composite ships the upper flange of the equivalent girder resembles that described for the later wood ships. Fig. 129 shows one arrangement suitable for small ships. The stringer plates on the beam ends are drawn in strong black lines under the wood planking. These stringers should always be strongly secured to the uppermost strake of the side plating (termed the- chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3^3 " sheer-strake "), which is often made thicker or doubled, for the purpose of increasing the longitudinal strength. Composite ships, although they have not an iron skin, are usually fitted with deck- stringers and sheer-strakes. Early iron ships were often built with no plating on the upper decks, the arrangements of deck-planking and water-ways being similar to those in wood ships. Then stringers and tie-plates were introduced ; and, as ships increased in sizes and proportions, com- pletely plated decks were fitted. Now it is not uncommon, in the largest iron and steel ships, to find all the decks completely plated. This arrangement is of the greatest value to the structural strength ; and has prevented weaknesses which were of common occurrence in earlier ships of much less dimensions, but without plated decks. Wood planking is laid over the plating in passenger-steamers ; in cargo-vessels the deck-plating is often left uncovered. From the first the iron-built armourclads of the Koyal Navy have been fitted with plated decks, covered by wood planking. It will be understood, from the remarks made on p. 348, that within certain limits the wood and plating can act together in resisting tensile or compressive stresses. At the same time the wood decks are fitted chiefly for comfort or for sanitary reasons, and not primarily for purposes of structural strength. In the Great Eastern exceptional strength was provided at the upper deck, which was a cellular structure formed by two strong iron skins worked above and below deep longitudinal girders. There were no transverse beams such as are generally fitted to the decks of ships, and the longitudinal girders were effective both against longitudinal bending and as stiffeners to the skins, especially under compressive strains. In the largest vessels since built there has been no necessity to imitate this cellular construction of the upper deck, and the simpler, lighter,* and less costly arrangement above described has been found to answer all requirements. Next, as to the lower flanges in the equivalent girders of the different classes of ships. In wood ships the parts included in the lower flange vary considerably, according as hogging or sagging strains have to be resisted. The bottom planking up to the bilge, the keel, keelson, and binding strakes (6, Fig. 128) are all effective, although not equally effective, against both hogging and sagging strains. It was a common practice to fill in the openings between the ribs, from the keel to some distance above the bilge in large war-ships ; and this had a twofold advantage. In case of damage to the bottom planking the fillings kept the water out of the hold ; and, moreover, when the vessel tended to hog, and her bottom was brought under compression, the lower part of the frames was made into a practically solid mass 3 6 4 NAVAL ARCHITECTURE. [chap. ix. of timber, the fillings offering great resistance to change of form. When sagging took place, and the bottom was brought under tension, the fillings could lend no such help to the pieces lying longitudinally, and the difference was very considerable. In most wood ships the severest longitudinal bending moments were those tending to produce hogging, a fact which made the use of fillings of the greater value. To assist the bottom in resisting the tensile strains due to sagging, iron stringers were fitted in some few cases in lieu of the ordinary thick binding strakes ; but this arrangement was not so efficient as the use of iron strengthenings to the upper deck. In iron or steel ships without double bottoms the bottom flange of the girder is made up of the keel, keelson, side keelsons (s, Fig. 129), hold stringers (/*), and the bottom plating. These are all effective against both hogging and sagging strains ; and, as already explained, the difference in the sectional areas, effective against tension and compression respectively, is not nearly so marked as in the case of the corresponding part of a wood ship. The transverse frames, or ribs, of the iron or steel ship are usually 20 inches to 2 feet apart, there being nothing corresponding to the fillings of the wood ship. Fig. 129 by no means represents the universal practice of shipbuilders in the arrangement of longitudinal stiffeners to the bottom plating. There are very many varieties of side keelsons, hold stringers, keelsons, keels, etc., some builders preferring one arrangement, other builders preferring another arrangement. But they have one feature in common. The mainframes lie transversely like those of a wood ship, and do not contribute to the longitudinal strength. The longitudinal pieces are supplementary or subordinate to the transverse framing, and are either fitted in between the ribs (like s), to secure a direct connection with the bottom plating, or over-ride the ribs (like h, Fig. 129). For wood ships it is practically a necessity to place the ribs transversely, and in the earliest iron ships the arrangements of wood ships were naturally imitated to a considerable extent. The moderate size of the earlier iron vessels rendered unnecessary any longi- tudinal strengthenings to the bottom other than were furnished by the engine and boiler bearers, fitted primarily as supports to the propelling apparatus. But as the sizes of ships increased, the longitudinal strengthenings to the bottom were multiplied, and in some cases the bottom was thus strengthened, while the top flange of the girder was left almost uncared for, the result being a great disproportion between the strength of the top and bottom flanges. There are, of course, many local strains to be borne by the bottom of a ship — such as those due to grounding, the carriage of cargo, and chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3 6 5 possible concentration of weights — which are not paralleled by any strains that have to be borne by the decks ; but to give greatly disproportionate strength to either flange involves a bad distribution of the material. The use of iron and steel upper decks and broader stringer plates has partially corrected an evil formerly prevalent in merchant ships, but the upper flange is still in many cases much weaker than the lower. If ships fail, they usually yield to hogging strains ; but cases have occurred where the upper flange of the "equivalent girder has yielded to the ^compressive strains incidental to sagging. The shallow-draught steam-ship Mary, mentioned on p. 345, is alleged to have foundered in consequence of the upper deck crushing up when she met with heavy weather. A wood deck properly fastened lends great assistance to a thinly plated deck when subjected to compressive strains, The transverse system of framing iron and steel ships of the mercantile marine has been continued, and will probably be continued, because it facilitates rapidity of construction and is less costly, under ordinary conditions, than the rival system in which the continuous frames are placed longitudinally. No doubt the best combination of strength with lightness is obtained when the main frames are placed longitudinally, at least in the parts of the bottoms below the bilges. On the other hand, the possible saving in weight is not found by private shipbuilders a sufficient inducement to depart from long-established practice. Consequently in ships with single bottoms and transverse frames the necessary strength is given to the lower flanges of the equivalent girders by means of strong bottom plating combined with numerous side keelsons, hold stringers, etc. Many, if not most, of these longi- tudinal pieces are now fitted " inter-costally " — that is, between the ribs or transverse frames — and attached at their outer edges directly to the skin plating. This is advantageous in many ways. The longitudinal stiffeners thus arranged can assist the skin efficiently, not merely against hogging or sagging strains, but against the strains incidental to water-pressure, grounding, and other causes which have been dealt with in the previous chapter. With these arrangements and closely spaced transverse frames, ample strength has been secured in the bottom flanges of some of the largest merchant steamers yet constructed, in which it has been thought undesirable to introduce cellular double bottoms. Composite ships resemble most iron and steel ships in having the main frames transverse ; and the bottom flanges of their equivalent girders differ chiefly in that they include wood keels and bottom planking. The latter especially loses, as compared with plating, in its resistance to. tensile strains due to sagging moments, No o 66 NAVAL ARCHITECTURE. [chap. ix. equally intimate connections can be made between the intercostal side keelsons of a composite vessel and the bottom planking, as are possible between such keelsons and the bottom plating of an iron or steel ship. Nor can the composite ship have the help of fillings between the frames like those of a wood ship. Although the transverse system of framing has been so generally adopted in the mercantile marine, there have been many ships in which longitudinal framing occupied the chief place. The Great Eastern, was the most notable example, and her structural arrange- ments, due to the joint labours of the late Mr. I. K. Brunei and Mr. Scott Russell, furnished good evidence of the possibilities of the longitudinal system.* Other and much smaller merchant ships have been built on very similar principles ; and in all the large ships of the Royal Navy great prominence is given to longitudinal framing. Such framing is of the greatest advantage in the lower parts of ships. The comparatively flat surfaces of the bottom plating below the bilge are best stiffened against buckling by longitudinal frames, which form strong girders well secured to the bottom plating, and contribute to the effective area of the lower flange of the equivalent girder for the upright position. At the bilge there is usually considerable transverse curvature in the bottom plating, a fact which gives it great stiffness in itself against buckling under compressive strains ; so that at the bilge longitudinal frames are not much required for the purpose of preventing buck- ling. Very frequently external bilge-keels, fitted just at this part of the bottom primarily to check rolling, also form good stiffeners to the plating, besides adding their own sectional areas to the lower flange of the girder. Above the bilge, and below the lower deck, longitudinal frames are again of great use, especially in adding to the longitudinal strength when the ship occupies an inclined position, and is subject to hogging or sagging moments. For parts of the structure lying above the lower deck, other considera- tions enter and make longitudinals of less importance ; in fact, the decks themselves with their stringers, etc., form most efficient longitudinal stiffeners. Sometimes, where a lower deck does not extend throughout the whole length, but is broken for some reason, its stringer plate is continued in order to form a stiffener, as shown by I, Fig. 129. As a rule the decks need no aid from intermediate * For much interesting information evident from the details therein given concerning the construction of thiB ship, that, at a very early period after the and her predecessors, the Great Western introduction of iron ships, Mr. Brunei and Great Britain, see the life of Mr. perceived the great advantages attaching Brunei, published by his son. It is to longitudinal framing. chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 367 longitudinal frames, the only framing required in the upper parts of ships being vertical and transverse. Such framing stiffens most efficiently the almost upright side plating, gives facilities for attaching the beams to the side, and answers other purposes. The extent to which it is adopted must of course depend upon the special conditions of each class of ship. Widely spaced vertical frames sufficed in the upper parts of the Great Eastern; whereas in armoured ships these frames are often very closely spaced, in FIG. 130. order to assist in strengthening the target formed by the armoured side. Tig. 130 illustrates the last-mentioned case ; below the armour the main frames are longitudinal, as shown, but behind the armour the principal frames are vertical, being spaced 2 feet apart (see the section at cd). The longitudinal girders worked between the strakes of the wood backing are not fitted primarily with a view to increase the longitudinal strength of the structure, although they have this effect, but are intended to increase the resistance of the o 68 XAVAL ARCHITECTURE. [chap.ix. target formed by the side of the ship against penetration or damage by projectiles. Looking a little more closely into the arrangements illustrated in Fig. 130, it will be evident that the lower flange of its equivalent girder includes the skin plating, both outer and inner, as well as the numerous and strong longitudinal frames. These frames, as already explained, are of great value in preventing buckling under hogging strains or water pressure, and in resisting the tensile strains due to sagging, even when there is only a single outer skin. But their efficiency in these respects and the strength of the lower flange of the girder are both very greatly increased by the adoption of the inner skin plating, forming a double bottom. This cellular construction has been proved by experiment to develop most efficiently the strength of a structure formed of plates and bars, any one of which, taken singly, has little strength to resist bending. This is particularly true under compressive strains, and was first demonstrated in experiments made before the tubular bridge across the Menai Straits was constructed. Although longitudinal frames play such an important part in connecting the two skins and stiffening the bottom, their direct contribution to the moment of resistance of the equivalent girder section is not relatively great. This will appear more clearly on refer- ence to the exemplar calculations for an armoured ship on pp. 353, 354. The inner and outer skins are the largest contributors to the moment of inertia of the lower flange, and the longitudinals might be left out of the calculation without seriously affecting the result. Their presence in the structure is, however, of great importance ; for without them the joint action of the two skins in resisting bending moments would not be secured. In order to give efficiency to longitudinal framing, frequent " sections of support " must be provided by means of transverse bulkheads or " partial bulkheads," as is further explained hereafter. Having made this provision, the amount to which the main longitudinal frames require to be reinforced by subordinate transverse frames, depends upon the necessities of local strength in the bottom. In armoured ships of the Eoyal Navy the " bracket-frames " are 4 feet apart, and this amount of stiffening to the bottoms is found sufficient to meet all the ordinary strains to which the ships are subjected during construction, launching, docking, or service afloat. In cases of grounding also, although these are rare in war-ships, this bracket- system of construction has stood the stress of service exceedingly well. The Iron Duke, for example, grounded twice on the China station, once on a soft bottom and secondly on a rocky bottom. On this second occasion the outer bottom was bulged in, the framing chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 369 in the double bottom was bent and broken over a considerable length., but the inner bottom remained intact, and the ship was safely navigated to port after she was got off. The case of the Apollo, which struck the Skelligs during the naval manoeuvres of 1892, was even more remarkable. Since 1877 a remarkable extension of the use of cellular double bottoms has taken place in the mercantile marine. The change must be mainly attributed to the enterprise of a few leading shipbuilders, and to the support given to the movement by the professional officers of the Eegistration Societies. One great reason . for this rapid progress is to be found, no doubt, in the more general recognition of the commercial advantages attending the use of water- ballast; the gain in safety has also had some weight, and is becoming increasingly evident to shipowners. Limits of space prevent us from attempting to trace in detail the various methods of construction adopted by different firms, or to contrast these with the corresponding methods of construction in war-ships. All that can be done is to choose a good example of common practice, such as is illustrated in Fig. 131, and to sketch the main features. Above the turn of the bilge the main frames are vertical and have the usual spacing, about 2 feet. At the turn of the bilge there is a continuous watertight longitudinal frame (AA, Fig. 131), and upon this the vertical frames are stopped short, their heels being connected to the longitudinal by bracket-plates (B). The longitu- dinal AA has its outer edge connected by a continuous angle-bar to the bottom plating, while its inner edge is similarly connected to the inner skin plating ; in this way the longitudinal forms a watertight side boundary to the ballast-tank, or cellular bottom. Within the double bottom the main frames are longitudinal as indicated on the section. The transverse framing consists of "gusset" or " bracket " plates, with angle-bars on their edges and ends connecting them to the two skins and the longitudinals ; these bracket-frames are spaced . 4 feet apart, just as the corresponding frames in the armoured ships are spaced. Intermediate between the bracket-frames, simple angle- bar transverse frames are fitted (as shown on lower section) to give additional support to the skin-plating, and to provide for taking the ground as merchant ships frequently have to do. In many cases a different plan of framing is adopted within cellular double bottoms. The main frames are placed transversely about 2 to 2 J feet apart, and formed of plates lightened by holes, with angle- bars on the edges, extending from the keel to the continuous longitu- dinals (AA, Fig. 131) which form the side boundaries of the double bottom. The longitudinal frames in the double bottom are then worked in short lengths (intercostally) between the transverse frames. 2 b ;7o XAVAL ARCHITECTURE. [chap. IX. Very similar arrangements have been carried out in some cruisers of recent construction and of moderate dimensions. The discontinuity of the transverse framing at the side boundaries of the double bottom requires to be carefully provided for, and when this is done no dif- ficulty arises in the maintenance of transverse strength. ~ Above the side longitudinals (AA) deep transverse frames or partial bulkheads are commonly fitted at intervals of 10 or 12 feet, and carried up to the lowest complete deck. The outline of such a strengthener is indicated by dotted lines in the diagram. From this brief explanation it will be seen that the cellular system now widely used for merchant ships, although similar in chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 37 l principle, differs in details from the longitudinal system previously described for armoured ships. The greater amount of support given to the bottom is desirable in merchant ships, which have to take the ground. Experience has shown that a vessel can be built on this cellular system, and given all the advantages of a water-ballast tank, as well as greater safety, with no greater weight of material than would be used in a vessel of the same dimensions built on the ordinary transverse system. The cost of workmanship in the cellular system is probably somewhat greater than in ships with a single bottom. Cellular double bottoms necessitate the sacrifice of some of the hold- space as compared with the transverse system of framing without any provision for water-ballast. But as compared with other methods of forming water-ballast tanks, the cellular system is more simple and efficient, while it takes less away from the hold-space. One very common arrangement for water-ballast consisted in building upon the floors a series of longitudinal girders which carried an inner skin, extending across the ship from bilge to bilge, and connected in a watertight manner to the outer bottom plating. These ballast-tanks, or partial double bottoms, answered fairly well, and the material used in their construction contributed somewhat to the general structural strength ; but not nearly to the same extent as the material in the cellular bottoms. It is now not uncommon to find the cellular system applied throughout the whole length of a ship, in order to gain the greatest power of controlling the trim by the admission of water-ballast into the spaces near the extremities. In many cases, however, the double bottoms of merchant ships only extend over portions of the length. Continuing the investigation of the equivalent girders for different classes of ships, attention must next be directed to the webs or vertical portions, marked EE in Fig. 124. In ordinary wood ships the outside and inside planking is worked in one thickness, as shown in Figs. 125 and 128. The individual planks or " strakes " are comparatively narrow, the numerous butts and edge seams being caulked. This planking, with the water-way and shelf-pieces under the beams, and the diagonal strengtheners, form the web of the girder. The ultimate strength of these parts against cross-breaking strains is no doubt ample in all or nearly all cases ; and what has to be regarded is rather their strength to resist the racking strains which always accompany bending. Eeverting to the case of the beam discussed on p. 349, it will be seen that, although the total of the tensile forces experienced by any cross-section equals the total of the compressive forces, these two resultants act in opposite directions, and therefore tend to rack or •distort the beam,- this racking strain reaching its maximum at the 37 2 NAVAL ARCHITECTURE. [chap. ix. neutral surface, and gradually decreasing to nothing at the top and bottom of the beam. So long as the beam is in one piece, or so long as the pieces forming its web are well connected together edge- wise, there is no difficulty in meeting this racking strain. But if a beam were constructed of which the web consisted of strakes or narrow planks placed edge on edge, and having little connection edgewise, then obviously, as the beam bent, these planks would be made to slide upon one another by the racking strains.* And if these strakes were crossed at right angles by ties, corresponding to the ribs or timbers of a wood ship, these ties would add little to the strength of the web against racking. For (to quote the well-known illustration of Sir Eobert Seppings), if a field-gate be made of pieces all lying parallel or at right angles to one another, its resistance to distortion of form will be very small. On the contrary, if the strakes forming the web are crossed by diagonal ties — corresponding to the cross-bar of the gate — there will be a great addition to the strength of the combination against racking and distortion of form. Such are the simple principles upon which the use of diagonal " riders " or ties in wood ships was principally based. The side planking above the bilge has in itself little strength to resist racking strains ; and in many cases these strains have been so severe as to show marked evidence of their action. When the line-of-battle ship Caesar stopped on the launching ways and broke considerably, it was in the planking near the middle of her depth that working was most apparent ; the diagonal riders also showed signs of severe straining. Moreover, it is a matter of common observation that, when the caulk- ing of the seams of planking in a wood ship becomes slack and needs Tenewal, she is much more liable to working longitudinally. This circumstance is easily explainable, seeing that, when well caulked, there is a much greater resistance to the relative motion of the planks which racking strains tend to produce. Diagonal riders furnished, however, the best corrective for this source of weakness, when a single thickness of planking was worked.f When first introduced into the Eoyal Navy by Sir Eobert Seppings, early in the present century, these riders consisted of massive timbers, worked inside the transverse ribs of the ship. Sub- sequently iron-plate riders were substituted for the timber riders, and with very great advantage. In Fig. 128 these riders are indicated in * For a well-known illustration of edgewise through adjacent strakes of the the ahove statement, the reader may skin planking, in order to prevent rack- turn to the springs of railway-carriages. ing. A similar plan of bolting is some- t In some small vessels built by the times adopted in certain portions of the late Mr. Ditchburn, bolts were driven bottom planking of ordinary wood ships. chap, ix.] STRUCTURAL ARRANGEMENTS. OF SHIPS* 373 both the cross-section and the inside view, being marked r, r. It will be observed that they are worked inside the ribs, and inclined 45 degrees to the vertical. Wood-built merchant ships are usually furnished with similar iron riders, which are often worked outside the timbers; and that arrangement has some advantages in point of strength, although it is not so convenient to execute during the con- struction of a ship. Whether fitted inside or outside, the riders are usually inclined so that their upper ends slope towards the midship section of the ship ; near the middle of the length (as shown on the inside view, Fig. 128) the two systems of riders belonging to the fore and after bodies respectively are made to cross each other at right angles. In some cases where special strength was desired, this duplicate arrangement of the riders has been carried right fore and aft ; but the more common plan was to have one system only. It will be observed that, as usually arranged, these iron riders are very efficient aids against hogging strains, which are those most injurious to wood ships. When hogging takes place, the ends must drop relatively to the middle, a change of form which would bring the iron riders under tensile strains, the kind of strains which they are best fitted to resist. Against compressive strains these thin narrow bands of iron cannot be nearly so efficient as against tensile strains, so that, as commonly fitted, riders are not of much service against sagging strains, except amidships, where the two systems overlap one another. It is amidships that the severest strains are experienced, so that the crossing of the riders there is a great advantage. Composite ships of the mercantile marine were usually built with a single thickness of planking, and consequently needed diagonal strengthened. One common plan of fitting these was to have rider plates riveted outside the iron frames, and inclined 45 degrees to the vertical. The upper ends of those riders were attached to the sheer strake, and the lower to another detached longitudinal tie, formed by a strake of plating worked at the bilge. Composite ships of the Eoyal Navy are built with their outside planking in two thicknesses. The edge-seams of the planks in the inner thickness are each covered by a plank of the outer thickness ; the seams of the outer thickness are similarly covered by the planks of the inner thickness* A strong edgewise connection is thus made in the double skin, and consequently diagonal rider plates are dis- pensed with. Other composite ships have been constructed with the skin planking in two thicknesses, one or both of which had the planks worked diagonally ; it was then unnecessary to fit diagonal rider plates to assist the skin against racking strains. This diagonal system of planking has also been adopted in some special classes of wood ships with great success. The royal yachts 374 NAVAL ARCHITECTURE. [chap. ix. are examples of this system of construction. Three thicknesses of planking are employed, the two inside being worked diagonally, and the outer one longitudinally. The two diagonal layers are inclined in opposite directions, and the skin thus formed possesses such superior strength to the skin of an ordinary wood ship that there need be comparatively little transverse framing above the bilges. Direct experiments with models, and the experience gained with ships thus built demonstrated its great superiority in the combination of strength with lightness. The royal yacht Victoria and Albert, built on this plan, with her unusually powerful engines and high speed, although subjected to excessively great sagging moments (see p. 315), has continued on service for forty years with complete exemp- tion from signs of weakness. Like many other improved systems of construction, this was found more expensive than the common plan ; but if wood had not been so largely superseded by iron and steel, much more extensive use would have been made of the diagonal system. Large steam and sailing launches employed in the Koyal Navy are still built on a somewhat similar plan ; the skin planking is in two thicknesses worked diagonally, with the two layers inclined in opposite directions. These boats answer admirably, and have frames only on the flat of the floor, where the wear and tear of grounding have to be borne. Iron and steel ships have outer skins formed by numerous plates,, each of which is strongly fastened at the edges, as well as the butts, to the plates adjacent thereto. Such a combination is very strong against longitudinal racking strains, and needs no supplementary strengthening such as the diagonal riders of wood or composite ships. Many proposals have been made, and several plans have been patented for using diagonal strengthenings in iron ships, the superiority of an iron skin, and its capability of resisting and trans- mitting strains in all directions, not having been apprehended. From the bilges upwards, the outside plating forms the principal part of the web of the equivalent girder section in ships like that in Fig. 129, p. 362 ; and when properly stiffened, it acts this part most efficiently when the ship is upright. When she is considerably inclined, some parts of the same plating contribute strength to the flanges of the girder-section for that position, as already explained. Vessels with double bottoms extending far up the side, or with wing-passage bulkheads like that in Fig. 130, p. 367, gain much on vessels with single bottoms, since the additional skin contributes to the strength of the web of the girder for the upright position, and to the strength of the flanges of the girders for inclined positions. Any other longitudinal bulkheads which extend over a considerable length in the ship may also be regarded as contributing chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 375 to the longitudinal strength, and one of the most valuable additions of this kind that can be made to a ship is a middle-line bulkhead like that shown in Figs. 22-29, p. 32, for an ironclad of recent type. The longitudinal bulkheads fitted in the Great Eastern added greatly to her ^longitudinal strength. Such bulkheads are, however, generally fitted with a view to increase in safety or accommodation; the increase in structural strength is a secondary consideration. Mention may be made, in passing, of a plan upon which a few iron ships have been built, intermediate in character between ships with transverse frames and others with longitudinal frames. The main frames in these special vessels were placed diagonally, some- what after the fashion of riders, and therefore crossed the probable lines of fracture of the plating in ordinary iron ships, which line, it has been said, would lie in a transverse plane. It was hoped, thereby, either to divert the line of fracture from this transverse plane to some longer and stronger diagonal line, or else to make the diagonal frames add to the strength of the transverse section which gives the smallest effective sectional area to the bottom plating. The plan has not found favour with shipbuilders, nor is it comparable to the longitudinal system, in cheapness and simplicity of construction or in combination of lightness with strength. Vessels designed for service in shallow waters often have their hulls strengthened longitudinally by girders. It has been shown that the depth of any cross-section of a vessel has a great influence upon the amount of its resistance to bending strains ; and in these special vessels the depths of the hulls are so small as to render supplementary strengthenings essential. The American river steamers before mentioned furnish good examples. Their wood hulls were extremely shallow, and had to carry an enormous super- structure of saloons, etc., although they had in themselves little longitudinal strength. To supply this, a " hog frame " was con- structed. It consisted of a strong side keelson fitted along the flat floor of the vessel, at some distance out from the keel. Upon this keelson were erected a series of timber pillars, and along over the heads of the pillars a strong continuous timber beam or tie was carried, diagonal struts being fitted between it and the keelson. A light but strong timber girder of considerable depth was thus firmly combined with the shallow hull, and made to help it efficiently against hogging. In other light-draught vessels built for river or coast service, with iron or steel hulls, arrangements have been adopted similar in principle to the foregoing, iron or steel lattice girders having been substituted for the more cumbrous and less efficient hog frame. These vessels, being designed for smooth-water service, are not subjected to longitudinal strains of so severe a 37 6 NAVAL ARCHITECTURE. [chap. ix. character as those experienced by ships at sea, and, what is still more important, their strains remain nearly constant in character as well as intensity. Hence their case is much more easily dealt with in the manner described, than is that of a seagoing ship which has to bear rapid and extreme variations of longitudinal bending strains while in addition she may be rolling from side to side. At the same time, there is considerable range for the exercise of ingemiity in securing the lightness of construction demanded by shallow draught. The conditions of the problem resemble more closely those of bridge construction than those connected with the construction of seagoing ships, with which we are more especially concerned. Figs. 182 and 133 furnish illustrations of this class; being respectively a side view and cross-section of a tug-boat built for the Godavery river from the designs of the late Mr. J. E. Napier.* The draught of water was not to exceed one foot ; it was conse- quently necessary to make the structure as bight as possible, and steel was used. The hull proper was that of a shallow open boat, about 3J feet deep ; it was formed, as shown in Fig. 133, of steel plates \ inch thick, with each strake of plating stiffened by a longi- tudinal angle-bar. The transverse frames consisted of angle-bars, spaced 9 feet apart, and therefore quite subordinated to the longi- tudinal frames. The hull proper, being so shallow and without a deck, could not contribute the necessary longitudinal strength; but this was obtained in a very ingenious manner. An awning was necessary to furnish protection from a vertical sun and tropical rains ; it is marked a, a in the diagrams, and is about 10 feet above the bottom. To convert this into an efficient upper flange, it was formed of steel plates ^ inch thick, each strake being stiffened by a longitudinal angle-bar. Transverse angle-bars were fitted, 9 feet apart, vertically over the corresponding transverse frames of the hull, and diagonal braces (e, o, Fig. 133) connected the corresponding transverse stiffeners to hull and awning, preventing the latter from being pulled or blown over. Lattice girders (6, b, Fig. 133) formed by diagonal and vertical bars, as shown in Fig. 132, were fitted on each side to strengthen the connection between the awning and the hull, and to enable them to act together in resisting longitudinal bending. The diagrams explain further particulars. The vessel was driven by paddles placed under the sloping stern ; the boiler was placed at the bow, where there was also a steam capstan ; and * The drawings and particulars are taken from vol. viii. of the Transactions of the Institution of Naval Architects. chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 377 37^ NAVAL ARCHITECTURE. [chap. ix. the tow-rope was secured near the middle of the length and led along over the awning. Besults of Calculations of Longitudinal Strength. — The comparison of a ship to a girder in her resistance to longitudinal bending is extremely useful in connection with structural arrangements; and the construction of the " equivalent girder " enables a fair approxi- mation to be made to the moment of resistance to longitudinal bending at any selected cross-section of a ship. It is necessary, however, clearly to recognize the assumptions made in these pro- cesses of calculation, and not to treat them as rigorously exact or as including all the conditions of practice. For instance, in an equivalent-girder calculation, such'as that on p. 353, it is taken for granted that the various parts of the structure are combined and supported so that they can act together. In practice, if the builder does not provide proper connections, or adequately meet local strains, " buckling " or other local failure may occur, the ultimate strengths of the various parts of the structure may not be developed, and the comparison to a well-constructed girder does not hold. Moreover, in a ship at sea the problem is made much more complicated than in bridge or girder work, by the movements of the vessel and the action of the waves upon her hull. A bridge or girder is fixed, and, although it is exposed to the action of the wind, to variations of temperature, and to both " dead " and moving loads, it is possible to approximate to the worst conditions it has to resist, and to provide a reasonable margin of strength. Experience is of immense value in determining this margin, but mathematical calculations are essential to all new departures. A ship at sea, rolling and pitching among waves, is simultaneously subjected to longitudinal, transverse, and local strains, of which a description has been given in the preceding chapter. Many of the pieces in her structure have to assist in simultaneously resisting all these strains; and it has been shown that exact estimates of their magnitude are scarcely possible. Hence it follows that purely theoretical calculation, based upon the equivalent-girder method, cannot be trusted in determining the scantlings of various portions in the structures of ships. The calculations which can be made are of value, especially for purposes of comparison between different ships, or the analysis of structural strength in a particular ship. They require, however, to be associated with the results of experience gained on service with actual ships. Some of the best lessons in structural arrangements have been derived from failures which made apparent weaknesses or dispro- portionate distributions of strength, that might not otherwise have been suspected. Keeping in mind the foregoing considerations, attention may CHAP. IX.] STRUCTURAL ARRANGEMENTS OF SHIPS. 379 now be turned to some of the calculations made for the strengths and stresses of various classes of ships. Much work of this kind has been done during the last twenty years for iron and steel ships belonging both to the Eoyal Navy and to the mercantile marine. In these calculations the maximum bending moments are estimated in the manner described on p. 311, for the two extreme positions of support illustrated by Figs. 113 and 114. These estimates, it has been shown, probably assign greater values to the bending moments than are experienced in practice. The equivalent girder is constructed, and its moment of resistance to bending estimated (as described on p. 346) for the weakest section nearly amidships. Having this data, the corresponding maximum tensile and com- pressive stresses on the material can be determined by the formula given on p. 352. These stresses are obviously not to be regarded as actually occurring in all cases, or being frequently experienced in any case. Ships may be long at work, and not meet " end-on " waves of the critical dimensions assumed. Ships of great length are less likely to do so than are shorter ships. For war-ships calculations made in the manner described show stresses on the material of comparatively moderate amounts. In armoured frigates of the Minotaur type, for example, the maximum tensile stress on the upper deck, when the vessel is balanced on a wave crest, was found to be only 5 tons per square inch of sectional area, or about one-fourth the ultimate tensile strength of good iron plates such as were used in those ships. In the central citadel type (No. 6, in the:;table on p. 315), the maximum bending moment occurs when astride a wave hollow ; and the corresponding maximum tensile stress on the bottom was found to be 5£ tons per square inch, or about one-fifth of the ultimate tensile strength of good steel plates. In the turret-ram and belted cruiser (mentioned in the same table), the maximum stress on the material was found to be only from 2 tons to 2J tons per square inch ; and in the Devastation class, only l£ ton per square inch. In the Boyal Sovereign class, the maximum stress was found to be 3£ tons per square inch when the vessel was on a wave crest. In these estimates the armour has been treated simply as a burden, not contributing to the structural strength, although it really does so to some extent. These examples show that armoured vessels have ample strength against all the principal longitudinal bending strains. Their hulls are constructed comparatively lightly, yet if the scantlings were determined solely with reference to the longitudinal bending strains, in many cases they might be still further reduced." The lower limit of scantlings in these vessels is, as a matter of fact, determined chiefly by the strength necessary 380 NAVAL ARCHITECTURE. [chap. ix. to resist local strains, and by considerations of durability. It will not be overlooked that the necessities for protection in the form of armoured sides or thick decks exercise great influence over the distribution of much of the material in these classes of ships, and curtail the possibilities of the designer. Unarmoured war-ships have also been found to have very moderate stresses under the assumed conditions. The Iris, for example, although very lightly built of mild steel, has a maximum tensile stress of 5 tons per square inch on the material in the upper deck, and a smaller compressive stress (4-6 tons) on the material in the bottom, when balanced on a wave crest. The swift cruiser, Blake, has a maximum tensile stress of 4 - 7 tons per square inch when similarly circumstanced. These moderate calculated stresses for all classes of iron and steel-hulled war-ships have been accompanied by a practical absence of any serious signs of working or weakness under longitudinal bending strains. With very few exceptions, it may be said that there has been an entire absence of any such signs, and no indica- tion of the need of greater scantlings for successfully withstanding the strains experienced when afloat. Corresponding calculations for merchant ships of all classes are now accessible. The results are very diverse, as might naturally be anticipated from the great differences between various types.* In the smaller classes the scantlings found necessary to give sufficient local strength and durability provide an ample margin of longi- tudinal strength according to the equivalent girder method. The calculated stresses for these smaller vessels are often very small; whereas in the larger vessels they are much greater than the corre- sponding stresses in war-ships. The late Mr. W. John, whose labours in this department were most valuable and extensive, published the following figures in 1874, for types of iron ships then afloat, as illustrations of the increase in maximum strain accompanying increase in dimensions. All these ships were supposed to be about eight beams, and eleven depths in lengthy and their scantlings agreed with the then current practice for first-class vessels. The maximum bending moment was assumed to occur on a wave crest, and to equal one-thirty-fifth of the product of the weight of a ship into her length. * See papers in the Transactions of 1878 ; and in the Transactions of the the Institution of Naval Architects for North-East Coast Institution of Engi- 1874, 1877, 1878, and; 1892 ; in the neers and Shipbuilders for 1889, 1890, Transactions of the Institution of Engi- and 1893. neers and Shipbuilders in Scotland for chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3^1 Register tonnage of Maximum tension on vessel. the upper works. Tons per square inch. 100 1-67 500 3-95 1000 5-19 1500 5-34 2000 5-9 2500 7-1 3000 8-1 Other examples showed that if the proportions of length to breadth and depth were increased, the vessels were subjected to greater stresses ; and in one vessel over 400 feet long a maximum stress of nearly 9 tons was found. Vessels having less proportions of length to breadth and depth sustained smaller stresses. The general adoption of plated decks in iron and steel ships of more recent construction has been most advantageous. Material has thus been added to the upper flanges of the equivalent girders, which were formerly weak in proportion to the lower flanges. The neutral axis has also been raised. Formerly that axis was often situated only from 30 to 40 per cent, of the total depth above the bottom of the equivalent girder for hogging moments. Consequently the material in the upper flange was about twice as far distant from the neutral axis as the material in the lower flange. As the stress on the material, within the limits of elasticity, is proportional to the distance it is placed from the neutral axis, for a given hogging moment the tensile stress on the upper deck was about twice as great as the compressive stress on the bottom. Such a great dis- proportion of stresses was objectionable, and has been much reduced by the changes in practice above mentioned. In war-cruisers it does not exist, the distribution of material bringing the neutral axis very nearly up to the middle of the depth of the equivalent girder, and making the tensile and compressive stresses approximately equal. The same thing. is true in many modern merchant steamers. But it is also true that in some types the old disproportion of stresses remains. Cases may occur in which the most serious strains with certain cargoes correspond to sagging moments astride wave hollows, and -in which (owing to the low position of the neutral axis) the material in the upper decks is subjected to large compressive stresses in proportion to the simultaneous tensile stresses on the bottom. This is a most undesirable condition, since the deck-plating is far better adapted for resisting tension than compression. The calculated stresses on the material in iron and steel merchant a 382 NAVAL ARCHITECTURE. [chap. ix. ships, for the two extreme hypothetical positions of support among waves, depend upon the stowage of cargo assumed and upon the structural arrangements. Homogeneous cargoes just filling the hold- spaces are generally assumed. But there are many types of cargo- steamers, each with special structural arrangements, and consequently generalizations are not possible respecting the intensity of the stresses. The following facts are of interest. In a number of cargo- steamers 300 to 350 feet in length, having about 8 to 9 beams and 11 to 12 depths in their length, the maximum stresses (tensile for wave crest) have been found to vary from 3£ to 6£ tons per square inch. Vessels of approximately the same dimensions and propor- tions, but differently constructed and varying in their speeds and coefficients of fineness, have been estimated to be subjected to tensile stresses of 8 to 9J tons per square inch. A tank steamer of the " shade-deck " type, 345 feet long, 45 J feet broad, and 35| feet depth (to shade-deck), has had her condition examined carefully.* With oil stowed principally amidships, the maximum stresses occur astride the wave hollow ; they vary from about 6 to 7 tons per square inch (compressive), and from 5£ to 7£ tons (tensile), according to the assumptions made as to the upper flange of the equivalent girder. "With an ordinary cargo, less concentrated amidships, the stresses are less serious, varying from 2£ to 3£ tons per square inch. In a Transatlantic passenger-steamer, about 500 feet long, 52 feet broad, and 33£ feet deep, the maximum tensile stresses were estimated at 6J tons per square inch. On the whole, these recent calculations in most cases show proportionately less values for the stresses than were obtained by Mr. John for steamships built twenty years ago. Similar calculations have been made for sailing ships. In examples having lengths of 210 to 230 feet, the maximum tensile stresses have not exceeded 3J tons per square inch. Attempts have been made to deduce practical rules from the comparison of stresses estimated on the equivalent-girder method, with the results of actual experience. For iron ships built to class at Lloyd's, the late Mr. John siimmarized the results of his investiga- tions as follows: When local strains have been properly met, and ships have been well built, the calculated maximum tensile stresses on the upper works may reach 6 to 7 tons per square inch, without any sign of weakness. Calculated tensile stresses of 7 to 8 tons per square inch are occasionally associated with some signs of weakness ; when these stresses reach 8 to 9 tons per square inch, experience shows that strengthening becomes absolutely necessary. In a fixed * See a paper by Mr. Kendall, in Coast Institution of Engineers and Ship- the Transactions of the North-East builders for 1892-93. chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3 8 3 iron bridge the corresponding stresses under the maximum working load to be frequently carried would not be allowed to exceed 4 to 5 tons per square inch. But as explained above, the comparison of ships to girders cannot be treated as absolute, nor the stresses calculated on the equivalent-girder method as exact. At the same time, this method of analysis and comparison is of great service in determining the scantlings of ships of new types, on the basis of past experience with other ships. Transverse Strength. — The strength necessary to prevent changes in the transverse forms of ships is chiefly provided by the following parts of the structures : (1) the transverse frames or " ribs ; " (2) the skin plating or planking ; (3) the decks, including the beams, plating, and planking thereon ; (4) the pillars or other supports to the decks ; (5) transverse bulkheads and partial bulkheads. As a simple illustration of general principles, take the case of a single-bottomed ship framed on the transverse system illustrated by Fig. 129, p. 362. Conceive two imaginary planes of division to be drawn, midway between any transverse frame and the frames adjacent to it on either side. These planes will cut off a strip of the skin plating, having a length fore and aft equal to the frame-spacing, and along the centre of this strip will be secured a " rib." Similarly, on each deck a strip of planking or plating of equal length will be cut off; and, if a beam is fitted at the selected frame, this beam will form a stiffener to the strip of planking or plating. Consequently the portion of the ship supposed to be cut off may be regarded as a hoop-shaped girder, the upper member being formed by the segment of the upper deck and its supporting beam, and the curved portion by the strip of the skin-plating and its stiffening rib. The fact that the skin and decks are continuous of course affects the resistance to change of transverse form ; and the existence of longitudinal framing secures the joint and concurrent action of adjacent parts of the structure in that resistance. Considering for simplicity only one hoop-shaped girder, its power to resist changes in transverse form may be approximately estimated when the thicknesses of plating and planking are known, and the sizes of ribs and deck-beams are ascertained. Moreover, it will be seen that the power of resist- ance to change of form must be increased greatly when there are decks below the upper decks, the segments of which form approxi- mately horizontal ties and struts to the hoop-shaped girder. Similarly, pillars reaching from the floors to the upper deck, and strongly secured to the floors and deck-beams, constitute vertical ties and struts. Or if there be longitudinal bulkheads, their seg- ments play the same part as pillars. Following out this general idea, it will be convenient to consider 3^4 NAVAL ARCHITECTURE. [chap. ix. the contributions to the transverse strength of the several parts of the structures above enumerated. The transverse frames or ribs in various classes of ships will be taken first, as these were the earliest, and are still the principal, means of giving transverse support to the skin. In wood ships the ribs are made up of several lengths (or futtocks), bolted or dowelled at the butts, as shown in Fig. 128, p. 361, or con- nected together in some other way. Adjacent pieces in any one rib are comparatively free to bend inwards or outwards in relation to one another. No single rib has much strength to resist change of form. The shipbuilder, therefore, has recourse to the plan known as " shifting the butts " (see inside view Fig. 128), making adjacent ribs succour the butted rib, by having their butts at some distance from the weak joint. Formerly, transverse timbers (or " riders ") were fitted inside the ribs to add to the transverse strength. When diagonal riders were used they also gave support to the ribs ; but in later prac- tice, when diagonal iron riders were employed, the ribs were left with little internal stiffening, except in the form of thick longitudinal planking and diagonal " trusses " from the bilges to the lower deck. The ribs of iron, steel, and composite ships are ordinarily formed from the bilges upwards, by angle, Z, or channel bars of con- siderable length. In most merchant vessels each rib consists, of a '• frame " angle riveted to the skin, and a " reversed frame " riveted to the athwartship flange of the frame angle. The frame and reversed frame thus make up a Z-shaped section (see Fig. 129, p. 362, enlarged section of rib placed below the upper deck). Z-bars are now largely used for war-ships, and channel bars for merchant ships. Greater lightness is thus secured without reduction of strength, and labour is economized. Greater lengths of bars are also available, and the necessity for strapping or welding butts is avoided. The progress in the manufacture of iron and steel has thus greatly assisted ship- builders in preparing the ribs and increasing their strength. From the remarks made on p. 352, it will be seen how important to the transverse strength of the typical hoop-shaped girder are the Z-form of the ribs, their depth, and the existence of the inner flange on the ribs. Turning to the enlarged section in Fig. 129, it will be obvious that the neutral axis must be very close to the skin ; and that the inner flange, being most distant from that neutral axis, adds largely to the strength. Increase in the depths of the ribs also increases stiffness. This principle is now largely made use of in merchant ships in the form of " web-frames," or " partial bulkheads." * * See in this connection a valuable Read and Jenkins, Transactions of the paper " On the Transverse Strains of Institution of Naval Architects for 1882. Iron Merchant Vessels," by Messrs. chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3§5 Below the bilges of iron, steel, and composite ships different modes of construction are followed. When there is no cellular double bottom, an arrangement like that in Fig. 129 is adopted. Deep floor-plates are fitted, gradually increasing in depth towards the keel. Eeversed bars are riveted to the inner edges of the floor- plates, or these edges are flanged. The outer edges, of the. floor- plates are connected to the skin plating by frame-angles. Each rib is thus formed into a strong but light girder, capable of assisting in resistance to transverse strains. In ships built with cellular double bottoms (like that illustrated by Fig. 131, p. 370), instead of the deep floor-plates, bracket-frames or lightened plate-frames stiffen and connect the inner and outer skins. It will be obvious that in such ships the inner skin contributes greatly to the transverse strength. A strip of that skin forms the inner flange of the hypothetical hoop-shaped girder, and the distribution of the material for resistance to transverse bending is much improved thereby. Care is required, of course, at the parts where the cellular bottom terminates, and ordinary transverse framing begins. The heels of the frames above the bilges are secured by brackets to the bounding longitudinals of the double bottom, and these, with other simple devices, are found sufficient in even the largest and swiftest steamships. . . The cellular system of construction for war-ships, illustrated by Fig. 130, p. 367, differs in many respects from the arrangements common in ordinary merchant ships. In the larger cruisers and armoured vessels the transverse frames are spaced 4 feet apart in the double bottom, as against 2 to 2 \ feet in merchant ships. These transverse frames are formed on the bracket system, and worked in short lengths between the longitudinals. Above the bilges where the inner bottom terminates, bracket-frames of considerable depth are fitted in the armoured ships, and connected with the frames behind armour, which are commonly spaced only 2 feet apart. The efficiency of the armoured target necessarily exercises great influence upon the framing and its connections, in many cases involving numerous breaks or discontinuities. By attention to details, however, it is found possible to meet all these conditions and yet to obtain ample transverse- strength. The unarmoured portions of the upper works and of the extremities are usually supported by transverse frames formed of Z-bars. In the smaller classes of cruisers, with protective decks and light plating on the cellular double bottoms, it has been preferred to have the transverse frames from 2 to 3 feet apart, in order to stiffen the bottom plating more efficiently. A common method is to have strong outer frame-bars extending in one length from the vertical 2 c o 86 NA VAL ARCHITECTURE. [chap. ix. keel up to the protective deck. The longitudinals for min g the side boimdaries of the double bottom are pierced by these frame-bars, but made watertight around them. The longitudinals within the double bottom are " scored " over the frame-bars and connected to the outer bottom plating by short angles. The transverse framing in the double bottom is made up of bracket-plates between the longitudinals. In this manner construction is simplified and cheapened. Above the protective decks and outside the double bottom the transverse frames are usually formed of Z-bars. In all war-ship construction, when cellular double bottoms are employed, the system of transverse framing is arranged so that adequate support may be given to the outer and inner skins for all ordinary conditions of service, while the two skins are so connected as to ensure their joint action in resisting the principal strains imposed upon the structure when ships are afloat. At the same time it is preferred not to give to the framing in the double bottom such strength or rigidity as would involve the transmission of heavy blows or shocks on the outer skin to the inner skin. Experience with many ships which have grounded proves that these intentions have been realized, especially in steel-built ships. Serious injuries to outer skins have bent and broken them, and the lower portions of the supporting frames, but have left the inner skin uninjured, and have preserved the buoyancy of the vessels sufficiently to enable them to reach port. The case of H.M.S. Apollo, mentioned on p. 334, is one of the most recent and striking illustrations of this feature in war-ship construction. The spacing of transverse frames in vessels built on the longi- tudinal system advocated by the late Mr. Scott Eussell was considerably greater than that in armoured ships, being from 12 to 20 feet in some cases. These transverse frames were made very deep and strong. They were formed of plates fitted in between the longitudinals, with stiffening angle-bars on the edges of the plates. Mr. Eussell termed these strong frames " partial bulkheads ; " and from these and the transverse bulkheads he obtained all the transverse stiffness required even in the Great Eastern, which had a cellular double bottom, and a cellular upper deck. In all such vessels the longitudinal frames were made strong and numerous, and upon them came the duty of distributing over intervening spaces, the strength of the bulkheads and partial bulkheads. The principal disadvantage of the system was the comparatively large areas of the outer skin — from 40 to 60 square feet — left without direct support. Hence it was decided, in adopting the bracket-frame system of fram- ing for armoured ships, to lessen the frame-space to 4 feet, keeping the strong plate-frames at intervals of about 20 feet, and fitting chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3 8 7 brackets at intermediate positions. The work of building was also facilitated by these departures from the original longitudinal system. Deck-beams, planking, plating, and pillars greatly assist in preserv- ing the transverse forms of ships. The first duty of the beams is to support the decks with their loads ; this was the purpose for which beams were originally fitted. But the beams have other uses. As the various transverse strains previously described are brought to bear upon the structure, the tendency at one time may be to increase the distance between opposite sides of the ship, and at another instant to decrease it. In other words the beams have to act as ties and struts alternately between the opposite sides. Similarly, the pillars were first fitted as struts or supports to the beams, to assist in supporting the decks ; but as the vessel rolls in a seaway, the strains tending to produce alteration of transverse form sometimes produce an increased thrust upon the pillars, and at others produce a pull or tension, if the pillars are well secured at both the heads and heels. Should the pillars be only capable of acting as struts, and not as ties, one important part of their possible usefulness is lacking, because they are powerless to resist any increase in the heights of the decks above . the keel. Longitudinal bulkheads, such as the " wing- passage" bulkhead shown in Fig. 130, or the coal-bunker bulk- heads usually fitted further inboard in war-ships, if well stiffened and connected at their upper edges to the decks, and at the lower edges to the outer or inner bottom, obviously exercise great influence in maintaining transverse form. The beams of wood ships are ordinarily of wood, of rectangular cross-section, and formed of different pieces, joined together by more or less elaborate scarphs, some of which are illustrated in Figs. 137- 141. The beam-ends very frequently rest upon a shelf-piece (see Fig. 128), which is bolted to the inside of the frame timbers, and are so secured to it (by dowels, etc.) as to be capable of with- standing a considerable force tending to pull the beam away from the side. Above the beam-end another strong longitudinal timber, the " water-way," is securely bolted to the timbers and strongly connected with the beam, greatly increasing the strength of its connection with the side. The beam is thus made capable of acting as a tie between the opposite sides. Its action as a strut is secured by accurately fitting its ends against the inside of the timbers. Thus far the arrangement is satisfactory, but it involves considerable skill and cost in scarphing the pieces that form the beam, and connecting the beam with the water-way, shelf-piece, etc. The rectangular form of cross-section is necessarily inferior to the flanged form ; and this is an unavoidable defect with wood beams. These considerations led to 388 NAVAL ARCHITECTURE. [chap. ix. the extensive use of iron beams in the later wood ships of the Eoyal Kavy ; similar care being taken to make good the connection of the ends of these beams with the side, in order that they might act as struts or ties. Wood pillars also fell into disuse in wood ships, iron pillars of less weight being readily made more efficient as ties and no less efficient as struts. Iron and steel ships have iron or steel beams of various sectional forms, all of which have more or less of that flanged form which has been shown to be so helpful to the association of strength with lightness. These beams can now be obtained from the makers in one length even for the largest ships, and so connected as to be capable of resisting both tension and compression. Their ends are very simply and strongly secured to the frames (see Figs. 129 and 130), the stringer plates on the beam-ends greatly strengthening the connection of the beams with the side. Tubular or flanged pillars can be associated with the beams, and made to resist both tension and compression. In every way, as regards strength and simplicity, the iron or steel ship has the advantage of the wood one in the character and connections of the beams and pillars. The composite ship in these particulars resembles the iron ship. It has been explained above that deck-flats, whether formed In- wood planking or iron or steel plating, assist the deck-beams greatly in the maintenance of transverse form. A completely plated deck, for example, if well stiffened by strong beams and bulkheads, is practically rigid when subjected to strains tending to alter the transverse form. If a ship has a series of such decks, the transverse frames or ribs really have little more to do than to stiffen the sides between the strong decks, or between the lowest of these decks and the bilges. In merchant ships of large size two or three completely plated decks are now common, and they are of the greatest value in the maintenance of the transverse form as well as in resisting longitudinal bending. This twofold usefulness has been previously mentioned, and it is as applicable to the skins as to the decks of ships. In armoured ships strongly plated "protective" decks are now the rule ; and these decks contribute greatly to the transverse strength, being assisted by other plated decks which are built for structural purposes only. Protective decks are also common in war- ships which have no side armour, and although fitted primarily for protection to machinery, magazines, etc., they are valuable additions to the transverse strength. In many cases the transverse framing of war-ships is worked in separate lengths above and below protective deeks, or behind armour. With proper connections no difficulty is experienced in the maintenance of strength. The lower decks of ships often extend over only a portion of the chap, ix.] STRUCTURAL ARRANGEMENTS OF SHIPS. 3 8 9 length, or are considerably weakened by having large openings cut in them. Merchant ships frequently have no lower decks in wake of the cargo holds, and consequently there is not nearly the same strength of connection between opposite sides at those parts as would be secured by a strong deck with its beams. To compensate in part for this loss of strength, it was formerly the practice to fit a few strong beams — known as hold-beams — in the cargo spaces. In very many cases where such precautions were not taken, serious working and change in transverse form resulted. Instead of hold-beams, deep plate-frames or partial bulkheads are now commonly fitted as previously explained. Perhaps the greatest point of difference between the action of the beams in wood and iron ships is to be found in their comparative resistances to change of the angles between the decks and the sides of the ship. The strains tending to produce such changes have been previously described ; and their effects on wood ships were so serious as to cause shipbuilders to bestow great attention upon beam-knees and their connections. A vast number of plans for beam-knees were proposed. Formerly, before iron strengthenings became general, cumbrous timber knees were fitted ; and in countries where timber is abundant such knees are even yet employed. Forged iron knees are, however, now much more generally employed, and are more efficient than timber knees, as well as less bulky. But even with the best of these arrangements— such as the knees shown under each beam- end in Fig. 128 — heavy rolling in a seaway produced sensible changes of angle. The usual indications of these changes were loosening of the fastenings which secured the iron knee to the side and to the beam-end ; and in the larger classes of wood frigates and line-of-battle ships in the Royal Navy these indications were not uncommon. The reasons for the superior resistance of iron and steel ships to any corresponding change will be obvious on comparing Fig. 128 with Figs. 129 and 130. The beam-ends of the iron and steel ships are shaped into strong knees, far more capable, from their form, of preventing change of angle. These stronger knees are fitted against the sides of the frames, and strongly riveted to them : the frames themselves are riveted to the skin, and in very many cases the stringer plates on the beam-ends are also directly connected with the skin, so that the beam-end cannot change its angle relatively to the side of the ship without shearing off numerous rivets, or fracturing plates and angle-bars. With properly proportioned knees and riveting, change in the angle made by the decks of iron and steel ships with the sides may be almost entirely prevented. Imperfect fastenings in the beam-knees may permit, and in some 39° NA VAL ARCHITECTURE. [chap. ix. cases have permitted, working at the junction of the decks and sides even in these ships; especially when they have happened to be associated with a considerable amount of flexibility in the frames to which the beams are attached. But these cases can only be regarded as examples of a defective application of principles which, when properly applied, lead to satisfactory results. Similar knees are formed on iron beams fitted to wood ships. Instead of attaching the beam-arm directly to an iron frame, as can be done either in an iron or composite ship, it has then to be secured to the side by means of angle-bars riveted through the beam, and bolted to the side planking and timbers. This plan is more efficient in preventing change of angle than ordinary knees fitted to wood beams, but is not so efficient as that of iron and composite ships, the connection with the side not being so perfect. Sometimes deep plate-knees are fitted below some of the beams in iron and steel ships, reaching from one deck to that next below it, for the purpose of stiffening the side. The beams forming the boundaries of large cargo-hatches or boiler-hatches in some merchant ships are treated in this manner, and made deeper and stronger than the other beams, for the purpose of compensating for the loss of transverse strength produced by cutting off the beams to form the openings in the deck. The growing use of partial bulkheads in the holds of merchant ships has been mentioned above : at the stations where they occur deepei beams are fitted, as shown (by dotted lines) in Fig. 131. In iron and steel-built ships of the Navy also, " partial bulkheads " are frequently fitted at intervals between the main and upper decks, in order to stiffen the sides and to assist the beam-knees in preventing change of angle. Each of these partial bulkheads is very simply formed by a plate 3 or 4 feet wide, connected at its upper end to the beams or stringer plate of the ixpper deck, at its lower end to the stringer plate on the main deck, and also attached to the side plating. Not unfrequently it is a convenience to be able to dispense with knees to lower deck beams ; a case in point is illustrated by Fig. 30, p. 36. If the ship has a sufficient number of transverse bulkheads, this disuse of beam-knees is no source of weakness. Moreover, it will be remembered that the transverse racking strains described in a previous chapter are likely to be more severe on the upper and main decks than on the lower decks. These racking strains chiefly cause the alterations of angle between the decks and sides, as well as deformations at or near the bilges ; but it is especially at the upper parts of the structures of ships that their effects require to be provided against by strong beam-knees and partial bulkheads. Transverse bulkheads, when properly constructed, add greatly to chap. IX.] STRUCTURAL ARRANGEMENTS OF SHIPS. 39* the transverse strength of all ships, but are most valuable in iron or steel ships having the main frames placed longitudinally and the transverse frames widely spaced. The cross-sections at which such bulkheads are placed may be regarded as practically unchangeable in form, under the action of the severest transverse strains experienced by a ship, provided the thin plating which forms the partition be efficiently supported by angle-bars, T-bars, Z-bars, or other forms of " stiffeners " riveted to its surface. A good arrangement of the stiffeners is that which places one set vertical and the other horizontal, the plating being thus prevented from buckling in any direction. The decks and platforms which meet the bulkheads lend very material help by stiffening them and thereby preventing change of form. When longitudinal bulkheads are associated with transverse bulkheads the two systems afford mutual support. Having thus secured great local transverse strength, it becomes necessary to provide the means of distributing it over the spaces lying between any two bulkheads ; this end is best accomplished by means of strong longitudinal frames, which are carried from bulkhead to bulkhead, and rest upon them just as the girders of a bridge rest upon the piers. The efficiency of the transverse bulkheads as stiffeners to the structure depends upon their strength and numbers, the distance between consecutive bulkheads, and the capability of the longitudinal framing to distribute the strength of the bulkheads. Ordinary iron or steel ships, having comparatively few bulkheads, do not gain so much from their help as ships with bulkheads spaced more closely. The desire to have large cargo-spaces in the hold, free from break or interruption, overrides, in many cases, considerations of increased safety and greater strength. At intervals between complete transverse bulkheads, " partial " bulkheads, formed by deep plate-frames with angle-bars on both inner and outer edges, are now commonly fitted. But there are considerable spaces in the length of ordinary merchant ships for which the transverse frames have to furnish the principal part of the transverse strength to the lower part of the structure, and the fewness of the bulkheads is one reason for retaining the close spacing of these frames. Supposing a large number of transverse bulkheads to be fitted in an iron or steel ship, the distribution of their strength over the bottom mainly depends upon the longitudinal stiffeners — keelsons, hold stringers, etc. These include very various arrangements, of very various degrees of efficiency ; but in none is the distribution so simply and efficiently made as in vessels where the main frames are longitudinal. Longitudinal bulkheads, when they are fitted either at the middle line or towards the sides (or wings), largely assist in the distribution of the strength of transverse bulkheads. In short, 392 NAVAL ARCHITECTURE. [chap. ix. all the pieces lying longitudinally, which are efficient against longi- tudinal bending strains as well as against some local strains, are also valuable distributors of transverse strength. Composite ships are often fitted with transverse iron or steel bulk- heads, the vessels of that class belonging to the Koyal Navy being exceptionally well subdivided. These bulkheads contribute much transverse strength, which is distributed very similarly to that for ordinary iron or steel ships, except that the longitudinal pieces are not so well connected to the skin. Closely spaced transverse frames are trusted, however, to supply the chief part of the transverse strength. Wood ships of the later types in the Eoyal Navy, and in some foreign navies, have been furnished with transverse iron bulkheads, and the results have been very satisfactory ; but there was greater difficulty in making the bulkheads sticcour parts lying between them in wood ships than there is in iron or steel ships ; and the attach- ment of the bulkheads to the sides was not so efficient as it is in either iron or composite ships. ( 393 ) CHAPTEE X. MATERIALS FOE SHIPBUILDING: "WOOD, IRON, AND STEEL. Three classes of materials have been extensively used in shipbuild- ing. From time immemorial wood ships have been constructed, and that material was exclusively employed for seagoing ships until the year 1838. Iron had been used for building canal boats half a century before ; and from 1821 had been employed in steamers built for river service, some of which made over-sea voyages to the places where they were regularly engaged. In the British mercantile marine from 1840 onwards iron steadily 'gained on wood ; at first by slow degrees, but subsequently very rapidly. In 1850, out of 133,700 tons of new shipping added to the British Begister only 12,800 tons were iron ships ; in 1860, out of 212,000 tons added 64,700 tons were iron ; in 1868, out of 369,000 tons added 208,000 tons were iron ; in 1880, out of 404,000 tons added 384,000 tons- were iron ; in 1891, out of 670,000 tons added less than 9000 tons were of wood. In fact, except for small vessels, wood shipbuilding has practically disappeared. The progress of iron-shipbuilding has been concurrent with the development of steam navigation, and was essential to that develop- ment. In 1850, out of 275,000 tons of British mercantile steamers on the Begister, 218,000 tons were of wood. In 1860, out of 686,000 tons of steam shipping, 536,000 tons were of iron. In 1868, out of 1,341,000 tons, wood ships represented only 122,000 tons, and iron over 1,200,000 tons. The building of wood seagoing steamers has practically ceased for many years past ; and in 1891 the total (nett) tonnage of wood steamships built was less than 600 tons. The Boyal Navy presents a similar picture. In 1850 the tonnage (B.O.M.) of wood ships had a total of 99,000 tons, against 19,500 tons for iron ships. In 1860 the proportion of wood to iron was even greater than at the earlier date, 420,000 tons against 34,800 tons. But with the construction of armoured ships iron hulls became general ; and in 1870 the total tonnage of wood ships had fallen to 386,000 tons, while that of iron ships had nearly quadrupled since 1860, becoming 130,200 tons. No wood-hulled 394 NAVAL ARCHITECTURE. [chap. x. fighting ship was laid down for the Royal Navy after 1873, and the last examples were of comparatively small size. All the armoured ships begun after 1866 haTe iron or steel hulls ; and so have other classes, except sloops and gunboats, most of which have been built on the composite principle, with wood skins, but iron or steel framing. In other countries, where shipbuilding timber is plentiful and cheap, wood ships are still constructed of considerable size and in large numbers. These are principally sailing ships. The inevitable tendency in all such cases is, however, towards the substitution of iron or steel hulls for wood, because of the commercial advantages thereby obtained. Having driven wood from its pre-eminence as a shipbuilding material, iron, in its turn, has given place to steel. Prior to 1870 steel was used to a very limited extent, and chiefly in cases where extreme lightness of hull or shallowness of draught were essential. Taking the twenty years from 1850 to 1870, over 3,600,000 tons of iron ships were built for the British mercantile marine, while only 27,000 tons of steel ships were constructed ; and from 1866 to 1875 only three small ships were built of steel in the United Kingdom. In the Royal Navy steel was used continuously from 1864 to 1875 for certain portions of the internal framing of iron ships and armoured vessels, but always under special precautions. Early in 1873 the French began to use so-called " mild steel," or " ingot-iron," in the construc- tion of war-ships. The Admiralty followed this example in 1875, ordering two despatch vessels to be constructed wholly of steel ; and in 1877 the use of the same material in the mercantile marine received the sanction of Lloyd's Register. Since 1875 the progress made in the use of mild steel has been extremely rapid. In the Royal Navy it has entirely superseded iron, and the experience gained with the new material has fully justified the change. In the mercantile marine slower progress was made at first, but there has been a very general adoption of steel in later years. In 1878 only 4500 tons of steel shipping were classed at Lloyd's ; in 1879, 16,000 tons ; in 1880, 35,400 tons ; and in 1881, 41,400 tons. In the latter year the total tonnage of steel ships was less than 6 per cent, of the aggregate tonnage of iron and steel ships. Four years later (1885) this had become nearly 35 per cent. ; in 1887 it exceeded 80 per cent. ; in 1889, 94 per cent. ; and in 1892 was nearly 98 per cent. The amount of iron shipbuilding remaining is distributed over a number of vessels of very moderate size. Iron shipbuilding is, therefore, virtually extinct in this country, except for small vessels. Besides wood, iron, and steel, other materials have been used in the construction of small vessels. Certain bronzes, for example, chap, x.] MATERIALS FOR SHIPBUILDING. 395 have been employed in experimental torpedo boats and steamboats. Aluminium has been used in a few cases for the bulls of yacbts and steamboats. In these exceptional cases it has been desired to demonstrate the capabilities of the materials employed, especially in regard to their freedom from corrosion such as iron and steel ships undergo unless proper care is taken. Aluminium has been used, not merely for this purpose, but also because of its remarkable association of strength with lightness, as compared with iron or steel. Whatever developments may be made in future in any of these directions, or in the use of alloys of nickel and other metals with steel, it is only necessary in this work to consider these three materials that have been largely used in the past. Although wood and iron are now practically obsolete, it will be interesting to examine briefly into their qualities as shipbuilding materials. By so doing it will be seen why iron was preferred to wood, and subsequently had to give place to steel. Moreover, this discussion will enable many important features in ship-construction not treated elsewhere in this volume, to be touched upon and illustrated. The structure of a ship is necessarily made up of many pieces, and the strength of the structure depends upon their individual strength, as well as their skilful combination. In considering the capabilities of any material, it is therefore necessary to examine into the behaviour of individual pieces when subjected to tensile, com- pressive, bending, or torsional strains ; and also to investigate the behaviour of combinations of pieces under similar strains. Of these strains torsional are of much less importance than the others, with the exception of a few pieces, such as the rudder-head. Tensile and compressive strains, as has been explained in previous chapters, are of the first importance; bending strains are also of importance in relation to many parts of the structure, such as the deck-beams, transverse and longitudinal framing, and unsupported areas of the skin plating subjected to water pressure. Belative Strengths and Weights of Single Pieces of Wood, Iron, and Steel. — It will be convenient to consider first the resistances of single pieces of wood, iron, and steel to tensile and compressive strains. Take a simple tie-bar, for example, and suppose it fixed at one end, while a tensile force is applied at the other. As the force is gradually increased the bar will begin to stretch, and up to a certain point the elongations will be directly proportional to the stresses. After this point is passed increase in stress is accompanied by rapidly increas- ing extensions. Finally, a certain amount of stress produces rupture. This determines the ultimate strength of the bar. The upper limits within which extensions are proportional to stresses are usually termed the " limits of elasticity," or shortly " elastic limits." For 39<5 NAVAL ARCHITECTURE. [chap. x. different materials the ratios of the ultimate to the elastic stress vary considerably. Formerly it was the practice to fix the elastic limits by the further consideration that within them, if the stresses were removed, the bar should return to its original length, and that there should be no " permanent set " or elongation. It is now known, by the use of improved measuring appliances, that " permanent sets " of very small amounts do occur for values of the stress much below the elastic limit as above defined. In practice the tensile stress brought upon a tie-bar of iron or steel and frequently repeated is rarely allowed to exceed one-half or one-third of the elastic stress. Consequently, sensible permanent set is avoided, as it clearly ought to be if the strength is to be maintained. Let the bar, for example, be L feet long, and let it be observed to stretch L -*- n (feet) under a stress of P lbs. per square inch of the sectional area of the bar : then for any other stress Q we must have — Elongation = ^ v — r » If it were possible, without passing the limits of elasticity, to double the length of the bar, and E were the stress which would produce this elongation, we must have — E L L = — x — ; whence E = P». This is confessedly a hypothetical case, since no bar could be stretched to double its length without exceeding the limits of elasticity ; but the hypothesis can be advantageously used in practice. The quantity E is termed the modulus of elasticity, and its comparison for various substances furnishes a ready means of estimating their relative efficiencies in resisting change of form. Within certain limits this mode of comparison is applicable to compression as well as extension. To illustrate this formula two examples may be taken. A piece of English oak was found to stretch x^sa P 8 ^ 0I " its length under a load of 1680 lbs. per square inch. For it — Modulus of elasticity = 1152 x 1680 = 1,935,000 (nearly). A steel plate was found to stretch yuVou V wi °^ i* s l^gtb under a load of 32,000 lbs. per square inch. For it — Modulus of elasticity = 10 ' 0Q0 x 32,000 = 29,091,000 (nearly). With specimens of timber considerable difficulties arise in deter- mining fair average values for the moduli of elasticity and for the ultimate tensile and compressive strengths. Even when the utmost care has been taken to season timbers, considerable variations are CHAP. X.J MATERIALS FOR SHIPBUILDING. 597 found to exist, not merely in different logs of the same description of timber, but in the strengths of different pieces cut from various parts of the same tree. Such causes as the existence of knots, cross- grain, etc., affect the strength, and it is very different lengthwise of the grain from what it is across the grain. This fact explains the diverse results obtained by various experimentalists. From the best results available the following table has been compiled for a few of the timbers most commonly used in shipbuilding : — * Timbers. Average weight per cubic foot. Tensile strength. Compressive strength. Modulus of elasticity, Rankine's values. British oak . Dantzic oak Dantzic fir . English elm Pitch pine . Teak . African oak Sabicu Pounds. 54 52 36 35 40 48 62 57 Pounds per sq. in. 7,600 to 10,000 4,200 to 12,800t 2,240 to 4,480 5,500 to 13,500t 4,600 to 7,800 3,300 to 15,000f 4,800 to 10,900 4,300 to 6,900 Pounds per sq. in. 7,600 to 10,000 ■ 6,800 to 8,700 7,000 to 9,500 5,800 to 10,000 6,500 to 9,800 6,300 to 12,000 10,000 to 11,000 6,500 to 9,000 1,450,000 1,190,000 1,958,000 700,000 1,226,000 2,400,000 As an illustration of the difficulties just mentioned, it may be stated that more recent experiments than those used by Eankine, conducted with great care in the Eoyal Dockyards, gave a modulus of elasticity of 1,300,000 only for teak, and of about 1,900,000 for English and Dantzic oak. The average modulus proposed by Ean- kine for the more important shipbuilding timbers when acting in association with iron or steel was 1,750,000, and this may fairly be accepted. A fair average value of the compressive strength of these timbers is probably about 3 to 3£ tons per square inch ; and their average weight is about 48 lbs. per cubic foot. Professor Eankine proposed to take about 5J tons as the average ultimate tensile strength of shipbuilding timbers. More recent experiments would indicate that this is too high an estimate, and that a fairer one would be about 3 tons per square inch. Good iron, such as was formerly used in the hulls of her * These figures are based upon the experiments of Barlow, Tredgold, Hodg- kinson, and others, of which an excellent summary is contained in the late Pro- fessor Kankine's work, " Shipbuilding, Theoretical and Practical," as well as upon the more recent and valuable ex- periments recorded in " Timber and Timber Trees,'' by Mr.. Laslett, late Admiralty Inspector of Timber. Sir W, Fairbairn's tables have also been examined in comparison with the others. t Doubtful values ; Mr. Laslett gives 5700 lbs. as the upper limit for teak, 7400 lbs. for Dantzic oak, and 6700 lbs. for elm. 398 NA VAL ARCHITECTURE. [chap. x. Majesty's ships, had an ultimate tensile strength of from 18 to 22 tons per square inch. Samples cut lengthwise from plates showed about 16 to 20 per cent, greater tensile strength and considerably greater ductility than samples cut crosswise from the same plates. All this iron was subjected to systematic testing before being used. In the mercantile marine similar tensile and bending tests were not commonly made on the iron used. The '■' brand " of the maker was usually accepted as evidence of good quality, supplemented, of course, by the practical tests involved in working the material into ships. Considerable variations occurred under this system in both strength and ductility ; but it was understood that good iron should have an ultimate tensile strength of about 20 tons per square inch in samples cut lengthwise from plates or bars. The weight of iron per cubic foot is about 480 lbs. Eankdne gave 28,000,000 as the modulus of elasticity for good wrought iron; possibly this is a somewhat high estimate. Ductility, as measured by the ultimate extension before rupture took place, varied greatly. In good speci- mens of iron having an ultimate tensile strength of about 21 tons per square inch, Mr. Kirkaldy found the mean ultimate extension in a length of 10 inches to be about 9"6 per cent, for lengthwise samples, and about 3-2 per cent, for crosswise samples. The elastic limit of good wrought iron appears to lie at from 50 to 60 per cent, of the ultimate tensile strength. Authorities differ widely as to the ultimate resistance to com- pression of wrought iron. Kankine fixed it at from 27,000 to 36,000 lbs. per square inch ; and Fairbairn (on the authority of Eondelet) at 70,000 lbs. Experiments on short cylinders, having lengths vary- ing from 11 to 2 diameters, made by Kirkaldy, showed the "elastic stress " to vary from 31,000 to 33,400 lbs. per square inch. These experiments were carried on to pressures of 100,000 lbs. per square inch, when the cylinders became " barrel-shaped," and were depressed over 40 per cent, of their length. At 50,000 lbs. per square inch the corresponding depressions were from 2 J to 4 per cent, only.* This shows that for practical purposes, supposing " buckling " to be prevented, wrought iron under compression can offer at least as great a resistance as to tension before sensible " break-down " occurs. In the comparatively thin plating of the skin or decks failure by " buckling " under compression, rather than crushing under direct thrust, has to be guarded against by suitable stiffeners. Steel of the " mild " quality now used in shipbuilding is a * These experiments were made on of England Institute of Mining and behalf of Mr. Wigham Richardson, who Mechanical Engineers in December, communicated the results to the North 1883. chap, x.] MATERIALS FOR SHIPBUILDING. 399 material which is in many respects superior, and in no respect inferior to iron. It can equally well withstand all the operations of the shipyard ; is very ductile and malleable ; about 25 to 30 per cent, stronger, under tensile strain, than the best iron ship-plates ; and only 2 to 2\ per cent, heavier for equal volumes. Most of the varieties of steel used in shipbuilding before 1873 had the serious disadvantage of lacking uniformity in strength, ductility, and malleability. If these serious faults were avoided by exceptional care in manufacture, the price of the material became so high as to be practically pro- hibitive except in very special cases. Not unfrequently steel plates made under practically similar conditions, and presumably of the same quality, displayed, when tested, singular differences in their qualities. Consequently the shipbuilder and shipowner had not the same assurance of safety with steel as was possible with iron. More- over, it was found with these earlier descriptions of steel that much greater care was required in the manipulation during the various processes of building — such as punching, bending, forging, and riveting — than was needed in the corresponding operations on iron. These steels were much stronger than iron, having tensile' strengths from 30 to 50 tons per square inch, as against 18 to 22 tons for good iron. On account of their greater strength these varieties of steel were used in exceptional cases, notwithstanding their known faults and greater cost. Vessels for river service like that illustrated in Pigs. 132 and 133, p. 377, steamers for the Channel service, blockade-runners, and other classes in which lightness of hull was the most important condition to be fulfilled, were all built of steel. Most of these early steel ships performed their work well, and some of them displayed remarkable durability under very trying con- ditions of service. The failures and difficulties to which allusion has been made were chiefly experienced in the shipyard. Mild steel is practically free from the defects mentioned above. It can be produced in large quantities, of uniform quality, and at a cost which does not compare unfavourably with that of good wrought iron. The tensile strength of the material now in common use is not so high as that of earlier varieties of steel, but the ductility is much greater. From 26 to 32 tons per square inch represent the limits of tensile strength not commonly exceeded ; the elongation of a sample before fracture under tensile strain frequently reaches 25 to 30 per cent, in a length of 8 inches. But there is reason to believe that still higher tensile strength, up to 35 or 40 tons per square inch, may be obtained, if desired, in association with excellent working qualities, and without that degree of hardness which would make the steel take a "temper " when heated to a low cherry-red and plunged into water having a temperature of about 80° Fahr. 4-00 NAVAL ARCHITECTURE. _:. [Chap. x. Another property of mild steel deserving notice is the practical equality of the strength and ductility of samples cut lengthwise or breadthwise from plates. With iron, as above stated, the samples cut lengthwise woidd have about one-fifth or one-sixth greater tensile strength and much more ductility than the crosswise samples from the same plate ; and care has to. be taken in many parts of iron ships to adjust the plates and butt-straps in the manner most favourable to this inequality of strength. Closely connected with this uniformity of strength and great ductility is the capacity of mUd steel to bear rough usage. Under percussive strains — produced by the blows of steam-hammers, falling weights, the explosion of gun-cotton, etc — mild steel has been proved greatly superior to the best wrought iron. In cases of collision, grounding, etc., ships built of mild steel have had their plating bulged and bent without cracking, under circum- stances which would have broken through less ductile iron plates. In the shipyard much work can be done on steel cold, which could only be done on iron after heating. One most important feature in the working qualities of mild steel should be mentioned. It shoidd not be subjected to percussive strains or shocks when at a •' blue-heat "—say from 430° to 580° Fahr., at which heat its ductility is at a minimum. The "elastic limit" for mild steel has been found to vary from about 55 to nearly 80 per cent, of the ultimate strength, and GO per cent, is probably a fair average value. For superior qualities of iron, about the same percentage of the ultimate strength probably represents the elastic limit. Hence it follows that, notwithstanding its greater ductility, mild steel can bear " working strains " having as great a ratio to the ultimate strength as superior wrought iron can bear. This is an important matter : mild steel may be trusted with working tensile stresses from 25 to 30 per cent, greater than superior iron. Under compression mild steel also gains as compared with iron although perhaps to a less extent than under tension. Experiments made with short cylinders of steel, similar to those described for wrought iron, showed the elastic stress to vary from 34,300 to 36,000 lbs. per square inch, or a gain of about 10 per cent, as compared with iron. Under loads of 50,000 lbs. per square inch, the steel cylinders sustained depressions practically as great as those sustained by the iron cylinders. As above remarked, these experiments do not repre- sent the conditions of practice, where compressive, strains, if they cause failure in portions of a ship's structure, usually do so by buck- ling. In steel ships, where plating is thinner than with iron, there is a greater necessity for carefully arranging the stiffeners and supports of plating in order to prevent buckling. chap, x.] MATERIALS FOR SHIPBUILDING. 4 OT The modulus of elasticity for mild steel, determined from a large number of experiments, is about 29,500,000, or about 5£ per cent, above that given by Eankine for wrought iron. An important factor in relation to the use of steel in the mercantile marine is the introduction of systematic tests for all the material used. In this way strength and uniformity are guaranteed ; whereas with iron, as explained above, no corresponding tests were made in building merchant ships. In the Boyal Navy, where systematic tests of iron have always been the rule, only a few changes in the test conditions have been necessary for steel. A simple comparison may now be made between single pieces of wood and iron when subjected to tensile or compressive strains. Take British oak as a standard timber. Its weight per cubic foot is given in the table as 54 lbs., or say one-ninth that of iron; the mean ultimate strengths there given are about 4 tons per square inch, or about one-fifth that of iron. Here, then, the timber apparently gains upon iron in ultimate strength for a given weight. Under the conditions of practice, however, it is less favourably situated. The builder could have no certainty that any piece of oak would reach the tabulated average strength. Some specimens of oak tested have had only one-eighth the ultimate strength of iron. Again, in practice it is not ultimate strength which must be considered, but that limit of force that may be safely repeated many times without distressing the material. This may be described as the elastic or working strength ; and with timber there is a very different range of elasticity from that obtaining in iron. With the latter material the working strength may be taken as about one-fifth of the ultimate strength ; in other words, a " factor of safety " of 5 is sufficient. With timber experience points to the desirability of using factors of safety nearly twice as great— 8 to 10. Under tension a factor of safety of 10 is not excessive, giving about four-tenths of a ton per square inch of sectional area as the working limit for oak. For iron the corresponding limit would be about 4 tons per square inch, or ten times as great, while the weight is only nine times as great for equal sectional areas of iron and wood. Hence it is seen that iron has the advantage in the ratio of strength to weight, under the conditions of practice. Steel would have a still greater advantage. Under compression a factor of safety of 8 might be accepted ; the working load for the oak would then be about half a ton per square inch. For wrought iron the corresponding load would be about three tons. Here the oak would gain on the iron if the single struts con- sidered were similar in cross-sectional forms — say solid rectangles or circles such as timber struts must be. Iron or steel struts, however, may be made with hollow or " flanged " cross-sections, and in this 2d 4-02 NAVAL ARCHITECTURE. [CHAP. X. way have their resistance to compression greatly increased, so gaining upon wood struts of equal weight and length. It will be noted, moreover, that pieces in the structure of a ship have to bear at Tarious times both tensile and compressive strains ; while in practice the tensile strains are usually most severe. A brief reference will suffice to the relative capabilities of wood, iron, and steel when subjected to lending moments. The condition of a bent beam has been described at p. 349. Failure, when it occurs in such a beam, usually begins either at the upper or lower surfaces most distant from the neutral axis. The bounding layers of the material are subjected to excessive tensile or compressive strains and give way. There is no doubt that in solid wood beams of rectangular cross-section the intimate connection of the parts with one another influences the ultimate resistances of the material in the bounding layers under bending moments, as compared with the ultimate tensile or compressive strengths of the same material. This influence may be marked, as in the following cases given by Eankine : — Timbers. Strength in pounds per square inch. Tensile. Compressive. Gross breaking. Dantzic oak Jamaica mahogany Pitch pine .... 12.7S0 7,800 7,720 8,800 8,740 16,600 9,800 Such considerable differences are, however, the exceptions rather than the rule, and do not appear in the timbers most used. For practical purposes, therefore, in solid timber beams as well as in flanged iron or steel beams, the ultimate resistances to bending strains of the material in the bounding layers may be taken as fairly approximating to the ultimate resistances to tension and compression above described. The advantages obtainable with flanged forms of beams, as compared with beams of rectangular cross-section, have also been illustrated at p. 352. In their capacity to be manufactured or built up into such flanged forms, iron and steel gain greatly upon wood. Steel also gains upon iron, becaxise its greater ductility and its homogeneous character permit it to assume, in the process of manufacture, sectional forms which were either impossible or most difficult and costly to produce in iron. These remarks apply not merely to deck beams, but to frames, stiffening bars, pillars, and many other parts of the structures of ships which are subjected to chap, x.] MATERIALS FOR SHIPBUILDING. 403 bending strains. Instead of solid masses of timber, flanged forms of iron or steel will give the necessary strength with less weight. Fig. 134 contains a few examples of the great varieties of FIG. 134. a TIIITI References, a, T-bar. e, T-bulb. 6, angle-bulb. /, bulb-plate with angle-bars c, Z-bar. r/, made beam. d, H-bar. h, box beam. sectional forms in iron and steel which the manufacturer places at the service of the shipbuilder. The simple angle-bar is sometimes used as a beam ; its form may be seen from the sections /, g, h, in Fig. 134, and differs from the T-bar in having a top flange on one side only of the vertical web. Neither the angle nor the T form is well adapted for resisting bending strains, because of the absence of a bottom flange. The angle-bulb (b) is a great improvement in this respect, and is used for light decks or platforms as well as under completely plated decks. Z-bar (e) is used for frames behind armour for transverse framing, and for longitudinal stiffeners, but not often for beams. Channel-bars, differing from Z-bars in having both flanges on one side of the web, are now largely used instead of Z-bars. H-bar (d) is expensive, and is not used so much as the made beam (g) of similar cross-section. Not unfrequently, instead of having double angle-bars on the upper edge of the made beams, to a deck covered with iron or steel plating, only single angle-bars are worked, a portion of the deck plating above the beam then forming the upper flange. Sections e and / may be regarded as interchangeable ; the latter was formerly much in use, but since manufacturers have been able to produce the section e with ease and at moderate cost, the shipbuilder naturally prefers to obtain the finished form. The box-beam h is only used where exceptional strength is required, to support some concentrated load, or to furnish a very strong tie. Of the other sections sometimes used it is needless to speak ; they all, or nearly all, exhibit the general characteristic of top and bottom flanges, or bulbs connected by a thin vertical web. Even for the largest ships, beams of these sections are now procurable in one length, which is another great advantage as compared with the two-piece or three-piece wood beams required in large ships. 4°4 NAVAL ARCHITECTURE. [chap. x. A comparison may be made between tbe weights and " working strengths " of wood and iron beams, in order to illustrate the preceding general statement. For this purpose the following figures will suffice, although they do not pretend to exactness. Taking 20 tons as the ultimate tensile strength of the iron, and a " factor of safety " of 5, the working strength will be 4 tons per square inch. Then for a flanged iron beam such as is ordinarily used we may assume — Safe bending moment (working ) , , .• i depth ,, „ , N v => J- = -i tons X sectional area X — £ — strength of beam) . . ) 3 The sectional area being expressed in square inches, and the depth in inches, the bending moment will be expressed in inch-tons ; that is to say, by the product of a load in tons into a leverage in inches. For example, take a beam of section d, Fig. 134, 12 inches deep, with top and bottom flanges, each 6 inches wide, and web and flanges i inch thick. Sectional area = (12 + 6 + 6)£ = 12 sq, in. 12 Safe bending moment = 4 tons X 12 sq. in. x — = 192 inch-tons. Since iron weighs about 480 lbs. per cubic foot, this beam would weigh about 40 lbs. for each foot of length. A teak beam of rectangular section weighing 40 lbs. per foot of length, may be assumed to have a sectional area of about 120 square inches. If 12 inches deep like the iron beam, it would be 10 inches broad. Take the working strength (as on p. 401) at four-tenths of a ton per square inch, a factor of safety of 10 being employed with an ultimate tensile strength of 4 tons. Then for the rectangular form of beam- Safe bending moment = -4 ton x sectional area X e ^ 6 = -4 x 120 x 12 x i = 96 inch-tons. That is to say, with equal weights the teak beam could be trusted only with one-half the bending moment which the iron beam could bear. A steel beam would be still stronger in relation to its weight. Supposing the problem differently stated. What would be the dimensions and relative weight of an oak beam capable of sustaining the same bending moment as the iron beam in the preceding illustration. Let the oak beam be supposed of a square section, its depth and breadth being x inches. Then, as before chap, x.] MATERIALS FOR SHIPBUILDING. 4°5 Bending moment = 4 tons x x 2 X \x = 192 inch-tons x 3 = 2880 x = 14| inches (roughly) Sectional area = 202 sq. in. = 14 sq. ft. Weight per foot length = 14 sq. ft. x 54 lbs. = 75*6 lbs. Each foot of length of the oak beam would therefore weigh about 90 per cent, more than each foot of the iron beam, although capable of bearing only the same load. Relative Strengths of Combinations of Wood, Iron, and Steel. — Passing from single pieces subjected to tension or compression, to the conditions of practice where such pieces have to be combined and to act together, the advantages of iron and steel over wood become more apparent. Under compression :a combination of pieces of timber is most favourably situated. This has already been explained (at p. 363) when illustrating the resistance to hogging strains offered by the lower parts of wood ships. Two planks or timbers, with a plain " butt " joint, or flat end to each, will effectively transmit a thrust, provided only that the two ends are well fitted to one another, and are prevented from changing their relative positions. On the contrary, when several pieces of timber have to be com- bined in order to resist tensile strains, their resistance compares much less favourably with that of a combination of iron plates or bars than does the ultimate tensile strength of a single piece of timber with that of a single piece of iron. Against tension a butt- joint is obviously quite ineffective. In Fig. 129, p. 361, if any two:timbers abutting on one another in a rib or frame were considered to act alone, and to be subjected to a strain tending to separate the butts, they could oppose no resistance except the friction of the dowel, which would be very trifling. If a " strap " of wood or iron were fitted over the butts and bolted to the timbers, it would resist the force tending to open the butts ; and it has been shown that the weakness of the butts in any rib is, so to speak, covered by the strength of the unbutted ribs lying on either side. In many wood ships the timbers of consecutive ribs were bolted together, in pairs, to increase the strength/ of the frame. In the case of the water-way fitted upon the beam ends of a wood ship (Fig. 128) the various pieces were plain-butted; but the butts were covered by strong carlings fitted underneath, and to these the water-way pieces were dowelled. This was an exceptional arrangement, however, the almost universal plan adopted where two pieces of timber had to be joined end-to-end, in order to form a tie, being to " scarph " or over- lap the ends in some fashion more or less complicated and expensive. 406 NAVAL ARCHITECTURE. [chap. x. Take the keel, for example, in a wood ship ; the adjoining pieces were secured by what is termed a " tabled scarph." Fig. 135 shows the two parts of the scarph thrown back to exhibit the projecting FIG. 135. "tabling" and the sunken recesses into which the tabling fits. Fig. 136 shows the two parts in place, with the fastening bolts which assist the tabling in resisting tensile strains tending to open the scarph. The plan was an excellent one, but necessitated considerable FIG. 137. b @ I / ©M o *j i PUj i^® ® j\j • Oj I Wm FIG. 138. skill and cost of workmanship in fashioning the scarphs so that they might fit accurately. The same thing is true in the beam-scarphs, illustrated in side view by Fig. 137, and in plan in Fig. 138. This is termed a " hooked scarph," metal wedges or keys (k, 1c, Fig. 138) FIG. 139. © ® A. iH FIG. 140. being driven to tighten up the scarph, and bolts and treenails being used to fasten it. This hooked scarph replaced the simple but less compact and satisfactory method illustrated in Figs. 139 (side view) and 140 (plan). The fastenings in this case consisted of dowels chap, x.] MATERIALS FOR SHIPBUILDING. 4°7 treenails, and metal bolts. Still another method of scarphing is illustrated in Fig. 141, and is known as a " plain scarph," being free from tabling and hooks. It is not nearly so strong against tensile strains as the preceding plans ; but neither does it involve such care and expense in fashioning. The keelsons, shelf-pieces, and some other longitudinal ties, were frequently scarphed in this manner. It will be noted that in the last plan, and the preceding one, the fastenings have to contribute the whole resistance to separation of the scarph under tensile strains; and when these strains are acting, there is a tendency for the wood to yield in wake of the comparatively small and hard metal bolts. The greater hardness and small size of the metal fastenings FIG. 141. in a wood ship is a fruitful source of weakness and working. Parts, at one instant under tension, tend to yield in wake of iron or metal bolts ; soon after, under compressive strains, the tendency disappears, to be followed almost immediately by its reappearance, if the ship is floating amongst waves. It will of course be understood that we are here dealing with tendencies only, and not with actual yielding ; the existence of a large reserve of strength often preventing the tendency from passing into a sensible change of form. When ships are weak, it is otherwise, and then working takes place. The use of timber treenails as fastenings in the outside planking of a wood ship, or of coaks and dowels, also of hard wood, is from this point of view a considerable advantage. Coaks in particular, and treenails in some degree, have a larger " bearing " surface on the wood planks, etc., than have metal bolts ; besides which they are not so hard, both of which differences tend to lessen the local yielding of the pieces fastened by them. An assemblage of wood planks or timbers, such as is found in the outside planking, or the flat of a deck, is not usually dealt with by scarphing adjoining pieces together. Plain butt-joints are then had recourse to (see Fig. 125, p. 347), and the weakness of the butted strakes on any transverse section is met by the device, previously explained, of "shift of butts." This is, how- ever, tantamount to a reduction of the total sectional area by one-fourth, when resistance to tensile strains is being considered ; and the holes for bolts and treenails necessitate a further deduction. Such are the best results obtained either in timber-ties (like the keel, or beam, or shelf-piece) or in an assemblage of planking. 4° 8 i\A VAL ARCHITECTURE. [chap. x. Either scarphing of an elaborate and expensive character must be adopted, or shift of butts must be trusted. In all cases, more- over, the greater hardness and small surface of the metal bolts tend to produce yielding of the wood in wake of them when the parts are under tension. In every one of these particulars iron and steel gain upon wood. The rivets forming the fastenings of piece to piece are of the same degree of hardness as the plates or bars ; so that yielding in wake of them is not to be feared. "What must be secured is that the riveting is properly done, and the holes in the plates, etc., well filled by the rivets. Again, when two plates or bars have to be joined to form a tie, nothing can be simpler than the connection. The pieces may either be lapped and riveted, as in Fig. 142, or butted and strapped, as in Fig. 143. In either case the shearing strength of the rivets may be made to fix the ultimate resistance of the tie under tension. With the lap joints of Fig. 142 the resistance to FIG. 142. FIG. 143. aol 1 ■ GO oo| o °l 1 too ooj ool 1 •OO oo; ool 1 JOO OOJ ool 1 |oo oo; ool I Joo oo; ooj compression is also measured by the shearing strength of the rivets ; whereas in Fig. 143, if the butts are carefully fitted, the rivets in the straps need not sustain any shearing strain under compression, so long as the plates are prevented from buckling. The butts in a strake of plating are not necessarily such sources of weakness as are the butts in a strake of planking, because the butt-strap gives great tensile strength to the butts, and may be made to render the section of the plating in wake of a line of butts quite as strong as its section in wake of the lines of rivet-holes at adjacent transverse frames.* Shift of butts is had recourse to also in assemblages of plating, but it is of less importance than in assemblages of wood planking. On the whole, in a well-built vessel, the effective sectional area of an assemblage of plating against tensile strains is probably not far from seven-eightJis of the total sectional area, as compared with five-eighths for the skin of a wood ship. It is unnecessary to repeat what was said in the previous chapter respecting the further gain of the iron skin, on account of * See a paper contributed by the 1873. The subject is too technical to author to the Transactions of the be discussed in these pages. Institution of Naval Architects for chap, x.] MATERIALS FOR SHIPBUILDING. 4°9 the efficient edge connections of strake with strake, although this is an important advantage. When subjected to lending moments, combinations of iron and steel plates and bars can be easily converted into flanged or hollow girders, or into cellular structures, capable of bearing equally well tension or compression. The double bottoms of iron and steel ships have already been fully described; and many other illustrations have been given in previous pages of the facts to which attention is again directed, because of their important bearing on the associa- tion of strength with lightness. It is consequently unnecessary to amplify the statement. From the nature of the material, timber must be used in solid masses, and not in flanged forms ; the several pieces in a combination have connections which are weak under tension ; and these imperfect connections are costly and difficult to make, besides being liable to working and increased weakness with repetitions of severe straining forces. Comparative Weights of Wood, Iron, and Steel Ships. — From the foregoing statements, it will be obvious that with equal structural strength a ship of given size and type can be built with a less weight of iron than would be necessary with wood, and with a less weight of steel than of iron. Savings in the weight of hull render possible corresponding increases in the carrying power. The extent to which these savings may be carried varies in different classes of ships ; and there is a necessity to bear in mind the character of the service for which a ship is designed, when comparing her weight of hull with that of a ship of a different class. Besides the materials worked into the structure for the purpose of giving it strength and rigidity, more or less considerable weights are added in the form of fittings or accommodation, which contribute but little, if at all, to the structural strength, and yet are included in the weight of hull. Cargo- steamers, for example, have a minimum weight devoted to fittings, the hold-spaces being kept clear for cargo. Passenger-steamers, on the contrary, are elaborately fitted for the accommodation of passengers, and considerable weights are involved. War -ships are still more elaborately fitted, every portion of the interior being devoted to and arranged for specified purposes of stowage or accom- modation, while the subdivision is very minute. Every endeavour is made to utilize bulkheads, platforms, partitions, etc., fitted primarily for accommodation as contributories to the structural strength. But after this has been done there remains a considerable weight of material, reckoned into the hull, yet really constituting only a load to be carried. This group includes fittings in magazines, shell- rooms, store-rooms, cabins, crews' quarters, etc. ; and arrangements for pumping, drainage, ventilation, electric lighting, working the 4 1 NAVAL ARCHITECTURE. [chap. x. cables, hoisting the boats, and other necessary services. Further, considerable weights are expended on strengthening the bows for ramming, the sides behind the armour-plating, the decks, etc., for carrying guns and withstanding the shocks of gun-fire, and meeting- other requirements incidental to the use of ships as fighting machines. As between different types of war-ships, these supplemental demands for fittings and strengthenings necessarily vary greatly. The height of freeboard ; numbers, disposition, and protection of guns ; system of hull-protection, engine-power, and speed, — all affect the weight of hull. Hence broad comparisons of weights of hull — say as percentages of the load displacements — require to be supplemented by detailed analysis, and the ship-designer is careful to separate in his calcula- tions the weights of materials contributing to the structural strength, from the weights of accessories and fittings. Generalizations respecting the variations in structural weights accompanying variations in dimensions, have been attempted repeatedly by capable investigators. The late Mr. W. Froude was one of the first to attempt the solution of this problem. He showed that, for similar ships placed on similar waves, the longitudinal bending moments varied as the cubes of the lengths, and directly as the breadths ; or as the fourth power of the lineal dimensions. Treating the parts of the structure contributing resistance to longi- tudinal bending as a box-girder, he remarked that the stress on the decks, bottoms, and sides varied as the quotient of the bending moment divided by the depth. Consequently, if the stress was to be kept at a constant maximum value in similar ships, the sectional areas of materials in decks, bottoms, and sides would have to be varied as (length) 3 x breadth -r- depth ; and the structural weights as the (length) 4 x breadth -r depth. That is to say, the structural weights, for equal stresses under longitudinal bending in ships of different dimensions, should vary as the fourth power of the lengths ; or as the four-thirds powers of the displacements.* It has been shown in the previous chapter that the stresses on ships of large dimensions exceed those usually experienced in ships of smaller dimensions. Further, it has been explained that considerations of local strength or durability, especially in vessels of small size, frequently determine the minimum scantlings which can be accepted and so cause the stresses incidental to longitudinal bending moments to be smaller than could be accepted apart from these considerations. Nor must it be forgotten that in ships of similar form, but greatly differing dimensions, the structural arrangements are different, the * See a paper on " Useful Displacement," in the Transactions of the Institution of Naval Architects for 1874. chap, x.] MATERIALS FOR SHIPBUILDING. 41 1 numbers of decks are not identical, the bottom is differently built, or other changes made, affecting the equivalent girder for longi- tudinal bending and the resistance offered to transverse change of form. In these and other ways, in practice, the theoretical condi- tions assumed in generalizations of the character described are departed from. This remark applies also to the able investigation published by M. Normand, in 1892.* His conclusions may be summarized. For equal stresses under longitudinal bending moments, in ships of different absolute dimensions and different ratios of length to depth and breadth, he considers the structural weights should vary as — /length\§ ... , N * ^deithJ * ( dls P lacement ) The weights of transverse framing, bulkheads, beams, etc., are assumed to vary as (displacement) 3 in ships where the absolute dimensions only are varied. The total structural weights (longi- tudinal and transverse) are assumed to vary as — /lengt M 4 ) x (displacement) 3 • depth M. Normand justly adds, "Whatever may be the true law of "variation of weight as a function of the ratio of the length to "the transverse dimensions (depth and breadth), it is certain that "a notable lightening can be realized by diminishing that ratio." This is a confirmation of a long-accepted principle in ship-con- struction. The ordinary method of making comparisons between ships is avowedly inaccurate except when applied within comparatively narrow limits of size and to ships of similar type. It expresses the weight of hull — including both structure proper and fittings — as a percentage of the load-displacement. Keeping in mind the foregoing remarks, the following facts will be of some value, and will illustrate the advantages obtained by changing materials of construction. In wood-built ships of the Royal Navy the weight of hull (including fittings) was about 50 per cent, of the load displacement. In wood-built ships of the mercantile marine, less elaborately fitted, the hull weighed from 35 to 45 per cent, of the displacement. Even the largest wood-built ships were of very moderate size, proportions, and speed, as compared with the iron and steel vessels which have succeeded them. And this fact must be borne in mind when com- paring percentages for weights of hull. * See Bulletin de 1' Association Technique Maritime, No. 3. 4 r 2 NAVAL ARCHITECTURE. [chap. x. In iron-built cargo-steamers and sailing ships the weight of hull may be taken as from 25 to 30 per cent, of the displacement. For ships of equal dimensions, it has been estimated that the change from wood to iron effected a saving of about one-third on the weight of- hull. Iron passenger-steamers, with their elaborate fittings, have relatively greater weights of hull, varying from 45 to 55 per cent, of the load-displacements. In such vessels the percentage of weight, contributing little, if at all, to the structural strength, is from twice to thrice as great as the corresponding percentage in vessels which are purely cargo-carriers. Armoured war-ships with iron hulls were at first heavily built, the hulls (including fittings) averaging about 55 per cent, of the displacement. These were armed on the broadside principle, and many of them were of considerable length. Improvements in structural arrangements and reductions in length resulted in savings in weight of hull, bringing it down to 40 to 45 per cent, of the displacement in the later broadside ships. Turret-ships with mode- rate freeboard, and carrying, at most, four heavy guns, had weights of hull amounting to 30 or 35 per cent, of the displacement. The iron hulls of the Kussian circular ironclads weighed only about 20 per cent, of the displacement. For iron-built unarmoured ships of the Eoyal Navy, the weights of hull ranged from 40 to 50 per cent, of the displacement ; and iu troop-ships was practically the same as in passenger-steamers. Perhaps the savings in weight will be more fully realized if an example is given. The Black Prince, one of the earliest seagoing ironclads, was of 9250 tons displacement, and her iron hull weighed nearly 5000 tons. The Alexandra, one of the latest broadside iron- clads, with iron hull, was of 9500 tons displacement, and her hull weighed only 3800 tons. By improved construction, fully 1000 tons was, therefore, transferred from hull to carrying power in the Alexandra. Steel ships, being built of a stronger material, are lighter than iron ships. In the earlier steel vessels, wherein material of high tensile strength was used, the reductions in scantlings usually varied from one-third to one-fourth of the scantlings used in iron for ships of the same sizes. In a few cases the reductions were even greater, amounting to one-half as compared with iron, the tensile strength of the steel rising as high as 50 tons to the square inch. With mild steel of the quality now used, having an ultimate tensile strength of 26 to 32 tons per square inch, less reductions are made. Lloyd's Eules at first permitted of a reduction of 20 per cent, on the plates and frames of a ship built of mild steel as compared with a similar ship built of iron. This reduction in scantlings, of course, did not chap, x.] MATERIALS FOR SHIPBUILDING. 4 J 3 apply to a considerable number of items included in the hull — such as forgings, fittings, woodwork, etc. Lloyd's now have separate tables for the scantlings of steel ships. Some authorities estimated that, on the original basis of reduction, the use of steel effected a saving of 12 to 15 per cent, on the weight of iron which would have been used in a ship of the same dimensions. In steel cargo-steamers of recent construction, the saving is said not to exceed 7 or 8 per cent, as compared with iron. It is this saving, and the consequent increase in carrying power which has chiefly led to the rapid sub- stitution of steel for iron in recent years; although the greater uniformity and ductility of the material, its excellent working qualities, and improvements in manufacture, tending to great reduc- tions in cost, have all contributed to the result. Steel ships are being built instead of iron because they are commercially more successful. Two illustrations may be given of the gain in carrying-power. Eirst, take an ordinary type of partial aWning-deck cargo-steamer, for which the length is about 290 feet, and load-displacement 5000 tons. The weights would be distributed somewhat as follows, if 10 per cent, is saved on structural steel : — Iron ship. Steel ship, tons. tons. Iron or steel in hull 1100 1000 Other weights of hull and outfit ... . . . 300 300 Total weight : hull and outfit . . 1400 1300 Machinery 260 260 1660 1560 Carrying power : cargo and coals .... 3340 3440 Displacement 5000 5000 Supposing the ordinary supply of coal to be 340 tons, the iron ship would carry 3000 tons of cargo, and the steel ship 3100 tons, or about 3 per cent. more. Second, take a passenger-steamer of good speed, about 500 feet long and load-displacement of 12,500 tons. The weights may be distributed as follows, if 14 per cent, is saved on structural steel :— Iron ship. Steel ship, tons. tons. Iron or steel in hull 5000 4300 Other weights of hull and outfit . . . . . 1650 1650 Total weight : hull and outfit . . 6650 5950 Machinery 1750 1750 8400 7700 Carrying power:. cargo and coals 4100 4800 Displacement .... .12,500 12,500 4H NAVAL ARCHITECTURE. [chap. x. In this case the use of steel practically adds one-sixth to the carrying power ; and if a constant weight of coal is assumed for hoth ships, the proportionate gain would be greater on the remunerative freight. For instance, if 2000 tons of coal were necessary, say, on the Atlantic service, the iron ship could carry 2100 tons of cargo, and the steel 2800 tons — one-third more. The relative importance of the gain in carrying power in this and other cases may vary considerably in ships of different types, engaged in different trades, and performing voyages of different lengths at various speeds. When ships are built to perform definite voyages at stipulated speeds, then the use of steel instead of iron enables either heavier dead- weight cargoes to be carried on a given displacement, or a stipulated dead weight to be carried in a ship of less displacement and less cost. The relative costs of iron and steel ships are necessarily dependent upon many circumstances, but chiefly upon the comparative prices paid for the materials. In 1877 steel was about twice as costly as iron in common use, which was (as explained above) an untested material, whereas steel was always tested rigorously. In the Eoyal Xavy, where equally searching tests were applied to both materials, only a very short time elapsed before mild steel could be procured at a lower price than superior iron. The same thing happened in the French Navy. As the sources of supply of steel have been increased, while the processes of manufacture have been developed, so the price of steel has fallen. In 1880 steel was about 50 per cent, dearer than iron of ordinary shipbuilding quality. Even as prices then stood, it was considered profitable in many trades to build steel ships. The rapid advance of steel since 1887 is, however, largely to be attributed to its lower price. In 1887 steel was about one-third dearer than iron; in 1891 it was only about 10 per cent, dearer. Mild steel for shipbuilding has hitherto been made almost entirely from haematite ores, the greater part of which have been imported. It has been proved, however, that steel made from native British ores by the " basic " process can be used with safety, and this fact will probably exercise a sensible influence on the future supplies of steel.* The development of cast steel in recent years has been remark- able, enabling shipbuilders in many cases to dispense with costly forgings, and to obtain the substituted castings at moderate cost and * See papers by the author in the 1888. As to the relative prices of iron Journal of the Iron and Steel Institute and steel, see the presidential address of for 1891 and 1892 ; and the Transactions October, 1892, to the North-East Coast of the Institution of Naval Architects for Institution of Engineers and Shipbuilders. CHAP, x.] MATERIALS FOR SHIPBUILDING. 4 J 5 in a comparatively short time. Stems, sternposts, shaft-brackets, rudders, etc., are now commonly made of cast steel instead of forged iron or steel. In war-ships the gain is most considerable, their ram-bows and under-water steering appliances necessitating special structural arrangements. The use of mild steel in the hulls of war-ships has enabled substantial savings to be made on the weights contributing to the structural strength. In these vessels, as previously explained, iron of high quality fulfilling specified tests was always used. The tensile strength of mild steel may be taken as about 30 per cent, greater than that of the best qualities of iron formerly employed ; but, having regard to all the circumstances, it was decided not to reduce scantlings more than 15 per cent, as compared with iron in any parts of the structures, and to secure the greater strength possible with steel of this relative thickness. Many internal portions of the iron structures had previously been made as thin and light as was consistent with durability ; consequently for them the use of steel gave no saving in weight. Notwithstanding these limitations, the change from iron to steel led to considerable additions to the carrying power of war-ships, and facilitated the marked increase in their engine powers and speeds which has taken place since 1875. Some of the results obtained could scarcely have been realized with iron. Torpedo- boats, for example, built of excessively light steel plating and framing, have hulls strong enough to carry extremely powerful propelling machinery. In these remarkable vessels, with relatively high freeboard, the hulls weigh only about 30 to 35 per cent, of the displacement, including all fittings. The propelling apparatus commonly weighs more than the hulls; while loads of armament, coals, and equipment are carried weighing in the aggregate nearly as much as the hulls. Yet in actual service at sea indications of weakness have been extremely rare, and nearly always local in character. As an illustration of the distribution of the weights in a steel- built first-class battle-ship of the present day, the following figures may be given : — Percentage of displacement. Materials contributing to structural strength . . . .18 Accessories and fittings to hull 20 Total weight of hull 38 Propelling machinery and coals 15 Armour and protective material on decks, etc 30 Armament and equipment . . . . . . . .17 100 41 6 NAVAL ARCHITECTURE. [chap. x. In the last group are included large weights of machinery used for auxiliary purposes, such as working the heavy guns, doing the cable work, hoisting heavy boats, etc., besides the guns and their mountings, ammunition, torpedoes, provisions, stores, etc. The protective material, especially the deck plating, is so disposed that it shall assist in resisting both transverse and longitudinal strains as far as possible; but its primary purpose is to give defence. This summary indicates how small a portion of the total displacement has to furnish the greater part of the strength required to resist strains incidental to service at sea, to the attainment of high speeds, and the carrying of great weights of armour and of armament. For a typical swift protected cruiser of high speed, large coal- supply, and heavily armed, the weights are distributed as follows : — Percentage of displacement. Material contributing to structural strength .... 205 Accessories and fittings to hull 17 - 5 Total weight of hull 38-0 Propelling machinery and coals 35-0 Protective material 16 - Armament and equipment 11-0 100-0 Developments in Dimensions and Speeds. — The use of iron and steel hulls has been accompanied by great increase in the dimensions, proportions, and speeds of ships. No such developments would have been possible with wood. In the later periods of wood shipbuilding for war purposes, when it was considered undesirable to adopt iron hulls because of their supposed inferiority to wood when exposed to an enemy's gun-fire, there were many evidences that the limits had been reached for which the material was suitable. Great engine power, considerable lengths, and high speeds were features which could not well be secured in wood ships. The latest and largest frigates in the Koyal Navy, the swift cruisers built in America during the Civil War, and many other similar cases, illustrated this fact. Such vessels required considerable repairs during their short periods of service, and soon fell into disuse. First with iron, and now with steel, it has been shown that there are no such limitations as occurred with wood. Commercial considerations, in fact, govern the sizes and speeds of mercantile vessels ; and other considerations — cost in great measure — determine the upper limits of size for war- ships. The Great Eastern was a crowning example of the capabilities of iron. She was 680 feet long, 83 feet broad, of nearly 19,000 tons (gross tonnage), and had a load displacement of over 32,000 tons chap, x.] MATERIALS FOR SHIPBUILDING. 4*7 when laying submarine telegraph cables. Throughout her period of service, extending over twenty years, she was proved to possess ample structural strength. No other vessel has yet been built of equal size. In- the Atlantic service, however, recent progress has narrowed the gap between the largest mercantile steamers and the Great Eastern. The Campania and Lucania of the Cunard line are 600 feet in length, 65| feet in breadth, 12,500 (gross) tons in measurement, with a load displacement of 18,000 to 19,000 tons. On service it is anticipated they will eventually average about 22 knots per hour, developing 25,000 H.P. to 30,000 H.P.* This is a wonderful advance in half a century. The Great Britain of 1840, built of iron, was regarded at the time as a vessel of extraordinary dimensions. Her length was 290 feet, breadth 51 feet, and register tonnage 3270 tons, with an original load displacement approaching 6000 tons. The wooden Great Western, which preceded her in 1838, was large for those days. Her length was 210 feet, breadth 35£ feet, and load displacement 2300 tons. On every other line of steamship traffic similar increases in dimensions and speeds have taken place, and have been made possible only by the use of iron and steel. In war-fleets the use of these materials has been equally associated with developments in size and speed. The table on the following page illustrates this fact. It deals exclusively with ships of the Eoyal Navy, in which, concurrently with the changes indicated in the table, there have been remarkable advances in powers of offence and defence, weights and thicknesses of armour, and weights and powers of guns. Comparative Durability of Wood, Iron, and Steel Ships. — For some years after the introduction of iron ships it was a matter of dispute whether they would prove as durable as wood ships. The experience of half a century has settled this matter definitely in favour of iron ; and the disappearance of wood shipbuilding in this country makes any statement on the subject one of historical interest only. A very brief summary of facts will suffice, therefore. There are many examples of great durability in wood ships. These are exceptional cases, however, and did not enable shipbuilders to increase the average durability of wood ships. The Sovereign of the Seas, built at Woolwich in 1635, was rebuilt forty-seven years later, and the greater part of the original materials are said to have been again used. The Royal William, built about 1715, remained on service for ninety-four years with only three slight repairs. In the * An admirable account of these remarkable vessels appears in Engineering of April 21, 1893. 2 E 4i8 XAVAL ARCHITECTURE. [chap. x. mercantile marine there have been instances also, chiefly in small vessels engaged in special trades, of continued service for about a century. On the other hand, there are numerous instances where wood ships, hurriedly built of unseasoned timber, have rapidly decayed Class of ship. Wood, unarmoured. Largest sailing threa-deokers 1S15 1S59 two-deckers ; 1860 ,, ,. frigates Wood, armoured. Largest class Iron, unarmoured. Swift cruising frigate . Iron, armottred. Early broadside ships . Modern Turret ships of moderate freeboard . Steel-, protected. Pirst-olaas cruiser Steel, armoured. Turret ships of moderate freeboard . Barbette ship of high free board 1857 1863 1866 1SS9 1861 1S65 1873 1S69 1871 1874 1888 1885 1885 1889 Name. St Vincent Victoria . Duncan Orlando . Lord Warden Inconstant Warrior . Minotaur . Hercules . Alexandra Devastation Dreadnought Inflexible . Blenheim . Victoria . Trafalgar . Royal Sovereign tons. 4,700 6,950 5,700 5,600 7,840 5,780 9,100 10,600 8,700 9,500 9,290 10,890 11,900 9,000 10,470 11,940 14,200 i •° h - V. £ & 3 •9 C feet. 205 4,190 260 2,820 252 4,000 800 6,700 280 7,360 337 5,470 380 6.700 400 S,530 325 8,600 325 6,650 285 8,000 320 S.000 320 20,000 375 14,000 840 12,000 345 13,000 880 feet 58} 60 58 52 59 50i 58 59J 59 631 62} 633 75 65 70 73 75 and become unserviceable. Cases in point are to be found in the gunboats built for the Eoyal Navy during the Crimean War; and in the war-ships built for the United States Navy during the Civil War. A consideration of all the facts on record leads to the conclu- sion that in wood ships built of seasoned materials, and with all proper precautions to preserve the timbers and planks from dry-rot and other kinds of decay, from twelve to sixteen years is a fair estimate of average durability for seagoing vessels properly used and kept in good repair. After that period wood ships may be kept going, but the repairs would be usually considered too costly to be undertaken. Iron is not subject to the internal sources of decay to which timber is liable. Worms or marine animals cannot penetrate iron as they do comparatively soft timber. Imperfect ventilation and many chap, x.] MATERIALS FOR SHIPBUILDING. 4*9 other circumstances which cause wood to rot do uot affect iron ■similarly. Moreover, in a well-built iron ship there ought not to be any sensible working of the several parts and their fastenings ; whereas in wood ships of large size the entire prevention of such working is practically impossible, and in it is found a fruitful source of weakness or decay. In iron ships the special danger requiring to be guarded against is corrosion or rusting of the surfaces of plates and bars. This danger is by no means insignificant, and the principal ■causes of corrosion will be dealt with hereafter, as well as the precautions necessary for its prevention. Here it will suffice to say that corrosion is practically preventible ; and that the experience of half a century proves that with proper treatment, and at moderate expense, the structures of iron ships can be maintained in a sound And efficient state for very many years. Their woodwork and fittings, of course, require renewal or repair - as in wood ships. Experience shows that the period of employment of iron ships, when they are properly cared for, and apart from accident, is usually ■determined by other considerations than deterioration or decay in the structures. Improvements in shipbuilding and marine engineering, following one another in rapid succession, make it impossible to -continue the employment of older vessels in the trades for which they were originally built, in competition with vessels of more recent •date. Consequently these older vessels gradually pass into other trades, and finally reach the stage when they are broken up ; not because they are worn out or past repair like wood ships, but because they can no longer be profitably employed. In order to indicate the possible durability of iron ships apart from these commercial considerations, a few facts may be stated. In the early days of iron shipbuilding the conditions necessary to ihe preservation of iron hulls were not so well understood as they are now. Yet many of these vessels served for long periods. The first iron steamer, the Aaron Manby, built in 1821, lasted thirty-four years. The Nemesis and Phlegethon, the earliest iron war-ships built for the East India Company in 1839, were employed for more than twenty years. The Great Britain, the first iron screw-steamer for Atlantic service, built in 1840, continued at work as a steamer for- forty years, and was then turned into a sailing ship. The troop-ship Himalaya of the Eoyal Navy, built for the Peninsular and Oriental Company in 1855, is still (1893) on active service, and in good condition as to structural strength. The iron-hulled ironclads of the Eoyal Navy (Warrior and Minotaur classes) dating from 1859-61, are as strong as ever in their iron structures, and not yet past active service. Steel ships, properly cared for, will undoubtedly prove equal to iron ships in durability. In some respects experience appears ; to 4 2 ° NA VAL ARCHITECTURE. [chap. x. indicate the necessity for special precautions in the treatment of steel, particularly under engines and boilers. The less thicknesses of plates and bars accepted with steel as compared with iron make it very desirable to ensure the protection of the surfaces from corrosion by cleaning and painting or cementing. These are, however, matters of practical detail easily arranged, and, subject to these precautions, steel ships will doubtless resemble iron in passing out of service in the mercantile marine chiefly because of the introduction of improved types. Some of the earlier steel-built steamers, with very light scantlings, have continued at work for very long periods. The first ships of the Royal Navy built of mild steel have now been afloat nearly twenty years, and are as strong and sound in structure as they were originally. The Corrosion of Iron and Steel Ships. — Reference has been made to the danger of serious rusting and corrosion in the structures of iron and steel ships unless proper care is taken. The subject is important, and will be further noticed. The conditions tending to promote corrosion are of many kinds, operating both inside and outside ships. Parts of the hull above water are least likely to suffer ; but even these on the outside have to sustain the action of air, water, and weather, and in the inside are exposed to changes of temperature, the condensation of vapour, and other circumstances tending to cause rust. Parts of the hull under-water are much less favourably situated. The outside surface of the bottom plating is immersed in corrosive sea-water, and differently constituted sea- waters affect iron or steel in different ways. In the hold-spaces the plating, frames, etc., often have to sustain the action of bilge-water, which has a strong corrosive action if left unchecked. Coal and many other substances carried as cargo may produce a chemical action on the surfaces of plates and bars which accelerates corrosion. Under engines and boilers the drippings of oily matters into the bilges, and their accumidation there under relatively high tempera- tures involve special dangers. In machinery and boiler spaces there are great alternations of temperature, the condensation of steam upon the surfaces of plating and framing, and the production of gases more or less effective in aiding corrosion. Galvanic action may be set up in parts of the structure immersed in sea or bilge-water by the metallic connection of copper, brass, or lead pipes with the hull. In such cases there is a risk of corrosion becoming both rapid and local. These are the principal causes of corrosion, and their enumeration will show how many and varying are the conditions upon which the rate of corrosion would depend if left unchecked. Other than extraneous causes affect practical results. The want of homogeneity in the various parts of the same plate or bar may cause corrosion to chap, x.] MATERIALS FOR SHIPBUILDING. 4 21 begin or accelerate its progress. Plates and frames of apparently identical quality are often differently affected by corrosion, and so are different parts of the same plate or frame. Patches are dis- covered where corrosion has proceeded with extreme rapidity, or " pitting " takes place, and corrosion is greatly localized. No general laws can be formulated respecting the rates of corrosion of iron and steel. Laboratory experiments, or the exposure of sample test-pieces to conditions intended to represent those of service, while they are valuable sources of information, cannot take the place of experience in actual ships. A brief reference to some of the results obtained from these experiments will suffice.* As illustrations of the different rates of corrosion arising from differences in the water acting on iron or steel, the following facts may be cited. Mr. Mallet found that iron boiler-plates immersed in clear sea-water lost from *007 to '009 lb. per square foot per month ; whereas in foul sea-water the loss was about twice as great. Mr. Parker found that iron discs of which the surfaces were bright, the " scale " having been removed, lost from -0136 to "0163 lb. per square foot per month in sea-water, and three times as much ("042 lb.) in bilge-water. Steel discs similarly treated lost "0172 lb. in sea-water, and -0436 lb. in bilge-water. Dr. Calvert and Mr. Johnson found that iron lost -0056 lb. per square foot per month when immersed in a vessel of sea-water, and -0204 lb. when immersed in the sea. These experiments have proved also that the oxides of iron and steel are electro-negative to those materials ; so that when a plate or bar immersed in sea-water has upon it the manufacturer's " scale," or becomes rusty, the rate of corrosion on any exposed portions of the surface will be accelerated by the galvanic action set up on them by the oxides. Extensive trials made by the Admiralty in the early days of steel shipbuilding showed this to be true, particularly for steel ; and as a result the manufacturer's scale, which adheres much more strongly to steel plates than to iron, is now removed from the surfaces of plates that will be immersed in sea or bilge water before they are used in her Majesty's ships. For this purpose the plates are immersed in a bath of dilute hydrochloric acid, and subsequently washed with fresh water. In this manner at small expense clean * See inter alia papers by Mr. R. 1865; by Mr. Parker and Professor Crum Mallet, in Reports of British Association, Brown in Journal of the Iron and Steel 1841-43, and in vol. xiii. of the Tran- Institute for 1881 and 1888 ; and by motions of the Institution of Naval Professor Lewes in vols, xxviii. and Architects; by Dr. Calvert and Mr. xxx. of the Transactions of the Institu- Johnson in Transactions of the Literary tion of Naval Architects, and Philosophical Society of Manchester, 4 22 NAVAL ARCHITECTURE. [chap. x. surfaces can be obtained, and pitting or rapid local corrosion greatly lessened or prevented. Some private firms follow the same practice for steel plates. As a rule, however, merchant ships are built in the open air, and builders are content to allow the surfaces to rust for a time, trusting to " scaling " before painting to remove the dangerous oxide. This answers well for iron ships, and is the usual practice for steel ships. Illustrations of the possible effects of scale upon corrosion are given by Mr. Parker, who states that in sea-water black discs of iron and steel with the scale left on had their rates of corrosion increased from 2 to 3 times, as compared with bright discs with the scale removed. In other test-pieces immersed in bilge- water, many of the discs with scale on suffered less than the bright discs ; but in practice this is not found to be true. Laboratory experiments indicate a slightly greater rate of corrosion in steel than in iron. There are, however, so many varieties, of steel that caution is necessary in dealing with the results. The earlier experimentalists probably tested steels of higher tensile- strength than that now used ; these lost from 6 to 7 per cent, more than iron when immersed in sea-water. Kerm's experiments of 1877 showed a correspondingly greater loss for steel — about 18 per cent. Mr. Parker's experiments with mild steel showed that under similar conditions it lost by corrosion nearly at the same rate as the superior qualities of wrought iron. Galvanic action, set up on iron or steel plates and bars by copper, brass, or lead pipes and.fittings in metallic connection with the struc- tures of ships and immersed in sea or bilge-water, may greatly accelerate local corrosion, and in many cases holes have in this way been eaten through the skins of ships. Caution is necessary, therefore, to prevent such galvanic action, and there is no great difficulty in doing so. To illustrate the greatly increased rate of corrosion incidental to galvanic action, r a few examples may be taken from the results of the experiments recorded by Mr. Mallet. An iron plate immersed alone in clear sea-water was found to lose during a certain period a quantity which we will denote by unity : it was then immersed for an equal time in clear sea-water with an equal surface of the following metals electro-negative to it, and the corrosion increased as follows : — Experiments. Relative corrosion. Iron plate in contact with copper „ „ ., brass .... „ „ ., gun-metal . ,. tin . „ . „ „ lead .... 4-96 3-43 6-53 8-65 5-55 chap, x.] MATERIALS FOR SHIPBUILDING. 4 2 3 Other laboratory experiments, made on an extensive scale, have given different results for the relative intensities of the action of the various metals on the iron ; but they fully confirm the fact that a greatly increased rate of corrosion results from galvanic action. The first two materials, copper and brass, are those of which the ship- builder has need to take most heed in arranging the sheathing or fittings of iron or steel ships. Under the conditions of practice, the losses in thickness by corrosion are usually less than those indicated by the laboratory experiments, which are made on bare plates, and mostly on small surfaces, over comparatively short periods. There are cases, however, where the skin plating and frames of ships have corroded more rapidly than the laboratory samples would lead one to expect. For example, in H.M.S. Megsera, built at an early period of iron ship- building when the proper, means for preservation were not so well understood, fifteen years' service reduced the thickness of many plates on the bottom by fully \ inch. The corresponding loss in weight per square foot was about 10 lbs., or about an average of •0555 lb. per month, if the wear is assumed to be uniform over the surface of the plates. This will be seen to exceed considerably the greatest losses above-mentioned for iron plates immersed in foul sea- water or bilge-water. Laboratory experiments differ among them- selves as regards rates of corrosion for the reasons above stated. It may be interesting to add, however, that a large number of these experiments indicate a loss of thickness for iron plates immersed in sea-water not exceeding £ inch to f inch in a century. Turning from laboratory experiments to experience in actual ships, with structural arrangements designed to facilitate examination, cleaning, and painting, and with proper care taken to remove rust and scale from the surfaces in order that they may be protected by paint, varnish, or cement, it may be said that serious corrosion need not be feared in iron or steel ships. Periodical inspection, cleaning and painting are absolutely essential to the preservation of such ships. Neglect of these simple precautions may cause serious deterioration. With ordinary care in designing the structures, there need be very few parts not readily, accessible when ships are cleared for survey and repairs. There should be none, bounded by the skin plating, absolutely inaccessible, unless they are filled with cement or other water-excluding material. Under engines and boilers there may be places difficult of access in some types of ships ; but, as above explained, these are just the parts where there is the greatest need for precautions against corrosion, and in arranging the structures access should be secured. There are very many kinds of " protective " paints, varnishes, and 4 2 4 NAVAL ARCHITECTURE. [chap. x. cements in use for the prevention of corrosion on the insides and outsides of iron and steel ships. Rival claims to superior excellence are naturally put forward ; but it would be out of place here to say more on the subject than that shipbuilders and shipowners can now procure many trustworthy " protectives," each of which possesses some special excellence. Facts might be multiplied in support of the very slow deterioration of iron and steel ships properly con- structed and cared for. No better evidence of this can be found than in the provisions of Lloyd's Eules, which do not contemplate an exhaustive survey and drill-tests of the actual thickness of plating until ships have been twelve years afloat. Less searching surveys have to be made at intervals of four years. If these prove satisfactory, another exhaustive survey and drill-testing is not required until a further period of twelve years has elapsed. Should plates have lost a good deal in thickness, they must be renewed ; but such cases are not common in ships properly cared for and maintained. The iron-built ironclads of the Warrior and Minotaur classes are now thirty years old ; the original bottom plating remains, and the vessels are practically as strong as ever. Steel ships have not, of course, a similarly long guarantee from experience. Some of the earlier ships built of high tensile steel have remained efficient for over twenty years, although their plating is very thin. Nearly as long experience has been obtained with the first ships built of mild steel ; and here also it has been most satisfactory on the whole. One special precaution in steel ships — the removal of the manufac- turer's scale — has been already mentioned. Another point of practical importance is that in new steel ships the protective coatings may not adhere so well at first to the surfaces as they do in iron ships. Consequently it is desirable to examine closely and in some cases to renew these coatings at first rather more frequently than in iron ships. This relative disadvantage disappears at later stages in the history of steel ships, when the protectives have become firmly adherent to the surfaces. " Pitting " has occurred in some steel- plated ships to a larger extent than is usual in iron ships. When the scale has been thoroughly removed, however, the liability to pitting is greatly diminished. Under engines and boilers in some steel-built ships of the mercantile-marine, considerable corrosion is said to have occurred ; and it has been recommended to use iron floors and plating at these parts. General practice has not, however, followed this recommendation ; and, as the steel manufacture extends, the use of iron for the minor parts of the internal structures is becoming less common than it was at first. An alternative plan is to use at these parts the full thickness in steel which would be used in iron. chap, x.] MATERIALS FOR SHIPBUILDING. 4 2 5 In torpedo-boats and other small vessels with very light scant- lings of steel, another method of preventing corrosion has been used. The outside plating, floor-plates, lower parts of bulkheads, etc., have been " galvanized ; " that is to say, the surfaces have been first cleaned in an acid bath, and have subsequently been dipped into a bath of zinc. A coating of this metal is formed in this way, and upon it the protective paints or varnishes are applied. Methods for electrically depositing zinc are now being worked out, as alter- native and possibly preferable to the old process of " galvanizing." The regulations issued by the Admiralty for the preservation of iron and steel ships contain the best summary of the precautions necessary for that purpose with which we are acquainted. It will be sufficient to summarize the main points. Galvanic action of copper, brass, or lead upon the hull is to be prevented by making the lower pieces of suction-pipes, etc., which are immersed in the bilge- water, of iron, steel, or zinc or zincked iron wherever that is possible. Where copper or brass pipes are unavoidable, they are to be well painted or varnished, and covered with canvas in order to reduce their action on the iron. The gun-metal screw-propellers are also to be painted for the same reason, and bands of zinc, termed " pro- tectors," are to be fitted near them, in order to concentrate the galvanic action of the propellers upon the protectors and save the bottom plating: this plan has answered admirably. In order to preserve the inner surfaces of the bottom plating below the bilge from the injurious effects of the wash of corrosive bilge-water from side to side as the ship rolls, cement is used, and has proved of great ■advantage to both merchant and war ships. Other surfaces of plates and bars in the interior are protected by suitable paints or com- positions. All parts of the hull are ordered to be made as accessible as possible for inspection and repairs. In cases where parts are necessarily inaccessible under ordinary circumstances — such as under the boilers or engines, etc. — careful records are to be kept of them ; and when opportunity offers, as during a thorough repair at a dock- yard, all such parts are to be opened up and inspected. When a ship is in the reserve or on service, all accessible parts are to be inspected once a quarter, cleaned and painted when necessary. A more thorough survey is made by dockyard officers at specified periods when ships are at naval ports ; then the only parts left unvisited are those which cannot be reached without great difficulty — as, for instance, spaces which can only be attained by lifting the boilers or machinery. The use of double bottoms facilitates a thorough examination, especially of the inner surface of the outer plating, and all the parts of the inner plating underneath engines and boilers. The outer surface of the bottom plating is to be sighted 426 NAVAL ARCHITECTURE. [chap. x. at least once a year ; it is protected by some anti-corrosive paint or composition, and if the annual examination shows it to be necessary, this protective material is renewed. Such are the main points in the Admiralty regulations. Con- formity to them must prevent any serious corrosion taking place ; for rusting ought to be detected in its earlier stages, and the surfaces, being frequently cleaned and coated, ought not to suffer greatly. The system has now been in force for many years, and has worked most satisfactorily. In a modified form it is applied also to the preservation of the ironwork in the composite ships of the Eoyal Navy. The Fouling of Ships. — When ships have been long afloat, various growths of marine plants and animals are found upon the bottoms. Such growths are usually described by the term " fouling." Their character and extent depend upon many conditions, but their effect upon the speed is always prejudicial. It will be shown hereafter that a very moderate degree of roughness in the bottom of a ship involves a relatively large increase in fluid resistance to her motion, and in the power required to attain a certain speed. Consequently fouling is a matter of considerable practical importance, particularly in iron and steel ships. Wood ships are subject to fouling unless their bottoms are covered with suitable metallic sheathing. In naval, history frequent references are made to the marked superiority as regards the main- tenance of speed .possessed by metal-sheathed ships over ships with the wood planking, exposed or simply coated with some protective material. Copper, Muntz metal, and zinc are the three kinds of metal sheathing which have been most extensively employed on the bottoms of wood and. composite ships. Although primarily employed to prevent serious fouling, these metal sheathings, of course, [also protect wood planking from the attacks of worms and other marine animals. The anti-fording properties of copper sheathing are due to the fact that the action of sea-water upon its surface produces salts which are readily soluble, and do not adhere strongly to the uncorroded copper beneath. Hence the salts, instead of forming incrustations, are continually being washed off or dissolved away, leaving the sheathing with a smooth, clean surface, and preventing the attach- ment of plants or animals. Some chemists have ascribed importance to the poisonous character of the salts of copper in preventing foul- ing; but the foregoing is undoubtedly the more important feature, and is commonly termed " exfoliation " of the copper. The rate at which this wasting of the copper proceeds varies greatly under different circumstances and with different descriptions of copper^ chap. x.J MATERIALS FOR SHIPBUILDING. 4 2 7 and formerly this subject received much attention, the aim being to secure the minimum rate of wearing consistent with the retention of anti-fouling properties. For this purpose Sir Humphrey Davy sug- gested to the Admiralty the use of " protectors," formed of iron, zinc, or some metal electro-positive to copper. When these pro- tectors were put into metallic connection with the copper sheathing and immersed, galvanic action resulted, the protectors were worn away, and the rate of wearing of the copper was decreased in propor- tion to the ratio of the surface of the protectors to the surface of the sheathing. When the protector had about -yfo of the surface of the sheathing, there was no wasting of the copper. With a smaller pro- portionate surface of the protectors the copper wasted somewhat ; but even when the protectors had an area of only 10 Vo' part that of the sheathing, there was proved to be a sensible diminution in the rate of wearing. The limits of protection from fouling appeared to be reached when the surface of the protectors equalled t \~q P ar t of the surface of the sheathing. After experience on actual ships it was found, however, that preservation of the copper by this means led to rapid fouling, and the plan was abandoned. Nor has any substitute been since found, the practice being to exercise great care in the manufacture of the copper, and to regard its wasting as the price paid for preventing fouling. Muntz metal— an alloy of copper and zinc in the proportions of about 3 to 2 — has been used largely as a substitute for copper, especially in the ships of the mercantile marine, and appears to answer fairly well, being, of course, much cheaper than copper. Such alloys are supposed by some persons to have the advantage of not producing powerful galvanic action upon iron immersed in sea-water and metallically connected with them ; but this property has not been definitely established. On the other hand, it appears that, after being long immersed, the alloy tends to alter in composition. Muntz-metal sheets have been found to become brittle after being some time in use ; and the explanation given is that, the zinc being electro-positive to the copper, galvanic action is established between the two metals in the alloy, and part of the zinc removed. Muntz metal bolts have also been found to perish through galvanic action, under certain circumstances, when immersed in sea- water. The addition to the alloy of a third metal, such as tin even in very small quantities, appears to prevent this objectionable change. In the Eoyal Navy an alloy known as " naval brass " is used instead of Muntz metal for securities in gun-metal castings, or in connection with copper sheathing, under water. This alloy consists of 62 per cent, of copper, 37 per cent, of zinc, and 1 per cent, of tin. It answers admirably for bolts, and trials have been made with it 4 2 § NAVAL ARCHITECTURE. [chap. x. rolled into sheets and plates of a thickness suitable for the bottoms of ships. As regards strength and ductility the trials were satis- factory ; but difficulties arose in connection with the riveting and watertight work on the thicker plates. The great expense of naval brass sheets, as compared with iron or steel, would prevent their extensive use in ship-work apart from other considerations ; but in certain special circumstances their use might have been permissible had the trials proved wholly satisfactory. In fact, somewhat similar alloys have been used for the construction of a few torpedo-boats. Zinc is another material which has been largely used for sheath- ing the bottoms of wood ships. When immersed in sea-water, the salts formed on the surface of a zinc sheet are very much more adherent to the uncorroded zinc than are the corresponding salts of copper, and are comparatively insoluble — or perhaps, we should say, are slowly soluble — by ordinary sea-water. Hence it appears that a coating of oxychloride of zinc, etc., is likely to form on the sheath- ing, not being washed away or removed like that on copper ; and consequently zinc does not possess such good anti-fouling properties as copper, nor present such a smooth surface. It lasts for a con- siderable time under ordinary conditions. In some waters, however, and those of the tropics especially, zinc sheathing has been found to perish very quickly, owing probably to such a composition of the water as favom-ed the rapid solution of the salts formed on the surface, the exposure of the uncorroded zinc, its rapid oxidation, and so on. One commission on the African coast is said to have sufficed to strip the bottom of zinc and leave the wood exposed in H.M.S. Trinculo, fouling of course ensuing. Other cases are reported where zinc sheets £ inch thick have, under exceptional conditions, been worn through in- the course of twelve months. Under ordinary con- ditions, zinc sheathing is much more durable ; in fact, to increase its anti-fouling qualities, it has, in some cases, been put into com- munication with a metal, such as iron, which is electro-negative to itself, in order that the galvanic action which is produced may have the result of keeping the surface of the zinc freer from incrustations to which marine plants and animals can adhere. Fouling is a much more serious matter in iron or steel ships. It may take place to a considerable extent without any considerable corrosion accompanying on the outer surface of the bottom plating ; but as a rule it may be said that corrosion and fouling, although distinct, are closely related. Corrosion, when it is developed on a large scale, certainly tends to make fouling more rapid. When pro- tective paints or compositions do their work well and minimize corrosion, there is much less risk of serious fouling. Some persons have affirmed that if all rusting were prevented, the bottoms of ships chap, x.] MATERIALS FOR SHIPBUILDING. 4 2 9 being kept smooth and clean, the plants and animals could not attach themselves. There are many objections to this opinion, but it is needless to dwell upon them. In practice, the bottom plating, being subject to continuous immersion in corrosive sea-water, and to the wear and tear of service, cannot possibly be kept smooth and clean. Even with the best protective and anti-fouling compositions applied to the bottoms, iron and steel ships cannot remain afloat in sea-water more than a year without becoming so foul as to suffer a serious loss of speed. Very frequently this result is reached in a much shorter period. For economical reasons steamships of high speed are frequently docked, and have their bottoms cleaned and recoated twice or thrice in the year. The prevention of fouling has naturally attracted much attention, numberless proposals having been made with the object of checking the attachment and growth of marine plants and animals, which go on more or less rapidly on iron and steel ships in all waters, and espe- cially in warm or tropical seas. Various soaps, paints, and varnishes of a greasy character have been proposed for the purpose of rendering the attachment of these marine growths difficult, and of securing a gradual washing of the bottom when the ship is under weigh. Many others have been suggested having for their common object the poisoning or destruction of these lower forms of life. Sheets of glass, slabs of pottery, coatings of cement, enamelling, and many other plans for giving a smooth polished surface to the bottom, in order to prevent the adhesion of plants and animals, have been recommended, and in several instances tried, but not with much success. In fact, it wpuld be difficult to point to any other subject which has been the basis of so many schemes and patents with so little practical advan- tage. Between 1861 and 1866 over a hundred plans were patented for preventing fouling, and in the subsequent period inventors have been quite as busy. No cure for fouling has yet been devised, nor, from the nature of the case, is one likely to be discovered. Much has been done in the improvement of anti-fouling compositions, par- ticularly in relation to their rapid application under practical con- ditions when ships are docked for cleaning and recoating. This improvement has been associated with similar changes in the pro- tective (or anti-corrosive) compositions. The result has been an efficient protection of the bottoms from corrosion, a reduction in the cost, and more uniform results with the anti-fouling compositions than were common heretofore. Docking accommodation has also been largely increased in all parts of the world, thus adding greatly to the facilities for cleaning and recoating the bottoms of iron and steel ships. War-ships benefit as well as merchant ships from the increase 43° NAVAL ARCHITECTURE. [chap. x. in docking accommodation. For certain classes of war-ships, how- ever, it has been considered necessary to retain copper sheathing, so that they might keep the sea for long periods without serious fouling and loss of speed. Hence has arisen the construction of "composite" and "sheathed" ships. Composite ships, as already explained, differ from iron or steel ships in having wood skins, to which metallic sheathing can be nailed. Formerly that method of construction was used in the mercantile marine, chiefly for sailing ships. The China tea-clippers were so built. Now the plan is rarely used, except for yachts. In the Eoyal Navy and in foreign navies the system has been extensively employed for gunboats, sloops, and corvettes, up to about 2000 tons displacement. The principal difference between mercantile and naval practice is found in the outside planking of composite ships. Merchant ships have usually had one thickness of plank, secured to the ribs by screw- bolts. When these bolts have been of iron, they have often deteriorated rapidly under galvanic action, resulting from the copper or Muntz-metal sheathing. With brass bolts much more satisfactory results have been obtained. Composite ships of the Boyal Navy, as explained at p. 373, have two thicknesses of planking. The inner thickness is fastened to the frames with naval brass screw-bolts, and the outer thickness is secured by copper through bolts spaced between the frames. This plan has been found to answer well for long periods of service. For larger classes of war-ships having greater engine-power, it has long been the practice to complete the iron or steel hulls with skin-plating in the usual manner, and then to work wood planking outside the skin-plating in order to attach copper sheathing. A very large number of these sheathed ships are now employed in the Eoyal Navy and in foreign navies. The Inconstant, Active, and Volage, dating from 1868, are still on service, furnishing con- clusive evidence of the durability of vessels of the class, and of the possibility of securing the anti-fouling properties of copper sheathing in association with the strength of iron or steel hulls. First cost is, of course, considerably higher than in unsheathed ships ; and, although the wood sheathing adds greatly to the local strength of the bottoms, and somewhat to the general structural strength, as a rule the hull proper would be sufficiently strong without the wood. In other words, the extra cost and weight of the wood and copper sheathing and of the bronze castings usually employed in sheathed ships for stems, stern-posts, rudders, etc., must be regarded as the price paid for securing the maintenance of speed during long periods afloat, and the avoidance of frequent dockings and recoatings such as are necessary in unsheathed ships. chat, x.] MATERIALS FOR SHIPBUILDING. 43 l Many plans have been used for attaching the wood planking to sheathed ships. That generally employed in the Eoyal Navy nntil 1887 had the wood planking worked in two thicknesses. The inner thickness was secured to the skin-plating by iron screw-bolts, and the outer thickness to the inner by brass or yellow metal screw- bolts passing into but not through the inner planking. In this way it was hoped to avoid metallic connection between the copper sheathing and the skin-plating and bolts of the inner thickness of planking. The copper sheathing was not brought into contact with the metal stems, stern-posts, valves, etc., and every precaution was taken against galvanic action being set up which would lead to deterioration of the hull and fastenings. Experience shows that these arrangements have answered admirably with one exception. There has in no case been evidence of serious galvanic action or deterioration on the skin-plating. The fact that the copper sheathing has maintained its anti-fouling qualities confirms this conclusion. On the other hand, there have been many cases where the iron bolts securing the inner thickness of planking have wasted to a serious extent, owing to the presence of water between the planking and the skin-plating. The renewal of these bolts has been a costly and difficult matter, with two thicknesses of planking worked in the manner described. After full consideration, therefore, and in view of all experience gained, it has been decided to use only one thickness of planking in future sheathed ships of the Koyal Navy, securing this to the steel skins by naval brass screw-bolts. Special arrangements are made to prevent the lodgment of water between the wood planking and the skin ; and to avoid any local corrosion of the skin in the neighbourhood of the bolts. With these pre- cautions there is no reason for anticipating galvanic action on the hull, and there can be no deterioration of the fastenings. Simplicity of attachment enables the planking to be readily removed for examination or repair of the hull ; whereas with two thicknesses this is a troublesome matter. Experience with ships so sheathed as yet extends only over four or five years. So far as it has gone it has been entirely satisfactory, both as regards the preservation of the skin-plating and the anti-fouling qualities of the copper sheathing. One special danger is necessarily incurred by all copper-sheathed iron or steel ships. Any damage to the bottom which stripped off the bottom planking and exposed a portion of the skin, might place that portion of the skin within the influence of powerful galvanic action ; for it would be immersed in the same sea-water as the copper sheathing, be almost certainly in metallic connection there- with, and have concentrated upon its comparatively small area the 43 2 NAVAL ARCHITECTURE. [chap. x. action of the Tery laxge surface of copper sheathing. The result might be very rapid corrosion of the skin, and possibly its perforation by holes. Such an accident, capable of stripping off wood planking firmly attached to the hull, must of course be exceptional in severity, and of very rare occurrence. The Warspite, sheathed with two thicknesses of wood and coppered, ran on the rocks in 1892, and seriously damaged her wood keels and some portions of the wood planking. In all such cases the least possible delay should be permitted in exaniining and repairing the damage, and if this is done no serious consequences can result. Zinc sheathing has been tried instead of copper on a few iron ships in the Eoyal Navy, and on some iron ships in the mercantile marine. If it could hare secured a fair degree of freedom from fouling, it would have been preferable, because its electrical relations to iron and steel would have prevented any galvanic action being set up causing the latter to suffer, and because first cost would have been lessened. At first promising results were obtained in the Eoyal Navy; but there is reason to believe that these were due in no small measure to the fact that the ship in which the trials were made was stationed for most of the year in the estuary of a river and in brackish water. Subsequently, on foreign service, the zinc sheathing of this ship became very foul when at sea, and was cleaned to a large extent when the vessel ascended rivers and entered fresh water. In another instance which came under the author's notice, a zinc-sheathed ship, belonging to a foreign navy, which had been several years afloat, and was found on docking to be remarkably clean, owed her condition in part, no doubt, to having been lying for some time before she was docked in comparatively fresh water. Taking experience with zinc-sheathed ships, as a whole it has been unfavourable, and the system has fallen into disuse. It appears that, after a very short period of immersion in sea-water, zinc becomes so rough on the surface as to largely increase factional resistance. Cases have occurred where swift cruisers, zinc- sheathed, have performed their speed trials soon after being un- docked with unsatisfactory results as compared with vessels of practically identical form, either copper-sheathed or with clean painted iron bottoms. In the relative roughness of the zinc surface was found the cause of the inferior performance. It has, therefore, become the custom to coat the bottoms of zinc-sheathed ships with anti-fouling compositions when they are docked. Zinc sheathing has, however, two advantages over unsheathed iron or steel skins: corrosion of the outer surface of the iron skin is rendered practically improbable by its presence. Further, when zinc-sheathed ships have been afloat for long periods, the fouling of their bottoms is, as a rule, chap. x.J MATERIALS FOR SHIPBUILDING. 433 much less than that with bare iron. The vastly superior qualities of copper as an anti-fouler have led to its general use in the Eoyal Navy, and no zinc sheathing has been used for many years. It may, however, be found useful in stationary ships, or vessels of low speed. Various plans have been tried for attaching zinc sheathing to iron hulls ; that commonly used in the Eoyal Navy was as follows : A single thickness of planks (3-inch to 4-inch) was bolted outside the skin-plating ; to this the zinc sheets were nailed : the strakes of planking were not caulked, but the water which found its way under the sheathing could pass freely through the seams to the iron skin. Iron stems and stern-posts were employed ; and by various means a certain amount of metallic connection was made between the zinc and the iron hull, such connection being desirable in order to keep the surface of the zinc freer from incrustation. The practical diffi- culty was to adjust the relative amounts of the surfaces of iron and zinc, contributing to galvanic action on the latter, in such a manner as to prevent too rapid or too local wearing of the zinc without interfering with its anti-fouling properties. On wood ships zinc usually lasted for a considerable time, but was not very successful in preventing fouling ; there it had but little metallic contact to produce galvanic action. On some merchant ships the zinc has been laid almost directly upon the iron skin, with felt or some similar material interposed, and its rate of wear has been so quickened that a single voyage has sufficed to destroy it. Allusion has already been made to plans for constructing vessels with skin-plating which shall be practically incorrodible. In torpedo- boats and yachts, various bronzes and aluminium have been used. Proposals have been made also for using steel alloyed with such a percentage of nickel as would secure freedom from corrosion. With skins of this nature, not merely corrosion, but fouling, would no doubt be greatly diminished. On the other hand, first cost would be considerably increased as compared with ordinary mild steel skins ; while the use of wood sheathing with copper attached probably involves less first cost, and makes a bottom capable of bearing rougher usage. It is by no means improbable, however, that as the cost of aluminium or that of nickel-steel alloys is lessened by improvements in manufacture, the use of non-corrodible skins may be more extended. 2 F 434 NAVAL ARCHITECTURE. [chap. xi. CHAPTER XI. THE RESISTANCE OF SHIPS. No branch of the theory of naval architecture has a richer literature than that which forms the subject of this chapter. It would be a formidable task merely to enumerate the names of eminent mathe- maticians and experimentalists who have endeavoured to discover the laws of the resistance which water offers to the progress of ships ; and still more formidable would be any attempt to describe the very various theories that have been devised. Again and again has the discovery been announced of the "form of least resistance," but none of these has largely influenced the practical work of designing ships, nor can any be regarded as resting on a thoroughly scientific basis. In fact, a century and a half of almost continuous inquiry has firmly established the conviction that the problem is one which pure theory can never be expected to solve. Although earlier theories of resistance are now discarded, and the present state of knowledge on the subject is confessedly im- perfect, great advances have been made within the last half-century, and most valuable experimental data have been collected. The modern or " stream-line " theory of resistance may now be regarded as firmly established. Many eminent English mathematicians have been concerned in the introduction and development of this theory, as well as in the conduct of the experiments by which it has been put to the test. Of these two deserve special mention. The late Professor Eankine did much to develop the theory and practically apply it to calculations for the resistances and speeds of ships ; the broad generalizations which we owe to him have served as guides to later investigators.* The late Mr. W. Froude was the founder of the modern system of model experiments, by which the resistances of full-sized ships may be determined. These experiments are carried on upon the basis of the stream-line theory of resistance, * See diy. i. chap. v. of Shipbuilding, Theoretical and Practical, edited by Professor Rankine. chap, xi.] THE RESISTANCE OF SHIPS. 435 and have fully confirmed its soundness. At the same time they have greatly enlarged, and in many particulars have corrected, the information previously possessed respecting the resistance of water to the movement of ship-shaped bodies. In addition to this im- portant service, Mr. Froude did much to elucidate and popularize the stream-line theory. In fact, the best available descriptions of its great features are to be found in his published Lectures and Memoirs on the subject. Added to clear and masterly descriptions are the accounts of illustrative experiments ; so that readers having but a moderate knowledge of mathematics can understand the prin- ciples involved and the practical deductions.* The experimental establishment founded by the late Mr. Froude, with assistance from the Admiralty, was conducted by him for some years. Since his death the superintendence of the establishment has been placed by the Admiralty in the hands of Mr. R. E. Froude, who has admirably continued and extended the investigations commenced by his father. This experimental establishment has become an important section of the Constructive Department of the Admiralty ; and has proved of great value in designing modern war-ships of novel types and high speeds. A considerable amount of information of a general character obtained thereat, has been published, with Admiralty approval, chiefly in the Transactions of the Institution of Naval Architects. Similar experimental establishments have been created in Holland, Italy, and Russia, and one leading private shipbuilding firm in this country has done the same thing for the purposes of its own business. It is now generally recognized that only by direct experiment can the problems of resistance be certainly resolved. Possibly, as experimental data are accumulated, a fuller and more complete theory may be constructed. Before attempting a brief outline of the stream-line theory of resistance, in general accordance with the methods followed by Rankine and Froude, it will be desirable to give a few explanations of terms that will be frequently employed. Classification of Water-Besistanee. — Water is not what is termed a perfect fluid ; its particles do not move past one another with absolute freedom, but exercise a certain amount of rubbing or friction upon one another, and upon any solid body past which they move. Suppose a thin plate with a plane surface to be entirely immersed in water and moved end-on, or edgewise, it will experience what is termed frictional resistance from the water with which its surface comes into contact. The amount of this frictional resistance will * See Reports of the British Asso- the Institution of Naval Architects, vol. ciation for 1875 ; and Transactions of xv. and onwards. 436 NAVAL ARCHITECTURE. [chap. XI. FIG. 144. depend upon the area and the length of the plate, as well as the degree of roughness of its surface and the speed of its motion. If this plate is moved in a direction at right angles to its surface, it encounters quite a different kind of resistance, termed direct or some- times head resistance ; this depends upon the area of the plate and the speed of its motion. Should the plate be moved obliqiiely, instead of at right angles to its surface, the resistance may be regarded as a compound of direct and frictional resistance. Supposing either direct or oblique motion to take place, the plate wotdd leave an eddying " wake " behind it, as indicated somewhat roughly in Fig. 1J4, and the motion thus created amongst the particles con- stitutes a very important element in their resistance to the passage of the plate. If the plate is not wholly immersed, or if its upper edge is near the surface, and it is moved directly or obliquely, it will heap up water in front as it advances, and create waves which will move away into the surrounding water as they are formed, and will be succeeded by others. Such wave-making requires the expenditure of power, and constitutes a virtual increase to the resistance. If the plate were immersed very deeply, it would create little or no surface disturbance, and therefore require less force to propel it at a certain speed than would a plate of equal immersed area moving at the surface with a portion situated above that surface. If there were no surface disturbance, the resistance would be practically independent of the depth of immersion. This statement is directly opposed to the opinion frequently entertained, which confuses the greater hydrostaticdl pressure on the plate, due to its deeper immersion, with the dynamical conditions incidental to motion. It may, therefore, be desirable to add a brief explanation. Supposing a deeply immersed plate to be at rest, the pressures on its front and back surfaces clearly must balance one another at any depth. When this plate is moved ahead at a uniform speed, it has at each instant to impart a certain amount of motion to the water disturbed by its passage ; but the momentum thus produced is not influenced by the hydrostatical pressures on the plate, corresponding to the depth of its immersion. Water is practically incompressible ; apart from surface disturbance, the volume of water, and therefore the weight, set in motion by the plate, will be nearly constant for all depths, at any assigned speed. In other words, if there be no surface disturbance, the resistance at any speed is independent of the depth. This is equally true of the resistance to direct and chap. XI.] THE RESISTANCE OF SHIPS. 437 oblique motion of a plate through water, as well as of factional resistance, and the fact has been established experimentally. Colonel Beaufoy ascertained the resistances of a plate moving normally to itself, when submerged to depths of 3, 6, and 9 feet below the surface, and found them practically identical at all the depths. These experi- ments also served to establish the following very useful rule : The resistance per square foot of area sustained by a wholly submerged thin plate moving normally to itself through sea-water at a uniform speed of 10 feet per second is about 112 lbs. ; and for other speeds the resistances vary as the squares of the speeds. Independent experiments made at the Admiralty works by Mr. E. B. Froude have practically confirmed Beaufoy's result, giving 109 lbs. as the resist- ance per square foot for the speed of 10 feet per second in sea-water. The case where a thin plate is set obliquely to its line of motion is not so simple as that where it is at right angles. In Fig. 144 it will be noted that the stream-line motions are symmetrical, the water diverging and flowing over each edge of the plate, and obviously at the centre of the plate the water is at rest. A tow-line attached to the centre of the plate and extending forward in the direction of motion would therefore keep the plate normal to it, because the pressures on each side would be balanced. For oblique positions of the plate, it is equally true that the water must separate into two streams and escape over the edges ; only in that case the intensity of the pressure on the foremost part (near the " leading " edge) of the plate will be much greater than that on the other part. That is to say, the line of zero-pressure on the plate where the streams may be supposed to diverge is nearer to the leading edge than to the after edge of the plate. This point is further discussed in Chapter XVIII., in connection with the action of water on rudders. For the present attention is directed chiefly to the laws which govern the total normal pressures on plates set obliquely to their line of motion, and it must be admitted that the existing state of knowledge is not satisfactory or complete. It was formerly assumed that for an angle of obliquity a of a plate to its line of motion, the normal pressure thereon varied with the square of the sine of the angle of obliquity. For any speed — Oblique resistance (tow-rope tension) = direct resistance x sin 3 a. Another theory, supposed to hold for small valves of a, was that the normal pressure varied as the sine of the angle of obliquity ; so that — Oblique resistance = direct resistance x sin 2 a. Beaufoy made experiments for the purpose of determining the tensions on a tow-line, when a wholly submerged plate was set at 438 NAVAL ARCHITECTURE. [chap. XI. various angles to its line of motion and moved at various speeds. From the remarks of the experimentalist, it is evident that the results obtained were not regarded as entirely trustworthy, but it may be of interest to summarize them. This is done in the following table, where "resistances" indicate the tow-rope tensions in the line of motion. For oblique positions of the plate these tensions may be termed " oblique resistances," as distinguished from direct resistance when the plate is at right angles to the line of motion. Beaufot's Expemmests ox Resistances of Submerged Plaxe Surfaces. Angles of plane] with line of > 90° 80° 70° 60° 50° 40° 30° 20° 10° motion . .J Sines of angles . 1 •985 •940 •866 •766 •643 •5 •342 ■174 (Sines) 2 of angles 1 •97 •88 •75 •587 •413 •25 •117 •03 (Sines) 3 of angles 1 •96 •83 •65 ■45 •26 •125 •04 •005 Resistance . 1-00 •915 •845 •828 •722 •579 •321 •272 It will be seen on investigation that Beaufoy's results do not agree with either of the formulae which had been generally accepted ; and it is known that the formulae were not based upon a full con- sideration of the phenomena attending the flow of water past a plate. M. Joessel, of the French Navy, conducted a series of experi- ments on thin plates moving in water, with special reference to his plan of balanced rudder. Hence he deduced a formula for the normal pressure on a plate set at an angle a to its line of motion, which is probably one of the most trustworthy yet proposed. Let P = the direct resistance on a plate moving normally to itself at a certain speed; P t = the normal pressure when the plate is inclined at an angle o to the line of motion, and has the same speed of advance. Then M. Joessel's formula is — p i = : sm a 39 + "61 sin a xP. It will be seen that this formula gives ratios of Pi to P consider- ably above those obtained by Beaufoy. At 20 degrees, for instance, Joessel gives this ratio as "57, and Beaufoy as - 32 ; at 40 degrees Joessel gives '82, and Beaufoy -579 ; at 60 degrees Joessel gives -93, and Beaufoy '828. Lord Bayleigh has obtained, by mathematical reasoning and neglecting the effect of eddy-making at the back of a plate, a formula very similar to Joessel's, viz. — -r, 2ir sin a „ sin a _ I"i = — — ^— X P = „„„ . „ . — X P. 4 + ir sin o •637 + "5 sin a chap, xi.] THE RESISTANCE OF SHIPS. 439 Here the pressures P and Pi are only those on the advancing face of the plate, and the solution does not profess to fully represent the conditions of practice. Another interesting series of experiments has been made by Mr. Calvert, in connection with his inquiry into the best forms of screw- propellers.* The experiments were made on small solids, with plane front surfaces and convex backs, representing sections of the blades of screw-propellers. The plane faces were set at various angles of obliquity to the line of motion, and the solids were moved at various speeds. Keeping the vertical measurements of the plates constant, their breadths were varied. Especial attention was bestowed on small angles of obliquity, from 13 degrees downwards. Although a very large number of experiments were made, and the method was most carefully studied in order to obtain trustworthy results, Mr. Calvert frankly admits that his conclusions are open to possible amendments if experiments were made on a larger scale, embracing 'a greater range of speeds. Even when thus limited those conclu- sions are of considerable interest. The most important are : (1) that the normal pressures were found to vary as the T85 power of the velocity, and not as the square ; (2) that the pressures did not increase directly with increase in breadth, but at a less rate, the actual rate of increase varying for different angles of obliquity. If P is the normal pressure (in pounds) on the plane surface, of which B is the breadth and D the vertical measurement, Mr. Calvert gives the fol- lowing empirical formula for velocity V in feet per second, and angle of obliquity a to the line of motion : — P = 6 x (V) 185 xB»xD sin a. to is a quantity to be determined by direct experiment ; and Mr. Calvert graphically records values of m for all angles of obliquity up to 90 degrees, where it is unity. For less angles to diminishes in value, the diminution being very rapid for very small values of a. At 30 degrees m is said to be about "6, at 13 degrees about 4, at 8 degrees about "32, and at 5 degrees about *2. This formula will be seen to be similar to one of the earlier formulae, in that the normal pressure on the plane face varies with the sine of the angle of obliquity. The variable function of the breadth used in estimating the pressure is entirely dependent upon the experiments, and these, as above stated, are not sufficiently extended to establish its correct- ness. There are, however, reasons for assuming that the conditions * See the detailed account of the of the Institution of Naval Architects method of experiment and the results for 1887. obtained appearing in the Transactions 44° NA VAL ARCHITECTURE. [chap. xi. of the stream line motions past an oblique plate may cause a sensible reduction in pressure on the after part. Fractional Resistance. — ^Numerous experiments have been made to determine the Ji-ictional resistances of thin plates moved through water ; the most valuable are those conducted by the late Mr. Froude for the Admiralty. Frictional resistance is measured by the momen- tum imparted in a unit of time to a current or " skin " of water which is then adjacent to the surface. This skin of water has a motion given to it in the direction of advance of the plate; while the particles within it move in frictional eddies. The extent to which the frictional resistance causes disturbance — that is to say, the " thickness of the skin " — varies with the velocity and other circum- stances of the motion. From instant to instant the frictional current thus created is left behind by the moving surface, and a " frictional wake " is formed which follows the surface. The forward motion of this wake is gradually communicated to larger masses of water, its velocity is consequently decreased, and finally it ceases to be per- ceptible.* The momentum imparted to the water in a unit of time by a plate moving at a given speed is (as above explained) inde- pendent of the depth of immersion and the corresponding hydro- statical pressure on the plate, any small variations in the density of the water produced by changes in that depth being neglected. The governing conditions of the frictional resistance are, in short, the area and length of the plate, its degree of roughness, and the speed of advance. Passing from these general considerations to the experiments ou actual plane surfaces, made by Mr. Froude, the results were sum- marized by him in the following tabular statement and prefatory remarks. Mk. Fkoude's Experimexts ox Sukface-fkictiox. This table represents the resistances per square foot due to various lengths of surface, of various qualities, when moving with a standard speed of 600 feet per minute, accompanied by figures denoting the power of the spesd to which the resistances, if calculated for other speeds, must be taken as approximately proportional. Under the figure denoting the length of surface in each case, are three columns, A, B, C, which are referenced as follows : — A. Power of speed to which resistance is approximately proportional. B. Resistance in pounds per square foot of a surface the length of which is that specified in the heading — taken as the mean resistance for the whole length. C. Resistance per square foot on unit of surface, at the distance sternward from the cutwater specified in the heading. * See Mr. Froude's paper in the Report of the British Association for 1874. CHAP. XI.] THE RESISTANCE OF SHIPS. 441 Nature of surface. Length of surface, or distance from cutwater, in feet. 2 feet. 8 feet. 20 feet. 50 feet. A. B. ■41 C. A. B. C. A. B. C. A. B. C. Varnish . 2-00 •390 1-85 •325 •264 1-85 •278 •240 1-83 •250 •226 Paraffin 1-95 •38 •370 1-94 ■314 •260 1-93 •271 •237 — — — Tinfoil . 2-16 •30 •295 1-99 ■278 •263 1-90 ■262 •244 1-83 •246 •232 Calico . 1-93 •87 •725 1-92 •626 •504 1-89 •531 •447 1-87 •474 •423 Fine sand 2-00 ■81 ■690 2-00 •583 •450 2-00 •480 •384 2-06 •405 ■337 Medium sand 2-00 •90 •730 2-00 •625 •488 2-00 ■534 •465 2-00 •488 •456 Coarse sand . 2-00 1-10 ■880 2-00 •714 •520 2-00 •588 •490 — — ""• Note. — Beaufoy's experiments made in the Greenland Docks (1794-98) gave values of A between 1*7 and 1'8, closely agreeing in this respect with the later experiments of Mr. Froude. From these experiments the following deductions have been made. First, that the law formerly assumed to hold is very nearly conformed to ; the frictional resistance varying approximately as the square of the velocity, when the area, length, and condition of the surfacei remain unchanged. Second, that the length of the surface sensibly affects the mean resistance per square foot of wetted surface ; and especially when very short plates are compared with plates of 50 feet or upwards. Mr. Froude explains this important experimental fact as follows : " The portion of surface that goes first in the line " of motion, in experiencing resistance from the water, must in turn " communicate motion to the water in the direction in which it is " itself travelling ; consequently the portion of the surface which " succeeds the first will be rubbing, not against stationary water, but " against water partially moving in its own direction ; and cannot, "therefore, experience as much resistance from it." For greater lengths than 50 feet, it appears that the mean resistance per square foot of area remains nearly the same as for the plate 50 feet long. A third important deduction is the great increase in frictional resistance which results from a very slight difference in the apparent roughness of the surface. For instance, the frictional resistance of a surface of unbleached calico — not a very rough surface — was shown to be about double that of a varnished surface. This varnished surface gave results just equal to a surface coated with smooth paint, tallow, or compositions such as are commonly used on the bottoms of iron ships. The frictional resistance of such a surface moving at a speed of 600 feet per minute would be about \ lb. per square foot, which would give a frictional resistance of about 1 lb. per square foot of immersed surface for the clean bottoms of iron ships when moving at a speed of about 12-8 knots. This unit is worth noting. 44 2 NAVAL ARCHITECTURE. [chap. xi. Mr. Calvert has experimented with a flat plank, 28 feet long, towed at different velocities on the surface of the water. By means of an ingenious system of pressure tubes projecting beneath the plank, he measured the velocity of the frictional wake at different points along the under-surface. At all speeds between 200 and 400 feet per minute, " the speeds recorded at distances of 1 foot, 7, 14, "• 21, and 28 feet from the leading end of the plank were respectively " 16, 37, 45, 48, and 50 per cent, of the velocity of the plank." Proceeding further, Mr. Calvert investigated the changes in velocity in the water along a vertical line from the underside of the plank. At 28 feet from the leading end, 6 pressure tubes were arranged with their open ends at various depths, and their indications were simultaneously observed. The conclusion reached was, that " the " velocity decreases in geometrical progression as the distance from " the surface increases in arithmetical progression." At J inch away from the under-surface, the velocity was one-half of the particles in contact with the surface, which were moving at half the velocity of the plank ; at If inch, the velocity was one-fourth ; at 5 to 6 inches away, the water was practically undisturbed. These results are unique and suggestive. The foregoing remarks on the resistance experienced by plane surfaces moving through water will assist the reader in following the discussion of the more difficult problems connected with the resistances of ship-shaped solid bodies. In many of the earlier theories of resistance the immersed surface of a ship was assumed to be subdivided into a great number of pieces, each of very small area, and approximately plane. The angle of obliquity of each of these elementary planes with the line of advance of the ship — her keel- line — was ascertained ; and its resistance was calculated exactly as if it were a detached plate moving along at the assumed speed. For quantitative purposes, experiments were to be made with small plates of known area moved at known speeds, and set at different angles of obliquity ; the resistances being observed. But obviously there was a radical error in applying unit-forces of resistance, obtained from the movements of detached plates, to the case of a ship where all the hypothetical elementary plates were associated in the formation of a fair curved surface, and none of them could have that eddying wake (like that in Fig. 144) which necessarily accompanied each experi- mental plate and formed so important an element of its resistance. This objection does not apply to the experiments made under the auspices of the French Academy of Sciences, during the last century, by Bossut, Condorcet, D'Alembert, Bomme, and others ; these experiments having been directed to the discovery of the resistances experienced by solid bodies of various forms moved at different CHAP. XI.] THE RESISTANCE OF SHIPS. 44- depths. Very few of the models tried, however, had any pretension to ship-shaped forms ; and this is also true of the subsequent experi- ments made in this country by Beaufoy. Satisfactory experiments on the resistances of ships can alone be made with ship-shaped models of reasonable dimensions. This is the principle upon which Mr. Froude proceeded in his experiments. Doubts were expressed at first respecting the correctness of the results deduced from models when applied to full-sized ships, but the experience of twenty years has thoroughly established the system. Stream-line Theory of Resistance. — The modern theory of resistance does not make any hypothetical subdivision of the immersed surface of a ship, but regards it as a whole. When such a surface, with its fair and comparatively gentle curves (like those in Fig. 145), is submerged and drawn through water, the particles are diverted laterally, and can glide over or past the ship without sudden or abrupt changes of motion, F[ „ 45 corresponding to those which occur when particles escape over the edge of the plate in Fig. 144. The paths of the particles are indicated roughly in Fig. 145 by the curved lines, the ship-shaped body being shown in black. After passing the broadest part of the vessel, the particles close in over the after part, and, gliding over the continuous surface, form a wake astern. In the modern theory, the total resistance is considered to be made up of three principal parts : (1) frictional resistance, due to the gliding of particles over the rough bottom of the ship ; (2) " eddy- making " resistance, which occurs chiefly at the stern ; (3) surface disturbance, or wave-making resistance. The second of these divisions only acquires importance in exceptional cases ; it is known to be very small in well-formed ships. It will, therefore, be necessary to bestow most attention upon frictional and wave-making resistance, to examine the conditions governing each, and to contrast their relative importance. It will be assumed throughout that the ship is either dragged or driven ahead at uniform speed by some external force which does not affect the flow of the water relatively to her sides. This is the condition always assumed when the resistance of a ship is being treated. , It is advantageous to separate propulsion from resistance, since the latter depends in all ships only upon the form, proportions, and condition of the bottom ; whereas there are many means of propelling ships. 444 XA VAL ARCHITECTURE. [chap. xi. Siippose the ship to be moving ahead at uniform speed through an ocean unlimited in extent and depth, and motionless except for the disturbance produced by the passage of the ship. Under the conditions assumed, there will obviously be no change in the relative motions of the ship and the water if she is supposed to remain fixed, while the ocean flows past her at a speed equal to her own, but in the opposite direction to that in which the ship really moves. This alternative supposition has the advantage of enabling one to trace more simply the character of the disturbances produced by introducing the solid hidl of the ship at a certain speed into water which was previously undisturbed. First, let the water be assumed to be frictionless, and the bottom of the ship to be perfectly smooth. These are only hypothetical conditions, but it is possible at a latter stage of the inquiry to introduce the corrections necessary to represent the actual conditions of practice. Take any set of particles situated a long distance before the ship, and moving in a line parallel to her keel. If the ship were not immersed in the ocean current, these particles would continue to move on in the same straight bine, which would be horizontal. When the ship is immersed her influence upon the motion of the particles may extend to a very long distance ahead, but there will be some limit beyond which the influence practically does not extend, and outside this, the particles whose motion is being traced will be moving at a steady speed in a horizontal line parallel to the keel. As they approach the ship> however, their path must be diverted in order that they may pass her ; and this diversion will be accompanied by a change in their speed. Supposing, for the sake of simplicity, that the particles main- tain the horizontelity of their motion, and are only diverted laterally ; then, as they approach the bow of the ship, they will move out sideways from the keel-line, and lose in their speed of advance. Xany considerations must govern the extent of this lateral diversion and loss of speed ; such as the form of the bow, the extreme breadth of the ship, and the athwartship distance from the line of the keel of the original line of flow of the particles. At the broadest part of the ship amidships the velocity of the particles of water must be greatest, because the breadths of the " streams " in which they flow are there less than at the bow, and the same quantity of water has to pass the two places. After the midship part of the ship has been passed, and her breadth begins to decrease, the path of the particles will converge towards the keel-line ; and their speed will again receive a check. Finally, after flowing past the ship, and attaining such a distance astern as places them beyond the disturbing influence of the ship, the particles will regain their original direction and speed of flow, provided that there is no surface chap, xi.] THE RESISTANCE OF SHIPS. 445 disturbance. This last-mentioned condition could only be fulfilled in the case of a vessel wholly immersed, at a great depth, below the surface of an ocean limitless in depth ; in the case of ships which are only partly immersed, the retardations and accelerations de- scribed must cause the formation of bow and stern waves, and these will be considered hereafter. Although it has been assumed, for the sake of simplicity, in the foregoing remarks that the particles maintain their horizontality of flow, it should be understood that the assumption is not supposed to represent the actual motion of the water in passing a ship. Diversion from the original line of flow is almost certain to have a vertical as well as a lateral component ; but as to the paths actually traversed by particles, we have little exact knowledge. Mr. Scott Eussell was of opinion that at the foremost part of a ship the particles moved in layers which were almost horizontal ; while at the stern the particles had a considerable vertical component in their motion, besides converging laterally. Professor Kankine asserted that " the actual "paths of the particles of water in gliding over the bottom of a " vessel are neither horizontal water-lines nor vertical buttock-lines, " but are intermediate in position between those lines, and approxi- " mate in well-shaped vessels to the lines of shortest distance, such " as are followed by an originally straight strake of plank, when bent "to fit the shape of the vessel." But, whatever paths may be followed, if at a considerable distance astern of a ship, wholly submerged in a frictionless fluid, the particles have regained their original direction and speed of flow, which they had at a considerable distance ahead of the ship, then their flow past the ship will impress no end-wise motion upon her. Professor Eankine laid down geometrical rules for constructing the paths, or " stream-lines," along which the particles of a friction- less fluid would flow in passing a body very deeply submerged, supposing the particles to move in plane layers of uniform thickness. Fig. 146 was constructed by Mr. Froude in accordance with these rules.* The form of the immersed body with its comparatively blunt bow and stern is indicated in black ; the curved lines indicate the paths of particles. Between any two of these stream-lines, the same particles would be found throughout the motion, and these would form a " stream " of which the stream-lines mark the boundaries. It will be noted that, as the streams approach the bow, they broaden, their speed being checked, and the particles diverted laterally ; the * See the address to the Mechanical described at pp. 106, 107 of " Shipbuild- Section of the British Association in ing, Theoretical and Practical." 1875. Professor Kankine's method is 446 XA VAL ARCHITECTURE. [chap. XI. amount of this diversion decreases as the athwartship distance of the stream from the keel-line increases, and at some distance athwartship the departure of the stream-lines from parallelism with the keel, even FIG. 146. when passing the ship, would be very slight indeed. As the streams move aft from the bow, they become narrowed, having their minimum breadth amidships, where the speed of flow is a maximum. Thence, on to the stern, the streams converge, broaden, lose in speed, and finally at some distance astern resume their initial direction and speed. Since there is no friction, there can be no eddying wake. So much for a vessel wholly submerged ; a ship only partly immersed would be differently situated, because even in a Motionless fluid she would produce surface disturbance. At the bow, where the streams broaden and move more slowly, a wave crest will be formed, of the character shown in Fig. 147 ; amidships, where the conditions FIG. 147. are reversed, some depression below the normal water bine may occur • and at the stern, where the conditions resemble those forward, another wave crest will be formed. Between the bow and stern waves a train of waves may also exist, under certain circumstances. The existence of such waves, when actual ships are driven through the water, is a well-known fact ; every one readily sees why, at the bow, water should be heaped up and a wave formed, but the existence of the stern wave is more difficult to understand. As remarked above, there is but one reason for both phenomena. A check to the motion of the particles is accompanied by an increase of pressure; the pressure of the atmosphere above the water is practically constant, and hence the increase of pressure in the water must produce an elevation above the normal level, that is to say, a wave crest. Conversely, amidships, accelerated motion is accompanied by a dimin ution of pressure, and there is a fall of the water-surface below the still-water level, unless the intermediate train of waves should somewhat modify the conditions of the stream-line motion. CHAP. XI.] THE RESISTANCE OF SHIPS. 447 These waves require the expenditure of force for their creation, and, when formed, they may travel away into the surrounding fluid, new waves in the series being created. In the case, therefore, of a ship moving at the surface of frictionless water, the only resistance to be overcome will be that due to surface disturbance. For the wholly submerged body which creates no waves there will be no resistance, when once the motion has been made uniform; the stream-lines, once established in a frictionless fluid, will maintain their motion without further expenditure of power. This remarkable result follows directly from a general principle, which is thus stated by Professor Eankine : " When a stream of " water has its motion modified in passing a solid body, and returns "exactly to its original velocity and direction of motion before " ceasing to act on the solid body, it exerts on the whole no resultant " force on the solid body, because there is no permanent change of "its momentum." In every stream surrounding the submerged body in Fig. 146, this has been shown to hold ; each stream regains its initial direction and velocity astern of the body. The partially immersed ship in the frictionless water differs from the submerged ship in producing surface disturbance. Perhaps the general principle will be better understood from one of Mr. Froude's simple and beautiful illustrations. Taking a perfectly smooth bent pipe (Fig. 148), he supposed it to be shaped symmetrically, and divided it into four equal and similar lengths, AB, BC, CD, DE. The ends of the pipe at A and E are in the same straight line ; a stream of frictionless fluid flows through it, and has uniform speed throughout. From A to B may be supposed to correspond to the forward part of the entrance of a ship, where the particles have to be diverted laterally, and react upon the inner surface of the pipe, as indicated by the small arrows /, /, /, the resultant of these normal forces being G. At the other end of the pipe, from D to E may be taken to represent the " run " of a ship, where the stream-lines are converging and tending to resume their original directions ; on DE there will be a resultant force J equal to G-. Similarly, the resultant forces on the other two parts BO and CD are equal. The final result is that the four forces exactly neutralize one another, and there is no tendency to force the pipe on 44 8 NAVAL ARCHITECTURE. [chap. xi. in the direction of the straight line joining A to E, although at first sight it would appear otherwise. The same thing will be true if, instead of being uniform in section, the pipe is of varying size, and if, instead of being symmetrical in form, it is not so ; provided only that at the end E the fluid resumes the velocity it had at A, and flows out in the same direction. The forces required to produce any intervening changes in velocity and direction must have mutually balanced or neutralized one another, as in the preceding example, before the stream could have returned to its original velocity and direction of motion. Applying these principles to the stream-lines surrounding a ship, it will be possible to remove one or two difficulties which have given rise to erroneous conceptions. It has been supposed, for example, that a ship in motion had to exert considerable force in order to draw in the water behind her as she advanced. As a matter of fact, however, the after part of a ship has not to exercise " suction " at the expense of an increased resistance, but sustains a considerable forward pressure from the fluid in the streams closing in around the stern. Any cause which prevents this natural motion of the streams, and reduces their forward pressure on the stern — such as the action of a screw propeller — causes a considerable increase in the resistance, because the backward pressures on the bow are not then so nearly balanced by the forward pressures on the stern. Again, it will be evident that — apart from its influence on surface disturbance — the extent of the lateral diversion of the streams, in order that they may pass the midship part of the ship, does not affect the resistance so much as might be supposed ; since the work done on the foremost part of the ship in producing these divergences is, so to speak, given back again on the after part where the streams converge. Yery considerable importance attaches, however, to the lengths at the bow and stern over which the retardations of the particles extend ; since these lengths exercise considerable influence upon the lengths of the bow and stern waves created by the motion of the ship. And, further, the ratios of these lengths of entrance and run to the extreme breadth of the ship must be important, as well as the curvilinear forms of the bow and stern, since the extent to which the particles are retarded in gliding past the ship must be largely influenced by these features ; and, as we have seen, the heights of the waves will depend upon the maximum values of the retardations. In other words, with the same lengths of entrance and run, differences in the " fineness " of form at the bow and stern may cause great differences in the heights of the waves created, and consequently in the energy required to create and maintain such waves. Frictional and Eddy-making Resistance of Ships. — Such are the chap, xi.] THE RESISTANCE OF SHIPS. 449 principal features of the stream-line theory of resistance for friction- less fluids and smooth-bottomed ships. The sketch has been necessarily imperfect, but it will serve as an introduction to the more important practical case of the motions of actual ships through water. Between the hypothetical and actual cases there are certain important differences. First, and by far the most important, is the frictional resistance of the particles of water which glide over the bottom ; secondly, friction of the particles on one another in association with certain forms, especially at the sterns of ships, may produce consider- able eddy-making resistance, although this is not a common case ; thirdly, friction may so modify the stream-line motions as to alter the forms of the waves created by the motion of the ship, and some- what increase the resistance. First, as to frictional resistance. Its magnitude depends upon the area of the immersed surface of the ship, upon the degree of roughness of that surface, or its " coefficient of friction," upon the length of the surface, and upon the velocity with which the particles glide over the surface. From what has been said above, it will appear that this velocity of gliding varies at different parts of the bottom of a ship, being slower at the bow and stern than it is amid- ships. Professor Eankine endeavoured to establish a simple formula for computing the resistances of ships when moving at speeds for which their proportions and figures were well adapted. Under these circumstances he considered that "the whole of the appreciable resistance " would result from the formation of frictional eddies ; in other words, that the wave-making factor in the resistance might be neglected. It is now known that this assumption was not a true one except for moderate speeds ; whereas it was applied by Eankine to considerable speeds. On the other hand, his method of approximating to the frictional resistance, and attempt to allow for variations in the velocities of gliding of the particles over the surface may still be studied with advantage. Eankine supposed that the wetted surface of a ship could be fairly compared with the surface of a trochoidal riband having the following properties : (1) the same coefficient of friction as the bottom of the ship ; (2) the same length as the ship ; (3) a uniform breadth equal to the mean girth of transverse sections of the wetted surface ; (4) an inflexional tangent, making an angle with the base of the trochoid, of which the value was to be deduced from a process of averages applied to the squares and fourth powers of the sines of the angles of greatest obliquity of the several water- lines in the fore body. For any trochoidal riband in which the angle made by the inflexional tangent with the base was , Eankine had previously obtained the following expression for the resistance due to frictional eddies: — 2o 45° NAVAL ARCHITECTURE. [chap. xi. Resistance = length X breadth. X coefficient of friction X (speed) 3 x (1 + 4 sin 3 ^ + sin 4 <(,). The last term was styled the "coefficient of augmentation." Hence — Resistance = coefficient of friction X (speed) 3 X " augmented surface." And his supposition was that for ships of good forms a similar ex- pression would hold, within the limits of speed usually attained. For clean-painted iron ships the formula was very simply stated : — Resistance = length x mean girth of wetted surface X coefficient of augmentation X (speed in knots) 3 -=- 100 _ augmented surface X (speed in knots) 9 100 This method of estimating the probable resistances of ships has been extensively employed by some shipbuilders, and is undoubtedly of use when the speeds to be attained are comparatively moderate. As the speeds increase, and the wave-making resistance assumes importance, the method necessarily fails ; the total resistance then varies with a higher power of speed. Mr. Froude investigated the frictional resistances of ship-shaped models, and as the result of a series of experiments came to a conclusion which greatly simplifies the calculation of this important factor, viz. that no sensible error is involved in calculating the frictional resistance " upon the hypothesis that the immersed skin is " equivalent to that of a rectangular surface of equal area, and of " length (in the line of motion) equal to that of the model, moving "at the same speed." Hence, it is only necessary to experiment with such a plane surface as will enable the proper coefficient of friction to be found, then to measure the immersed surface of the ship, and to apply the coefficient, neglecting the variations in speed of the particles at different parts of the surface. It has been suggested that this generalization requires further and more extended experimental verification before it can be accepted absolutely, especially for ships of great length. No doubt further experiments on planes and curved surfaces of greater length moved at higher speeds would be valuable, but they involve consider- able difficulties in execution. This method of estimating the frictional resistance on the immersed surface of a ship obviously takes no account whatever of the forms and proportions of ships. Two ships of very different forms, but of equal area of bottom, equal roughness, and equal length, will have the same frictional resistance for the same speed ; but they chap. XI.] THE RESISTANCE OF SHIPS. 45 T are likely to have different total resistances. The influence of form and proportion is greatest at high speeds, and it is chiefly felt in the direction of surface disturbance or wave-making ; eddy -making or wake formation also depends upon form, especially at the stern. The remarks made above respecting the general character of frictional resistances to the motion of planes, apply also to the case of the curved wetted surfaces of ships ; and, from an inspection of the coefficients of friction previously given, it is easy to see why foulness of bottom often causes a considerable reduction in the speed of ships. Furthermore, in comparing the frictional resistances of a small model and a full-sized ship, it is necessary to make the necessary corrections in the coefficients of friction on account of differences in length. Such corrections always appear in the records of model experiments. Model experiments have determined the actual value and the relative importance of frictional resistance in different classes of ships moving at various speeds. In all well-formed ships moving at moderate speeds a very large proportion of the total resistance is due to friction. At speeds of 6 to 8 knots, for example, with clean bottoms, frictional resistance has been found to represent from 80 to 90 per cent, of the total resistance. At full speeds in ships steaming at high speeds — 18 to 22 knots — friction has a less proportionate effect, but still represents from 45 to 60 per cent, of the total resistance. When the bottoms become foul, and the coefficients of friction are doubled or trebled as compared with clean bottoms, frictional resistance assumes greater relative importance. For a given speed a much larger expenditure of power and coal is required ; and for a given development of power there is a more or less serious loss of speed according to the degree of foulness. Second, as to eddy-making resistance. It is generally agreed that in well-formed ships with easy curves at the entrance and run (more particularly the latter), this factor in the resistance is com- paratively unimportant. Experiments indicate that eddy-making ordinarily bears a fairly definite proportion to frictional resistance ; and Mr. Froude estimated eight per cent, of the frictional resistance as a fair allowance for eddy-making in a well-formed ship, when (to revert to our old illustration) the stream-lines in a frictionless fluid would converge easily towards the stern, and have regained very nearly their original velocities and directions before they leave the ship. With a full stern, and abrupt instead of gently curved termi- nations to the water-lines of a ship, the particles of water cease to act upon her at a period when they still retain a considerable forward velocity; and the momentum thus created, and not given back in forward pressure on the stern, is a virtual increase to the resistance. 45 2 NAVAL ARCHITECTURE. [chap. xi. Behind the stern of such a vessel will lie a mass of so-called " dead- water," an eddying wake like that behind the plate in Fig. 144. Snch a form of stern is objectionable, and is never adopted unless its use is unavoidable in order to fulfil other and more important condi- tions than those affecting the resistance. It not merely increases resistance, but reduces the efficiency of propellers placed behind it. In order to diminish eddy-making resistance as much as possible, careful attention must be given to the forms of the various adjuncts to a ship, as well as to the shape of the ship herself. Outlying pieces — such as stern-posts, rudders, struts to shaft-tubes in twin- screw ships, supports to sponsons in paddle-steamers, etc. — may occasion a sensible increase to the total resistance if improperly shaped. No general rule can be laid down in this matter ; but Mr. Froude pithily expressed an important fact when he said, "It is " blunt tails rather than blunt noses that cause eddies." In other words, the after terminations of outlying parts should be made as fine as possible consistently with other requirements. Characteristics of the " Wake " of Ships. — When ships are well formed, and eddy-making is reduced to a Tninimmn , their motion through water is necessarily accompanied by a "wake," in which the water near to the stern has a forward motion impressed upon it. One of the main causes of this wake is frictional resistance, and the explanations given above for plane surfaces apply also to ship-shaped forms. The stream-line motions, and at certain speeds the waves produced by the advance of a ship, also influence the motion of particles in the wake. Certain general principles have long been recognized in relation to the movement of water in the wake of a ship which is towed. For example, it is agreed that the maximum forward velocity is likely to occur in particles which flow past the fuller portions of the stern at and near the water-line ; while much less velocity is impressed on particles which flow over the fine deadwood. Further, it is obvious that there must be a gradual loss of forward velocity with increase in the athwartship distance of particles from the hull, at any assigned depth below the surface. Variations of velocity must also occur with change in the longitudinal positions of particles, especially after the ship has passed clear ahead of them. In connection with experimental and analytical investigations into the efficiency of screw propellers, this problem of the wake has assumed greater importance, and has been more thoroughly investigated.* A large amount of informa- * See papers in the Transactions of R. E. Froude in 1883 and 1886 ; and by the Institution of Naval Architects ; by Mr. Calvert in 1893. the late Mr. Griffiths in 1879 ; by Mr. chap, xi.] THE RESISTANCE OF SHIPS. 453 tion has been obtained from model experiments, and much has been learnt from careful observations of the performances of ships. Naturally most attention has been given to the phenomena of those portions of the wake which affect the action of screw propellers, and are comparatively close to the stern. Valuable and extensive observations of this kind were made in 1891 by Mr. Calvert. A boat 28£ feet long and 3 feet 8 inches in beam was towed in smooth water at various speeds ; the towing appliances were fixed, and the screw was not in place. By means of a number of ingenious pressure-logs, the velocities of the streams at different points were measured by the heights of water in tubes. Photographic records were taken of these heights, and simultaneous values for different tubes obtained. The pressure-logs were free to turn both horizontally and vertically, and thus it was endeavoured to indicate the direction as well as the velocity of flow relatively to the ship. Measurements of this kind were made at a great many positions in the water surrounding the stern, and great care was taken to ensure accuracy. Apart from any claim to absolute accuracy, the great number of observations and their general agree- ment make the results specially interesting and important. Graphic and tabulated records have been based on these experiments, which show admirably the .velocities and directions of the " stream-lines " surrounding the stern of the experimental boat. These charts may be subject to some correction, but they give information such as has not been previously available for the whole region in which the screw-propeller would have to work. From them it appears that at a speed of 460 feet per minute, or 4'6 knots per hour, the experimental boat had a wake the particles of which, at some points close to the stern and near the water-line, had a forward velocity exceeding 60 per cent, of the velocity of the boat. This was no doubt in the frictional wake ; and a few feet athwartships away from the points where these high velocities were measured, the corre- sponding velocity was not more than 10 per cent. As the depths below the water-surface increased, and the streams flowed over the finer portions of the dead-wood, the forward velocity rapidly diminished and fell to not more than one-fourth that near the surface. These are but samples of the results which we owe to Mr. Calvert, whose work is likely to lead to similar investigations by other experimentalists. Although the motion of water in the wake varies so greatly, it has been shown, by means of a large number of model experiments, that in considering the action and efficiency of screw-propellers the wake may be assumed to be a current of uniform velocity, so far as the sectional area is concerned which influences the thrust and 454 NAVAL ARCHITECTURE. [chap. xi. slip of the propeller.* This mean velocity of the wake is usually expressed as a percentage of the speed of the ship, and termed the " wake percentage." For single-screw ships the propeller operates on a portion of the wake, where (as will be obvious from the fore- going remarks) the forward velocity should be greatest. The wake percentage for such vessels has been found to vary from 20 to 30. In twin-screw ships the propellers are carried at more or less considerable distances from the hull, both in the athwartship and the longitudinal directions. With full forms of sterns and twin- screws the wake percentage has been found to vary from 14 to 17, and with fine forms, with propellers well clear of the hull, it has fallen as low as 5 to 10. This matter will be again referred to in Chapter XVI. when dealing with the efficiency of screw- propellers. Wave-making Resistance. — The general character of the causes which create waves at the bows and sterns of ships moving in a frictionless fluid have already been sketched. Similar causes operate when the motion takes place in water, although the friction of the particles against each other and against the surface of the ship affect both the dimensions and positions of the waves. At the bow and stern, the motion of the particles of water relative to the ship has its minimum, and there are wave crests ; amidships the relative motion has its maximum speed, and there may be a wave hollow. In other words, considering the ship as in motion and the water as motionless except for the motion she impresses upon it, the particles of water at the bow and stern will have motion in the same direction as the ship; those amidships will have motion in the opposite direction. Besides these two principal wave crests at the bow and stern, there may be other minor waves created, the general principle being that wherever a crest is formed the particles attain a maximum speed in the direction of the advance of the ship; and where a hollow is formed the particles have a maximum speed in the opposite direction. The principal waves at the bow and stern are each followed by a train of waves, successive waves in the series having diminished heights. It will be remembered that throughout this discussion no propeller is supposed to be in action, which could modify the relative motions of the water and the ship. But it is worth notice that the action of propellers may create additional wave crests, or modify considerably those formed by the ship. Paddle-wheels, for example, placed nearly amidships, accelerate the sternward * See on this point papers by Mr. the Institution of Naval Architects for K. E. Froude, in the Transactions of 1883 and 1886. chap, xi.] THE RESISTANCE OF SHIPS. 455 motion of particles, and produce an additional wave. Screw- propellers, on the contrary, being placed aft, give sternward motion to the particles, and tend to degrade the stern wave, as well as to cause considerably greater resistance by partially destroying the forward pressure of the water upon the stern ; but they also create a local upheaval of the water, and confuse the phenomena of the waves. The laws which govern the wave-making resistance of ships are not yet fully understood, systematic investigation of the subject having been begun within the last half-century. Mr. Scott-Eussell was one of the earliest workers in this field, and made a large number of experiments, chiefly upon canal boats and small vessels, before putting forward his well-known " wave-line " theory of con- structing ships. The theory is not in complete accordance with more recent investigations, but it has the great merit of having enforced the importance which attaches to the wave-making factor in the resistance, unless the lengths of " entrance " and " run " in a ship are suitably proportioned to her intended maximum speed. By the •" entrance " is meant that part of the ship bounded by the stem and by the foremost athwartship section which has the full dimensions of the midship section ; the " run " is the corresponding length at the stern ; and the " middle body " or " straight of breadth," is .that part of a ship amidships where the cross-sections maintain the form of the midship section. The entrance and run have also been termed the "wave-making features," because the waves which accompany a ship are produced, as we have seen, by the accelera- tions and retardations of the particles of water resulting from the motion of the entrance and run relatively to those particles. It is obvious, oh reflection, that the lengths as well as the forms of entrance and run must greatly influence both the bow and the stern waves. During each interval occupied by a ship in advancing through a distance equal to the length of her entrance the sets of particles then contiguous thereto undergo accelerations which lead to the production of the bow-wave ; and this interval of time depends upon the ratio of the length of entrance to the speed of the ship. Similarly, importance must attach to the ratio of the length of the run to the speed. If a ship is formed so that these ratios are suitably adjusted for the maximum speed she is destined to attain, and the curves of the bow and stern are easy and fair, the wave-making resistance will not assume undue importance. When such a ship has reached her uniform speed, and the waves have been fully formed, the maintenance of those waves will require a certain expenditure of force which measures the wave-making resistance. The case is parallel to that of the deep-sea waves (described at p. 45<5 XAVAL ARCHITECTURE. [chap. xi. 217), which travel OTer immense distances without any great loss of speed ; but with this important difference, that, whereas the ocean-waves gradually become degraded, the waves accompanying ships, under the favourable conditions described, are kept to their full heights. If the lengths of entrance and run are not suitably adjusted to the maximum speed of the ship, the waves which are formed, or a certain portion of them, diverge from her path, carrying off into still water the energy impressed upon them. The ship has, there- fore, to be continually creating new waves, and the expenditure of force involved in this creation may form a very serious feature of the total resistance. Moreover, when the speed of a ship exceeds that of the waves which her entrance and run naturally tend to form, other series of waves make their appearance, even more important than the diverging waves, and requiring a Aery large expenditure of power for their maintenance. These waves have a length proportioned to the speed of the ship, and actually keep pace with her; although the wave-making features of the ship are not adapted to their formation on account of the inadequate lengths of entrance and run. It is now universally admitted that for every vessel there is a certain limit beyond which increased speed can only be secured at the expense of a very rapid growth in resistance. This limit is "somewhat less than that appropriate to the length of the wave which the ship tends to form," which length obviously bears a close relation to the length of entrance and run.* This general endorse- ment of a principle first enunciated by Mr. Scott Eussell naturally leads to a closer consideration of his wave-line theory. According to this theory the water displaced by the bow of a ship forms a " solitary " wave, wholly situated above the level of still water, and travelling as a heap of water. This bow wave is sometimes styled the "wave of displacement," and its companion stern wave is named the " wave of replacement." The latter wave Mr. Eussell supposed to be the leading wave in a trochoidal series resembling the deep-sea waves described in Chapter Y. In order to prevent undue wave-making, the theory prescribed that the length of entrance given to a ship should be at least equal to the length of the solitary wave having a natural speed equal to the maximum speed proposed for the ship ; and the length of run should be two- thirds the length of the entrance. Eules were also laid down for * The apparent exceptions to the pedo-boats and swift launches are dis- foregoing statement furnished by tor- cussed hereafter. chap, xi.] THE RESISTANCE OF SHIPS. 457 guidance in designing the forms of the entrance and run, so that the resistance might be minimized.* The rules of Mr. Scott Kussell for lengths of entrance and run may be stated in the following simple form : Let V be the maxi- mum speed of the ship (in knots per hour); L x be the length of entrance appropriate to the speed V, and L 2 the length of run (both lengths being expressed in feet) ; then — Lj = 0-562 x V 2 , L 2 = 0-375 x V 2 = fL 1 . For example, let V = 15 knots ; then, to avoid undue wave-making, the theory prescribes — Length of entrance = 0-562 x 15 2 = 126 feet ; Length of run: = 0-375 x 15 2 = 84 feet. With these dimensions Mr. Scott Eussell considered there might be associated any required length of middle body, the additional resistance for the assigned speed being chiefly due to friction on the enlarged immersed surface.f Of these two rules, that relating to the length of run was thought to have the greatest practical importance, many successful vessels having had a less length of entrance than that prescribed by the formula; whereas vessels with shorter runs than the formula prescribes have done badly. As a matter of fact, however, seagoing vessels usually have greater lengths both of entrance and run, in proportion to their maximum speeds, than are required by these rules ; and instead of having the run only two-thirds as long as the entrance, the lengths of entrance and run are commonly equal, or nearly so. It will be observed from the preceding formula that — L x + L 2 = 0-937 V 2 ; whence — V 2 = 1-067(11! + L 2 ) ; and V = 1-03^ L x + L 2 (nearly). So far as can be seen at present, this last equation enables a fair approximation to be made to the speed (V) at which a small increase in speed causes an increase in resistance altogether disproportionate to that which would accompany an equal increase in speed when the vessel was moving more slowly. Putting the equation in this form allows for any variations which may be desirable in practice in the ratio of the length of entrance to that of run ; although neither of * Particulars will be found in Mr. -f See further on this subject the Russell's work on "Naval Architecture;" experiments of Mr. Froude mentioned also in vols. i. and ii. of the Transactions at p. 460. of the Institution of Naval Architects. 45 8 NAVAL ARCHITECTURE. [chap. xi. these can become very short in proportion to the speed without pro- ducing increased resistance. Suppose, for instance, that the common practice is adhered to, and the lengths of entrance and run made equal to one another : it may be desired to know what are the lengths appropriate to a speed of 16 knots. Here — L t + L 2 = 0-937 X (16) 2 = 240 feet (nearly). Professor KanMne, in 1868, suggested another mode of deter- mining the limit of speed at which wave-making resistance begins to grow at a very disproportionate rate.* Taking the quotient of the volume of displacement divided by the area of the load-water section of a ship, he termed it the mean depth of immersion (&). The velocity of the waves which are formed by a ship he considered to be equal to that acquired by a heavy body in falling freely through a distance equal to half the mean depth of immersion; this velocity might therefore be expressed approximately by the formula — Telocity (feet per second) = 4\/2&. If the actual speed of the ship exceeded this natural velocity of the waves formed by her advance, those waves would become divergent, and the wave-making factor of the resistance would increase. In other words, the limiting speed for economical pro- pulsion was considered to be that expressed in the above formula. This theory was tested by observations made during the steam-trials of actual ships, and was fairly confirmed ; but the observations were not sufficiently numerous to justify the general adoption of the method. The experimental researches of the late Mr. Froude and of his son, Mr. E. E. Froude, have considerably advanced our knowledge of the general character of the waves which accompany ships. Those experiments have mostly been made on models; but the wave-phenomena thus observed have been repeatedly compared with similar observations made during the steam-trials of ships belonging to the Eoyal Navy. According to these observations, the waves produced by the motion of ships in deep water previously undis- turbed may be classified as follows : (1) waves produced by the advance of the bow ; (2) waves produced by the stream-line motions near the stern. Of these, the bow waves are more important. Each of these sets of waves may be divided into two distinct series : (1) diverging toaves, the crest-lines of which trail aft; (2) transverse waves, of which the crest-lines are nearly perpendicular to the keel- * See Transactions of the Institu- experiments made to test this theory tion of Naval Architects for 1868. The were conducted by Mr. John Inglis. chap. xi.J THE RESISTANCE OF SHIPS. 459 line of the ship. Mr. Eroude did not agree with Mr. Scott Eussell as regards the bow producing a solitary wave of translation; but considered that all the waves produced in deep water are gregarious (like deep-sea waves described in Chapter V.), successive crests following one another at regular intervals ; those intervals, as well as the heights of the waves, varying with changes in the speed of the ship. Taking the bow waves, for example, the highest crests appear near the bow of a ship, and against her sides. The lengths of the waves, measured outwards from the ship along the crest-lines, are only moderate, and they gradually die away to the level of still water towards the outer ends. The leading wave in each series is followed by a number of other waves, of which the heights gradually diminish as their distance from the bow increases, but the actual termination of the series of waves cannot be distinguished. Similar remarks apply to the two classes of stern waves. At low speeds neither the diverging nor the transverse waves attain such dimen- sions as to practically affect the resistance. At moderate speeds the diverging waves become apparent, and their crest-lines are com- monly inclined aft at an angle of 40 to 50 degrees to the keel-line. It appears that only the leading wave in the diverging series at the bow touches the side of the ship in most cases, the highest points in the following waves in that series being at some distance from the ship. In other words, as the wedge-shaped entrance is driven forward it " throws off on each side a local oblique wave of greater "or less size, according to the speed and the obtuseness of the " wedge, and these waves form themselves into a series of diverging " crests . . . which, after becoming fully formed at the bow, pass clear " away into the distant water and produce no further effect on the " resistance." The " length," measured normally to the crest-lines of these diverging waves, appears to agree, or nearly so, with that of deep-water waves travelling at the speed which the ship's speed would give if resolved normally to the crest-lines. As the speed increases so do these diverging waves increase in magnitude, and represent a larger amount of resistance ; and the wave phenomena are complicated still further by the appearance and rapid growth of the transverse series of waves as that limit of speed is approached where the wave-making resistance begins to grow rapidly in impor- tance. When that limit is passed the transverse series of waves becomes even more important, affecting the total resistance very largely and sometimes Very singularly. In Eig. 149 is reproduced a drawing prepared by Mr. Froude to represent the result of careful observations of the wave phenomena attending the motion at a relatively high speed of a model having a 460 NA VAL ARCHITECTURE. [chap. XI. long middle-body. The drawing indicates the positions of the diverging waves, while the profile of the wares in the transverse series is defined against the side of the model. This profile was FIG. 149. drawn from exact measurements, but the vertical scale is exaggerated for the sake of clearness, so that the waves appear about twice as high as they really were relatively to the model. Unlike the diverging waves, those in the transverse series appear directly behind one another, successive wave crests and hollows reaching the sides of the ship. In the diagram the distance from crest to crest is about 115 feet, the speed of the model corresponding to about 14£ knots per hour for a full-sized ship. It will be observed that (in accord- ance with the formula on p. 202) an ocean wave having this speed would be about 120 feet in length, so that there is a very fair agree- ment between the observed waves and trochoidal waves of equal speed. Hence it appears that as the speed of a ship is increased, so the lengths from wave crest to wave crest will increase in the ratio of the squares of the speeds ; and the positions of wave crests and hollows must vary, relatively to the ship, as her speed is varied. These variations in the relative positions of the waves and the after body of the ship were found, on analyzing the results of numerous experiments, to sensibly affect the resistance of models having identically the same entrance and run, with Fig. 149, but varying lengths of middle-body. The earlier investigations of the late Mr. Froude on this im- portant feature of wave-making resistance were made with a series of models having the same lengths and forms of entrance and run (160 feet), but varying lengths of middle-body — ranging from 340 feet down to nothing. The maximum speed appropriate to this length chap, xi.] THE RESISTANCE OF SHIPS. 4 61 of entrance and run, according to the formula on p. 457, would be rather less than thirteen knots ; and so long as this speed was not exceeded, the wave-making resistance remained nearly of constant amount for all the models. At higher speeds considerable differences in the wave-making resistance were produced by variations in the total lengths of the models. When the length and speed of a model were such that a wave crest of the transverse series was placed at or near the middle of the length of the run, the wave-making resistance was decreased. On the contrary, if the length and speed were so related that a wave hollow of the transverse series occupied the position named, an increase in the wave-making resistance took place. Hence Mr. Froude argued that the absolute length of a ship, as well as her length of entrance and run, must affect her resistance when moving at relatively high speeds ; and that variations in speed must influence the resistance by altering the relative positions of the hollows and crests of the transverse series of waves situated near the stern of a ship. These conclusions have been confirmed generally, and our know- ledge of the subject much extended by the investigations of Mr. R. E. Eroude.* It is impossible here even to summarize the valuable experimental results, and the provisional theory based upon the ex- perimental investigations. By means of elaborate observations of the wave-phenomena accompanying the motion of models through water, the general characteristics of the bow and stern series of waves, classified above, have been determined. Moreover, it has been shown that the variations in wave-making resistance accom- panying variations in speed, after a certain limit of speed has been passed in a given ship, may probably be explained by the " inter- ference " of waves belonging to the transverse bow series, with the leading wave in the transverse series originated at the stern. That is to say, "the height of the waves made, and the amount of the "resistance caused will be at the maximum or minimum according " as the crests of the bow-wave series coincide with the crests or "troughs of the natural stern-wave series. ... In either of these " two cases the crest of the resultant wave coincides with the crest of " the larger of the two components, while, if the crests of one series " fall on the slopes of the other, the resultant crest position will be a " compromise between the crest position of the components, though " nearer to the larger of the two." The increase or diminution in resistance produced by variations in the relative positions of the wave crests or hollows near the stern of * See the paper " On the Leading sistance of Ships." — Transactions of the Phenomena of the Wave-making Re- Institution of Naval Architects for 1881. 462 NAVAL ARCHITECTURE. [chap. xi. a ship is governed by various considerations. For example, the height of the leading transTerse wave in the bow series is affected by the form of the entrance of a ship and the speed at which she is driven. Again, the height of the crest in that wave of the transverse bow series which lies on or near the stern, as compared with the height of the leading bow wave, will depend npon the number of intervening waves, which number will depend upon the length and speed of the ship. The form of the stern and speed of the ship also influence the magnitude of the waves originating there, and so of the waves composed of the bow and stern series. These general considerations do not, however, enable an exact estimate to be formed of the magnitude of wave-making resistance in a ship of given form moving at a given speed, and for this purpose model experiments are essential. The following passage in the remarks of Mr. R. E. Froude deserves quotation, although it relates to a different aspect of wave- making resistance. He says, "It is a reasonable inference . . . " that the wave-making features of a ship will operate more effectively •'to make short waves if their displacement is disposed broadwise •' rather than deepwise ; and more effectively to make long waves if •' it be disposed deepwise rather than broadwise. Now, the diverging " waves being necessarily much shorter than the transverse waves, we " see that flaring-out the end sections of a ship, or increasing the ratio " of breadth to depth, will cmteris paribus tend to increase the resistance " due to diverging waves and diminish that due to transverse waves : "while giving U -sections or increasing ratio of depth to breadth will " have the opposite effects. These inferences are visibly corroborated " by the appearance of the wave systems caused in the cases referred " to. Again it is worth noticing that the experiments have shown "that, as a rule, moderately U-shaped sections are good for the fore- "body, and comparatively V-shaped sections for the after-body. ■'This would seem to show that in the wave-making tendency of " the after-body the diverging wave element is less formidable than "in that of the fore-body, and this inference corresponds with the " fact that the stern diverging- wave series is visibly less marked than "that of the bow." Another important deduction from model experiments may be mentioned, before concluding these remarks on wave-making re- sistance. Supposing that the lengths of entrance and run provided in the design for a new ship to be ample in proportion to her intended full speed, a diminution in the total resistance may be usually secured by adopting still greater lengths of entrance and run, with finer lines at the extremities and a greater extreme breadth, the displacement remaining unchanged. This is contrary to the opinion formerly CHAP. XI.] THE RESISTANCE OF SHIPS. 463 entertained as to the influence on resistance of an increase in the area of the immersed midship section ; but there is ample evidence of the truth of the principle. An excellent illustration is found in the experiments made with a model of the merchant steamer Merkara, and models of alternative forms but identical displacement.* The dimensions of .two of these vessels (in feet) were as under : — Models. Length. Extreme breadth. Mean draught. Entrance. Middle-body. Run. Total. Merkara . Model B . 144-0 179-5 72 Nil 144-0 179-5 360 359 37-2 45-88 16-25 18-0 The Merkara had an area of immersed surface of 18,660 square feet ; model B an area of 19,130 square feet ; the displacement in each case was 3980 tons. So far as surface friction went, therefore, the Merkara had a small advantage; as to eddy -making, the two ships must have been practically equal, and the difference in total resistance between the two would arise from differences in the wave- making resistance. On trial it was found that about 18 knots marked the limit of speed for the Merkara, where a slight increase in speed led to a disproportionately large increase in the wave-making resistance. At a speed of 19 knots the wave-making resistance of the model of the Merkara was found to be fully 60 per cent, of the whole resistance, whereas at the actual maximum speed of the ship — 13 knots — wave-making resistance was only 17 per cent, of the whole. For model B up to speeds of 19 or 20 knots no dispro- portionate increase in the wave-making occurred ; consequently the total resistance of B at a speed of 18 knots was only 75 per cent, that of the Merkara, whereas at 13 knots the difference in the resist- ances was very trifling. Applying the formulae of the wave-line theory to these two vessels, we have — For Merkara If the first bpdy have lineal dimensions D times those of the second, then — | = I> a (4) and further, if the velocities V! and V 2 are related to one another as the square roots of the lineal dimensions— Y;=VD;and(.^) a =D (5) Substituting from (4) and (5) in (3), we have at these " corresponding speeds "— | = DxD 2 = D ! (6) ±C 2 4^4 *VA VAL ARCHITECTURE. [chap. xi. Under this limited assumption, therefore, the law of comparison holds good. If in equation (3) Vx equals V2, that is, the speeds are equal in both bodies — | = | = D a (7) The wetted surfaces in each case are proportional to the two-thirds power of the displacements ; say W x and W 2 . Hence — *L = (™i)i (8) This is an expression to which reference will again be made in Chapter XVII. In addition to their primary and most important purpose — the determination of the resistances of ships — model experiments hare yielded much valuable information respecting the behaviour of ships when moving through still water. A few examples may be given. The recording apparatus enables a record to be kept of the vertical motions which the centre of gravity of a model performs as the speed is varied, and the changes of trim which take place. It has thus been ascertained that ships moving at ordinary speeds usually sink bodily below their still-water draught, and that at such speeds the bow usually sinks more than the stern. There will be no difficulty in accounting for these changes of level when the character of the stream-line motions, and the variations in the resultant pressures of the water upon the different parts of the length of a ship, are considered ; nor will it be a matter for surprise that when the cross-sections of the bow of a ship are V-shaped the sub- sidence is less than when those sections are U-shaped. Although the foregoing statement is fairly representative for ordinary conditions, it does not apply when ships are moved at velocities very high relatively to their dimensions. In torpedo-boats, for example, the ordinary laws hold good only for the lower speeds. Mr. Thornycroft has made some valuable experiments on this matter, and a brief summary of the results may be of interest.* A boat 67 feet long was driven at various speeds, the maximum being about 19 knots ; observations were made from which the vertical position of the centre of gravity and the trim of the boat could be determined at each speed. It was found that as the speed increased so the vessel sank more deeply up to about 12 knots ; after which the boat rose as the speed increased. At 12 knots the bodily * See the British Association Reports for 1875. chap, xi.] THE RESISTANCE OF SHIPS. 485 subsidence was about 5 inches, at 19 knots the bodily rise was 3 inches, these measurements being taken in relation to the still- water level. In this case the boat trimmed by the stern, as compared with her still-water trim, throughout the trials ; but it must be remembered that she was driven by her own propeller, and not towed. Experiments with models, made by Mr. Froude, have shown very similar results as regards mean draught and trim at very high speeds.* For example, a model about 10 feet long was towed at various speeds, the maximum being about 850 feet per minute — or 8J knots per hour. At first the trim altered very little from the still-water condition, but as the speed increased the bow gradually rose, while the stern fell. Ultimately at the maximum speed the bow had risen 2£ inches, while the stern had sunk to an equal amount with reference to their still-water levels. This model repre- sented a full-sized ship of 360 feet in length, and the maximum experimental speed represented a speed of more than 50 knots for the ship. The vertical displacements of the bow and stern of the ship, if moved at this very high speed, would have been more than 7 feet. Air Resistance to the Motion of Ships. — In the actual propulsion of a ship the air exercises an appreciable resistance, especially if she is a rigged ship. As to air resistance, there have been very few trustworthy experi- ments. Mr. Froude, in his experiments with the Greyhound, which was not rigged at the time, found that, when the speed of the wind past the ship was 15 knots per hour, it produced an effect on, the hull measured by a force of 330 lbs. For other speeds of wind past the ship, it was assumed that the effect varied as the square of the speed. In the case where a ship is steaming head to wind air resistance obviously must be greatest, since the speed of the wind past the ship then equals the sum of her own speed and that of the wind. The absolute force of the air resistance in the Greyhownd was thus found to be small ; but if the vessel had been masted and rigged, the resistance would have been greater. Mr. Froude did not expressly state, in his report on this experiment, what scale of allowance he employed in estimating the additional resistance due to the passage of the masts and rigging through the air ; but from the particulars which he subsequently furnished to the author, it appears that the total resistance of the masts and rigging was taken about equal to that of the hull. At a speed of 10 knots * See the very admirable Report on published as Parliamentary Paper (No. the proposals of the Rev. C. Ramus, 313) of 1873. 486 NAVAL ARCHITECTURE. [chap. xi. through stiU air, this would give a total air resistance of about 300 lbs., the corresponding total of water resistance being about 10,200 lbs.; making the air resistance about ^ part of the water resistance. If the ship steamed head to wind at a speed of 8 knots, the actual speed of the wind being 7 knots, it would pass the ship with a relative speed of 15 knots; the air resistance would then probably have a total of about 650 lbs., whereas (if the water were smooth) the total water resistance would be about 5600 lbs., the air resistance rising to about ^ of the water resistance. These results may not be exactly correct, but they are sufficiently so for illustrative purposes ; they explain the considerable decrease in speed in ships — especially rigged ships — steaming head to wind ; and they are so considerably in excess of what would have been predicted on purely theoretical grounds as to indicate the desirability of further experi- ments on the air resistance to rigged ships. Up to the present time, we have little information of an exact or trustworthy character on this important subject, and probably the steady decrease of sail- power in steamships makes it less likely that much will be added to existing knowledge. The experiments required are very simple. All that is necessary is to allow a ship to drift before the wind, to note the uniform speed which she will ultimately attain through the water, and to measure the velocity of the wind past the ship ; her condition aloft must also be recorded, as to spars on-end, running rigging rove, etc. The water should be approximately smooth, and the ship should owe her drift simply to the air pressure, not to tides or currents. The resistance of the water at the uniform speed of drift must then exactly equal the total air resistance ; and this water resistance could be ascertained by other experiments made either with the ship or with models. Accuracy would be increased and more valuable information obtained if the same ship were made the subject of several experiments, including two sets : one made with the same condition as to spars and rigging aloft, but with different forces of wind ; the second set made with different conditions of rig, while the actual speed of the wind remained constant. This is a matter which may commend itself to the attention of naval men when they learn the imperfect condition of our present knowledge of the subject. Other modes of making the required experiments might be suggested did space permit ; but it must suffice to add that, with the aid of suitable dynamometric apparatus and good anemometers, the air resistance corresponding to a certain speed of wind might be obtained with the ship moored instead of drifting. As to the air resistance on the hull only, there appears good reason for adopting the rule which Mr. Froude suggested, viz. that chap, xi.] THE RESISTANCE OF SHIPS. 4§7 if the above-water portions of the hull are projected back upon the midship section of a ship, and the total area (A) enclosing these projections is determined, then the air resistance on that area (A) will approximately equal the air resistance on the hull for any assumed speed. In the Qreyhownd the area A was somewhat less than 400 square feet ; Mr. Froude ascertained by experiment that at a speed of 1 foot per second the air resistance per square foot on a plane area is about equal to to^otv lb. A speed of 15 knots per hour equals about 25^- feet per second ; and since the air resistance varies as the square of the speed, the speed of 15 knots should cor- respond to a pressure of about 1'09 lb. per square foot of area. Hence the total air resistance on the Qreyhownd for a speed of fifteen knots past the ship should be about 436 lbs. by this law ; and by experi- ment it was determined to be 330 lbs. This approximate rule may be found useful for purposes of comparison between different types of ships ; and in mastless ships it will give a fair estimate of the total air resistance at any assigned speed of wind past the ships. Eigged ships present a more difficult problem, which can be best dealt with experimentally. Resistance when Motion is not uniform. — Throughout the preced- ing pages, the discussion has proceeded on the assumptions of uniform motion and still water. These are not the conditions of practice, but they are necessarily assumed for purposes of exact investigation. When motion is not uniform, but variable from moment to moment, other considerations have to be kept in view, even if the hypothesis of still water is maintained. Suppose, as before, that a ship is being towed. For uniform motion the tension on the tow-line equals the resistance. If at any moment the tension on the tow-line were increased, there would be an unbalanced force, tending to accelerate the speed of the ship. If after being increased the tension was maintained at a constant value, the ship would finally settle down to a higher speed at which the resistance once more balanced the tow- rope tension. During the interval before this balance was re-estab- lished, the motion of the ship would be accelerated. At p. 149, an explanation of the nature and mode of measuring accelerating forces has been given. It will thus be seen that, in order to estimate the acceleration of speed, it is necessary to know the weight of the ship and that of the water surrounding her whose motion is to be changed, as well as the amount of the unbalanced force tending to accelerate the motion. Mr. Froude's experiments on the Greyhound showed that the virtual weight of a ship in motion — that is, the sum of her own weight and that of the water influenced by her motion — might be taken at about 20 per cent, above the actual weight of the ship. If the curve of resistance of the ship for uniform motion is known, 488 NAVAL ARCHITECTURE. [chap. xi. then it is possible to trace her acceleration in velocity under the circumstances assumed, when the variation in the tow-rope tension is known. Similarly if the tow-rope tension were reduced, the retarda- tion in speed can be traced. And if the increase or decrease of tow- rope tension varied from instant to instant according to some given law, it would still be possible, mathematically, to determine the motion of the ship. In practice, when ships are not towed, but propelled by their own engines and propellers, circumstances commonly arise which interfere with uniform motion. Variations in the engine-power developed, changes in the depth of water, progress through tides or currents, and other causes, may produce alterations in speed even in still water. Consequently, for the scientific analysis of steam trials it is absolutely necessary to have the most detailed observations and records of facts if accuracy is to be obtained, and information gathered for future guidance. Ordinarily steam trials are not conducted in this maimer, and there is often a tendency to treat scientific methods as useless refinements. For most purposes it may be admitted that rougher methods, dealing with the performances broadly on the basis of the powers developed at various speeds, suffice for practical purposes. That admission, however, in no way lessens the value of the more scientific method of inquiry, particularly for vessels of new types. Resistance in a Seaway. — When water ceases to be smooth, the resistance it offers to the motion of a ship must obviously be affected. Observation and experiment tend to show that a very moderate degree of wave motion sensibly affects the resistance, increasing its amount for a given speed as compared with that in smooth water. In a seaway there are infinite varieties of roughness and correspond- ing variations in resistance, while the motions of ships in pitching and rolling also influence the speed. Under these circumstances any attempt to express the increase in resistance by an exact method must be hopeless. Experience proves, however, that for maintenance of speed in a seaway, considerable length, good freeboard, and moderate pitching are essentials. Greater size and weight give ships, other things being equal, a greater power of maintaining speed. This is established by the comparative regularity of the passages made by large ocean steamers, especially those on the Atlantic service, under very various conditions of wind and sea. In selecting the form of a new ship, particularly towards the extremities, service at sea must be kept in view no less than economical propulsion in smooth water; and it is fully recognized that some forms which would be admirable for smooth-water are not well adapted for a seaway. Experience alone can be trusted in deciding between these somewhat conflicting claims. ( 4§9 ) CHAPTEE XII. PKOPULSION BY SAILS. The efficient management of a ship under sail furnishes one of the most notable instances of skilful seamanship. In different hands the same ship may perform very differently. Changes in stowage and trim also affect the performance ; but such changes as an officer in command can make are necessarily limited in their scope and character ; and some ships can never be made to sail well, having radical faults in their designs. Without intruding upon the domain of seamanship, the naval architect requires, therefore, to study very carefully the conditions of sail-power, and the distribution of sails in a new design, if the completed ship is to be fairly successful. His success or failure greatly depends upon the possession of information respecting the performances and sail-spread of ships of similar type and rig. Having such information, the process by which the total sail-spread and the distribution of the sail are determined in the new ship is by no means difficult or complex. Taking the exemplar ships, and the reports on their sailing qualities, an analysis is made of the sail areas, the distribution of the sail longitudinally and vertically, the transverse stability, and some other particulars. Furnished with these data, and having regard to the known qualities of com- pleted ships, it is possible to secure similar, or perhaps improved, performance in the new design. Apart from experience, however, the naval architect would be unable to be equally certain of obtain- ing good results ; and in cases where great strides are taken in new designs, away from the sizes and proportions or sail plans of existing ships, the arrangement of the sail-power cannot but be, to a large extent, experimental. The Laws of Wind Pressure. — An acquaintance with the laws which govern the pressure of the wind on sails is obviously essential to accurate investigations of the behaviour of sailing ships. These laws have not yet been determined experimentally. Many theories have been framed for dealing with the problems involved in pro- 49° NA VAL ARCHITECTURE. [chap. xii. prdsion by sails, and deductions have been made therefrom as to the practical management of ships. None of these attempts at scientific treatment of the question has had much influence on practice. In fact, experiment and observation alone can be relied upon as a basis for scientific procedure. Up to the present time, experimental data, in regard to wind pressures on sails, are scanty. Similar experimental inquiry into the laws of wind pressure on plane and curved surfaces has been greatly advanced in recent years. As many of the results obtained have an intimate bearing on the performances of sailing ships, it is proposed to briefly summarize them.* The simplest case to be considered is that of a thin plate placed normal to the line of motion of the wind ; or the corresponding case of a thin plate moving normally to itself, and at uniform velocity through still air. All experimentalists agree that in this case the resistance, or normal pressure, varies as the square of the velocity, and may be expressed by the formula — E = A.A.V 2 . where B. = the normal pressure (say in pounds). A = area of the surface of the thin plate (say in square feet). V = relative velocity of the wind and the plate (say in feet per second). Tc = a constant coefficient for the same area and form of plate ; its value being experimentally determined. The pressure (E) includes both the positive pressure on the front face of the plate, and the negative pressure at the back due to eddy- making. A similar case for motion through water is described on p. 436. In the following table are summarized values of the coefficient h obtained by various experimentalists on small plates, mostly of rect- angular form, and not exceeding 3 to 4 square feet in area : — * An excellent account of early ex- Journals of the Royal Meteorological periments appears in Spon's " Dictionary Society, 1882-90 ; and in the Proceed- of Engineering." Beaufoy's experiments ings of the Royal Society for 1890-91. are described in the " Papers on Naval Details of the observations made by the Architecture " (vol. i.). Valuable in- late Lieutenant Paris of the French formation respecting wind pressures on Navy on board several ships, have been railway structures is given in Parlia- published in vol. xxxi. of the Bevue mentary Paper C 3000 of 1881, and in Maritime et Coloniale, and in his post- various " Memoirs on the Forth Bridge," humous work " Observations snr jles by Sir Benjamin Baker. Important con- Vitesses du Vent et du Navire : " Paris, tributions on anemometry, and experi- 1885. ments on wind pressure appear in the CHAP. XII.] PROPULSION BY SAILS. 49 * Experimentalist. Date. Value of K. Mode of experiment. Borda Thibault . Morin and Didion Beaufoy . Rouse Hutton . Paris Froude . Dines 1763 1832 1835 to 1837 1872 to 1880 1876 1888-90 •001841 •00206 •0019 ) •0016 ■00207 •00229 •00188 •00224] to \ •00239 J •0017 •00135 Plates moved through still air on a re- volving fan-wheel. Plate falling vertically. Plate exposed to wind. Plates exposed to wind for pressure; anemometric observations for speed. Observations made on board ship. Plate moved through still air in straight line at uniform speed. Plate moved through still air on a specially designed " whirling " machine. The earliest experimental information on this subject was obtained by the French. Morin and Didion used delicate chronometric apparatus ; and it is interesting to note that their results agree very closely with those obtained by Mr. Froude, who made his experiments under more favourable conditions than other experimentalists, so far as stillness of the air and uniformity of motion are concerned. Mr. Dines' experiments were conducted on a " whirling " machine in the open air, and are probably the best experiments of that kind yet made. At the same time, it is obvious that when plates are moved rapidly round on a " whirler," there is a possibility of the air being acted upon by the apparatus, and the results being somewhat in- fluenced by such action. This is clearly recognized in the account of the experiments, and may explain the lesser values of h as com- pared with the results of Mr. Froude, where the plate was moved rectilineally through still air. According to the latest experiments of Mr. Dines, a pressure of 1 lb. per square foot corresponds to a relative velocity of wind and plate of 27£ feet per second, or about 18£ statute miles, and about 16 knots per hour. His earlier results gave a velocity of rather over 17 miles per hour. Mr. Froude gave 24£ feet per second as the corresponding velocity, which gives 14£ knots, or about 16 \ statute miles per hour. On the whole it is con- sidered that the last-mentioned result is the most trustworthy. The two sets of experiments may be expressed as follows : if v be the velocity of wind in statute miles per hour — (Froude) Pressure on plate (in pounds) = -00366 x area (in square feet) X tf a (Dines) „ „ „ = -0029 x area (in square feet) X v a 49 2 NAVAL ARCHITECTURE. [chap. xii. These formulae may be compared with that proposed by the committee appointed by the Board of Trade subsequently to the Tay Bridge disaster. It runs as follows : — If P = maximum pressure in pounds on the square foot occurring during the storm to which v refers. v = maximum run of the wind in any one hour, measured in statute miles by an anemometer. Then P = -Olv 3 . This will be seen to be about three times the pressure which would be given by the mean of the foregoing coefficients based on the experiments of Froude and Dines. It must be noted, however, that the Committee contemplated a varying velocity of wind, and en- deavoured to express the maximum velocity and corresponding pressure in terms of the hourly run, which would average these alternations of velocity. The other formulae refer to uniform velocity of wind. The values of h in the table given by Lieutenant Paris, as the result of his observations on board ships, are relatively high. It is probable that this arose from unavoidable difficulties to which attention was called by Lieutenant Paris himself. The presence of rigging and sails necessarily produced eddies and currents of wind in the neighbourhood of the ship. No place of observation could be found, therefore, where measurements of the true velocities and pressures of winds could be made; and as regards velocities, the anemometric records which were adopted are open to doubt. Not- withstanding these limitations, the work done by Lieutenant Paris is of the greatest interest, and is unapproached by that done by any other observer under similar circumstances. The preceding formulas require correction when it is desired to obtain the pressures on plates of large area exposed to winds of certain velocities. It has been remarked that the values of h given above were determined experimentally for small pressure plates, and until recently direct experiments had not been made with large pressure plates. Experience had shown, however, that when the wind acts upon a large surface, there are gusts and currents of vary- ing velocity on various parts of the surface. Further, the fact that certain structures had successfully withstood great storms of wind afforded positive proof that the mean pressures per unit of area were much less than those corresponding to the maximum velocities indicated by small anemometers during the same storms. These anemometers may have been acted upon by " streams " in the wind currents, for which the velocities exceeded the mean velocities of the currents taken over the whole areas. In many instances the chap, xii.] PROPULSION BY SAILS. 493 situation and surroundings of the anemometers have affected their indications, and in others there have been obvious errors in the recording apparatus. On the whole, however, the broad conclusion based upon experience was that, for a given velocity of wind, large areas sustained a smaller pressure per square foot than smaller areas. Some of the earlier writers on propulsion by sails also recognized the fact that variations in the sizes and shapes of sails affected their propelling power, and various speculative explanations were given of the circumstance. To these theories, however, it is unnecessary to allude further. Direct experiments have been made on this subject in recent years. Those on the largest scale have been carried out at the Forth Bridge, and the results are most interesting.* Three pressure boards were erected. One was twenty feet long by 15 feet high ; the other two were circular plates each of \\ square feet in area. From a long series of records, it was concluded that the effective pressure per square foot on the large board averaged only about two-thirds the pressure indicated by the small and light plates. For instance, when the latter indicated 41 lbs. per square foot, the large board did not indicate more than 27 lbs., and in one case it indicated only 15 lbs. Other observations showed conclusively that the streams of maximum velocity and pressure in a wind current are of limited extent and local in character, and that the mean velocity of the current is much below that maximum. Experiments subsequently made by Mr. Dines confirm the con- clusions reached in the Forth Bridge experiments. Three boards were used : one, 6 feet by 7 feet ; a second, 3 feet square ; and a third, 1£ feet square. The respective areas were 42, 9, and 2£ square feet. Calling the pressure per square foot on the smallest board 100, that on the next larger was 89, while the correspond- ing pressure on the largest board was 78. The law of diminution of pressure per square foot with increase in area has not yet been determined. For that purpose further experiments are neces- sary. It has been established that the proportion of perimeter to area in a thin plate affects the mean pressure. This was supposed to be the case by some of the earlier writers on propulsion by sails. Mr. Dines proved experimentally that increase in perimeter, with a constant area, is accompanied by increase in mean pressure. One of his experiments is very interesting. Two rectangular plates were taken, each 48 inches long by 3 inches wide, the area of each being 1 square foot, and the perimeter 102 inches. For a certain velocity * See Sir Benjamin Baker's " Memoir " Engineering of February 28, 1890. For in the British Association Reports for Mr. Dines' experiments, see Journal of 1885, and the later records published in the Royal Meteorological Society for 1890. 494 NAVAL ARCHITECTURE. [chap. xii. of wind, the pressures on these plates were ascertained : first, when they were so distant from one another as to have no mutual influence ; second, when the two plates were placed with their adjacent long edges in contact, forming a plate 2 square feet in area, and with a perimeter of only 108 inches. In the second case the total pressure was less than 80 per cent, that in the first. Experiments have been made also on thin plates of the same area, but different forms. These changes in form, of course, affect the proportion of perimeter to area, and so influence mean pressure. Up to the present time only small-scale experiments have been made, and the subject is deserving of further investigation. It will be obvious that it has an important bearing on the relative value of sails of different shapes, particularly as between that class of sails which are approximately triangular, and those which are approxi- mately rectangular. Closely related to the foregoing investigations are those which have been made in order to determine the movements of wind currents when they impinge normally upon thin plates, and the consequent distribution of pressure over the surfaces of the plates. Mr. E. H. Curtis has done good work in this direction, experimenting with boards from 1 square foot in area up to 16 square feet.* On each board holes were formed in a series of selected positions, one being in the centre, and used as a standard. By means of tubes, the centre hole and any other hole could be connected simultaneously to pressure-gauge glasses containing water. Changes of level in the glasses gave the relative pressures of the wind on the front of the plate, at the centre, and at the selected hole. A series of observations gave corresponding results for all the holes, and so determined the distribution of pressure. These results may not be absolute indications of what happens in an unperforated plate, but the errors ought not to be large, and the general conclu- sions are interesting. The pressure gradually diminished in intensity from the centre towards the edges of the boards. For square boards of the different sizes tried, the law of distribution was approximately the same. A board having a side of 2^ feet and an area of 6J feet may be taken as an example. Calling the pressure at the centre 100, that at a point about midway between the centre and the edge was 90 ; at a point 13 inches from the centre it was 80 ; and close to the edge about 70. For a circular board 2 square feet in area, the pressure at the centre being 100, that on a circle having a radius equal to one-half the radius of the board was 90 ; for a radius 70 * See Journals of the Royal Meteorological Society for 1882-83. chap, xn.] PROPULSION BY SAILS. 495 per cent, of the radius of the board the pressure was 70 ; and for a radius 85 per cent, of the radius of the board it was 60. These re- ductions of pressure towards the edges, no doubt, result from the deflection of the wind currents from the centre over the front surface of the plate. Mr. Dines has approximated to the pressure experienced at the centre of the front of a board 1 foot square, and the simultaneous negative pressure at the centre of the back surface. For a velocity of wind of 60 miles per hour, he made the front pressure equivalent to 1"82 inch of water, and the negative pressure to - 89 inch. The sum of these (2*71 inches of water) represents about 14 lbs. per square foot. For this velocity of wind, the total pressure on a plate 1 foot square, according to independent experiments made by Mr. Dines, would be about 10| lbs., or about 75 per cent, of the maximum pressure at the centre. This is a practical confirmation of the pre- ceding results. In the Forth Bridge observations, two small pressure gauges were arranged in connection with the large pressure board. One was at the centre, one near a corner of the board. The indications of the small gauge at the centre were always in excess of the simul- taneous indications of the corner gauge, but the proportions varied greatly. Calling the indication at the centre 100, that, at the corner varied from 77 to 93 - 6. The mean of the indications of the small gauges exceeded the mean pressure per square foot over the whole area of the large board, which varied in the cases mentioned from 66 to 85. The effective wind pressure on the total area of the sail set on a ship must obviously be affected by the mutual influence of adjacent sails. That influence depends upon the relative positions of the sails and the spaces between them. The direction of the wind, its velocity, and the speed and course of the ship also affect it. Different styles of rig must be differently affected. To these general statements there can be no objection ; but there is little exact information respecting the actual effective wind pressures on the sails of ships of different classes under different cbnditions of sailing, or the influence of adjacent sails upon one another. Experiments made with plates, like those mentioned on p. 493, are suggestive of the results which may follow from variations in the distances between the edges of adjacent sails, especially with fore- and-aft rig. Supposing the two plates there mentioned to ex- perience a total pressure of 100 when placed 6 inches apart (twice their own width), that pressure fell to 91 when the edges were only 1 inch apart, and to 79 when the edges- were in contact. A plate 7 inches wide would have experienced about the same pressure as 496 NAVAL ARCHITECTURE. [chap. XII. these two plates, each 3 inches wide, with an open space of 1 inch between the edges. In square-rigged ships, portions of the sail set are necessarily to windward of adjacent sails, and consequently affect the pressure upon those sails. The distance apart of the two sets of sail is an important matter in such cases. Here also there is room for further investigation. In connection with bridge construction, and more particularly with the Forth Bridge, many experiments hare been made to determine the pressure on a series of girders placed parallel to one another or nearly so, and associated with horizontal platforms. The results are of great interest, but limits of space prevent any details being given. It has been shown, however, that problems which could not be solved by mathematical investigation are readily dealt with experimentally. This conclusion applies equally to the case stated above for adjacent sails. Wind Pressures on Oblique Plates. — When the wind impinges on a flat plate set obliquely to its direction of motion, the normal pressure is less for nearly all positions than it is when the plate is placed at right angles to the line of motion. Various mathematical formulae have been devised for calculating these normal pressures, resembling in form those given on p. 438. Experiments have also been made iu order to determine these pressures. Thibault made the most elaborate experiments of the kind amongst the earlier inquirers. Mr. Dines has in recent years gone much beyond what was previously accomplished. In Fig. 152 are shown four curves. Abscissae measurements correspond to the angles of inclination of the plate FIG. 152. to the direction of motion of the wind. Ordinates to the curves represent the corresponding normal pressures on the plate. The curve ADC represents the assumption that the normal pressure varies as the sine of the angle of inclination ; the curve AEC chap, xii.] PROPULSION BY SAILS. * 497 represents the assumption that it varies as the square of the sine. The curve ABC shows Thibault's experimental results ; that marked AHC shows Mr. Dines's. The last-mentioned is very peculiar in character, and differs altogether from Thibault's. Mr. Dines applied various independent tests, but the same character of curve (and particularly the very curious and sudden rise between 40 and 35 degrees of inclination) occurred in all cases.* If these latest results be accepted, as there seems good reason to do, then all previous estimates of effective normal pressures for angles of inclination of plates to the line of motion of wind up to 35 to 40 degrees are shown to be much below the truth. At 30 degrees, for example, Thibault's results are only 40 per cent, of Mr. Dines's ; at 20 degrees, 30 per cent. ; and at 15 degrees, 25 per cent. The matter is one of considerable practical interest, especially in connection with the behaviour of sailing vessels when " close-hauled " to the wind, both as regards the speeds attained and the angles of heel produced by wind pressure. In a square-rigged ship, for example, sailing as close to the wind as possible, the angle which the apparent wind makes with the sails may be as low as 15 degrees, and the normal pressure deduced from the latest experiments would then be about four times as great as the previously accepted rules would indicate. The propulsive and heeling effects of the normal pressures would be correspondingly increased. In the case of a plate set obliquely to its line of motion through water, it has been explained that the centre of pressure is nearer the leading edge than the after edge (see p. 437). Similar conditions hold good in plates on which winds act obliquely. More than one experimentalist has dealt with this matter, but Mr. Dines has most thoroughly investigated it. Taking his experiments made on a pivoted plate 1 foot square exposed to the action of wind, he found the centre of pressure was three-tenths of a foot from the leading edge for an inclination of 10 degrees, three-eighths of a foot for 20 degrees, and four-tenths for 30 degrees. The centre of pressure was before the middle of the plate, but at a gradually diminishing distance up to the time when the plate was placed normal to the wind. Mr. Curtis, in the series of observations above described, placed a board 1 foot square at an angle of 45 degrees to the direction of the wind. Calling the standard pressure at the centre hole on the board 10, the corresponding pressure at three-fourths the distance from the centre towards the windward edge was found to be 13, while that correspondingly placed to leeward was 6 - 4. Wind Pressure on Curved Surfaces and Sails. — In the course of * gese Proceedings of §oyal Society for 1890, No. 294. 2k 49^ NAVAL ARCHITECTURE. [chap. xn. his experiments (about 1832) Thibault attached small sails (about 1*2 square foot in area) to the arms of a fan-wheel, noting the resistances when they were tightly stretched as planes, and when they were allowed to " belly out " under the action of the air. Such small-scale experiments, of course, are no safe guide when applied to the enormously greater areas of the sails in a ship. So far as he went, Thibault concluded that the normal pressure on a curved sail was equal to that on a plane sail of the same shape and area. The effect of the curvature appeared to balance the reduction of the area when projected on a plane normal to the wind. Mr. Dines has experimented on curved sheets of metal, cylindrical in form, which, when laid flat, were of square form with an area of 1 square foot. These bent plates had their axes inclined to the wind at various angles, and their curvature was varied in different experi- ments.* They were tested with the concave and convex surfaces facing the wind. In this connection interest is limited to the former case, which corresponds to a sail " bellied " out. Taking the case of normal incidence, the plate was tried first as a plane, and then with varying curvatures. The projected area of the plate upon a plane perpendicular to the wind direction, of course, decreases as the curvature increases. In these experiments the depth remained constant, so that the plate which was square when flat had a narrowing rectangular projection as the curvature was increased. This fact should be kept in view when examining the following ex- perimental results — Chord. Versine. .= * J Relative pressure inches. inches. square foot. per square foot. 120 0-0 10 114 11-8 1-0 0-98 129 11-6 1-5 0-97 130 10-9 2-0 0-91 127 90 3-3 0-75 129 These figures are interesting when compared with Thibault's conclusion stated above. Further experiments were made with the axes of the curved plates inclined to the wind. For these oblique positions, such changes in curvature as were tried, did not appear to have a very marked influence upon the normal components of the wind pressure. The range of curvature was not a large one, and for such changes as were made in curvature the difficulty of carrying out the experiments increased as the inclinations of the axes of the cylinders to the direc- tion of the wind became smaller. Under these conditions the plates See Proceedings of Royal Society for 1891, No. 302. chap, xii.] PROPULSION BY SAILS. 499 had considerable vibratory motions, which sometimes tore them. This phenomenon is of interest in connection with the behaviour of sails in ships sailing close to the wind or " going about." As regards the effect of changes in inclination to the wind of curved plates when the curvature remains constant, these experi- ments indicated that the normal components of the wind pressure remained almost constant in value from normal incidence up to 40 degrees departure therefrom. As the departure from normal incidence increased, the normal components first diminished slowly, and then at 55 to 60 degrees of departure increased rapidly, as shown for the same angles on the curve AHC in Fig. 152. Subsequently the curve rapidly dropped, but for very small angles of inclination its character was not determined, for the reasons stated above. None of these experiments on curved plates or sails are on a scale sufficient for making trustworthy estimates for the pressures on large sails. Experience appears to show, however, that the more nearly plane the surfaces of sails can be kept the greater will be the pro- pelling force of the wind pressure. The opinions of naval officers in the days of sailing war-ships were summed up by Mr. Fincham as follows : " All slack canvas, whether sailing by the wind or large, " lessens the effect of the sail. Even before the wind, when the slack " reef is out the power which acts on the sail will be reduced very " considerably on the curved surface ; less even than the base of the ":same curve, or than if the sail were set ' taut-up,' but reduced to " the same ' hoist ' (or distance between the yards) as when slack." Reviewing the foregoing sketch of the laws of wind pressure, it must be admitted that much remains to be ascertained, although much valuable information has been recorded for thin plates and certain solid bodies. Accurate knowledge of the laws which govern wind pressures on large sails is almost entirely wanting. We cannot certainly express the pressure per unit of area on large sails corre- sponding to a given velocity of wind and to a certain angle of incidence ; and need further experiments on a larger scale, accom- panied by more accurate observations than are now common, re- specting the velocity and pressure of the wind. Such experiments would be by no means difficult to arrange, and they could be best conducted on board small sailing vessels, such as yachts, of which the stability had been ascertained by experiment and calculation. It would be necessary to place the vessel beam-on to the wind, to hoist certain sails, and to note the corresponding angles of steady heel. By means of anemometers, the velocity and pressure (on small areas) could be measured simultaneously, and the average pressure per unit of area on the sail set could be deduced from the righting moment due to the observed angle of heel. The areas and forms of 500 NAVAL ARCHITECTURE. [chap. xn. the sails set could be varied, and thus much valuable information could be obtained.* Classification of Winds. — It is usual to classify winds by their velocities, and by certain numerals indicating their " force." These velocities, for the most part, have been measured by revolving ane- mometers, with radial arms carrying cups. It was estimated by Dr. Robinson, who introduced this instrument, that the rate of rotation of the cups was one-third that of the wind. Later experiments, con- ducted by Dr. Eobinson himself and by other experimentalists, have shown that there is no constant relation between the rate of motion of the cups and the velocity of the wind. That relation varies with differences in the construction of the instrument, in the sizes of the cups, and the lengths of the arms, as well as with variations in the speed of the wind, especially in the form of gusts. According to the latest and best experiments, the value 3, originally assigned as the factor for multiplying the speed of the cups in order to obtain the speed of the wind, is much too high for anemometers of the Kew pattern, the mean value deduced being 2 - 17.f Hence it results that the recorded velocities for winds measured by anemometers accord- ing to the old scale are considerably above the truth. The positions in which anemometers are placed, and their sur- roundings, influence the currents of air impinging upon them, and probably account for some high readings. Moreover, as already stated (see p. 493), it is a well-known fact that in a wind current there are " streams " having velocities greatly exceeding the mean velocity of the wind over a large sectional area of the current. In records of maximum velocity measured by anemometers, all these causes of exaggeration may be in operation, and sometimes the re- cording apparatus is of a character that will still further exaggerate the true velocity, especially in gusts of wind. It has been usual hitherto to accept the following classification for winds, proposed by Admiral Beaufort, and known as the " Beau- fort Scale : " " Hurricane " (Force 12), speed assigned 60 to 100 knots per hour. " Storm wind " (Force 11), speed 45 to 50 knots an hour. " Heavy gale " (Force 10), speed about 40 knots. " Strong gale " (Force 9), speed about 34 knots. " Fresh gale " (Force 8), speed about 28 knots. " Moderate gale " (Force 7), speed about 23 knots. " Strong breeze " (Force 6), speed 15 to 20 knots. " Fresh * This recommendation was made them during a yachting cruise. No rc- by the author in 1881. About 1889-90 suits have been published, and his death the late Professor Jenkins consulted the caused a suspension of the work, author as to the prosecution of these t See Reports of Wind Force Corn- experiments, and it is understood that mittee in Journal of Meteorological he actually made some progress with Society for 1888 and 1890. chap, xii.] PROPULSION BY SAILS. 5 QI breeze " (Force 5), speed of about 14 knots. For the highest forces of wind the velocities are possibly over-estimated. If they were accepted, the pressures per square foot on plates placed at right angles to the wind would be very great, rising to about 50 lbs. per square foot for a hurricane. There are, it is true, anemometric records of velocities varying from 60 to 100 knots ; these are pro- bably in excess of the truth, for reasons given above. For engineering purposes, when dealing with the strength and stability of structures, measurements of pressure are more important than measurements of velocity. The Board of Trade Committee, to which allusion has been made, refer to wind pressures of 80 or 90 lbs. per square foot having been noted in this country under ex- ceptional circumstances, and treat 50 to 60 lbs. as unusually high pressures. Their recommendation was to use 56 lbs. per square foot. as a maximum wind pressure in calculations for railway bridges and viaducts. Probably the extraordinary pressures mentioned by the committee were not observed in such a manner as to command acceptance, since the velocities corresponding to 90 lbs. per square foot would be from 150 to 170 miles per hour by the formulas given on p. 491. Taking the observations made at the Forth Bridge from 1883 to 1892, with which we have been favoured by Sir Benjamin Baker, the maximum pressure recorded on a small board has been 41 lbs. per square foot, and on the large board 35 lbs. per square foot, corresponding by the formulas to mean velocities of from 100 to 120 miles per hour. The recommendation of the committee was therefore considerably on the side of safety. For nautical purposes it is usual to classify winds by the amount of canvas which a well-found sailing ship could carry with the respective forces of wind, such as "topgallant-sail wind," "topsail wind," "reefed topsail wind," "close reefed topsail wind," etc. It is commonly assumed that the " topgallant-sail wind," when all " plain sail " is carried on a ship-rigged vessel, corresponds to the " fresh breeze " (Force 5), and to 1 lb. pressure per square foot on a plate placed normally to it. There does not appear to be any absolute proof that this assumption is correct, but it is based on experience, and has many advantages as a working hypothesis in dealing with plans of sails. The Propulsive Effect of Wind on Sails. — Sails attached to ships are not fixed in position like the plates and sails considered above, but necessarily move with the ship. Hence, in dealing with the propulsive effect of a wind of which the absolute direction and force are known, it is necessary to take account also of the motion of the ship ; or, as it is usually expressed, it is necessary to determine the apparent direction and velocity of the wind. This can be done 502 NAVAL ARCHITECTURE. [chap. xn. easily in any case for which the course and speed of the ship, as well as the true direction and velocity of the wind, are known, the simple general principle being that the apparent motion of the wind is the resultant of the actual motion of the wind, and a motion equal and opposite to that of the ship. A vane at the mast-head would indicate the apparent direction of the wind, and not its true direction; an anemometer on board would measure the apparent Telocity of the wind. Take the simplest case : a vessel with a single square sail run- ning " dead before " the wind. If the speed of the wind is Y feet per second, and that of the ship r, as the direction of both motions is identical, the resultant of the actual speed of the wind and the reversed motion of the ship will be Y — v feet ; and this apparent motion will govern the propulsive effect. For example, let the speed of the wind be 15 feet per second ; that of the ship 5 feet per second ; the apparent speed of the wind will be 10 feet (15 — 5) ; and, accepting the coefficient given by Froude's experiments for impact on small planes, the normal pressure per square foot of area of sail will be given by the equation — Pressure = -*I— x 10 2 = — lb. 10000 100 The pressure of this wind on a fixed sail would be about 2£ times as great. From this simple illustration it will be seen that it is most important to determine accurately the apparent motion of the wind. As a second illustration, take the case of a vessel sailing on a wind close hauled, with the wind he/ore the beam. To simplify matters, let a single square sail be considered set on the yard marked XY in Fig. 153. AB represents the middle line of the ship, the outline of the " plan " being indicated. The line WW I repre- sents the actual direction of the wind ; let M\Y 1 represent (on a certain scale of feet) its velocity. The line CO shows the course of the ship, in- cluding the effect of "lee- way ; and on WJ) (which is drawn parallel to CO) a length W t D is set off to represent a motion equal and opposite to that of the ship, the same scale being used for WjT) as was employed for the length MWi. Join MD ; then MD represents in magnitude and direction the apparent velocity of the wind. MD is greater than the actual velocity MW\ ; but its direction makes a more acute angle with the sail on XY than does the actual direction WW> CHAP. XII.] PROPULSION BY SAILS. 503 The case of a ship sailing with the wind abaft the beam is illustrated in Fig. 154 ; the reference letters being similar to those in Fig. 153, no description is needed. Here the resultant MD is less than the actual velocity MWj ; but, as in the previous case, it makes a more acute angle with the sail on XY. With these two examples before him, the reader will have no difficulty in readily determining the apparent velocity and direction of the wind, corresponding to ob- served actual speeds and directions of the wind, and observed speeds of a ship on a certain course. But this is by no means a complete solution of the question which presents itself in practice, and takes the form : Given a certain actual direction and speed of wind, and the sail area and angle of bracing for the yards, what will be the course of the ship, and her speed of advance ? To answer the question fully and cor- rectly requires data beyond those at present possessed, but an approximate solution is possible. Eeverting to the case of a ship sailing on a wind (Fig. 158), suppose the apparent direction and speed of the wind to have been determined. Assume EM, Fig. 155, to represent the apparent direction and force of the wind, and FM to be the normal pres- sure on the sail. The normal pressure (as explained above and illustrated in Fig. 152) varies with the value of EM and with the angle of incidence ; it can only be determined experimentally. The pressure FM may be regarded as made up of three pressures : one of these (shown by GM) acts longitudinally ; the other (FG) acts athwartships ; and the third acts vertically, at right angles to the other two, which act hori- zontally. For moderate angles of steady heel under sail, such as are common in ships, the vertical component of the normal pressure is not of much importance, and it is usually neglected. In all cases, however, it tends to increase the immersion of a ship ; and in some cases, when the angle of heel is considerable, this effect may be noteworthy. Let it be assumed for the present that only the horizontal components FG and GM require to be considered. 5°4 NAVAL ARCHITECTURE. [chap. xn. When the motion of the vessel has become uniform under the action of a wind of constant force and unchanging direction, it will take place along some line, such as CC, lying obliquely to her middle line AB. This motion may be resolved into two parts : one, a direct advance in the line AB, the other a drift to leeward perpendicularly to AB. The angle made by the line CC with the keel-line AB is called the " angle of leeway." Its magnitude depends upon the ratio of the velocity of advance, or headway, along AB to the velocity of drift or leeway, and these velocities are governed by varying conditions. If a ship were running before the wind there would be no leeway, and her motion would closely resemble that described in the previous chapter, the effective wind pressure taking the place of the tow-rope, but being applied at a considerable height. Hence, when the motion has become uniform, the wind pressure will be opposed by an equal and opposite fluid resistance, and these forces will form a mechanical couple tending to change the trim, as was previously explained. The actual change of trim would, however, be small in most cases. For instance, in the Greyhound running dead before the wind at a speed of 6 knots, the resistance would be about 1£ tons, the moment of the couple less than 100 foot-tons, and the change of trim less than one inch. As a second extreme case, suppose a ship to have her sails braced fore-and-aft, with wind abeam, and to drift bodily to leeward, moving parallel to her original position, and making no headway. When uniform speed of drift has been obtained, a lateral resistance would be developed equal and opposite to the effective wind-pressure, and forming with it a mechanical couple, causing the ship to heel. This lateral resistance, for a given speed of drift, is obviously much greater than the resistance to headway at the same speed. The ratio of the two resistances may vary greatly in different classes of ships : on account of differences in form or draught, or in the areas of keels, deadwoods, and other approximately flat surfaces immersed. Such surfaces experience a lateral resistance resembling that offered to plane surfaces moving parallel to themselves, and are, therefore, very effective in checking leeway. The curved and approximately cylindrical portions of the bottom of a ship permit the particles of water to glide past them with less abrupt changes of motion, and therefore contribute less to the lateral resistance. Exact measures of that resistance have not been determined, similar to the measures for head-resistance described in the preceding chapter. Speaking generally, it is necessary for efficiency under sail, and weatherliness, that there should be considerable lateral resistance ; and in some classes of ships various devices are employed in order to increase the chap, xii.] PROPULSION BY SAILS. 5°5 lateral resistance, and to diminish leeway. In shallow-draught or flat-bottomed vessels, " lee-boards " are often fitted ; these boards can be dropped at the sides of the vessels, and made to project beyond the bottom. Sliding keels, or " centre-boards," are sometimes fitted so as to be housed in recesses formed within the vessels, or to be lowered below the bottom. Very deep keels and great rise of floor are also commonly adopted in yachts designed for racing, for the same purpose. A rough approximation is sometimes used for comparing the lateral resistances of ships of similar form, by assuming that those resistances are proportional to the resistances which would be ex- perienced by the immersed parts of their longitudinal middle-line planes if they were moved to leeward at certain speeds. This method of procedure can only be applied within the limits named, because two ships having the same area of middle-line plane might differ greatly in fineness of form, areas of keel, etc., and so have very different lateral resistances. A more trustworthy method of estima- tion consists in finding the aggregate areas of the keels, deadwoods, and other approximately fiat surfaces, and calculating their resist- ances by the formulae given on p. 437 ; while the remaining portions of the wetted surface would have their resistances estimated according to the formula for frictional resistance on p. 441. But ■even this mode of estimating lateral resistance can be treated only as approximate, not as exact. The conditions of actual practice in sailing ships lie between the two hypothetical cases, above described, of no leeway and no head- way. A sailing ship proceeding at uniform speed under certain conditions of wind and sail-spread, usually follows a course making an angle of leeway with her keel-line, and in doing so both heels and changes trim. From what has been said above, it will be seen that a priori estimates of the angle of leeway for a given ship and a certain set of conditions cannot be made with certainty. Experience shows that in successful ships the angle of leeway is seldom much more than 6 degrees, and rarely exceeds 12 degrees ; in less success- ful ships, or shallow-draught vessels with no drop-keels, the angle of leeway may be much greater. The tangent of the angle of leeway (AMC, in Fig. 155) equals the ratio of the speed of drift to the speed ahead. These speeds depend upon various conditions, some of which have been mentioned. It will be evident, for example, that variations in the angle (AMX) to which the yards are braced will affect both the absolute and the relative values of the transverse and longitudinal components of the wind pressure. If the normal pressure (FM) were known, we should have — 506 NAVAL ARCHITECTURE. [chap. xn. Transverse pressure FG , , - r „ : : — = r^ivf = cot -^ M -^- Longitudinal pressure "JM- Suppose A1IX = 30 degrees ; then — Transverse pressure = longitudinal pressure v 3. The speeds ahead and to leeward clearly do not depend simply upon this ratio of the longitudinal to the transverse wind pressures ; they are governed far more by the relative resistances of the water to the motion of the ship ahead and to leeward. Even if the two pressures were exactly equal, the resistance to leeway would be much greater than the resistance to headway, and the speed of advance would much exceed the speed of drift. Moreover, it must be noted that the magnitude and direction of the fluid resistance are affected by the action of the wind upon the sails. Heeling destroys that symmetry of form in the immersed part of the ship which exists when she is upright ; and thus the character of the stream-line motions is changed from that considered in the preceding chapter. Change of trim may also effect the resistance somewhat, but probably not to so serious an extent as heeling. Leeway, again, causes the vessel to move obliquely through the water, instead of along her line of keel ; and this oblique motion not merely involves additional resistance, but leads to an unequal distribution of the dynamical pressures on the leeward side. The most intense pressures are experienced on the lee bow, and this effect is enhanced by the heeling ; so that the tendency is.to make the bow " fly up into the wind." From this brief statement it will appear, therefore, that any exact determination of the speed and course as well as magnitude and direction of the fluid resistance experienced by a sailing ship is scarcely to be hoped for ; even when the force and direction of the wind, the spread of sail and bracing of the yards, are assumed to be given. But it will also be obvious that in every case when uniform motion has been attained on a certain course, the longi- tudinal and transverse components of the fluid resistance will balance respectively the corresponding components of the effective wind pressure. Confining attention for the moment to the longitudinal compo- nents, it will be evident that if the component of the effective wind pressure exceeds the corresponding component of the resistance, the velocity of headway will be accelerated. Eeverting to Figs. 153 and 155, it will be seen that this increase in speed must affect both the direction and velocity of the apparent wind, and so influence the value of the longitudinal component of the effective wind pressure. But so long as CM, Fig. 155, exceeds the longitudinal component chap, xil] PROPULSION BY SAILS. 5°7 of the resistance, so long will the speed be increased. If the resist- ance is small even at very high speeds, then it is theoretically possible for a vessel sailing on a wind to attain a speed exceeding that of the wind. In ice boats this condition is realized. There is practically no leeway, and the frictional resistance of the sledge or " runner " on which the boats run is exceedingly small even at high speed. With the wind varying from a point before the beam to an equal amount abaft the beam, speeds are said to have been reached about equal to twice the real velocity of the wind. When a ship, sailing at a uniform speed, under the action of a wind of which the force and direction are constant, maintains an unchanged course without the use of the rudder, it is clear that the resultant pressure of the wind on the sails and the resultant resistance of the water cannot form a couple tending to turn the vessel. Under these circumstances, therefore, these equal and opposite forces must act in the same vertical plane. If it were possible to determine the line of action of the resultant resistance for any assumed speed, on a certain course in relation to the direction of the wind, then it would follow that the sails should be so trimmed as to bring the line of action of the resultant wind pressure into the same vertical plane with the resultant resistance, if the course is to be maintained without the use of the rudder. The less the rudder is used in maintaining the course, the less will the speed of the ship be checked thereby. In practice, however, the theoretical conditions cannot be fulfilled, because the line of action of the resultant resistance cannot be determined in the present state of our knowledge, even under given conditions of speed and course ; because that line of action changes its position with changes in the speed, the angle of leeway, and the transverse inclination of the ship, not to mention the changes consequent on the alterations in the force and direction of the wind ; and because it is not possible to determine accurately the line of action of the resultant wind pressure on the sails, when set in any given position. The problem which thus baffles theory is, however, solved more or less completely in practice. The skilful seaman varies the spread and adjustment of his sails in order to meet the changes in the line of action of the resistance. In a well- designed vessel, the distribution of the sail is such that the com- manding officer has sufficient control over her movements under all circumstances. Some vessels, however, are not so well arranged for sailing purposes, and in them " ardency " or " slackness " when sailing on a wind may be practically incurable. " Ardency " is the term applied when a vessel tends to bring her head up to the wind, and she can only be kept on her course by keeping the helm a-weather ; the resultant resistance must then act 5°8 NAVAL ARCHITECTURE. [chap. xn. before the resultant wind pressure. The contrary condition, where the resultant resistance acts abaft the resultant wind pressure, and makes the head of the ship fall off from the wind, is termed "slackness," and can only be counteracted by keeping the helm a-lee. Of the two faults, slackness is regarded as the more serious ; for a vessel thus affected seldom proves weatherly. To avoid excess in either direction, the naval architect distributes the sails of a new ship, in the longitudinal sense, by comparison with the arrangements in tried and successful vessels, conforming to some simple rules which will be stated hereafter. From the foregoing explanations, it will appear that the greatest care must be taken in determining the angle to which the yards shall be braced, or the sails set, in order to secure the greatest speed when sailing on a wind. This is pre-eminently a question of sea- manship ; but it has engaged the attention of many eminent mathematicians, whose investigations remain on record. All these investigations were based upon certain assumptions, as to the effective pressure of a wind acting obliquely upon the sails, the apparent direction and velocity of that wind being known. In Fig. 155, for example, if EM represents in direction and magnitude the " pressure due to the apparent velocity " of the wind — that is, the pressure it would deliver upon a plane area, say, of one square foot placed at right angles to EM — the effective pressure (FM) would, according to the law formerly received, have been expressed by EM sin 2 EMX. It has been shown that this law cannot be accepted ; and therefore the elaborate deductions which have been made from investigations based upon it have now little interest. Even if the true law were determined, mathematical inquiries could never be trusted to replace the judgment of the sailor in determining the most efficient angle for bracing the yards or trimming the sails. So many varying circumstances have to be encountered in the navigation of a sailing vessel that theory can never be expected to take complete cognisance of them all. The decision as to the best mode of handling a sailing ship must rest, where it has always rested, in the hands of her commander. It will be seen, from the foregoing explanations, that when ships are sailing close hauled it is of very great importance to be able to bring the sails to comparatively small angles with the line of keel. In this respect square-rigged vessels compare unfavourably with fore- and-aft rigged vessels, since the bracing of the yards in the former has practical limits imposed upon it by the presence of shrouds, stays, etc. In yachts the " feet " of the sails are said to seldom exceed an angle of 10 degrees with the keel when sailing close hauled. In fore-and-aft rigged vessels, such as formerly existed in chap. xii.] PROPULSION BY SAILS. 509 the Eoyal Navy, the corresponding angle was from 13 to 17 degrees. It is to be observed, however, that- for all fore-and-aft sails not set on a stay, the angle at the foot is less than that at the head ; for fore- sails, jibs, etc., set on stays the converse is true. In square-rigged ships sailing close hauled the yards are seldom braced more sharply than 25 to 30 degrees with the keel, when ordinary arrangements of shrouds and stays are fitted. Some vessels, including the ill-fated Captain, have had specially contrived tripod supports, partly for the purpose of increasing the power of bracing up sharply. Experience proved that such sharper bracing was advantageous. One example may be given from the experimental squadron of 4827.* Most of the vessels tried could only brace their yards up to 27 or 30 degrees. One vessel could brace up to 17 or 19 degrees, and proved very superior on this point of sailing, although she had the least relative length. The other ships could only lie within 5£ points of the wind, whereas this vessel could lie within 5 points and constantly gain to windward. When the shipbuilder has done all in his power to permit of bracing the yards, the choice of the angle of bracing for particular yards on any point of sailing rests with the commanding officer, who must have regard to the efficiency of the sails as a whole, and may brace the yards to different angles on the various masts in order to minimize their mutual interference and obtain the best propelling effect. Experience also gives the means of deciding, in vessels of different rig and different under-water form, what dispo- sition of the sails gives the best result under any selected set of circumstances. The late Lieutenant Paris of the French Navy made a very large number of observations upon the behaviour of the training ship Jean Bart, when sailing on different courses with varying sail-spreads and forces of wind.f These observations included eight points of sailing ; and, on each of these points, four descriptions of sail-spread and six speeds. They extended over 138 days, and numbered about fifteen hundred. Although, from the nature of the case, it is not possible to generalize for all sailing ships from this series of observations on a particular vessel, the results recorded are of great value, and well repay the study of all interested in the performances of sailing ships. Only a few examples can be given. The Jean Bart, sailing as close to the wind as was possible, with her yards braced about 32 degrees from the middle line, could keep, it is said, within 5£ to 6 points of the true wind. Her mean speed * See " Papers on Naval Areliitec- f See his posthumous work, " Obser- turej" vol. ii. ; also Fincham " On Mast- Vations sur les yitesses relatives du Vent ing Ships." et du Navire." Paris : 1885. 5IO NAVAL ARCHITECTURE. [chap. xh. was found to be abotit four-tenths that of the true wind tinder these circumstances ; the apparent speed of the wind was about 20 per cent, greater than the true wind, and its line of action was inclined to the sails about 20 degrees less than the line of action of the true wind, or about 15 degrees to the sails. When the true wind was abeam, the mean speed of the ship was six-tenths that of the true wind. The yards were braced to an angle of 45 degrees, and the apparent wind was about 11 per cent, greater in Telocity than the true wind, and made an angle of about 23 degrees with the sails. This was the best point of sailing of the Jean Bart. When the true wind was two points abaft the beam, the mean speed of the ship was one-half that of the true wind. The apparent wind then acted nearly on an athwartship line, and the yards made an angle of from 22 to 30 degrees with the apparent wind, according to the amount of sail carried. The apparent speed of the wind was about 12 per cent, less than the true speed. Lieutenant Paris was careful to remark that there was an extreme variety in the relative speeds of the ship and the wind on a given point of sailing, even when no sufficient causes for the variation could be traced. As his attempts at classification were unsuccessful, he decided to take all the observations for each point of sailing, including changes in sail-spread, and as a rough-and-ready method to average the results, on the assumption that errors or variations might be considered to neutralize one another. His results, therefore, although apparently precise in their form of summarized statement, only express averages, and do not indicate limits of variation. They are superior, however, to any other published records of the kind. One other point in these observations deserves mention, because it has an important bearing on the speeds attained by sailing ships, especially in light winds. When the Jean Bart came fresh out of dock with a clean bottom, the gain in speed for a given velocity of wind, as compared with the performance when the bottom was foul, ranged from 12 to 21 per cent, according to the point of sailing, and averaged nearly 17 per cent. The explanation is simple. At moderate speeds (as appears from the remarks on p. 464), frictional resistance is the greatest factor in the total resistance of sailing ships. Foulness of bottom, therefore, at once makes itself felt. In the Koyal Navy it has been found, for similar reasons, that zinc- sheathed ships of equally good form and rigged in the same way are inferior in their rates of sailing to copper-sheathed ships, which have smoother bottoms after they have been a comparatively short time out of dock. Preparation of Sail Plans for Ships. — When the naval architect undertakes the preparation of the sail plan for a new design, he chap, xii.] PROPULSION BY SAILS. 5 l l deals principally with plain sail or working sail, and usually does not include in his calculations all the sails with which a ship may be furnished. Plain sail may be defined as that which would be commonly set in a fresh breeze (Force 5 to 6), which is assumed to correspond to a pressure of about 1 lb. per square foot of canvas. The following tabular statement shows concisely what sails are generally included in the plain sail of various classes of ships ; and although the sails not included are of value, especially in light winds, yet it will be obvious that those named in the table are the most important. Style of rig. Plain sail. Ship . Barque . Brig . Schooner Cutter . Jih, fore and main courses, driver, three topsails, and three top-gallant sails. As ship, except gaff-topsail on mizen-mast. As ship, exclusive of mizen-mast. Jib, fore stay-sail, fore-sail, and main-sail. Jib, fore-sail, and main-sail. Notes to Table. In brigs, one-half the main course and the driver are sometimes taken instead of the whole of the main course. In schooners, the fore topsail is sometimes included. In yawls, besides the sails named for cutters, the gaff-sail on the mizen is included. It will be understood in what follows that, except in cases specially mentioned, we are dealing only with plain sail, and not with total sail area. In arranging the plan of sails for a new ship, the naval architect has to consider three things : (1) the determination of the total sail- spread ; (2) the proper distribution of this sail in the longitudinal sense, including the adjustment of the stations for the masts ; (3) the proper distribution of the sail in the vertical sense, in order that the vessel may have sufficient stiffness. First : as to the determination of the total area of plain sail in new design. Other things being equal, the propelling effect of the sails of a ship depends upon their aggregate area. Wind pressure and the management of ships are necessarily varying quantities. Hence for equal speeds the area of plain sail in two ships should be made proportional to their respective resistances at those speeds. For speeds such as are ordinarily attained under sail, frictional resist- ance furnishes by far the larger portion of the total resistance ; and when the bottoms of two ships are equally rough — having the same coefficient of friction — the frictional resistances will be proportional 5 12 NAVAL ARCHITECTURE. [chap.xii. to the immersed or " wetted " surfaces of the bottoms. If the two ships are similar in form, but of different dimensions, the wetted surfaces will be proportional to the two-thirds power of their displace- ments ; for these surfaces will be proportional to the squares of any leading dimension — say the length — while the displacements will be proportional to the cubes of the same dimensions. Put in algebraical language, if W x be the displacement of one ship, Sx the wetted surface, and A, the area of plain sail ; while W2, Sj, and A 2 are the corresponding quantities for another similarly formed ship : then for equal speeds under sail we must hare — S. A 3 \W 2 J Suppose, for example, that W] = 8W 2 ; then — ±1 = f ?Z?\ f _ 8 | = 4 or Al = 4A, a 2 v w 2 ; Although the attainment of a definite speed under certain con- ditions does not form part of the design of a sailing ship, as it does in a steamship, yet it may be interesting to notice a roughly approxi- mate method for determining the sail-spread of a new ship when it is desired to give her greater speed than that of the typical ship or ships used as examples. Let it be assumed, as may be fairly done, that the resistance of these ships varies as the square of the speed's, within the limits of speed considered. Further, let it be assumed that the effective pressure (per square foot) of the wind on the sails is the same for both ships.* Then, if Y 1 and V 2 be the maximum speeds, and the other notation remains as before, we have — Ax = h(W$ X \V A 2 = £(W a )* x Y a 3 where Jc is a constant, and the same for both ships. Hence a 3 "Uv x IwJ is an equation from which the new sail-spread (A 2 ) may be determined approximately ; but for the reasons given above it has little practical value. Keeping to the ordinary assumption that equality of speed is * This latter assumption is not strictly The character of the correction required correct, since the difference in speed will be understood from the remarks must produce some difference in the ap- previously made, parent direction and velocity of the wind. chap. XII.] PROPULSION BY SAILS. 5 r 3 aimed at in the new and old sailing ships compared, it would no doubt be preferable when arranging the sail-spread of a new ship differing considerably in form from the exemplar ship to determine the resistances by model experiments, and then to proportion the saiUareas to those resistances. On the whole, the equation on the previous page, although obtained under the limitations stated, is considered a sufficient guide in most cases, when comparing the sail-powers of ships not similar in form, provided the dissimilarity is not very great. It is usual in the Eoyal Navy to compare the "driving powers " of the sails in different ships by the ratio — 2. ; Sail-spread : (displacement) 3 . But it is fully recognized that, if there is considerable difference in form, it is preferable to use the ratio — Sail-spread : wetted surface. It may happen that when the equation on p. 512 is used to determine the sail-spread for a new ship, it gives results which are inadmissible'. For example, a ship may not have sufficient stability to carry the sail-area which the formula would assign to her ; or it may be impossible to find room for the efficient working of the theoretical sail-spread. This statement is tantamount to another, which is fully borne out by experience, viz. that in ships of different types and sizes, different " driving powers " of sail have to be accepted, and the hypothetical condition of equal speeds abandoned. Formerly it was the practice to proportion the area of plain sail to the area of the water-line section of ships ; and this would agree with the foregoing rule so long as the condition of similarity of form was strictly fulfilled. But, when the vessels compared are dissimilar in form and proportions, it becomes preferable to express the sail-area as a multiple of the two-thirds power of the displace- ment, rather than as a multiple of the area of the water-line section. Very similar remarks apply to another method once commonly used, in which the area of plain sail was proportioned to the area of the immersed midship section ; a plan which was applicable only when the vessels compared were similarly formed. Still another method of stating the sail-spread is to express it as a multiple of the displacement (in tons). A ship of 3500 tons displacement with 24,500 square feet of plain sail would be described as having 7 square feet of canvas per ton of displacement. From the explana- tions given above, it will be seen that, if anything like a constant ratio of sailrarea to displacement were maintained, large ships would be much superior to smaller ships in driving power and speed. Hence it was the practice, in former times, to increase the ratio greatly as " ships diminished in size ; so' that the smaller classes 2l 514 NAVAL ARCHITECTURE. [chap. xu. might be as fast as, or faster than, the larger. This practice still holds good, in yachts and vessels designed to perform well under sail; as size is diminished the sail-spread is made proportionately greater, and the consequent risks are accepted, because it is recognized that the smallness of individual sails makes them easily handled. A full statement of the sail-spread considered desirable in different classes of ships would occupy space far exceeding the limits at our disposal.* The treatise on " Masting Ships " published some years ago by Mr. Finchani contains detailed information on the subject that can still be studied with advantage, embracing, as it does, not merely the particulars of sailing ships of various obsolete classes, but also those of the classes of unarmoured steamships of the Royal Navy designed before the ironclad reconstruction began. In this work the area of plain sail is expressed as a multiple of the area of the water-line section, and the following figures may be interesting. For ship-rigged vessels the area of plain sail was from 3 to 4 times the water-line area ; for brigs and schooners, from 3^ to 3f times ; and for cutters, from 3 to 3J times. These ratios were for sailing vessels ; in their unarmoured successors, possessing both steam and sail power, the ratio was not so high, and in a great many ship- rigged vessels fell to 2 or 3. In armoured ships of the Royal Navy, with good sail-power, the corresponding ratio is in some cases a little above and in others a little below 2. In sailing ships of the mer- cantile marine the corresponding ratio has been found to vary from 2| to 3 in a large number of examples, 2£ being a good average : but this mode of measuring the sail-spread is not commonly employed by private shipbuilders. Taking the ratio of sail-spread to area of immersed midship section, it appears that in the obsolete classes of sailing war-ships this ratio varied from 25 to 30 in line-of-battle ships, up to 30 to 45 in frigates, and 40 to 50 in brigs and small craft. This mode of measurement is still used in the French Navy, and M. Bertin thus summarized their practice. In the obsolete sailing line-of-battle ships the ratio was from 30 to 35, in frigates 35 to 40, for smaller classes sometimes as high as 50. In unarmoured ships, with steam and sail, the French practice gave ratios of sail-spread to midship section varying from 28 in line-of-battle ships to 40 in frigates and cruisers. In French ironclads the ratio has not exceeded 20. For * For many of the facts as to mer- the " Report on Masting," made by ■chant ships given hereafter, the author Lloyd's surveyors, he has also obtained has to thank the late Mr. John Ferguson valuable data. For the facts as to and the late Mr. Bernard Waymouth yachts, he is principally indebted to the (Secretary of Lloyd's .Register). From works of Mr. Dixon Kemp. chap, xh.] PROPULSION BY SAILS. 5*5 English ironclads, equipped for sailing, the ratio varied from 18 to 25 ; for unarmoured frigates of the older classes it was about 32, and for swift cruisers like the Inconstant, 26. For corvettes and sloops the corresponding ratios were 23 to 33. For sailing ships of the mercantile marine the ratio varied from 22 to 35 in a great number of ships examined, about 28 being a good average value. The ratio of sail-spread to displacement is not commonly used for war-ships, but is frequently employed for merchant ships. It is unnecessary to repeat the remarks made above as to the limitations within which this mode of measurement can be usefully employed. In a considerable number of sailing merchantmen this ratio has been found to vary from 4£ to 8, the largest ratio occurring in the ships of least displacement. For ships below 2000 tons displacement 6£ is a good average value ; for larger ships up to 4000 tons displace- ment 5J to 6 is a fair value. Simply as a matter of comparison, it may be stated that in the obsolete classes of sailing men-of-war the ratio of sail-spread to displacement varied from about 6 in the largest classes (4000 to 5000 tons displacement) up to 12 or 15 in frigates (of 1200 to 2000 tons displacement), and 20 to 30 in the brigs and small craft. For unarmoured ships of the Eoyal Navy, having steam as well as sail power, the ratio was about 5 to 7 for frigates, 5 to 6 for corvettes, and 9 to 12 for sloops. For the armoured ships it commonly varied between 3 and 4, rising to 6 in a few of the smallest vessels. Another mode of comparing sail-spreads occasionally used in the mercantile marine is to express the ratio of the sail-spread to the under-deck tonnage. For ships of similar class (as explained in Chapter II.) this tonnage bears a fairly constant ratio to the displace- ment at the deep load-line. Hence the practice now being described is open to the same objections as were urged against the preceding method. From 12 to 16 are common ranges in the ratio of sail- spread to under-deck tonnage, and 13 is a good average in ships of moderate size. Comparing these various classes by the ratio which the sail- spread bears to the two-thirds power of the displacement, the following results may be interesting. The numbers represent, for some typical ships of war, the quotient : — Sail^spread -f- (displacement)!. Sailing — Line-of-battle ships . . 100 to 120 Frigates Corvettes 5 120 to 160 Brigs Steam and Sail — Ironclad ships 60 to 80 Unarmoured — Frigates .... Corvettes J 80 to 120 Sloops 5*6 XAVAL ARCHITECTURE. [chap. xii. It will be remarked that the proportionate sail-power of the steam unarmoured frigates, etc., was, on the whole, less than that of the sailing Yessels, and that the armoured ships stand still lower in the scale. But it must be noticed that some of the steamships had finer forms and proportions than the sailing ships, so that their resistances were proportionately less. Further, it is important to note that the great increase in displacement which accompanied the construction of ironclads rendered it practically impossible to give to these heavy vessels a spread of sail comparable in propelling effect to that of the sailing line-of-battle ships, even if other and more important qualities had been sacrificed. Take, for example, the 80-gun sailing line-of-battle ship Vanguard, with a displacement of 3760 tons and sail-spread of 28,100 square feet, the quotient sail- 2 spread -f- (displacement) 5 was not much below 120. In the best equipped ironclads of moderate size built for distant services the corresponding quotient was about 75, and in most of the heavier ironclads it was less. In connection with the work of the committee on designs for ships of war in 1871, this matter was considered, and the Hercules ironclad was taken as a typical case. It was shown that if her sail power had been proportioned to the two-thirds power of her displace- ment (8800 tons) as in the sailing line-of-battle ship Vanguard, the total area of plain sail would have been increased from its actual value (about 29,000 square feet) to nearly 50,000 square feet. Having regard to the limitations in height of masts imposed by the conditions of stability, and to the number of masts which could be fitted in a ship 325 feet in length, it was obvious that such an increase in sail-area was impracticable. In fact, it was agreed that in armoured ships with single screws, the possible sail spread in most cases could not exceed that required to enable the ships to proceed under sail alone, in case of emergency, or when desired to economize fuel. Manoeuvring under sail, in the manner common before the ironclad period, was. admitted to be neither necessary nor possible under the new conditions. In twin-screw vessels sail was still more distinctly reduced to a mere auxiliary to steam, as the drag of the twin-screws was found to be serious when proceeding under sail alone. The general use of twin-screws since 1870, and the desire to diminish " top-hamper " in order to increase fighting efficiency, have caused the practical abandonment of sail power in all but the smallest classes of war-ships, so that the subject of sail equipment has ceased to have the importance it had formerly. Although it is not usual to express the sail-area of merchant ships in terms of the two-thirds power of the displacement, it may be interesting to state that in a great many cases examined, the chap, xii.] PROPULSION BY SAILS. S l 7 area of plain sail has been found to vary from 70 to 110 times the two-thirds power of the displacement, and 80 to 85 times seems to be about the average. There will, of course, be great differences in sail-spread according to the intended service, and the ordinary trader will carry much less sail than clippers built primarily for fast sailing. Yachts stand quite apart from other classes of sailing ships, and cruising yachts differ greatly from vessels built especially for racing. The latter are necessarily influenced greatly in sail equipment as well as design by the rules for measurement (or rating for com- petitive sailing) in force at the time when they are built. It is an interesting study to trace the influence of changes in these rules on the types and sail equipments. All that can be done here is to briefly summarize present practice. Under the Thames measurement and modifications thereof, no regard was had to sail-spread in settling the rating of yachts. The tendency, therefore, was to have large sail-areas, and to use large relative weights of ballast in order to give sufficient stiffness to the long narrow and deep type of yachts which were built under these rules. Since 1886 (see p. 76) the formula of the Yacht Racing Association takes account of sail-area, and the best authorities agree that as a consequence sail has been reduced in all classes of yachts. The sail-area used in that formula must not be confused with " plain sail " as defined above for cutters and schooners, but includes in addition to the lower sails there enumerated, the topsails, spinnaker, etc. Having regard to the great varieties of under-water forms in yachts, differences in areas of deadwoods, keels, etc., it is generally admitted that the fairest mode of proportioning sail-areas is to express them in terms of wetted surfaces. For British racing yachts four square feet of sail- area to one square foot of wetted surface is said to be a common value ; for American yachts, nearly six square feet of sail to one of wetted surface is usual. There are great differences in the proportion of sail-areas to displacements in different sizes of yachts for reasons given above, as well as in the proportion of sail-area to the two-thirds power of the displacement. In small yachts there are commonly from 100 to 150 square feet of sail per ton of displacement ; in large yachts the corresponding numbers vary from 55 to 80. In small yachts the quotient of sail-area divided by the two-thirds power of the displace- ment ranges from 230 to 300, and in some cases goes higher; in large yachts the corresponding numbers vary from 260 to 300. Mr. Dixon Kemp states that for British yachts the cube root of the displacement in cubic feet is usually found to be one-fifth of the square root of the sail-area ; while, it is one-sixth in American yachts. 5*8 NAVAL ARCHITECTURE. [chap. xii. If displacements are expressed in tons, this rule is equivalent to saying that the quotient of sail-area, divided by the two-thirds power of the displacement, is ordinarily about 267 for British yachts, and 385 for American yachts. Average values are obviously not very safe guides in these special classes of racing yachts. The figures given are interesting, however, as indicating the enormous relative spread of sail given to yachts as compared with sailing ships of all other classes mentioned above. Secondly : In the arrangement of sail-plans it is important to secure a proper longitudinal distribution of the sails, in order that neither excessive ardency nor excessive slackness may result, and that sufficient handiness or manoeuvring power under sail may be secured. It has already been shown that the difficulties attending any attempt at a general solution of this problem are insuperable, and we are now concerned only with the methods adopted in practice. The line of action of the resultant wind pressure changes its position greatly under different conditions ; the naval architect therefore starts with certain assumed conditions in order to determine the " centre of effort " of the wind on the sails. All the plain sails are supposed to be braced round into the fore-and-aft position, or plane of the masts, and to be perfectly flat-surfaced. The wind is then assumed to blow perpendicularly to the sails, or broadside-on to the ship, and its resultant pressure is supposed to act perpendicu- larly to the sails, through the common centre of gravity of their areas. This common centre of gravity is determined by its vertical and longitudinal distance from some lines of reference, those usually chosen being the load water-line, and a line drawn perpendicular to it through the middle point of the length of the load-bine, measured from the front of the stem to the back of the sternpost. Fig. 156 shows a full-rigged vessel with her sails placed as described, the centre of gravity of the area of plain sail, or " centre of effort," being marked C. A specimen calculation, illustrating the simple process by which the point C is determined, is given in the table on next page. When the centre of effort of the sail-area has been determined relatively to the middle of the load-line, it is usual also to deter- mine the longitudinal position of another point, commonly styled the " centre of lateral resistance." This is marked L in Fig. 156, and is simply the centre of gravity of the immersed portion of the plane of the masts — the same plane area which was referred to in an earlier part of the chapter as considerably influencing the leeway of a ship sailing on a wind. It will, of course, be understood that the point L is no more supposed to determine the true line of action of the resultant resistance than the point C is supposed to determine CHAP. XII.] •PROPULSION BY SAILS. 5*9 Calculation fob the Centre of Effort of the Sails of a Ship. Distances of centres J of gravity from middle of load-line. moment .of sails. Heights of centres Vertical Sails. Areas. of gravity moments of sails. Before. Abaft. Before. Abaft. load-line. sq. ft. feet. feet. Jib . 1,000 145 — 145,000 — 48 48,000 Fore course 2,300 85 — 195,500 — 36 82,800 „ topsail 2,500 83 — 207,500 — 74 185,000 „ top-gallant sail . 1,100 82 — 90,200 — 108 118,800 Main course 3,000 — 20 — 60,000 35 105,000 ,, topsail 2,600 — 23 — 57,500 76 190,000 „ top-gallant sail 1,100 — 25 — 27,500 110 121,000 Driver 1,600 — 120 — 192,000 40 64,000 Mizen topsail . 1,300 — 100 — 130,000 66 85,800 „ top-gallant sail Total area of plain sail 600 103 — 61,800 92 17,000) of effort » 55,200 17,000 638,200 528,800 Centre above 1,055,600 1?,000 528.800 62-1 feet. ) 109,400 Centre of effort before middle of load-line . 6-43 feet. Centre of lateral resistance abal Centre of effort before centre of t ditto lateral resistance 6'0 „ 12-43 feet. the line of action of the resultant wind pressure. But, on the other hand, experience proves that the longitudinal distance between the centre of effort and the centre of lateral resistance L should lie within the limits of certain fractional parts of the length of the load-line. From the drawings of a ship the position of the centre of lateral resistance may be determined by a very simple calculation; and the particulars required for an approximate calculation are easily obtainable from the ship herself, being the length at the load-line, draught of water forward and aft, area of rudder, and area of aperture in stern for screw, if the vessel be so constructed. The distance of the centre of effort before the centre of lateral 5 2 ° fi AVAL ARCHITECTURE, [chap. xii. resistance varies according to the style of rig ; and in determining it, regard must be had also to the under-water form of a ship. A full-bowed ship, for example, should have a greater proportionate distance between the two centres than a ship of the same extreme dimensions and draught, but with a finer entrance. In ships trim- ming considerably by the stern, and with a clean run, the distance between the centres should be made proportionately less. In ship- rigged vessels and barques the centre of effort is usually from one- fourteenth to one-thirtieth of the length before the centre of lateral resistance ; one-twentieth being a common value. The greater dis- tance (one-fourteenth) occurred in the old sailing ships of the Royal Xavy, with full bows and clean rims ; this has been almost equalled in some of the later masted ironclads, where the centre of effort has been placed one-sixteenth of the length before the centre of lateral resistance. The smaller distance occurs in screw frigates of high speed and fine form, such as the Inconstant; in the unarmoured screw frigates which preceded them, the distance was from one- twentieth to one-twenty-fourth of the length. In brigs, one-twentieth of the length is a fair average for the distance between the two centres. In schooners and cutters, the two centres are always very close together, their relative positions changing in different examples, and the centre of lateral resistance sometimes lying before the centre of effort. Mr. Dixon Kemp considers that for racing yachts the centre of effort of the sails should be placed about one-fiftieth of the length before the centre of lateral resistance ; and for cruising yachts recommends that they should lie in the same vertical line. For yawls the centre of effort should be a little further aft than in cutters or schooners. It is to be noted, however, that in a vessel with square sails the longitudinal position of the centre of effort will vary but very slightly, however wide may be the differences between the angles to which the yards are braced. On the contrary, in a schooner or cutter the centre of gravity of the plain sail must move forward with any angle of departure from the hypothetical position in the plane of the masts. In the designs of sailing men-of-war, it was formerly the practice to express the longitudinal position of the centre of effort in terms of its distance from the centre of buoyancy ; and it was generally agreed that the centre of effort should lie further forward than the centre of buoyancy. Chapman, the famous Swedish naval architect, laid down the rule that the distance between these two centres should be between one-fiftieth and one-hundredth of the length ; but considerable departures were made from this rule in practice. Cases occurred where the distance was as great as one-thirtieth of the length. CHAP. XII.] PROPULSION BY SAILS. 521 A similar practice still prevails in the designing of merchant sailing ships ; and even greater variations occur in the relative positions of the two centres. Cases have occurred where the centre of effort has been as much as one-twentieth of the length before the centre of buoyancy ; and others where it has been one-fiftieth of the length abaft. Such variations clearly indicate an absence of con- formity to any fixed rules, other considerations — such as convenience of stowage or accommodation^-largely influencing the longitudinal distribution of the sail. Having decided upon a suitable distance between the centre of effort and centre of lateral resistance for a new design, it is next necessary to station the masts and distribute the sail in such a manner that the required position of the centre of effort may be secured, in association with sufficient manoeuvring power and a proper balance of sail: In the following table the results of experi- ence with various classes of ships are summarized, all the vessels being supposed capable of proceeding under sail alone. The. length of a ship at the load-line, from the front of the stem to the back of the sternpost, being called 100, the other lengths and distances named will be represented by the following numbers.: — Big and class of vessel. Distance from front of stem. Base of sail. Foremast. Mainmast. Mizenmast. Ship or barque rig : — Obsolete classes of sailing \ ships of war . . . / Unarmoured war - ships, \ steam and sail . . / Sailing merchantmen Ditto (four masts) Brig Schooner* Cutter Yawl Ketch 12 to 15 13 to 18 20 to 22 14 17 to 19 16 to 22 36 to 42 38 39 55 to 58 56 to 59 53to 55 38 to 40 64 to 65 55 to 61 80 to 90 84 to 86 80 to 88 ( 64 to 66 < .Tiggermast ( 86 to 87 J C variable ) ] abaft | (sternpostj 90 125 to 160 160 to 165 160 to 170 170 to 190 The most successful sailing ships yet built, both in war fleets and in mercantile marines, have had three masts. In some of the earlier * These are Fincham's rules: in modern schooner-yachts no fixed rule appears to be" followed, the masts being placed much' closer together, in order ta increase the size of mainsail. 5 22 NAVAL ARCHITECTURE. [chap. xn. ironclads from 380 to 400 feet in length, four and five masts were adopted, in order to increase the sail-spread while keeping the centre of effort low. Although the masts could be well spaced in these long ships, and the sails on each kept far apart, the departure from precedent did not proTe successful. A few large ironclads intended to sail, as well as steam, have been " brig-rigged " on two masts, but not with much success. In merchant steamers of great length four or five masts are sometimes employed, and the Great Eastern had sis masts ; the sail power in all these cases is relatively small, and auxiliary to steam. Now that twin-screws are extensively employed in the largest passenger and cargo steamers, sail is practically abandoned in many cases. The new Cunard steamships of 600 feet in length have only two masts. Sailing ships in the mercantile marine have, in recent years, been largely increased in size ; and in vessels from 260 to 375 feet in length four and five masts have been fitted for the same reasons as are given above in connection with the earlier ironclads, viz. that a large sail-spread is secured in association with a comparatively low position of the centre of effort, and a sufficiently wide spacing of the masts to secure the efficient action of all the sails. These large vessels are designed primarily for increased carrying power, and not for the purpose of making faster passages than the smaller vessels formerly built. The " rake " given to the masts in different classes of ships requires a few words of explanation. In nearly all cases it is an inclination aft from the vertical line drawn through the heel of the mast ; but in vessels with " lateen " rig the foremast commonly rakes forward considerably. The following are common values for the rake aft. In cutters, from ^ to ^ of the length ; in schooners, for fore- mast, from -^ to ^, and for mainmast, from ^ to £ ; in brigs, for foremast, from to £$, for mainmast, from ^ to -f s ; in ships, for foremast, from to ^g, for main and mizen masts, from to ^. It is customary to have the greatest rake in the aftermost mast, and the least in the foremast. Graceful appearance, greater ease and efficiency in supporting the masts by shrouds and rigging, and the possibility of bracing the yards sharper when the masts are raked aft and the rigging led in the usual way, are probably the chief reasons for the common practice. The " steeve " given to the bow- sprit is also in great measure a matter of appearance ; but it is useful, especially in small vessels, in giving a greater height above water for working the head-sails in a seaway. In some large war- ships intended to act as rams, the bowsprits have been fitted to run-in when required ; the steeve was very small, but the height above water was considerable. The table also gives a length for the " base of sail," in terms of chap, xii.] PROPULSION BY SAILS. 5 2 3 the length of the ship, and this exercises an important influence on the manoeuvring power of a vessel. In Fig. 156 it would be measured from the foremost corner (or " tack ") of the jib to the aftermost corner (or " clew ") of the driver ; in other classes it would be measured between extreme points corresponding to those named. The base of sail is usually proportionally greater in vessels wholly dependent on sail-power than in vessels with steam and sail-power. Special circumstances may, however, limit the length of the base of sail ; and one of the most notable cases in point is to be found in her Majesty's ship Temeraire, a brig-rigged vessel of over 8400 tons displacement, where the departure from ship rig was made in order to facilitate the arrangements for heavy chase guns at the bow and stem. Experience has led to the formation of certain rules for deter- mining the proportionate areas of the sails carried by the different masts, with various styles of rig. According to Mr. Fincham and other authorities, in ship-rigged sailing vessels of the earlier classes, if the area of the plain sail on the mainmast was called 100, that on the foremast varied from 70 to 77, and on the mizenmast from 46 to 54. In the ships of the Eoyal Navy, the later practice has been to make the corresponding sails on the fore and main masts alike, except the courses ; and calling the sail-area on the mainmast 100, that on the foremast would commonly be from 90 to 95, that on the mizen 45 to 55, and the jib from 15 to 20, the latter agreeing fairly with the practice in sailing vessels. In barque-rigged vessels the sail-area on the mizen is often about one-third only of that on the main, the sail-area on the foremast having about the same propor- tion as in ships. In brigs the sail on the foremast varies from 70 to 90 per cent, of that on the main ; in schooners it is often about 95 per cent. In sailing merchantmen the distribution of sail varies consider- ably. The following appear to be good average values. Calling the sail-area on the mainmast 100 in ship-rigged vessels, that on the foremast varies from 90 to 95, and on the mizen from 55 to 60 ; the jib varies from 10 to 12. In barque-rigged vessels the corresponding numbers are : mainmast 100, foremast 90 to 95, mizen 25 to 30, jib 10 to 15. In four-masted ships the main and mizen carry about equal sail-areas ; calling this 100, the jib is about 8 to 10, the foremast 85 to 95, and the jigger 55 to 60 in some good examples ; in a four-masted barque the jigger has been found as little as 20 to 25. The handiness of a ship under sail, particularly in the earlier movements of any manoeuvre, is somewhat affected by the distance of the centre of gravity of the ship from the centre of effort. This 524 NAVAL ARCHITECTURE. [chap. xn. consideration was formerly treated as of great importance, but it now has little influence in the actual arrangement of sail plans. The longitudinal position of the centre of gravity for the load-draught is usually fixed by other and more important conditions; and its position changes considerably as the amount and stowage of weights on board are varied. It will suffice to say, therefore, that, when a ship is tiirning, her motion of rotation may be regarded as taking place about a vertical axis passing through the centre of gravity, which point simultaneously undergoes a motion of translation. Hence it follows that the turning effect of any forces will vary with the distance from the centre of gravity of their line of action. Suppose a ship to have all plain sail set, and to be balanced so that her course can be kept without using the rudder, the line of action of the resistance will lie in the same vertical plane with the resultant wind pressure, which may be supposed to pass through the centre of effort. Then, in tacking, the resistance tends to throw the head of the ship up into the wind and to assist the helm, but it tends to resist the helm in wearing. The further forward of the centre of gravity the centre of effort is placed, the greater will be the initial turning effect of the resistance when a manoeuvre begins. But as soon as changes are made in the sails which " draw " in order to assist the manoeuvre, and as soon as the action of the rudder is felt, the speed and course of the ship alter, and the initial conditions no longer hold, the line of action of the resistance changing its position from instant to instant. Lastly : in arranging the sail-plan of a ship, it is necessary to consider their vertical distribution, which governs the height of the centre of effort, and the " moment of sail " tending to produce transverse inclination. The specimen calculation on p. 519 shows the ordinary method of estimating the vertical position of the centre of effort when the plain sail is braced fore-and-aft. If the line of action of the wind is assumed to be horizontal, the steady speed of drift to leeward will supply a resistance equal and opposite to the wind pressure, and having a line of action approximately at mid-draught. This couple will incline the ship transversely until an angle of heel is reached for which the moment of stability equals the moment of the incHning couple. Let A = area of plain sail, in square feet ; h = the height (in feet) of the centre of effort above the mid-draught, when the ship is upright ; m = the metacentric height (GM) in feet of the ship ; D = the displacement (in pounds) ; p = the average pressure, in pounds per square foot, which the assigned velocity of the wind would pro- duce upon the sail-area when placed at right angles to the wind ; and a = the angle of steady heel. Then, within the limits of the chap, xii.] PROPULSION BY SAILS. 525 angles of steady heel reached in practice, the following equations may be considered to hold : — Moment of sail, to heel ship = A x h X p cos 2 a ; Moment of statical stability = D x m x sin a ; whence is obtained the following equation for the angle a : — . „ D . m sin' a -f- sin a — 1 = 0. A.p .h Since a is usually an angle of less than 6 or 8 degrees, this equation may, without any serious error, be written — D .m , . A.p .h sin a = 1 ; or sin a = -r^ 4 — A.p .h D .m Suppose, for example, that p = 1, and that, in the case of Fig. 156, D = 6,800,000; m = 3 feet; A = 15,600 ; and the mean draught 20 feet. Then h = 62 + 10 = 72 feet ; 15,600 x 72 468 1 . Sm a = 6,800,000 x 3 = 8^00 = 18 (nearly) ' a = 31 degrees (nearly). From the remarks made on p. 499 it will be understood that, in practice, the determination of the ayerage pressure p in this formula is not possible, in consequence of our want of exact knowledge of the laws governing wind pressures on sails. Consequently exact estimates of the angles of steady heel for ships corresponding to certain "forces" and velocities of wind, to certain assigned sail- spreads, and to certain angles of bracing for the yards, cannot be made on the basis of the preceding formula. The old assumption, resting upon no experimental data, is that for all plain sail in a ship-rigged vessel the average pressure of the wind on a surface normal to it may be taken as 1 lb. per square foot. A careful comparison of a large number of recorded angles of steady heel under all plain sail in ships whose conditions of stability and dis- tribution of sail were known, shows that the actual angles of heel exceeded those which would be obtained on the ordinary hypothesis. Various explanations may be given of the difference thus disclosed, but it is unnecessary to enter into a discussion of them, since direct observations, by means of anemometers, of the velocities and pressures of winds producing certain inclinations in ships under sail (such as have been suggested on p. 500) would settle the matter, and, apart from such observations, it. must remain open to doubt. On the basis of experience, practical rules have been framed by which to determine approximately the lengths of . the masts and 5 26 NAVAL ARCHITECTURE. [chap, xi i. yards, and the proportionate areas of the different sails, when pre- paring sail-plans. For these it is impossible to find space, and they can be consulted by readers desiring information of the kind in the standard works mentioned above. The heights of the masts and the depths of the sails were formerly proportioned to the extreme breadths of ships. Hence it became the practice to express the height of the centre of effort above the load- line in terms of the breadth. For ship-rigged vessels and barques, the ratio of this height to the breadth usually lies between 1 \ and 2 ; for brigs and schooners, between 1 \ and If ; and for the other rigs mentioned in the table on p. 521 it has nearly the same value. These approximate estimates are not to be put in place of exact calculations for the position of the centre of effort, but they are useful nevertheless. In order that the moment of sail may be estimated, the half-draught must be added to the height of the centre of effort above the load-line. If there be no similar vessels to compare with a new design, the problem of the vertical distribution of the sail takes the form of a determination of the height h of the centre of effort above the centre of lateral resistance. In that case the whole of the quantities in the formula given above, except the height \ feet, the sail-carrying powers in a great number of cases we have investigated lie between 14 and 18. Mr. W. John gave 12 to 20 as corresponding values with 3£ feet metacentric height. It may be desirable again to state that sailing merchantmen have forms and proportions such that, if they are stowed so as to secure the amount of stiffness assumed, they must have a large range of stability. But they are liable to be much less favourably situated, both as regards stiffness and range of stability, if improperly stowed. The spread of sail carried by yachts has been shown to be enormous in proportion to their displacement, and, their metacentric heights being moderate, their sail-carrying powers are small. In some very successful English yachts the sail-carrying power has been found to lie between 4 and 8. Eor cruising vessels it is usually greater than in racing yachts. In the Sunbewm, with auxiliary steam- power, it is 84. In match sailing, steady angles of heel of 20 to 30 degrees are said to be not uncommon ; but there is little risk of such vessels being capsized, as the ballast brings the centre of gravity very low, and they have extremely great range of stability (see curves on Fig. 63, p. 138). 528 NAVAL ARCHITECTURE. [chap.xii. The Dimensions and Proportions of Modern Sailing Ships. — Allusion has been made aboTe to the remarkable increase in the sizes of sailing ships that has taken place in recent years, and equally notable changes have been made in their forms and pro- portions. The construction of sailing ships has naturally been influenced by improYenients in steamships. Greater lengths, larger proportions of length to breadth, and finer forms have been adopted in sailing ships, with marked advantage in their working. Formerly it was assumed that the length of a sailing ship should not exceed four times the beam ; in many vessels having high reputations the length was not much more than three times the beam. Sailing ships of war were given these moderate proportions, no doubt, because extreme handiness was desired, as well as considerable stability, so that the angles of heel should not be great, and that the guns on the lee side could be fought. These vessels necessarily had to be loftier than merchantmen, to carry considerable weights of armament on the decks instead of cargo in the holds, and generally to fulfil conditions which were essentially different from those in the mercantile marine. Consequently there was far less latitude in the choice of forms and proportions. As steam-power was introduced and sail-power subordinated, great changes were made; primarily to improve steaming performance, but with the result in many cases of giving increased speed under sail. As an example, reference may be made to H.M.S. Inconstant, which has made runs at speeds of from 13J to 14J knots per hour under sail alone. The introduction of the so-called " clipper " type of fast-sailing merchantmen must be credited to the United States, although its fullest development is due to British shipbuilders.* Yessels of this type commonly have lengths from five to six times the beam, and in some cases the lengths have exceeded seven to seven and one half beams. Diminished Tesistance has been obtained by increased length and greater fineness of form,. and the performances under sail have been remarkable on voyages of great length, even in these days of rapid steam navigation. One or two examples may be given. The Tliermopylse made the passage from London to Melbourne in 60 days in 1868. On one occasion she ran 330 knots in 24 hours, with the wind strong abeam. The following tabular statement * For details on this subject see zine for October, 1891. The late Mr. Lindsay's " History of Merchant Ship- Waymouth, who designed the Thermo- ping," and very interesting articles on pylse and other vessels, also> su] "Clipper Ships" in Naval Science for much information to the author. 1873, and the English Illustrated Maga- CHAP. XII.] PROPULSION BY SAILS. 5 2 9 enables a comparison to be made between this famous clipper and the Pique, which was a sailing frigate of good reputation in the Boyal Navy : — Particulars. Length Breadth Displacement .... Area of plain sail Area of plain sail -f- (displacement)* Thermopylce. 210 ft. 36 ft. 1,970 tons 17,520 sq. ft. 110 Pique. 162 ft. 48^ ft. 1,912 tons 19,086 sq. ft. 124 The sail-spread of the Thermopylae was, therefore, less proportion- ally than that of the Pique; but her greater length and fineness of form diminished her resistance, and gave to the Thermopylse greater speed in making passages than the sailing frigate possessed. The Sir Lancelot, built by Messrs. Steele of Greenock, made the passage from China to England in 1869 in eighty-nine days, against the prevailing monsoon, covering about 14,000 miles in that time. During this voyage she ran over 305 knots in twenty-four hours; and during one week with fresh beam winds her daily run averaged nearly 260 knots. This vessel was not quite 200 feet long, about 33£ feet broad, of 886 tons register, and had an enormous sail-spread. Another clipper, the Melbourne, designed by the late Mr. Way- mouth, made a remarkable passage from England to Melbourne in 1876. It occupied 74 days, the conditions being unfavourable during part of the time. Erom the Cape fair winds were obtained, and 300 miles a day were averaged for seventeen consecutive days. In this period the three longest daily runs were 374, 365, and 352 miles. The Melbourne had a displacement of about 3500 tons, an area of plain sail of about 21,000 square feet, and the ratio of sail-spread to the two-thirds power of the displacement was about 90 to 1. These fast-sailing ships were built for special services, such as the China tea trade, where speed was of primary importance. In later years there have not been the same inducements for shipowners to imitate their predecessors, and sailing ships have been designed chiefly with a view to carrying large cargoes on very long voyages. There was a great revival in the building of sailing ships during the period 1889-92. In 1889 about 122,000 tons (gross tonnage) of sailing ships were built in the United Kingdom, rather over 9 per cent, of the total mercantile tonnage built. In 1890 the tonnage of sailing ships approached 142,000 tons, or about 11 per cent, of the total production. In 1891 the corresponding figures were nearly 230,000 tons, and over 18 per cent. ; and in 1892, 275,000 tons, and 2m 53° NAVAL ARCHITECTURE. [chap. xn. over 22 per cent. This revival was associated with the con- struction of very large sailing ships, of which the dead-weight carrying capacity is about 6000 tons, and the register tonnage from 3300 to 3800 tons, the lengths varying from 330 to 375 feet. These vessels are not rigged so loftily as the much smaller clipper ships above described, nor do they carry so much canvas in proportion to their size, although they have four or five masts. Steam and mechanical power are used to supplement manual labour in working the sails, for pumping, and for other purposes. Water ballast is also fitted in many cases. The two largest sailing ships yet built in this country are the France and Maria Bdekmer, both for foreign owners. The former, built by Messrs. Henderson in 1890, is 360 feet long, nearly 50 feet in beam, and has a carrying capacity of 6150 tons. The latter, built by Messrs. Russell in 1891, is 375 feet long, 48 feet beam, and has a carrying capacity of about 5700 tons. Both vessels have cellular double bottoms fitted for water ballast. The Maria Richmer was notable also because she had auxiliary steam-power in the form of triple expansion engines of about 650 H.P., which were capable of driving her, when fully laden, at a speed of 6 to 7 knots per hour. This adoption of auxiliary steam-power was a return to a former practice, and was primarily intended to be made use of in the region of calms or when contrary winds are experienced. A " feathering " screw was fitted, so as to reduce its drag when the vessel is under sail, as it was intended she should be ordinarily. She was lost at sea under unknown circumstances. Propulsion under Steam and Sail. — When ships possess fairly good sail-power as well as good steam-power, it is often found advantageous to use both means of propulsion. This is especially true in many classes of war-ships, and considerable economies of coal may be effected by the judicious use of sails as auxiliary to steam when making passages. Lieutenant Paris, in his observations on board the Jean Bart, endeavoured to appraise the gain in speed obtained by using both steam and sails, as compared with the speed realized with the same development of horse-power acting alone. His general conclusions were, that there is always a notable increase in speed ; that the gain is irregular according to circumstances, but usually greatest when sailing close-hauled. He suggested that the increase in speed might be supposed to be proportional to the apparent wind, and taken roughly, for the Jean Bart, at one quarter of a knot for each metre of velocity of the apparent wind. Professor Eankine dealt with this problem theoretically. He pointed out that the efficiency of the propeller was likely to be increased by the propulsive effect of the wind balancing a part of chap, xii.] PROPULSION BY SAILS. 53 l the resistance of the water to the motion of the vessel. But neglect- ing any such increase, he proposed the following approximate rule, which would be on the safe side. Suppose the respective speeds of the ship to be known under steam alone for the given development of power, and under sail alone for the known sail-spread and known force and direction of the wind ; then the cube of the speed under sail and steam will be nearly equal to the sum of the cubes of the speed under steam alone and under canvas alone. Lieutenant Paris gave one case for the Jean Bart which enables Eankine's rule to be roughly tested. On a certain course and with a certain spread of sail the ship could have made 5J to 6 knots under sail alone, while the engine could have driven her 5 - 8 knots in a calm. The actual speed with steam and sail was logged at 8 to 8£ knots. By Eankine's rule it would have been about 7£ knots. No doubt, in practice many circumstances influence the actual results obtained, besides those which any theory can embrace. This is particularly true of the state of the sea, and the course of the ship in relation to the waves. But that the use of sails as an auxiliary to steam-power on the whole conduces to economy, is placed beyond doubt by universal experience. The steadying effect of the sail in many cases affects the results obtained. Proportions of Yachts. — The proportions and forms of sailing yachts are necessarily influenced by the tonnage rule under which they are intended to compete. In most cases the proportions of length to beam have been between 4 to 1 and 6 to 1. Under the operation of "Thames Measurement," or similar rules (see p. 75), a severe penalty was put upon beam as compared with that on length, and no account was taken of depth. Consequently, up to 1886 there was a tendency to make British yachts relatively narrow and deep, giving them large weights of ballast. Subsequent changes in the rules for rating have tended to encourage the building of yachts of greater relative beam for racing purposes than were built under the old rules. For cruis- ing purposes the best authorities favour a proportion of length to beam varying from 4 to 1 up to 4f to 1. It does not appear that any of these British tonnage rules for yachts have failed to produce handy, seaworthy, and fast vessels. Some of them have attained very remarkable speeds in proportion to their lengths and sizes, cases being on record where they have reached 13 to 14 knots per hour, while the American yacht Sappho is said to have made 16 knots per hour for several consecutive hours when crossing the Atlantic. 53 2 NAVAL ARCHITECTURE. [chap. xm. CHAPTER XIII. STEAM PBOPULSION — MEASURES OF HOBSE-POWEK, AND PBOPULSIVE COEFFICIENTS. The problems incidental to steamship design are many and difficult. They admit of no general solution, because the conditions to be fulfilled vary greatly in different classes of ships. Speaking broadly, in any particular design it may be assumed that it is desired to attain a certain speed, with a specified load, and to associate with those conditions the power of traversing certain distances without taking more coal on board. There may be endless variations in the assignment of speed, load, and steaming distance. Frequently the circumstances of the intended service impose limitations on the draught of water, and sometimes these circumstances limit other dimensions. The materials and system of construction also influence the design. In the case of war-ships, the offensive and defensive powers exercise great influence on dimensions and form. Still, it is true generally that, whatever other conditions may have to be fulfilled, the designer of a steamship has to approximate to the engine-power and coal supply which must be provided, when determining the dimensions and form most suitable to the particular case. In much of this work the naval architect and marine engineer have a joint interest, although each has his independent responsi- bility. Upon the latter devolves the actual design and construction of the propelling apparatus. His skill is displayed in providing machinery and boilers which shall be compact, durable, strong, and efficient, economical in consumption of fuel, and as light as they can be made in proportion to the power developed. The requirements of the engineer also necessarily exercise considerable influence on the internal arrangements, especially in vessels of high speed. In the appropriation of suitable spaces for the machinery and boilers, the efficient ventilation of those spaces, the arrangements for carry- ing and working the coal, the construction of engine, boiler, and shaft-bearers, and many other details of the hull-structure, the engineer must be consulted, and his wishes met as far as possible. When the chap, xiii.] STEAM PROPULSION. 533 power necessary for the intended speed has been determined ap- proximately by the naval architect, and the engineer has made a sketch-design for the propelling machinery, the choice of the most suitable propeller for the new vessel is an important matter, in which both are interested, and which must be made by mutual agreement. Apart from such joint action, the best utilization of the power developed in the propulsion of the ship cannot be secured. The engineer supplies to the naval architect data regarding the pro- portion of weight to power in the propelling apparatus, and the probable rate of coal consumption. The naval architect has to embody these particulars as part of a design which shall fulfil specified conditions of speed, coal endurance, and carrying capacity, while provision is made for structural strength, stability, and sea- worthiness. In the preliminary stages the processes are necessarily ten- tative and subject to correction. The various features of the design are to a large extent inter-dependent. At the outset the dimensions, form, and displacement are undetermined. Yet upon them depend the power which the engines must develop to give the desired speed, the weight of the hull, and the weight of certain parts of the equipment. In the finished ship the sum of the weights of hull-structure, propelling apparatus, equipment, coals, and load must equal the displacement to the specified load-line. Apart from experience, a problem involving so many unknown yet related quantities could scarcely be solved. On the basis of experience, recorded data, and model experiments it is dealt with readily. Approximate dimensions and forms are first assumed. The weight of hull is then approximated to by methods explained in Chapter X., for the system of construc- tion which will be adopted, and the type of ship. An estimate for the probable engine-power is made, either on data obtained from the steam trials of previous ships, or from model experiments. The weight of engines and boilers is then ascertained for the horse- power, and the rate of coal consumption per hour calculated on the same basis, while the total weight of coal for the intended steaming distance at the desired speed is readily deduced. Adding together these first approximations to the weights of hull, equipment, machinery, and coal, and to the total adding the load stipulated to be carried, a grand total is reached which should equal the displacement pro- visionally assumed. If the sum-total is in excess or defect of the provisional displacement, corrections must be made on the dimensions originally assumed, with a view to obtaining a balance. For these corrected dimensions a fresh series of approximations is made to the weights of hull, equipment, machinery, and coal. A balance between the grand total of weights and the displacement corresponding to the form and dimensions is ultimately obtained. When no large 534 NAVAL ARCHITECTURE. [chap. xni. departure is made from past experience or precedent, this preliminary work is rapidly performed. Under other circumstances, the selection of the most suitable dimensions and form may involve the considera- tion of many alternatives. From the explanations given in previous pages it will be obvious that the naval architect has many other qualities to consider, in working out a new design, besides economical propulsion. He has to secure sufficient stability for the varying conditions of lading, good behaviour in a seaway, handiness, and ample structural strength. It may happen that the adoption of great length and fineness of form, while it enabled the specified speed to be obtained with a less expenditure of power, would involve an increased weight and cost of hull, more than counterbalancing savings on machinery and coal. Or the form which would be preferred for propulsion may not give sufficient stability for the variations in lading occurring on service. In short, the designer must consider the question in all its aspects, and endeavour to fulfil the conditions laid down for a new design in that manner which, on the whole, will give the best results, taking into account first cost and subsequent working. It is proposed in this and subsequent chapters to treat of steam- propulsion chiefly as it affects the work of the naval architect. Detailed descriptions of the remarkable progress which has been made in marine engineering during the latter half of the nineteenth century would be out of place. References must be made, however, to certain stages in that progress, because they have exercised such marked influence on steamship design. Even when thus restricted, the field of inquiry is very large, and deserves most careful study. It includes the consideration of all the circumstances which must be taken into account by the naval architect in designing a steamship, and cannot be dealt with adequately without recourse to mathematical investigations which cannot be introduced into this work. An en- deavour will be made, however, to indicate, in a form which may be generally understood, the principal results of such investigations, and to illustrate the principles by which the development of steam pro- pulsion has been guided. Measures of Hobse-Powee. Effective Morse-Power. — When a ship is towed at a uniform speed by some external force which does not interfere with the free flow of water past her hull, the strain on the tow-rope measures the resistance to her motion. Suppose this resistance to be R pounds, and the speed to be S feet per second. The product of the resistance into chap, xiii.] MEASURES OF HORSE-POWER. 535 the distance moved through in a second, measures the " mechanical work " done by the towing force. In symbols — Work done (per second) = E . S (units of work). A " horse-power " represents 550 units of work per second. Conse- quently — Horse-power (corresponding to work done) = — — This is termed the " effective horse-power," because it measures the " useful work " performed by the engines when the ship is propelled at the speed S. As an example, take the Greyhound, for which the towing experiments are described on p. 474. At the speed of 16 - 95 feet per second, the resistance was 10,770 lbs. The corresponding effective horse-power is given by the expression — E.H.P. = 1077 °^ 16 - 95 = 332H.P. 550 When a ship is propelled by her own machinery, she is very differently circumstanced from her condition when towed. For a given uniform speed, it must be true that the thrust or reaction of the propeller will equal the resistance of the ship ; only that resistance will be greater than the tow-rope strain for the same speed, because the action of the propeller modifies the stream-line system which surrounds the ship when towed. The propeller, besides driving the ship forward, sustains frictional and other resistances in its passage through the water, while in many cases it produces motions and consequent reactions of the water acted upon in directions not effective for propulsion. That is to say, there is a " waste " of work in the power delivered by the engines to the propeller, in consequence of these circumstances attending its action. Further, as between the power exerted by the engines and that delivered to the propeller, there is a sensible waste, because of the frictional and other resistances in the mechanism. Hence, in order to estimate efficiency of propulsion, it is necessary to supplement " effective horse-power " by " indicated horse-power," which measures the work done in the cylinders of the engine as the pistons move to and fro. Hereafter it will be shown how the separate efficiencies of engines (or mechanism) and propellers are estimated, and to what extent tow-rope resistances are augmented by the action of pro- pellers. Indicated Horse-Power. — This measure of the power exerted in the cylinders of an engine derives its name from the useful little instrument known as the "indicator." By its use diagrams are 536 NAVAL ARCHITECTURE. [chap. xm. drawn showing the variation of steam-pressure in the cylinders at different portions of the stroke of the pistons, and the mean pressure for the whole stroke is ascertained. Let p = this mean pressure in pounds per square inch. A = the total area of the pistons in square inches. I = the length of " stroke " of pistons. » = the number of revolutions per minute. Then— 2n .1 = speed of piston (feet per minute) p . A = total mean pressure on pistons (in pounds) p . A x 2nl = units of work done per minute. p. A x 2nl — qqaaa — = indicated horse-power. Indicated horse-power, therefore, depends upon (1) the mean steam pressure (p) ; (2) the " cylinder capacity " (A . Z) ; and (3) the number of revolutions per minute. Sometimes it is said to depend upon mean pressure, piston area, and piston speed ; which is only a slight variation of the other expression. This measure of power, of course, is not a complete representation of the efficiency of the propelling apparatus, nor does it take account of the efficiency of the boilers. It is, however, the method commonly employed in statements of the horse-power developed in ships moving at various speeds. For war-ships the tabulated powers of the engines are the average indicated horse-powers obtained, or specified to be obtained, on actual trials extending over a certain number of hours' continuous steaming, and carried out in accordance with certain fixed con- ditions. When " forced draught " is used, it is customary, in official returns for ships of the Eoyal Navy, to give the powers indicated under both " forced " and " natural " draught. In the Eoyal Navy, new ships fitted with ordinary boilers are tried by steaming for eight hours continuously under natural draught, and for four hours under " forced " draught. For ships fitted with the locomotive type of boiler, the periods of continuous steaming are 3 hours under forced draught, and 8 hours under natural draught. In all cases where forced draught is employed, the limits of air- pressure in the stoke-holds are defined. These trials are made with engines and boilers in perfect order, with good coal and well-trained stokers. It is recognized that the results obtained do not represent the engine-power which could be developed over long periods of continuous steaming at sea under ordinary conditions of service. For her Majesty's ships it is assumed that, under the latter con- ditions, the power which should be developed when steaming " with chap, xiii.] MEASURES OF HORSE-POWER. 537 all despatch " for long periods should be at least 60 per cent, of the power obtained with natural draught on the eight hours' trial. In very many cases this minimum is exceeded, and in some cases con- siderably exceeded, the actual development of power having ap- proximated to the specified natural-draught power over the whole period that the coal lasted.* The present practice in the French Navy is very similar to that above described. A French eheval vapeur is 32,549 foot-pounds per minute instead of 33,000 foot-pounds for the English horse-power; the proportion is as 9863 to 10,000. French practice tabulates both the maximum power indicated on a four hours' trial (essai a outrance), and the normal power indicated during a continuous trial of twenty- four hours. In ships not fitted with forced draught, the normal power appears to be about 70 per cent, of the maximum ; in ships fitted with forced draught, it falls as low as 40 per cent, of the maxi- mum. In other navies the conditions laid down for the trials made to determine the tabulated horse-powers differ in regard to duration of the trials, the extent of " forced " draught permitted, and other particulars. It is important, therefore, in making comparisons between the tabulated powers of war-ships in different navies to clearly ascertain under what conditions these powers have been indicated, and what proportion they bear to the powers likely to be realized over long periods of continuous steaming. Nominal Horse-Power. — Until 1872, in all official returns the engine-power of her Majesty's ships was given in " nominal " horse- power. The matter is now one of historical interest chiefly, but, as a similar practice still obtains in the mercantile marine, it may be useful to explain the rules formerly employed. A fictitious mean pressure of 7 lbs. per square inch was assumed. In screw-steamers the intended piston speed (feet per minute) was taken as the true speed. Then — Nominal horse-power = 7 x area of P istons x P iston s P eed 33000 In paddle-steamers — Assumed piston speed = 129-7 X (length of stroke) ^' 3S Nominal horse-power = 7 X area of pistons x assumed piston speed 33000 The actual piston speeds were often much in excess of the speeds * For details see a paper by the author in the Transactions of the Institution of Naval Architects for 1890. 53 8 NAVAL ARCHITECTURE. [chap. xui. assumed in the calculations, and the true mean pressures were much above the 7 lbs., but followed no constant law. Consequently there were very different proportions between the nominal and indicated horse-powers in different ships, and the former mode of measurement, being of no practical service, was abandoned. In the British mercantile marine there is no legal enactment for measuring engine-power corresponding to that for the measurement of tonnage described in Chapter H. Shipbuilders and marine engineers employ indicated horse-powers for their own purposes in designing steamships and their propelling machinery. The powers developed on trial are frequently stated in published descriptions of ships. In the official registers of ships, however, only " nominal " horse-powers appear. Formerly the rule established by the practice of Messrs. Boulton and Watt was generally employed ; it was very similar to the old Admiralty rule for paddle-steamers, the same effective pressure of 7 lbs. per square inch of piston area being assumed ; but the Assumed speed of piston = 128 ^/length of stroke. This rule was sometimes stated as follows : Let D 2 = sum of squares of diameters of cylinders (in inches) ; then — Nominal horse-power = -^ X D 2 X ^length of stroke. At present the rule most commonly employed takes the form — Nominal horse-power = Jq X D 2 . It is sometimes expressed by the equation — 1 nominal horse-power = 30 " circular inches " of piston area. This rule would correspond with that of Messrs. Boulton and Watt, if the piston speeds were assumed to be 200 feet per minute. Various proposals have been made with a view to improving the commercial method of measuring horse-power, but none of them has found general favour. In 1872, the council of the Institution of Naval Architects, having been consulted on the subject by the Board of Trade, replied as follows : " The term ' nominal horse- " power,' as at present ordinarily used for commercial purposes, con- " veys no definite meaning." ..." The majority of the committee " were of opinion that no formula depending upon the dimensions of " any parts of the engines, boilers, or furnaces could be relied upon " as giving a satisfactory measure of the power of an engine ; and " that even if the varieties of engines and boilers now in use could " be comprised under one general expression for the power, the pro- gress of invention would soon vitiate any such expression or "formula." The committee could not agree to any alternative chap, xiii.] MEASURES OF HORSE-POWER. 539 mode of measuring engine-power, but the plan which met with least objection was to take either the indicated power on a trial trip as the nominal power, or some submultiple, such as one-fowih of the indicated power. The latter method, at that date and for some years afterwards, was used in the French Navy, the nominal horse-power being about one-fourth of that indicated on the contractor's trial. As explained above, the French now use indicated horse-power, and have abolished the " nominal." The Council of the North-east Coast Institution of Engineers and Shipbuilders made a careful inquiry into this subject in 1888, adopting the basis of indicated horse-power, but endeavouring to formulate " normal " conditions under which all engines should be supposed to work when indicating the powers assigned to them. They proposed the following rule for "normal indicated horse- power " for surface condensing marine screw engines, working at any boiler pressure between 50 lbs. and 250 lbs. per square inch, under the specified conditions : — Normal indicated horse-power = (D 2 #S + 3H)»/P * 100 In this expression D = diameter of the low-pressure cylinder in inches, if there is only one such cylinder. D 2 = sum of squares of diameters of the low-pressure cylinders, if there be more than one. S = stroke of piston (in inches). P = working boiler pressure in pounds per square inch above the atmosphere. H = heating surface of the boilers in square feet. It was urged that this rule would be practically useful to both shipowners and engineers ; and that it took account of the efficiency of the boilers, as well as of those features in the engines — piston area, steam pressure, stroke, and piston speed — which govern the indicated horse-power. No general adoption of the rule has followed its publication* The rules issued by Lloyd's Eegister of Shipping contain a formula for the nominal power of triple expansion engines which may be quoted, although it is used only for special purposes. Taking the same symbols as above for stroke and heating surface, and calling D the diameter of the low-pressure cylinder in inches — Nominal horse-power = A ( -I ) * 2 V 100 15/ See vols. iv. and vi. of the Transactions of the Institution. 54° NAVAL ARCHITECTURE. [chap. xm. It has been pointed out that this rule and that last described can be brought into practical agreement by the following further assumptions. The working pressure P in the North-east Coast rule to be taken at 150 lbs. per square inch, the square root of the stroke to be substituted for the cube root, and the stroke assumed to be 72 inches. The result obtained by these changes to be divided by 5 for nominal horse-power. Propulsive Coefficients fok Steamships. Assuming that the "effective" and " indicated " horse-powers have been determined for an assigned speed in a particular ship, the ratio which the former power bears to the latter is usually termed the " propulsive coefficient," and often expressed in the form of a per- centage. For example, if the effective horse-power were 5000, and the indicated horse-power 10,000, the propulsive coefficient would be called 50. Comparatively few f ull-scale experiments have been made on ships or boats from which the propulsive coefficients could be determined. The most important were those made on H.M.S. Grey- hound, and described at p. 478. She was a single-screw ship built of wood, and the propulsive coefficient was about 42 for full speed. Mr. Isherwood made experiments on a single-screw steam launch, 54 feet in length.* His results give for the speed of 7 knots a propulsive coefficient of 67, which is an unusually high value. Mr. Yarrow experimented on a first class torpedo-boat 100 feet in length, and obtained a propulsive coefficient of 60 at a speed of 15 knots. By the comparison of model experiments with the results of steam trials, propulsive coefficients have been determined for many types of ships. Absolute exactitude cannot be attributed to estimates of effective horse-power based on model experiments. The correc- tion for frictional resistance when passing from the model to a full- sized ship is open to some doubt. It appears certain, however, that a fair approach to accuracy is obtained, and where full-scale experi- ments have been made this has been demonstrated. The case of the Greylwund has been discussed. As another example, it may be stated that the towing experiments made by Mr. Yarrow with a torpedo-boat agreed within 3 per cent, with the results of experiments with a model of the boat made in the Admiralty establishment. Assuming that estimates for effective horse-power deduced from model experiments may be trusted, the following are values of pro- * See Report of the Secretary of the tects for 1883. Full details of the United States Navy for 1874. For Mr. Greyhound experiments appear in the Yarrow's experiments see the Transac- same Transactions for 1874. tions of the Institution of Naval Archi- chap, xin.] PROPULSIVE COEFFICIENTS. 541 pulsive coefficients.* For single-screw ships with thick wood stern- posts and rudder-posts, about 40 ; with iron or steel stern-posts of less thickness, and fine forms of stern, from 50 to 55, rising in special cases to 60. For twin-screw ships of full form, fitted with horizontal engines and with propellers of moderate efficiency, from 40 to 45. For twin-screw ships of fine form, fitted with vertical engines, 50 to 55, and sometimes 60. For torpedo-boats and torpedo gunboats, with very quick-running engines, coefficients varying from 55 to 65 have been obtained. In these vessels the accurate measurement of the indicated ihorse-power is not an easy matter. At the present time, in dealing with estimates of indicated horse-power for ships of good form, on the basis of model experiments, the propulsive co- efficient 50 may fairly be taken. With fuller forms a lower value would be used, and in vessels of exceptional fineness and high speed a somewhat higher value. The designer has to exercise his judgment in selecting the coefficient appropriate to each type. In Admiralty practice there is no necessity to determine pro- pulsive coefficients for paddle-steamers. Experiments of this nature have been made, however, by the late Dr. Tideman and by one private firm, and have furnished valuable guidance in new designs subsequently undertaken with very high speeds. Efficiency of the Mechanism. — It may, at first sight, seem sur- prising that in a well-designed screw-steamer the indicated horse- power should be twice the effective horse-power. An examination into the causes of this waste work is therefore desirable. First, the efficiency of the mechanism must be noted, that efficiency being expressed by the ratio which the power delivered to the propeller or propellers bears to the indicated horse-power. Power has to be expended in overcoming frictional and other resistances in the moving parts of the propelling machinery and the shafting. A further deduction from the indicated horse-power is necessary to provide for driving the air-pumps, etc., worked off the main engines. In a few cases the efficiency of the mechanism has been determined by direct experiments. Most of these trials have been made on small vessels, and few trials have been conducted on marine engines of considerable power. Attempts have been made also to estimate frictional resistances from the analysis of results obtained on progressive steam trials. All these steps have added to available information, particularly in regard to the engines of screw-steamers. On the other hand, the efficiency of the * See papers by the late Mr. Froude K. E. Froude in the same Transactions in the Transactions of the Institution of for 1886. Naval Architects for 1876, and by Mr. 54 2 KAVAL ARCHITECTURE. [chap. xm. mechanism varies with the type of engine, the valves and valve- gear, the arrangements for working the pumps, and other circum- stances. Authorities differ, therefore, in their estimates for the percentage of the indicated horse-power delivered to the propellers in screw-steamers. For the experimental steam-launch above men- tioned, Mr. Isherwood placed it as high as 90 per cent., the work done on auxiliary appliances being very small. For a second-class torpedo-boat, Mr. Thornycroft made experiments showing only 77 per cent. Mr. Hall-Brown, after experimenting on triple-expansion engines of 900 H.P. and of 300 H.P. respectively, considered 85 per cent, a fair value. Mr. Blechynden, on the basis of similar ex- periments, arrived at the same result. For a well-adjusted modern marine engine in a screw-steamer, probably 80 to 85 per cent, of the indicated horse-power may be considered to be delivered to the pro- peller. The late Mr. Froude, by inference from data drawn princi- pally from "land-engines, fixed the percentage as rather under 70, but this was too low an estimate.* Frictional resistances account for most of this waste work. They may be arranged under two headings : (1) " Constant " or " dead- load " friction, approximately constant at all speeds, due to the dead weight of moving parts, tightness of piston-packings, friction of shaft bearings, etc. ; (2) friction due to the working load, varying with the thrust of the propeller and the speed of engines and ship. An interesting series of trials was made on H.M.S. Iris in 1878. The engines, which were of the horizontal compound type, driving twin-screws, were run at high speeds, disconnected from the screw shafting. At 90 revolutions, 400 H.P. was absorbed in overcoming the friction of the engines alone, and 170 H.P. in overcoming the friction of the screw shafting. The sum, 570 H.P., representing the power required to overcome the dead-load friction, was about 8 per cent, of the total indicated horse-power when the engines and screws were running at the same number of revolutions. Other experiments have given different values for the dead-load friction, ranging from 5 to 9 per cent, of the full indicated horse-power. For large ships 8 per cent, appeals a fair value, with bearings and packings well adjusted. For boats a smaller percentage is probable ; Mr. Isher- wood gave about 3 per cent, as the dead-load friction for the launch experimented with. The expression of the dead-load friction as a percentage of the maximum indicated horse-power, while generally adopted, is obviously not precise or complete. * See his paper in the Transactions and Mr. Blechynden in the Transactions of the Institution of Naval Architects for of the North-East Coast Institution of 1876; also papers by Mr. Hall-Brown Engineers and Shipbuilders, 1889-91. chap, xiii.] PROPULSIVE COEFFICIENTS. 543 The late Mr. Froude suggested a method for determining constant friction from the results of progressive steam trials carried down to very low speeds. This method has been extensively employed, but has been found to give widely varying results, ranging from 5 to 15 per cent, of the gross indicated horse-power at full speed. It would appear, therefore, that the method, while of value, should not be implicitly trusted under the conditions of practice. Mr. Froude himself recognized this, and, to secure trustworthy results, designed for the Admiralty a special form of dynamometer, which was intended to be put in the place ordinarily occupied by the screw on the end of the shaft, in order to measure the power delivered for various rates of revolution. By means of this instrument, it was intended to determine both the dead-load friction and the working-load friction. The instrument was partly constructed at the date of Mr. Froude's death. It was subsequently completed, and a few trials made with it under the direction of Mr. R. E. Froude. Up to the present time, however, it has not been possible to carry the experiments very far, owing to more pressing work having to be done, and to difficulties in finding vessels both suitable and available for the trials.* Apart from actual measurements of the power delivered to the propellers, estimates, however carefully made, must be open to some doubt. Since the dead-load friction represents a constant mean pressure on each square inch of the piston area, its relative importance in- creases as the speed of a steamer decreases. In war-ships, which usually cruise at speeds much below their full speeds, this is specially important. In Mr. Isherwood's experiments, while the dead-load friction represented less than 3 per cent, of the total indicated horse- power at 8 - 5 knots, it exceeded 9 per cent, of the indicated horse- power at 5 knots. In the trials on the Iris, it was shown that at 18 knots' speed the dead-load friction absorbed 8 per cent, of the indi- cated horse-power (7500 H.P.). At 9 knots, only about 800 indicated horse-power was required to drive the ship, and about 30 per cent, of that power was absorbed by dead-load friction. At still lower speeds, the relative importance of this friction increased. Various suggestions have been made in order to diminish these frictional losses at low cruising speeds. Most of them involve the subdivision of the machinery, or plans for throwing certain portions of the engines out of work when ships are proceeding at low speeds. This matter is further discussed in Chapter XVI. Less information is available respecting friction due to the work- ing load than has been obtained respecting dead-load friction. For * A description of the dynamometer, found in the Proceedings of the Institu- and the principles of its design, will he tion of Mechanical Engineers for 1877. 544 NAVAL ARCHITECTURE. [chap. xiii. the experimental steam-launch, Mr. Isherwood fixed about 7 per cent, of the maximum indicated horse-power, or 7 - 5 per cent, of that horse- power less the power for constant friction, as the friction of the load. This value has been adopted by other engineers for engines of large power, but, so far as can be seen, without experimental verification. The late Mr. Froude, as a rough approximation, assumed the friction of the load at full power to be about equal to the dead-load friction, which would represent, on the basis of the statement made above, about 8 per cent of the indicated horse-power at full speed. This agrees fairly well with the assumption that the total waste work between the cylinders and the propeller in a well-designed and carefully adjusted marine engine aggregates about 15 to 20 per cent, of the indicated horse-power. The subject obviously requires fuller experimental investigation, and dynamometric trials would settle many doubtful points. Common experience shows that unless care is taken in the adjustment of the moving parts of the machinery and shafting, as well as in the due proportioning of bearing surfaces to the loads and speeds, the waste : work on friction may very greatly exceed the values given above. These losses are preventable, and need not be further dwelt upon. Waste Work and Augmentation of Resistance diie to Action of Propellers. — Accepting the waste work on the mechanism as 15 to 20 per cent, of the indicated horse-power at full speed, there remains to be accounted for about 30 to 35 per cent., if the standard value of the propulsive coefficient is taken at 50. This represents the waste work due to the action of the propeller. In Chapter XVI, the efficiency of screw propellers is discussed. Here it will suffice to point out the principal causes of loss. Obviously when a screw is rotating in water and delivering thrust, its blades must experience frictional and edgewise resistances of a more or less serious nature. In the Greyhound experiments it was found that when the two- bladed screw revolved freely as the ship moved ahead at 10 knots, the additional resistance amounted to 11 per cent, of the net resist- ance without the screw. In Mr. Isherwood's experiments on a steam-launch, the corresponding increase in resistance produced by the free revolution of different screws varied from 8£ to 21 per cent, of the net resistance, the higher values occurring with experimental screws having the larger number of blades and greater blade area. For the despatch vessel Iris it was estimated, on the best data available as to coefficients of friction, that at full speed the waste work on the screws might vary as widely as from 6 to 20 per cent, of the work represented by indicated horse-power at the full speed, according to the pattern of screw used and the number of blades. chap, xiii.] PROPULSIVE COEFFICIENTS. 545 The action of propellers also produces augmentation of the resistance corresponding to the condition of being towed at a given speed. For screws the augmentation may be considerable. Its value depends chiefly upon the form of the stern of a ship, her speed, and the dimensions, number, and position of the screws. Mr. Isher- wood, on his steam-launch with a single screw, found the augmenta- tion to be about 11 per cent, at 1\ knots. Mr. Yarrow found it to be 16£ per cent, in his torpedo-boat. For ships with thick stern- posts and full forms, with single screws in the usual position, the late Mr. Froude considered 40 per cent, a fair value for augmentation, the rudder-posts representing about 10 per cent. The late Dr. Tideman made numerous experiments of a similar character on models, and found considerable variations in the augmentation with ships of different forms. Subsequent experiments have shown that in single-screw ships the augmentation varied from 20 to 40 per cent., the lower value corresponding to the finer forms. For twin- screw ships the augmentation varied from 25 per cent, in full ships to 6 per cent, in very fine ships. In some torpedo vessels of very high speed, with twin-screws placed well clear of the hull, the augmenta- tion has been only 2 to 3 per cent. The explanations given on p. 448 as to the movement of water in the wake of ships when towed, will make it clear why there are such considerable differences in the augmentation occurring with twin and single screws. They will also assist to an understanding of the experimental results obtained by the late Mr. Froude. He found that when a single screw was placed about 30 per cent, of the extreme breadth of a ship clear of the stern, the augmentation was only one-fifth as great as when the screw occupied its ordinary position. It will be shown hereafter that such a change of position, while it reduces augmentation, also lessens the utilization by the propeller of the energy in the frictional wake. In fact, the probability is that the gain in one direction is practically neutralized by loss in the other. Experiments show that the efficiency of a well-designed screw working under favourable conditions does not exceed 70 per cent. Frequently a lower efficiency is obtained. If 80 per cent, be taken as a fair measure of the efficiency of the mechanism, ihen it will be seen that with a fairly good efficiency of the screw (allowing for both augmentation of resistance and utilization of wake), a propulsive coefficient of 50 is not unreasonable. 2 N 54 6 NAVAL ARCHITECTURE. [chap. xiv. CHAPTEE XIV. PBOGKESS IN: MARINE ENGINEEKING — ITS INFLUENCE UPON STEAM- SHIP DESIGN. In order to understand the influence which improvements in marine engineering have had upon steamship construction, it is necessary to obtain a general idea of the lines upon which that progress has proceeded. The changes introduced into marine engines and boilers in recent years are most remarkable. Their effect upon weight and coal consumption requires to be noticed, since this is a matter of importance to shipowners and shipbuilders. Without entering into technical details, which find their proper place in engineering treatises, it is proposed, therefore, to sketch briefly the principal advances that hare been made, and to indicate the various types of propelling apparatus now placed at the service of the naval architect by the marine engineer.* Increase in steam pressure has been the chief aid to progress in marine engineering. The extent of that increase will be gathered from the following statement of practice in the Koyal Navy. Up to 1850 the load on safety-valves, as a rule, was not more than 10 lbs. per square inch. Ten years later the corresponding load was 20 lbs. In 1865 it had risen to 30 lbs. About 1870 the load had been increased to 60 lbs., in association with engines on the " compound " principle. By successive steps, loads of 90» lift, and 130 lbs. per square inch were adopted during the next fifteen years. In 1885 triple expansion engines were introduced into her Majesty's ships, and the loads on the safety-valves hav& * Readers desirous of further study- for 1872, 1881, and 1891 ; the Transac- ing this subject may refer with advan- tions of the Institution of Naval Archi- tage to the following publications : "The tects for 1888, 1889, and 1892 ; and the Marine Steam-engine," by the late Mr. Transactions of the North-East Coast Sennett ; " Manual of Marine Engineer- Institution of Shipbuilders and Engineers, ing," by Mr. Seaton ; the Proceedings of 1887-92. the Institution of Mechanical Engineers chap, xiv.] PROGRESS IN' MARINE ENGINEERING. 54Z since gradually risen to 150 or 160 lbs. per square inch with boilers of ordinary type. The mercantile marine has usually been in advance of the war? fleet in the use of higher steam-pressures. A careful analysis has given the following figures. In 1872 the average boiler pressures (load on safety-valves) of a number of typical merchant steamers Was 524 lbs. per square inch ; in 1881 the corresponding average was 774 lbs., and in 1891, 158*5 lbs.* Pressures of 200 lbs. per square inch have been employed in some cases with cylindrical boilers of ordinary type and " quadruple " expansion engines. In a few instances, with special forms of "tubulous" or "water-tube'' boilers, pressures of 210 to 400 lbs. per square inch have been adopted. The last-mentioned pressure must be considered experi- mental under present conditions. This considerable increase in steam pressure has resulted in great economies in coal consumption and has been in other respects advantageous. It would be out of place here to enter into a discus- sion of the laws of thermo-dynamics, which prove these results to be necessary consequences of increase in steam pressure and the accom- panying increased rate of expansion of steam in the cylinders. The essential facts in the generation and use of steam may be briefly enumerated, however, in order that the principal causes of economy may be understood. The efficient combustion of coal in a boiler demands careful stoking and a proper supply of air. Subject to the fulfilment of these conditions, the combustion of each pound of coal produces a certain "total heat of combustion," dependent upon the quality and chemical composition of the coal. This total heat of combustion is expressed in "thermal units" of definite value, which (according to Joule's law) are convertible into units of " mechanical work." When coal is burnt on the fire-grates of a boiler, the intention is, of course; to evaporate water contained in the boiler and to convert it into steam of a given pressure. Necessarily there are certain losses from the total heat of combustion of the number of pounds of coal burnt, say, in each hour. These losses chiefly result from radiation, conduc- tion, the waste heat of gases passing up the funnel, and imperfect combustion due to inefficient stoking or air-supply. All these sources of loss have been carefully investigated, and much has been done to minimize their amount. That portion of the total heat of combus- tion which is applied to the evaporation of the water in the boilers produces steam of certain pressures and "temperatures in certain * • See Mr. Blechynden's paper in the Proceedings of the Institution of Mechanical Engineers for 1891 '. -.: 54 8 NAVAL ARCHITECTURE. [chap. xiv. quantities per hour. Knowing the pressure of the steam, " the total heat of evaporation " of each pound of steam can be expressed in thermal units. It has thus been shown that the total heat of evaporation per pound of steam increases but slowly with increase in pressure. For a pressure of 30 lbs. per square inch on the boiler (a load of about 15 lbs. per square inch on the safety-valves), the total heat of evaporation of a pound of steam is 1157 thermal Units ; whereas for a pressure of about 160 lbs. per square inch it is only 1190 units. Consequently, if all other things remained constant, the number of pounds of steam evaporated by the combustion of a pound of coal would be practically the same for all pressures that have been used in marine boilers, say from 20 up to 200 lbs. per square inch load on the safety-valves. In practice, other things have not remained constant. As pressures have increased, changes have necessarily been made in the types of boilers and furnaces. These changes have affected the efficiencies of combustion and evaporation, and so have influenced the rate of evaporation per pound of coal burnt on the grates. Still the theoretical result, above stated, even when modified by the conditions of practice, is of great importance in its bearing on the use of higher steam-pressures. A certain weight of steam of high pressure can be produced with only a small increase in the weight of coal required to produce an equal weight of steam at lower pressure. The higher pressure is accompanied by higher temperature, and has the capacity for performing more mechanical work during expansion to a given minimum pressure and temperature. This higher rate of expansion in the cylinders is the great source of economy with increased steam pressures. The steps performed in using the steam are as follow : First, a certain volume of steam at the full initial pressure is admitted into the high-pressure cylinder, the piston of which performs a certain portion of the stroke under this full pressure. Next, the volume of steam so admitted is allowed to expand until it fills the high-pressure cylinder, after which it passes into other cylinders and completes its expansion. In a com- pound engine there are two stages of expansion, although in engines of large power there are frequently two low-pressure cylinders. In a triple expansion engine there are three stages. For a given engine the weight of steam used per stroke can be cal- culated from the volume of the cylinder or cylinders, when the terminal pressure at the end of the stroke has been ascertained by the indicator diagram. The communication with the condenser is opened when the expansion is completed, and the steam passes out of the cylinder into the condenser. Upon the efficiency of the condenser, measured by its so-called " vacuum," depends the " back pressure " in the cylinders during the return stroke. This back chap, xiv.] PROGRESS IN MARINE ENGINEERING. 549 pressure has to be deducted from the mean steam pressure in order to obtain the effective mean pressure used in calculating the indicated horse-power by the formula given on p. 536. The mechanical work which can be done by the expansion of steam may be expressed in terms of the range of temperature between the initial and terminal conditions, due allowance being made for back pressure. Con- sequently, for each pound of steam generated in the boilers and used in the cylinders, an increase in the initial pressure and temperature, if associated with a practically constant terminal pressure — that is to say, with a greater ratio of expansion — enables more mechanical work to be performed. It has been shown that in the boiler practically the same weight of coal has to be burnt to evaporate this pound of steam at high or low pressure. Hence it follows that with higher initial pressure and greater ratio of expansion, back pressure being constant, a higher mean effective pressure on the pistons is obtained during each stroke, and the indicated horse-power is increased for a given expenditure of coal.* Efficiency in the condensers and reduction of back pressure will be seen to have an important influence upon the effective mean pressure and the work done. The introduction of surface condensa- tion has been of great importance. The sea-water used to condense the steam is then kept separate from the steam ; comparatively pure water is obtained by condensation, and is available for further use in the boilers. Experience proves that the use of pure fresh water is essential to continued efficiency in boilers generating steam of high pressures. Unavoidable losses of steam occur in service. To make up for these losses evaporators and distillers are now universally adopted, and in many cases reserves of fresh water for use in boilers are carried in special tanks or in compartments of the double bottom. Further economy is realized by means of " feed-heaters," utilizing what would otherwise be " waste heat " in order to raise the tempera- ture of the feed-water supplied to the boilers. By " superheating " the steam, jacketing cylinders to prevent liquefaction, and many other devices of which no account can be given here, engineers are constantly endeavouring to reduce the losses incidental to the use of steam, and to lessen the expenditure of coal. * In the " Marine Steam-Engine " the pressure of 40 lbs. per square inch and late Mr. Sennett has dealt with this sub- ratio of expansion 3*6, let the mechanical ject at length in a popular manner, work done during expansion be called From his illustrations the following 100. Then for an initial pressure of figures may be taken. Steam is sup- 100 lbs. and ratio of expansion 8-4 the posed to expand in a single cylinder corresponding work would be 186, and with a terminal pressure of 10 lbs. per for 200 lbs. initial pressure and ratio of square inch (absolute) and a back pres- expansion 15 - 5 the corresponding work sure of 3 lbs. (absolute). For an initial would be 258. 55° NAVAL ARCHITECTURE. [chap. xiv. With increase in steam pressures successive stages of expansion nave been introduced. TJp to 30 lbs. per square inch, all the expansion was performed in the cylinders to which admission took place. These are termed " simple " or " single " expansion engines. Two stages of expansion were adopted with 60 lbs. per square inch, the engines being on the- " compound " principle. With higher pressures " triple " expansion is employed. " Quadruple," expansion has now many advocates, but with pressures of 180 to 200 lbs. per square inch triple expansion has so far maintained itself in general iavour. In all these plans the fundamental idea is to restrict within moderate limits the range of temperature in each stage of expansion, and thus to reduce the losses inevitable when there is a great range of temperature in a single cylinder, which is alternately open to supply and exhaust at either end. There are many different arrangements of the cylinders and cranks, even with a given system of expansion. Compound engines of moderate power commonly have only two cranks and two cylinders ; whereas with engines of large power, there are often two low-pressure cylinders and three cranks. The latter plan has given excellent results, and has been adopted also, so far as the number of cranks and cylinders is concerned, for many triple expan- sion engines. Some triple expansion engines have only two cranks, two of the cylinders being placed in line, " tandem " fashion. Others have four cylinders — two low-pressure — and four cranks. Another plan has five cylinders on three cranks, two pairs of cylinders being arranged tandem fashion. The last-mentioned plan has been adopted in the Campania and Lucania of the Cunard Line, for two sets of engines developing 30,000 HJP. Quadruple expansion engines demand the use of at least four cylinders, but the numbers of cylinders and of cranks are varied by different designers. These arrangements, while they are primarily the concern of the marine engineer, have a great interest for the naval architect and shipowner, because they affect the space occupied by the machinery, and influence the possible vibration of the ship's structure. Increased rate of revolution and piston speed is another striking feature in engineering progress, tending to economy in the weight of machinery in proportion to the power developed, as explained on p. 536. The formula there given shows that indicated horse-power depends upon number of revolutions, area of pistons, and length of stroke. Increase in-the number of revolutions, therefore, enables a given horse-power to be produced from cylinders of less capacity ; and this reduced capacity may be realized either by smaller area of pistons or shorter stroke. Higher speed of piston and greater rate of revolution have been very marked in recent practice. In the chap.-xiv.] PROGRESS IN MARINE ENGINEERING. 55 J Koyal Navy up to 1860, about 400 feet per minute was a fair piston speed. This was gradually increased to 550 or 650 feet. Since 1880 piston speeds of 800 to 950 feet per minute have been attained when developing: maximum powers on steam trials. In ordinary service lower speeds, of course, would be obtained. Under the conditions of ordinary service in the mercantile marine, revolutions and piston speeds have been very sensibly increased in recent years. Mr. Bleehynden states, as the result of the analysis of a large number of. representative screw-steamers, that between 1872 and 1891 the average number of revolutions per minute increased from 56 to 64, and the average piston speeds from 376 to 529 feet per minute. In swift passenger-steamers the length of stroke is greater than 'in war-ships, and the number of revolutions is not so high ; but the piston speeds are fully as great as those above mentioned for war- ships. Battle-ships and large cruisers in the Boyal Navy have engines of about 4 to \\ feet stroke, with about 100 to 105 revo- lutions at maximum power on trial, and about. 80 revolutions for full speed when continuously steaming at sea. Passenger-steamers of recent design have strokes of 5 to 6 feet, and revolutions at sea of 70 to 85 per minute. For cargo-steamers strokes of 3£ to 4 \ feet are used, with revolutions ranging from 65 to 75 per minute. Proposals have been made by eminent engineers to introduce quicker-, running engines in cargo-steamers, and it is possible some change may be made.* There is, however, a close connection between the rate of revolution of the engines and the efficiency of screw pro- pellers, and this will always influence engine design in ships of ! low speed with large carrying capacity. At the present time (1893) piston speeds of about 1000 feet per minute have been regarded as- a maximum for large marine engines. ; In the earlier period of screw-propulsion, when , slow-running engines were in use, gearing was employed in order to increase the. speed of revolution of the screws. Now that quick-running engines have been introduced, and their capabilities demonstrated in torpedo craft and cruisers, proposals have been made to use gearing in order to reduce the revolutions of the propellers below the revolutions of the engines. It is suggested that sensible savings might thus be effected in the weight of the engines developing a certain horse- power, while the revolutions of the screws might be adjusted so as to secure maximum efficiency. The suggestion clearly is not im- practicable, but so far no use appears to have been made of it, and there are unavoidable disadvantages associated with gearing. * See papers by Mr. Boyd and Mr. . of the North-East Coast Institution of Hall-Brown in vol. 6 of the Transactions Engineers and Shipbuilders. 55 2 NAVAL ARCHITECTURE. [chap. xiv. Two items, as explained above, are involved in piston speed, viz. rate of revolution and stroke. Between the cases of a torpedo- boat engine making 350 revolutions per minute with a stroke of 18 inches, that of a cruiser making 140 revolutions per minute with a stroke of 42 inches, and that of a Trans- Atlantic steamer making 80 to 85 revolutions per minute with 66 inches stroke, there are very obvious differences which would not be represented by mere statements of the piston speeds, although they would have to be recognized by the designers of the engines, and might have an important bearing upon the vibration of the ship's structure. High piston speeds demand excellence of materials and workman- ship, ample bearing surfaces, and a proper margin of strength. The extensive use of steel instead of iron, both in forgings and castings, has been of great value to engineers in carrying out improvements in the moving parts and framing. Savings in weight have been effected without diminution in strength, but often at increased cost, by means of hollow shafting, special forms of engine-framing, and close attention to the design of details. The extended use of twin-screws in ships of large engine power has enabled the sizes of cylinders and weights of moving parts to be kept down. Progress in steel manufacture also has greatly aided the marine engineer, as well as the shipbuilder, both in the direction of substituting a stronger material for iron, and in giving to the user his material in sectional forms better adapted to the association of strength with lightness. Types of Marine Boilers. — New types of boilers have been devised for the purpose of generating steam of higher pressures. In this direction great activity is still being displayed. At first, with steam pressures below 10 lbs. per square inch, the boilers used had internal flues. Tubular boilers were next introduced, with flat surfaces and approximately box-shaped; hence they are commonly described as the " box-tubular " type. Their distinctive feature was the employment of groups of small tubes, through which the products of combustion passed on their way from the furnaces to the uptakes. These tubes were surrounded by the water-space, and were ordinarily placed above the tops of the furnaces, so that they formed an important part of the heating surface. This type of boiler remained in general use in the Eoyal Navy for fully twenty years, and proved satisfactory for steam pressures of about 30 lbs. per square inch. They depended entirely for strength against internal pressure on the stays fitted between the flat surfaces. When steam pressures rose to 60 lbs. per square inch, the box form had to be abandoned in favour of cylindrical boilers (usually circular, but sometimes oval in cross-section) fitted with circular furnaces. The arrangements of chap, xiv.] PROGRESS IN MARINE ENGINEERING. 553 tubes remained much as in the earlier types. The cylindrical type (sometimes described as the "tank" boiler) continues in use, although steam pressures of 180 to 200 lbs. are now employed. In the mercantile marine they are almost universally fitted, and in war-ships they are employed except in special classes. For con- tinuous service they have proved very efficient. On the other hand, they carry comparatively large weights of water, and are not adapted for the quick raising of steam. The construction of cylindrical boilers of very large size, capable of working under high steam pressures, has been made possible, in great measure, by the remarkable extensions of steel-manufacture in recent years. Steel plates of very large dimensions and suitable thickness can now be obtained. That material has also facilitated the production of improved forms of furnaces, front plates, and combustion chambers. With steel the several parts of boilers can be flanged or bent into forms well adapted for combination, and for resisting pressure, to an extent impossible with iron. Moreover, in boiler-construction machine work has been substituted for manual labour in many directions, such as flanging, bending, drilling, riveting, and caulking. Apart from these mechanical devices, the progress realized in the use of high steam pressures with this type of boiler could not have been made. The " locomotive " type of boiler has been used extensively in vessels of the torpedo-flotilla in recent years, and in most cases has been associated with high steam pressures, and very quick running engines. A few larger ships of war have been fitted with groups of locomotive boilers, when it was desired to economize weight as much as possible. Compared with cylindrical boilers, the locomotive type is very light for the power developed. Single locomotive boilers fitted in torpedo-boats have given 45 to 50 H.P. (indicated) per ton of boiler and water in boiler, on trials of three or four hours' duration under forced draught. Groups of locomotive boilers have given from 30 to 35 H.P. on similar trials, with moderate forced draught. Higher results are claimed by some foreign engineers for groups of locomotive boilers. Groups of cylindrical boilers worked for 3 or 4 hours, under the highest forced draught considered suitable for the type, have given 20 to 25 H.P. per ton of boiler and water in boilers. It is within the truth to say that, apart from the use of the loco- motive boiler, before water-tube boilers were introduced, the small swift classes of torpedo-boats, and torpedo-gunboats could not have been produced. Difficulties have arisen in some cases where groups of locomotive boilers have been used. The torpedo-ram Polyphemus of the Koyal Navy was originally fitted with locomotive boilers, which were 554 NAVAL ARCHITECTURE. [chap. xiv. removed after many trials, cylindrical boilers being substituted. Less serious, but still considerable, difficulties nave been met with in vessels of the torpedo-gunboat class both in this country and abroad, and a more moderate indicated horse-power than was first anticipated has had to be accepted. The qualities which ensure to locomotive boilers fitted in ships .great evaporative power appear to make their management more difficult than that of cylindrical boilers, when groups of boilers have to be worked. The figures above stated indicate that the results obtained with a single boiler are very sensibly better than the results obtained with groups, and experience shows this to be true generally. Locomotive boilers have been tried in seagoing ships of the mercantile marine, and in a few foreign cruisers designed for general sea-service. Under these conditions the type has not proved suc- cessful. The propriety of fitting a combination of cylindrical and locomotive boilers was also considered many years ago in the Admiralty, but the difficulties with the Polyphemiis' boilers caused the plan to be dropped. In that instance, the desire was to economize as much as possible the weight of boilers which would ordinarily be held in reserve. War-ships at cruising speeds usually develop only 10 to 15 per cent, of their maximum power. This reserve is only drawn upon on the occasions when full speed is required. The Italian battle-ship Lepanto is actually fitted on this plan, and the results are said to be satisfactory.* In recent practice " water-tube " boilers have become formidable rivals of the locomotive type, even in the small swift vessels, where the latter have been almost exclusively used for ten years past. The distinctive feature in water-tube boilers is the circulation of the water and steam within tubes, which are acted upon externally by the products of combustion. In these boilers the weight of water is relatively small, the construction is admirably adapted for high steam pressures, steam can be very quickly raised and kept under command, and there is a considerable economy in weight relatively to power developed. Some boilers of the type are suitable for the use of forced draught; others are not. Many varieties have been tried for land service, with considerable success. Experimental water-tube boilers were also tried many years ago in mercantile steamers, with unsatisfactory results. In recent years there has been a renewal of the experiment under new conditions, including the use of fresh water in the boilers. The results have been satisfactory on the whole, and there is reason to anticipate an extended use of water- * See a paper by Colonel Soliani in the Transactions of the Institution of Naval Architects for 1889. chap', xiv."] PROGRESS IN MARINE ENGINEERING. 555 tube boilers.* In France the type is, at present, being employed for all classes of war-ships in construction, and many mef chant ships are similarly fitted. Considerable experience has been obtained in this country with boilers of the type designed by the principal 'builders of torpedo-boats. For some years Messrs. Thornycroft have almost exclusively used water-tube boilers, in preference to locomotive. It is difficult to obtain exact information respecting the relative weights of locomotive and water-tube boilers. Mr. Thornycroft has claimed, for a single water-tube boiler with moderate forced draught; a development of 68 indicated horse-power per ton of boilers, water, and boiler-room fittings. He estimated this as a gain of about 40 per cent, for the water-tube type. Advocates of the locomotive boiler do hot admit such a great superiority. Groups of water-tube boilers do not appear to realize such a high performance as is claimed for single boilers. A valuable series- of trials with the Thornycroft type were conducted in the Danish cruiser Geiser during 1892. From the published official report, it appears that with eight boilers, worked under an air pressure of less than 1 inch 6f water, about 30 H.P. were obtained per ton of boilers, water, etc. With 2 inches of air pressure it was estimated that about 40 to '50 per Cent, more power would have been realized, say 45 H.P. per ton as a maximum. This is only two-thirds as great power as was claimed for a single boiler. The total indicated horse-power in the ■Geiser was 3157 H.P. for a total boiler-room weight of 108 tons. Comparing this with practically the same weight in a torpedo- gunboat of the Boyal Navy fitted with four locomotive boilers, and developing about 2600 H.P. for 1 inch of air pressure, the water- tube boilers have an advantage of about 20 per cent. Probably about the same relative superiority would be maintained with 2 inches of air pressure. Another series of trials with boilers of the Thornycroft type was made in 1893 on board the torpedo-gunboat Speedy of the Royal Navy. Under an air pressure in the stoke-holds of about six- tenths of an inch of water, about 28 I.H.P. were obtained per ton of boiler-room weights during a trial of eight hours. With an air pressure of 1*7 inch of water, about 43 I.H.P. per ton were obtained during a trial of three hours. As compared with a 'group 1 of locomo- *. For particulars of the past history Engineers for 1889-90 ; Journal of the and present position of this type, refer- Royal United Service Institution for ence may be made to the following publi- January, 1891, and February, 1893. An cations : Transactions of the Institution excellent report on this type of boiler of Naval Architects for 1876 and 1889 ; as exemplified at the Paris Exhibition of Proceedings of the Institution of Civil 1889 was prepared by M. de Maupeou. 556 NAVAL ARCHITECTURE. [chap. xiv. tive boilers fitted in a sister ship, those results showed a gain of over 30 per cent, for the water-tube boilers. Definite information in regard to the capabilities of water-tube boilers will be largely increased at an early date. In the French Navy several types are under trial, some of them in large ships where it is proposed to develop from 14,000 to 18,000 H.P. In the Eoyal Xavy, various types of water-tube boilers are being fitted in vessels building for the torpedo flotilla; and the cruisers of the Poioerful class are to have water-tube boilers developing about 25,000 H.P. Several other systems of water-tube boilers are to be tried in vessels now building for the torpedo flotilla. The results will probably have a marked influence on future practice. As applied to merchant ships for general sea-service, recent ex- perience with water-tube boilers is limited, but not unsatisfactory on the whole. About 20 to 25 H.P. per ton of boiler-room weights is said to have been obtained over long periods with natural draught. This performance, if correctly reported, compares well with that mentioned above for cylindrical boilers under the highest forced draught thought suitable, which could be continued only for a few hours. Cylindrical boilers with triple-expansion engines, working under natural draught, develop 16 to 18 H.P. per ton of boilers and water in boilers, which is about 25 per cent, less than is claimed for the water-tube boilers under the same conditions of draught. This claim is not admitted absolutely by advocates of the cylindrical type, who consider that, when both space and weight are taken into account, that type has still much in its favour for marine purposes and long- distance steaming. The Danish Admiralty has constructed a sister ship to the Geiser, with six cylindrical boilers, intended to give the same indicated horse-power with natural draught as the water-tube boilers give with about 1 inch of air pressure. This is hardly a fair comparison, since the cylindrical boilers could be forced to a moderate extent without difficulty. The relative boiler-room weights are said to be 168 tons and 108 tons. Subsequent experience with these two vessels should give much valuable information. Besides their relative lightness, water-tube boilers have some incidental advantages over the other types. They can be put together on board ship, or repaired without removal. Much smaller openings are needed in the decks for getting the boilers into or out of place. The operations of boiler-making are less onerous than with the other types, and lighter plant suffices. But their greatest advantage, especially in war-ships, will be found in their capacity for raising steam quickly. The most important question remaining to chap, xiv.] PROGRESS IN MARINE ENGINEERING. 557 be determined by experience, and which experience alone can resolve,, is the comparative durability of water-tube boilers. Cylindrical boilers, properly treated, remain unaltered in efficiency for long periods. Boilers of the type have continuously worked for twenty years at full pressure. In the earlier trials with water-tube boilers made many years ago two principal difficulties arose : defective circulation and rapid pitting or corrosion of the tubes. The first difficulty has been overcome in later types. Pitting and corrosion of tubes have not been as thoroughly dealt with, although it is probable these risks have been much diminished. The use of fresh water only, and other devices for preventing deposits on the inner surfaces of the tubes ; arrangements for keeping clean the outer surfaces, and pre- venting overheating in certain parts of boilers ; improvements in the manufacture of tubes, and modes of protecting them by zincing or other coatings ; — all tend to give greater durability. The failure of a tube, however, practically puts the whole boiler temporarily out of use until it can be reached and plugged. In the design of water- tube boilers, therefore, it is recognized that ease of access for ex- amination and repairs is an important feature. Further, it is pre- ferred to subdivide the total steam-generating power more extensively, and to have a larger number of water-tube boilers than would be adopted if cylindrical boilers were fitted. In this way the temporary loss of a single boiler is less felt if repairs are necessary ; and in war-ships at cruising speeds only a limited number of the boilers need be at work. Methods of accelerating Evaporation in Boilers. The evaporative power of boilers has been shown to depend greatly upon the quantity of coal burnt per hour, and upon the supply of air being appropriately adjusted so as to secure efficient combustion of the coal. Ordinarily, in steamships the funnels are depended upon for creating a " draught " of air into the furnaces, and the supply of fresh air is obtained by means of ventilators, or " downcast " shafts, leading from the upper decks to the stoke- holds. At a very early period in steam navigation cases occurred in which it was found necessary to supplement the natural (or funnel) draught by appliances intended to quicken that draught and increase the air supply. In recent years renewed attention has been given to the subject, and many plans have been tried. Steam Blast. — Until 1880 war-ships were commonly fitted with this means of quickening the draught. Steam jets could be delivered at the base of the funnel, and the rate of combustion increased from 40 to 50 per cent, for short periods. This involved a very consider- 55 8 NAVAL ARCHITECTURE: [chap. xiv. able waste of steam, and was prejudicial to economy in coal con- sumption. While the rate of combustion was so greatly accelerated, the indicated horse-power was increased only about 15 per cent. In other words, the coal consumed per indicated horse-power per hour was increased about one-third, while the increase in horse-power was only about one-seventh of the power realized with natural draught. As higher steam pressures were used, fresh water in the boilers became essential, and the objections to this system became more serious. It has now fallen into disuse. Air Blast. — Instead of steam jets M. Bertin suggested the use of jets of compressed air. In this way the draught could be quickened, and the steam used in the engine of the air-compressors could be condensed. On trial it was found that an increase of 40 per cent. could be obtained upon the indicated horse-power realized with natural draught, with about 20 per cent, increase on the coal burnt per indicated horse-power per hour.* After these trials it was pre- ferred to use " closed stoke-holds " in the ships of the French Navy, and to adopt forced draught. Induced Draught. — Instead of using steam or air jets at the base of the funnels, it has been more than once proposed to " induce " the draught by means of fans placed in the same position, and driven by steam-engines. Mr. Martin has worked out one of these plans, and trials have been made with it in the Royal Navy. Other inventors have proceeded on similar lines, developing certain novel features. Messrs. John Brown and Co., of Sheffield, while retaining the fan in the uptake, have arranged that the air supplied to the furnaces shall pass through a series of tubes placed in the uptakes. It is asserted, as the result of experiment, that this utilization of heat which would otherwise be wasted, and consequent heating of the air before it enters the furnaces, favour both the rate of combustion and the* economy of coal consumption. Important experiments are now in' progress with this system on several large steamships. One advantage- claimed for it is the possibility of obtaining good evaporation with inferior qualities of coal. It is also asserted that these results can be maintained over long periods without leakage of tubes or other injury to cylindrical boilers. With all plans of induced draught the stoke-holds remain open, and all the operations therein proceed as under ordinary funnel draught. . Forced Draught. — Under this designation several plans may be included, which have in common the delivery of air under pressure to the furnaces by means of steam-driven fans or blowers. These * See a Memoir by M. Bertin in tne PrOcekdings of the Society d'Encourage- ment pour Plndustrie Nationale, 1877. chap, xiv.] PROGRESS IN MARINE ENGINEERING. 559 plans may be arranged in two classes : the " closed ash-pit," and the " closed stoke-hold." The "closed ash-pit " system was employed in some of the earliest steamers. In recent years it has been revived and extended ; in some instances for the purpose of enabling inferior qualities of coal to be used, and in others to increase the evaporative performance of the boilers either in ordinary work or under special circumstances. In all cases the stoke-holds remain open as with natural draught, but the ash-pits are closed, and air is delivered to the furnaces either below the fires, or both below and above, or below and in the com- bustion chambers. The " Ferrando system " has been extensively used in cargo- steamers, and is stated to have given excellent results, both as regards economical working and good evaporative power when using cheap and inferior qualities of coal. Its distinctive features are the employment of special firebars, and the supply of air to the ash- pits below the fires. The system worked out by Mr. Howden has been applied to many merchant steamers, including some of the largest and fastest vessels afloat. It embodies arrangements of the character mentioned above, for utilizing heat, that would otherwise be wasted, in raising the temperature of the air supplied to the furnaces. There are special fittings by means of which the amount and pressure of the air can be regulated before admission to the furnaces both above and below the fires. With this system it is alleged, on the basis of extensive experience, that large evaporative power can be combined with an economical rate of coal consumption, and the boiler-room weights reduced. When work has to be done on the fires, and the furnace doors are opened, the forced draught must be temporarily shut off. It is necessary also to make inde- pendent provision for the ventilation of the stoke-holds. These two features apply to all forced-draught systems with closed ash-pits. The "closed stoke-hold" system has been extensively used in recent years. Its success in torpedo-boats led to its extension to larger war-ships, and it has also been applied in many steamers of the mercantile marine.* Each stoke-hold is made practically air- tight, and powerful fans or blowers are used to deliver air into the closed stoke-holds, producing a sensible amount of pressure. As this air can only escape through the furnaces, the draught is " forced," more coal is burnt and more steam produced. In order to maintain the pressure while permitting entrance and egress, special " air-locks " have to be constructed. This closing of the stoke-holds and the * See papers on this subject in the 'Transactions of the Institution of Naval- Architects for 1883-and 1888. 560 NAVAL ARCHITECTURE. [chap. xiv. difficulty of getting into or out of them have been objected to, and undoubtedly involve some inconveniences. On the other hand, there are certain advantages. All the operations of stoking, cleaning fires, etc., proceed as with natural draught and in open stoke-holds. The stoke-holds are kept comparatively cool and well ventilated by the same air supply as serves for the furnaces. It has been urged that the rush of cold air into the furnaces when the doors are opened for firing involves the danger of sudden chilling of some portions of the boiler, and of tube leakages. While there may be some risk of the kind, its magnitude has probably been over-estimated by opponents of the closed stoke-hold system. Undue forcing of the draught in order to increase the rates of combustion and evaporation is obviously unwise, since it may impair the efficiency of the boilers for subsequent service. Much depends upon the type of boiler used. In the Boyal Navy it has been the rule, with cylindrical boilers, to limit the air- pressure in the stoke-holds, when proceeding at full speed for long periods, to \ inch of water. The term " natural draught " is now usually applied to this steaming condition with stoke-holds closed and an air pressure not exceeding £ inch, which does not exceed what a tall funnel would give under favourable conditions. In some swift mail-steamers fitted on the closed stoke-hold system, air pressures of I inch to 1 inch of water have been used for long periods without injury to cylindrical boilers. For short periods, as on the four hours' contractors' trials of her Majesty's ships, the stoke-holds were formerly put under an air pressure of 2 inches with cylindrical boilers. Now the upper limit is fixed at or about 1 inch of water. With 2 inches of air pressure the maximum indicated horse-power obtained has been from 60 to 70 per cent, above that obtained with natural draught. With 1 inch of air pressure, the corresponding increase is about 20 to 25 per cent. Exact determinations of the relative rates of coal consumption under natural and forced draught are wanting. Under the higher forced draught condition named, the coal burnt per indicated horse-power per hour would probably increase sensibly as compared with natural draught. Two causes account for this. First, forcing the draught and burning a much larger weight of coal would tend to be wasteful of fuel ; second, the engines would be worked less expansively when using the larger quantities of steam. With moderate forced draught (1 inch of air pressure) it would appear that economy in coal consumption should be well maintained. For groups of locomotive boilers, the rule of the Eoyal Navy is to permit an air pressure in the stoke-holds not exceeding 1 inch of water (as the so-called " natural draught ") for full-speed continuous steaming on service, and 3 inches as the air pressure for contractors' 3-hour trials. Formerly it was thought not excessive to obtain 60 to CHAP. Xiv.] PROGRESS IN MARINE ENGINEERING. 56 1 80 per cent, above the natural-draught development of power with high forced draught. The later practice is to be satisfied with about 40 per cent. In torpedo-boats, each fitted with one large locomotive boiler, much higher stoke-hold pressures have been used without injury to the boilers. In some instances air pressures have reached 6 to 8 inches of water. This experience naturally leads to the remark that the air pressure in a stoke-hold is not the sole measure of the extent to which a boiler is or may be forced. Eegard must be had to the heating surface of the boiler, the coal burnt, and the heat transmitted in a unit of time. For each type of boiler, experience is the best guide in deciding on the limit of forcing consistent with continued efficiency. "While the locomotive boiler is better adapted to forcing than the cylindrical, the higher air pressures used with that type involve a higher rate of expenditure of coal per indicated horse-power per hour. As already stated, the locomotive type is used only in classes of war-ships where the accomplishment of high speeds for short •periods is a matter of the greatest importance. Economy of coal consumption necessarily has to be sacrificed at such times. Under ordinary working conditions the locomotive type compares much more favourably with the cylindrical in its rate of coal consumption.' Some types of water-tube boilers are not adapted for high forced draught. Others have been forced to a considerable extent without injury. So far as experience has gone, however, the preference is for moderate forcing under service conditions with such boilers. Fan-draught: Open Stoke-holds. — In many cases powerful fans have been fitted, delivering air to the stoke-holds independently of closing either the stoke-holds or the ash-pits. It is thus possible to increase the evaporative power of boilers very sensibly as compared with natural draught, more especially in cases where the supply of air is made difficult by the necessity for having limited openings in decks, or indirect passages to the stoke-holds. Fan draught is also of great value under unfavourable conditions, such as hot weather, calms, or following winds, giving a command of steam not possible with funnel draught and ordinary ventilators. All the methods of assisting draught above mentioned are of value within proper limits, and subject to the maintenance of the boilers in an efficient condition. In War-ships it may be of immense importance to obtain an increase of power or speed for a limited time. In merchant ships similar conditions may arise when in hot climates, saving a tide in entering port, or facing contrary winds. "Teh years' experience in the Eoyal Navy has given much valuable information for future guidance, and has confirmed the' view that 2o 562 NAVAL ARCHITECTURE. [chap. xiv. appliances for forcing or assisting draught, if employed within proper limits, are most valuable aids to efficiency. Weights and Eates of Coal Consumption. In concluding this brief and necessarily imperfect sketch of engineering progress, it may be of interest to present in a tabular form the weights, rates of coal consumption, and some other parti- culars of the types of propelling machinery still in use in the Eoyal Navy, An epitome of the history of marine engineering since 1860 is represented in ships remaining on the active list. Beginning with the earliest ironclads of the Warrior and Minotaur classes, and con- cluding with the latest battle-ships and cruisers with vertical triple- expansion engines, this table indicates clearly the advances to which reference has been made above. The indicated horse-powers used in estimating weights are those corresponding to the full-speed contract trials. For ships of recent date, fitted withjiorced-draught appliances, the results of the " natural draught " trials of eight hours' duration are used. It will be easy to estimate, from the particulars given on p. 560, how the proportion of weight to power would be reduced if. the forced-draught developments were taken into account. The coal consumptions correspond to the full-speed condition. At lower cruising speeds in war-ships, the rates of coal consumption per indi- cated horse-power per hour are usually above those for full speed. For the earlier vessels the rates of coal consumption can only be regarded as approximately correct.* Weights and Rates of Coal Consumption for War-ship Machinery. Type of Weight Bate of coal Date. Boiler pressure. Piston speed. per indicated horse- power. consumption per indicated horse-power per hoar. Boiler. Con- denser. Engine. lbs. per ft. per sq. in. minute. lbs. lbs. 1850-1360 20-25 Bos-tubular Jet (Simple-expansion :1 I horizontal j Ditto 360-450 380-400 5-51 1860-1870 30-35 Ditto Surface 500-660 330 3i-3* 187O-1S80 60-65 Cylindrical Ditto 1" Compound hori- \ I aontal or vertical J 650-650 360 2* 1880-1885 90-130 Ditto Ditto Ditto 600-800 310-330 2+ 1885-1892 1890-1893 130-155 165 Ditto f Locomotive : \ I in groups 1 | Locomotive : | Ditto Ditto ( Triple-expansion : \ I vertical ) Ditto 700-900 800 260-300 150-180 2--2J 2-2i 1890-1893 180-200 < single large > [ boiler J Ditto Ditto 900-1000 70-80 Note. — The particulars tabulated are for "natural-draught" trials, except for the single locomotive boiler in torpedo-boats, for which the trials are under forced draught. In the case of cylindrical boilers, air pressures not exceeding i inch of water, and with locomotive boilers not exceeding 1 inch, come under this category. * For much fuller details see Mr. Durston's paper in the Transactions of the Institution of Naval Architects for 1892. chap, xiv.] PROGRESS IN MARINE ENGINEERING. 5 6 3 For merchant steamers it is customary to express the weight of machinery and rate of coal consumption in terms of the average horse-power indicated on service, and not on contractors' trials. Merchant ships work under much more uniform conditions of speed than war-ships, and are designed to steam at certain speeds (except for the influence of wind and weather) with certain maximum loads on board. Passenger-steamers are built to cover certain distances from port to port. War-ships, as explained above, have to perform their ordinary duties at very low speeds and powers, compared with the full speeds and powers which they are capable of developing. Hence it is usual to take the contractors' trials as the fairest standard when comparing different types of war-ships. When com- parisons are made between war and merchant ships, however, it is necessary to estimate the seagoing performances of the former in terms of the trial performances. According to the established practice of the Eoyal Navy, the minimum power which ought to be developed continuously as long as the coal lasts is 60 per cent, of that obtained on the natural-draught eight hours' trials. In many cases a higher percentage has been obtained, and in some ships the full specified natural-draught power has been realized on a 96 hours' trial at sea. Taking the ordinary estimate of 60 per cent., it will be seen from the foregoing table that the weight of propelling machinery in modern war-ships fitted with triple-expansion engines and cylindrical boilers varies from 400 to 500 lbs. per indicated horserpower for continuous steaming, an increase of two-thirds above the tabulated weights. Turning to merchant ships, and using the same basis for esti- mating weights in terms of the average horse-power indicated on continuous steaming, it is found that considerable differences exist between different types of steamers. In a number of examples of cargo-carrying steamers of moderate speed worked under compara- tively easy conditions, with low piston speeds, compound engines, and cylindrical boilers, the weights have varied from 480 to 500 lbs. per indicated horse-power. For triple-expansion engines in a number of similar ships, the corresponding weights have been from 450 to 470 lbs., and in a few cases 600 to 650 lbs. per indicated horse-power.* For fast passenger-steamers, weights of 400 to 500 lbs. per indicated horse-power have been common with triple-expansion engines and natural draught ; while weights of 300 to 350 lbs. have occurred in steamers of very great power fitted with forced or assisted draught. It. will, be seen, therefore, that the latest practice in the Eoyal Navy * See, a paper by Mr., Hall in vol., iii. builders; and Mr. Blechynden's paper of the Transactions of the NorthrEast above mentioned. Coast Institution of Engineers and Ship- 564 NAVAL ARCHITECTURE. [chap. xiv. and that in the mercantile marine do not differ much when expressed on the same basis. It is generally assumed that war-ship machinery is much lighter than that in passenger-steamers ; but the opinion is based upon the different modes of expressing the relation of weight to indicated horse-power. What has been said above as to the ordinary cruising speeds of war-ships being very low need not be repeated. But it involves, as a consequence, very small demands on either engines or boilers during the greater period of service of war-ships ; whereas merchant ships are worked at uniformly high power in proportion to maximum capability. This constancy of condition in merchant ships, while it makes greater demands on the strength of the machinery, is advantageous in other respects. It favours economy in coal consumption, and tends to preserve in a highly effi- cient condition the bearings and all working parts of the mechanism. Economy in Coal Consumption. — The principal sources of economy in coal consumption have been shown to consist in higher steain pressures, greater rates of expansion, and improved condensers. Other improvements have favoured economy, such as feed-heaters, steam jacketing, more efficient valves and valve gear, and better combustion of fuel. In the table on p. 562 are given the successive steps in increased economy. Since 1860 the rate of coal consump- tion has been climinished about 60 per cent, in her Majesty's ships. The use of the compound engine effected a saving of from 40 to 50 per cent., and the balance has been due to the triple-expansion engine. Starting from the compound engine, the use of triple expansion has effected an economy of about 18 to 20 per cent. In the mercantile marine similar but greater economies have been effected. Average results for merchant ships on service are said to work out as follows : * In 1872, with compound engines and about 52£ lbs. boiler pressure, the coal consumption was 2-11 lbs. per indicated horse-power per hour. In 1881, with compound engines «nd about 77£ lbs. boiler pressure, the corresponding consumption was 1-828 lbs. In 1891, with triple-expansion engines and 158£ lbs. boiler pressure, the consumption was 1-522 lbs. There is a great mass of evidence in support of the statement that with triple- expansion engines at the present time the consumption of coal per indicated horse-power per hour on service is from 1£ to If lb., and in some instances is below 1£ lb.f * See Mr. Blechynden's paper above resume of the facts respecting coal ex- mentioned, penditure in war-ships, see a paper by t See reports in the Proceedings of Mr. Riley, R.N., in tie Journal of the the Institution of Mechanical Engineers, Royal United Service Institution for 1889-93 ; of the Research Committee on July, 1893. Marine Engine trials. For an excellent chap, xiv.] PROGRESS IN MARINE ENGINEERING. 5 6 5 Comparing these figures with those tabulated for war-ships, mercantile practice is seen to give superior economy, and no doubt does so. There are many reasons for this superior economy. The constancy of the conditions as to speed and power under which merchant ships work is an important factor. In such ships there is much greater freedom in arranging engines and boilers than can be obtained in war-ships, where considerations of armament and protection often hamper the designer. The boilers can be made more roomy, and combustion under natural draught more efficient. The steam can be worked more expansively under the conditions of full speed than it is ordinarily worked under similar conditions in war-ships. On the other hand, it must be stated that the figures given in the table for war-ships are based on a large number of trials, extending over considerable periods, and with the indicated horse-power accurately determined as well as the weight of coal burnt. Similar trials can hardly be carried out in merchant ships on service. The coal consumed on a voyage is known, of course, within narrow limits ; but the average indicated horse-power is not accurately determined, and any over-estimate of that power would involve an under-estimate of the rate of coal consumption. Exact trials have been made, however, on merchant steamers by the Research Committee of the Institution of Mechanical Engineers and others, and these substantially confirm the results based on ordinary service. For war-ships making long passages, much better results have been obtained than are shown in the table, which deals with averages. The Thunderer, for example, steamed at full sea-speed to Madeira and back, on a consumption of 1*66 lbs. of coal per indicated horse-power per hour — a result comparing well with mercantile practice. Equally good results have been obtained with other battle-ships and cruisers on long runs at high speed. Could every- thing in war-ships be adjusted so as to secure maximum economy at the full sea-speed as is possible in merchant ships, greater economy of coal would be obtained. This cannot be done, because of the great range of power over which war-ships have to work. At low speeds the rate of coal consumption is higher than at the full sea-speeds. The reasons for this are obvious, since engines capable of developing a certain maximum power only develop about 10 to 15 per cent, of that power at cruising speeds. Moreover, when cruising in com- pany, war-ships are bound to keep a large reserve of steam available, which makes against economy. At cruising speeds, therefore, the rate of coal consumption per indicated horse-power is necessarily increased as compared with that at full sea-speed. The difference in the rates varies greatly in different ships. Sometimes it is about 5^6 NAVAL ARCHITECTURE. [chap. xiv. 10 to 15 per cent, greater at low than at full speeds ; in other cases it is 20 to 30 per cent, greater. For locomotive boilers the rate of coal consumption at the higher powers is usually somewhat greater than with cylindrical boilers, but the difference is small at lower powers. Results obtained with water-tube boilers of good type compare favourably with those for cylindrical boilers. In the Danish cruiser Geiser, Thornycroft boilers on an eight hours' trial burnt 1*77 lbs. of coal per indicated horse-power per hour, when developing about 80 per cent, of the full power. Similar results have been obtained in French cruisers with other types of water-tube boilers and triple-expansion engines, the consumption varying from 1£ to 2J lbs. of coal per indicated horse-power per hour. In torpedo-boats with water-tube boilers and feed-heaters, M. Normand claims to have obtained even greater economy in coal consumption. With some forms of artificial draught there appears to be a ppsitive economy in the rate of coal consumption as compared with natural draught. This is possible if the natural-draught conditions did not give an ample supply of air for combustion of the fuel. In general, however, with forced draught the rate of coal consumption tends to rise somewhat as compared with good natural-draught performance. Moderate forcing is, as a rule, practised in merchant ships, and with this there is no loss of economy. In war-ships, with closed stoke-holds at the higher air pressures, the rate of coal con- sumption increases somewhat. Such pressures are intended to be xised only for short periods in cases of emergency, when the attain- ment of the highest speeds is of paramount importance. Under these circumstances economy in coal consumption is necessarily subordi- nated to the development of greater horse-power. No discussion can be attempted here of the possible use of liquid fuel in ships, or of the applications which the system has already received. Its advocates assert that for a given weight of liquid fuel carried by a ship, a much greater weight of steam can be produced than by an equal weight of coal. Hence it would be possible either to increase the distance which a ship coidd steam, or to diminish the weight of fuel required to cover any assigned distance. High authorities estimate that 10 lbs. of petroleum refuse may be con- sidered equal to 14 or 16 lbs. of good coal, when proper arrange- ments are made for burning the liquid fuel. Incidental advantages obtained with liquid fuel are complete control of the supply of fuel to the boilers by mechanical arrangements easily manipulated by a few men ; the practical abolition of the laborious work of stoking and coal-trimming, and more perfect combustion. Hitherto the use of liquid fuel has been comparatively limited. In the mercantile chap, xiv.] PROGRESS IN MARINE ENGINEERING. 5^7 marine this has been due mainly to commercial considerations. In war-ships partly to considerations of defence, and to the results of experiments. The difficulty of obtaining supplies of liquid fuel in many parts of the world, the comparatively limited sources of supply and total supply available, have also had great weight. Some foreign navies are employing liquid fuel for torpedo-boats, and in large vessels are using it to supplement and assist the combustion of coal in the furnaces. This subject has received, and is receiving, con- siderable attention both in this country and abroad.* Examples of the Influence of Engine Design upon Ship Design. — Illustrations might be multiplied of the effect which improvements in marine engines and boilers have had upon steamship design. Space is available for only a few striking cases. In the Eoyal Navy during the period 1888-93, several of the older armoured ships have been fitted with new engines and boilers. The outlay has been considerable, but the resulting advantages are great. Take, for example, the Thunderer, designed in 1869, and fitted with box tubular boilers with 30 lbs. pressure, surface con- densers, and horizontal engines. The total weight of propelling machinery and boilers was about 1050 tons. On the measured-mile trial 6270 H.P. were developed during six consecutive runs, the cor- responding speed being 13-4 knots for the period of the trial, which probably did not exceed two hours at full power. With a total 6oal stowage of 1350 tons the ship could cover about 4500 knots at 10 knots. The total weight of machinery and coals was about 2400 tons. New triple-expansion engines, of the inverted cylinder type, and cylindrical boilers, carrying 145 lbs. per square inch, were fitted in 1889-90. The total weight of the new propelling apparatus was under 800 tons, and on trial with natural draught 5500 H.P. were developed on a continuous trial of 8 hours, while 7000 H.P. were developed for 4 hours with very moderate forced draught. Under the latter condition the speed was over 14 knots; with natural draught it was about 13J knots. The superior economy of the new arrangements has enabled the same distance to be covered as before, with about 950 tons of coal instead of 1350 tons. The total weight of machinery and coals for this distance has, therefore, been reduced to less than 1750 tons, as against 2400 tons originally ; and 650 tons disposable weight have been secured, which can be devoted to other purposes. At full speed the relative economy in coal consumption is greater with the new engines than it is at * An admirable summary of facts Navy, and embodied in a paper for the bearing on this subject has been made Engineering Congress at Chicago, 1893. by Colonel Soliani of the Boyal Italian 5 68 NAVAL ARCHITECTURE. [chap. xiv. cruising speeds, such as 10 knots. An actual trial has been made with the ship from Spithead to Madeira and back. The average indicated horse-power was about 4500 H.P., or over 80 per cent, of the specified natural-draught power ; the mean speed was 13 knots, and the coal burnt per indicated horse-power per hour was 1§ lb., probably about one-half that which the old machinery would have expended at the same speed. It is improbable that with the old machinery and boilers such a development of power could possibly have been obtained on a voyage of 2600 knots, and if it could have been realized, instead of burning 675 tons of coal for propulsion, about 1350 tons would have been expended. Facts such as these, and the economy in expenditure on coal which has been secured during the remaining period of service of this ship, justify the large expenditure incurred in the refit. For ocean steaming at high speeds over long distances economy in coal consumption is the determining factor in commercial vessels, and the longer the voyage the greater are the gains of the modern type of machinery. As an example, take a passenger-steamer trading to Australia, and averaging at sea about 16 knots, with 6000 H.P. With compound engines such as were in use in 1881, the daily con- sumption of coal for propulsion would have been about 125 tons per day, or from 3700 to 3800 tons for the voyage. With triple-expan- sion engines such as are now fitted, the daily consumption would be about 100 tons, or from 3100 to 3200 tons for the voyage. A saving of 600 tons on the coal burnt does not, of course, measure the gain, because what is saved in weight of coal carried can be made available for freight-earning. If desired, the economy in coal consumption can be utilized in adding to the size and speed in new steamers, while keeping practically to the same expenditure of coal. On the Atlantic service this has been done, and by the adoption of triple- expansion and higher steam pressures, vessels of greater size and engine power have been produced, which steam a knot faster and yet burn no more coal than their predecessors of smaller size do with compound engines at a lower speed. As an example of the possible influence of liquid fuel, the case may be taken of an Atlantic steamer averaging 20 knots, and burn- ing about 1900 tons of coal on the voyage. Accepting the relative values of coal and liquid fuel above stated, about 1300 tons of petroleum refuse should be equivalent to the 1900 tons of coal, and 600 tons of disposable weight would be obtained. This might be added to the weight of cargo if desired, and would constitute a very substantial addition thereto. Or it might be distributed partly in additional boilers and engine power, and partly in fuel, enabling a higher speed to be realized in a ship of the same form and dimeni chap, xiv.] PROGRESS IN. MARINE ENGINEERING. 5 6 9 sions. Or it would enable a ship of less size to be produced, having the desired qualities of speed and carrying power. In cargo-steamers, no less importance attaches to the types of engines and boilers employed, economy in working being essential to successful competition. The horse-power developed in the ordinary type of cargo-carrier working at a speed of 9 to 10 knots is very moderate, and the expenditure of coal is small ; but the aggregate gain — including reduction in coal carried and burnt, and the corresponding increase in cargo — has led to the rapid introduc- tion of triple-expansion engines in the place of compound.* To illustrate this, take a vessel of 5000 tons displacement averaging 9£ knots at sea, and indicating about 1000 to 1100 H.P. With compound engines of the type used in 188.1, the hourly consumption would be about 17 cwt., and the daily consumption about 20£ tons. With triple-expansion engines of recent types, the same speed could be obtained with a daily consumption of about 16 to 17 tons. A voyage of 3000 knots would occupy about 13 days ; with compound engines about 265 tons of coal would be burnt, and with triple- expansion engines about 215 tons. The total dead-weight carrying capacity would be about 3400 tons ; with compound engines, the cargo would therefore weigh about 3140 tons, and with triple- expansion engines, about 3190 tons. It has been estimated by ship- owners that each ton added to freight may be regarded as equivalent to from £6 to £7 per annum. So that in freight-earning the saving of 50 tons on coal carried would represent from £300 to £350 per annum, besides the saving on the coal. The latter saving requires further assumption to be made of the total time per annum the steamer is running, and the price of coal. Supposing the vessel to be running 240 days in the year, the total saving would be about 950 tons of coal, and if £1 per ton is taken as the average price paid for coal at home and abroad, this saving will represent £950. Adding the freight value, the total annual economy is from £1200 to £1300. These figures are put forward as illustrations only, and must not be treated as exact measures of the economy which might be realized. This case also represents the remarkable economy of a modem cargo-steamer. Each ton of coal burnt suffices to drive 5000 tons' weight of ship and cargo about 13£ knots. An average expenditure of £1 on coal, therefore, transports 3000 tons of cargo over the distance named. There are, of course, other working expenses to be considered, besides the charges on capital account and depreciation, but into any estimate of these it is not proposed to enter. * See a valuable paper bearing on Institution of Engineers and Ship- this subject by Mr. Hall, in vol. iii. of builders ; also a paper by Mr. Boyd, in the Transactions of the North- East Coast vol. vi. of the same Transactions. 57° NAVAL ARCHITECTURE. [chap. xiv. The last illustration may be taken from cross-channel steamers. A certain class still in actual service were fitted with low-pressure boilers and simple-expansion engines applied to paddle-wheels. The indicated horse-power on trial was 2800 H.P., and the measured-mile speed 18J knots. The total weight of machinery and boilers was 320 tons. If it were possible to substitute screws for paddles on this service, using the torpedo-vessel type of machinery and locomotive or water-tube boilers, with forced draught, the same power could be obtained for a total weight of about 140 tons, or less than one-half the actual weight. Here there would be a large saving on the quick- running engines and screws as compared with slow-running engines and paddle-wheels. Moreover, limitations of draught or considera- tions of steadiness might lead to the adoption of paddle-wheels even if locomotive or water-tube boilers and high pressures of steam were employed. With special forms of screw-propellers, however, a very limited draught could be acoepted without undue sacrifice of efficiency. ( 571 ) CHAPTEE XV. MARINE PROPELLERS. — FUNDAMENTAL PRINCIPLES OF ACTION: WATER-JETS AND PADDLE-WHEELS. The selection of the type of engine for a new steamship is closely associated with the choice of a suitable propeller. In some cases the character of the service for which a ship is designed virtually decides the choice of a propeller, and the type of engine is governed by the consideration of the efficiency of the propeller. The paddle-wheel has been in use from the earliest days of steam propulsion, and still continues to be employed for ships of shallow draught, chiefly in smooth-water service. Experimental screw-propellers were also used at a very early period, but it was not until 1836 that this class of propeller began to be applied to ships in a practical manner, and the Archimedes, the first seagoing steamer, was launched in 1838. At the present time, for seagoing service screw-propellers are universally employed ; and for channel or coasting service, screws have taken the place of paddle-wheels to a large extent. Special forms of screw- propellers are now used even in vessels of very shallow draught, wherein until recently paddle-wheels were exclusively employed. The chief practical difficulty with paddle-wheels, applied in large seagoing steamers, arose from the variations in performance produced by changes in the draught of water and the immersion of the floats, as well as from the influence of rolling motion upon the efficiency. In performing long voyages, the consumption of coals and stores produced a considerable lightening of the draught, and decrease in the immersion of the paddle-floats. That fact necessarily involved a diminished efficiency at some portions of the voyage. Paddle-floats which at starting were too deeply immersed, might be insufficiently immersed at the end. By means of water ballast this difficulty could be overcome, of course, at the cost of an increased mean draught and larger expenditure of engines-power ; but the plan has not found favour, because in other respects the screw-propeller is so superior to the paddle-wheel. Boiling motions involve alternate deep sub- mergence and emergence of paddle-wheels placed outside the main 57 2 NAVAL ARCHITECTURE. [chap. xy. breadths of ships. In the one case the revolutions are retarded, in the other greatly accelerated ; and these alternations involve serious straining actions as well as losses in propelling effect. With screw- propellers pitching at sea may cause racing and loss of efficiency, and with twin-screws of large size in relation to draught, rolling may cause some variations in efficiency ; but in no case are the losses so serious as with paddles. The considerable increase in breadth necessary with paddle-wheels, is a further argument against their use in large ships. By common consent the paddle-wheel is now used only under con- ditions where the voyages are short and mostly in smooth water. The variations in draught are then trifling, and fairly uniform efficiency is maintained. Under these circumstances the paddle- wheel as a propeller does not compare unfavourably with the screw. Its use, however, involves the employment of a slower-moving and heavier type of engine. While the paddle-wheel has thus been subordinated to the screw-propeller, it must not be overlooked that for a long period the swiftest steamships were driven by paddles, and that some of the latest and swiftest Channel steamers are similarly propelled. Her Majesty's yacht Victoria and Albert, built in 1854-55, attained a speed of 17 knots, which was then most remarkable ; the Holyhead packets of 1860 attained 18 knots ; the Viceroy of Egypt's yacht Mahrousse, built in this country in 1865, reached the same speed ; and recent Channel steamers have attained 21 to 22 knots. The water-jet or hydraulic propeller cannot be regarded as a serious competitor with the screw or paddle-wheel, but it has attracted so much attention and been so strongly recommended that it cannot be left unnoticed. This form of propeller was made the subject of a patent in 1661. Mr. Euthven has the credit of bringing it into practical use in 1839, when he constructed two boats for experimental purposes. Other vessels were built between this date and 1866 with hydraulic propellers, including a floating fire-engine and the Nautilus, a river steamer 115 feet long. The Admiralty then authorized the application] of the system to the armoured gunboat Waterwitoh, 162 feet long and of 1160 tons displacement, in order that it might be tried in competition with twin-screws fitted to similar vessels. This is the largest experiment with the hydraulic propeller yet made, and the results were not sufficiently satisfactory to induce any extended use of the system in war-ships. Since 1866 further trials have been made on small vessels in Sweden, Germany, and this country. The latest vessel so propelled is a steam lifeboat built for the National Lifeboat Institution by Messrs. Green, with machinery by Messrs. Thornycroft. In that instance the hydraulic system was adopted because it was thought more suitable than the screw for service in rough water, where the screw might race greatly, and in shallows chap, xv.] MARINE PROPELLERS. 573 where an ordinary screw might be fouled. A greater expenditure of power was accepted m order to secure these contingent advantages. In the great majority of screw steamers there is a single screw, placed in an aperture between the body of the ship and the stern- post to which the rudder is hung. In a few cases the single screw has been placed abaft the rudder, which has been suitably formed to be worked either under the shafting, or in two parts, one above and one below the shafting. By moving the screw further aft from the stern of the ship, |it was anticipated that economy in propulsion would be increased. This change in position undoubtedly decreased the augmentation of resistance due to the screw action. On the other hand, the screw was not so well placed to utilize the energy in the frictional wake, and the net result on propulsion did not give the gain anticipated. In addition, there were practical difficulties in the arrangement. The screw was more exposed to accidental injury ; the steerage was not so good, especially ;when gathering way ; and the movement of the rudder affected the flow of water to the propeller. After a considerable trial, therefore, the system was abandoned. There have been many proposals to place single screws much further forward than the usual position, either in tunnel-shaped cavities formed in the vessel or directly underneath her. An interest- ing experiment of this kind was made by Messrs. Herreshoff in a torpedo-boat purchased by the Admiralty. The screw was placed under, the boat at a considerable distance before the stern. The results were fairly satisfactory, but there was no good basis for com- parison of efficiency with the ordinary plan. Mr. Yarrow made a trial on similar lines in a torpedo-boat of larger size. In that case the results obtained with a screw working below the boat were very inferior (measured by the speed obtained with a given indicated horse-power) to results with a screw in the ordinary position. General experience confirms the opinion that this position gives the ' best results for steerage and propulsion. For efficiency the stern must be formed suitably to permit the free flow of water to the propeller, and care must be taken to diminish the resistances of stern-posts and rudder-posts, especially in wood or composite vessels. Experiments have shown that with very thick stern-posts and rudder- posts, the augmentation of resistance may be practically doubled, as compared with what would happen if these appendages were of small thickness and suitably shaped. ■ Twin-screws, one placed under each counter, were tried at a very early period. Their use was practically limited to vessels of shallow draught or relatively high speed until 1865-70. For blockade-run- ning during the American Civil War, for special services in shallow water, and in certain coast-defence vessels, twin-screws were "used. 574 NAVAL ARCHITECTURE. [chap. xv. An experimental armoured twin-screw vessel, the Penelope, was built for the Royal Navy in 1866-67. Soon after, twin-screws were adopted for the Audacious class, and in the ill-fated Captain. The general use of twin screws in seagoing war-ships of deep draught dates from 1S69, when the so-called " mastless " type of moderate freeboard turret-ship (Devastation class) was introduced. Since that date twin- screws have been gradually growing in favour in the Royal Navy, and at present single screws are fitted only to sloops or gunboats having good sail power, or to torpedo-boats. Most of the larger classes of torpedo-boats, or " destroyers," have twin-screws. Foreign fleets have adopted a similar practice. In the mercantile marine twin-screws have been much more recently adopted in seagoing ships of deep draught. Prior to 1889 few such ships were at work. Most of the largest and swiftest passenger- steamers since brought into service have had twin-screws ; and the system is growing in favour. On the Atlantic service, with its very high speed and limited draughts of water at some of the principal ports of call, twin-screws have been found necessary to the utilization of the great engine power. It is, however, a notable fact that in many of the largest cargo-steamers recently built — in which only moderate engine powers have to be utilized, and the draught of water is ample for single screws — twin-screws have been preferred for other reasons. Many authorities maintain that, for vessels trading to the East, twin-screws are more liable to damage than single screws when passing through the Suez Canal. Some very important vessels now on that service already have twin-screws. As speeds are in- creased under the stress of competition, and larger powers have to be utilized on a draught practically fixed, it may be anticipated that, as on the Atlantic service, twin-screws will be more extensively used. From the explanations given in Chapter XVL, it will be under- stood that by subdividing the power, having two sets of machinery and twin propellers, smaller diameters of screws can be employed than are possible with single screws. All the moving parts of the machinery can be made of less size and weight, and the straining forces due to reciprocating motion can be lessened. Shafting can be reduced in diameter, its manufacture facilitated, and the risk of fracture diminished. The duplication of machinery and propellers makes the risk of total disablement much less. A twin-screw ship, with one engine and propeller at work, and using the helm to keep her course, is perfectly under control, while she can make fair speed. Cases are on record, of quite recent occurrence, where twin-screw passenger-steamers have proceeded with one screw at speeds only two to three knots less than their full speed with both screws. Twin- screws also give greater handiness. In war-ships this has long been chap, xv.} MARINE PROPELLERS. 575 recognized. In the mercantile marine it has been found of great advantage in " slewing " long ships in limited space, in entering docks, and under other circumstances where a single-screw ship would be almost helpless. Water-tight subdivision in the machinery compartments can also be secured by means of longitudinal bulkheads between duplicate engines, as explained on p. 33. It was feared that twin-screws would, be more liable to damage than single screws when ships were entering or leaving docks, going alongside wharves, or taking the ground. Precautions have been taken in some instances to reduce the projection of twin-screws, and bring the shafts closer to the middle line. In some vessels one screw is placed somewhat before the other, an aperture being formed in the deadwood, so that the screw discs may overlap. It appears, however, from experience with ships fitted in this manner working side by side with other ships with the twin-screws not overlapping, and consequently projecting further from the middle line, that free- dom from accident is not much increased by overlapping. In fact, with reasonable precaution in management, the risks of injury to twin-screws in large ships do not seem great. With small ships of high speed, having relatively large screws, greater care must be taken. Duplication of machinery and propellers probably involves the occupation of somewhat more space, and a larger staff may be needed than with a single engine and screw. These disadvantages do not appear to be of any relative importance when set beside the gains obtained with twin-screws, even in cases where there is no necessity, on the score of propulsive efficiency, to use the latter, as in the large cargo-steamers of moderate speed above mentioned. There is an increasing use of twin-screws in other mercantile marines also. At the commencement of 1893 it is stated that there were in exist- ence 112 twin-screw ships of over 1000 tons gross tonnage in all mercantile marines, and 35 twin-screw ships are reported to have been launched in this country during that year. This is a very small proportion of the total number of steamships, but in this number are included a very large proportion of the most recent and swiftest ocean-going steamers. Formerly there was an impression that single screws were more efficient as propellers than twin-screws.* Enlarged experience has demonstrated that twin-screws are at least as efficient, and under many circumstances more efficient. This has been proved in all * As a matter of historical interest, tects for 1878. Interesting particulars of reference may be made to a paper con- early experience with twin-screws in tributed by the author to the Transac- merchant steamers will be found in the tions of the Institution of Naval Archi- same Transactions for 1864-66. 57 6 NAVAL ARCHITECTURE. [chap, xv sizes and classes of war-ships, and more recently in mercantile experience. Some of the highest propulsive coefficients yet obtained have been reached in twin-screw ships (see p. 541). With a given draught the smaller diameter of twin-screws carries with it deeper immersion, and this tends to increased efficiency in smooth water, while at sea it diminishes the chance of racing when a ship is pitch- ing. The smaller diameter and different position in relation to the stem of twin-screws tend to decrease the augmentation of resistance due to their action, as compared with single screws. On the other hand, they are not so favourably placed for utilizing the frictional wake. Care must be bestowed upon the arrangements and forms of the struts, tubes, etc., which are necessary when the shafts are carried outboard with twin-screws. If, as is now frequently done, the stern is " bossed " out to carry the propeller-shafts, equal care must be taken to obtain suitable forms for the after-terminations. When such care is taken, the broad fact is established that twin- screws, with all their attendant advantages above enumerated, do not involve lessened efficiency. Twin-screws are not so well adapted as single screws to the use of sail power. Auxiliary sail power may be of service in economizing coal, even in twin-screw ships. It is possible sometimes, with a favourable wind, to use one screw in association with sail, or to run before the wind, using both sail and screws. For vessels of war, in- tended to make passages under sail alone, single screws are a prac- tical necessity. In the mercantile marine, as twin-screws have been adopted, sail has practically disappeared. Increased dimensions in ships has reduced the propulsive value of even the full-sail equip- ments formerly carried, and the duplication of propelling apparatus has rendered sail of little importance as an auxiliary to steam power. In twin-screw war-ships, with few exceptions, only steadying fore-and- aft sail is now carried. Experience shows, moreover, that in nearly all cases, even at low cruising speeds, it is most economical to use both screws, rather than to work one screw, allow the other to revolve or drag, and use small helm to keep the course. Another method of using two screws, adopted in the "cigar" ships built by Mr. Winans, and in certain tugs, has been to run the shaft throughout the length, and to have a screw at each end. This plan cannot conduce to efficiency, seeing that the forward screw derives no benefit from the frictional wake, and its action must seriously affect the stream-line motions proper to the rate of advance of the vessel. Possibly the primary object has been to gain power for rapidly reversing the course without turning. Some ferry-boats have been fitted with two continuous shafts, a screw being carried at each end of each shaft. Trials have also been made on a few vessels chap, xv.] MARINE PROPELLERS. 577 with two screws placed at the stern, one abaft the other, and rotating in opposite directions. One screw is mounted on an annular shaft, which rotates round a solid shaft carrying the other screw. This is the arrangement adopted in locomotive torpedoes, to ensure straight running. Multiple screws, carried by independent shafts and placed at the stern, have been adopted in certain vessels of shallow draught and considerable power. Some of the shallow-draught vessels built for service on the Mississippi during the American Civil War had four screws. The Kussian circular ironclads have six screws. Such special cases can be better dealt with, however, in future, if the necessity arises, by using special forms of propellers adapted to the light draught. Triple-screws have also been used in many instances, and have been recently adopted in several swift cruisers, and in some battle- ships built abroad. The Kussian imperial yacht Livadia, built hi this country in 1880, has three screws. A model of this remarkable vessel was tested by the late Dr. Tideman, in the experimental establishment at Amsterdam. The augmentation of resistance is said to have been 22 per cent, of the tow-rope strain. This is high as compared with twin-screw ships of good form, but may be accounted for partly by the peculiar form of the Livadia. Eeference to her performances under steam is made in Chapter XVII. It will there be seen that the draught of water was very light ; but in this case the diameter of the screws was not limited by the draught, the lower portion of their orbits being much below the keel. A very interest- ing series of trials with triple-screws was made in France during 1884-85, with a small vessel (about 33 feet long) built for the purpose from the designs of M. de Bussy.* This vessel was really a model of a battle-ship about 340 feet long and of 9600 tons displacement. The form of the stem was arranged with special reference to the use of three screws, and differed considerably from ordinary practice. Possibly this fact somewhat affected the results when two screws only were used. Experiments were made with the three screws placed in one athwartship plane, as compared with two screws similarly placed. The latter had somewhat the advantage. The two outlying screws were then placed some distance ahead of the central screw, and a considerable improve- ment was found to result. In fact, the broad conclusion reached by the experimentalists was that in this vessel, when the best * For details, see M. Marchal's paper ticulars of the Italian trials with triple- in the Transactions of the Institution of screws, see a paper by Mr. F. C. Mar- Naval Architects for 1886. For par- shall, in the same Transactions for 1888. 2p 57 8 NAVAL ARCHITECTURE. [chap. xv. arrangements for both triple and twin screws had been made, with equal disc-areas {i.e. with larger diameters in the twin-screws), equal efficiency was obtained. Triple-screws were also tried about 1886-87 by the Italian naval authorities on torpedo gunboats of the Tripoli class. From the details which have been published, it appears that the utilization of power by the three screws was fairly satisfactory. On the other hand, it must be noted that in later vessels of the class, twin-screws have been preferred to triple. It is reasonable to suppose that, as higher speeds are attained and larger powers have to be utilized, since the limits of draught for ocean-going steamers are fixed by practical considerations, triple- screws may become necessary to efficiency. At the present time (1893) a number of swift cruisers and some battle-ships belonging to foreign navies are being constructed with triple-screws, not because the draught is inadequate for twin-screws, but because the arrangement is preferred on other grounds. With triple-screws smaller diameters suffice. The subdivision of power into three sets of machinery instead of two, in association with the smaller screws, makes it possible to employ quicker-running engines of less height and stroke than with twin-screws. Such engines can be kept lower in the vessels, and therefore more readily installed under protective decks fitted at or near the water-line. Further, it is hoped — and this is probably one of the chief reasons for the change from twin- screws —that at low cruising speeds greater economy in coal con- sumption will be realized than is possible with twin-screws. The intention, under these circumstances, is to work only the central engines, to disconnect outlying screws, and allow them to revolve freely. In this way the waste work on the two idle sets of machinery would be avoided, and it has been shown (see p. 543) that at low powers this amounts to a considerable percentage of the total work done. On the other hand, the work done in making the idle screws revolve, or dragging them through the water, would be incurred. Experience will decide where the balance of advantage lies. Lastly, it is anticipated that, by placing a central screw immediately before a rudder, steerage will be sensibly improved. This matter has been most carefully studied in connection with the design of ships of the Koyal Navy, from a period antecedent to any of the experiments above mentioned. Up to the present time it has been considered that, with the speeds and powers required, the balance of advantage is with twin as compared with triple screws. The utilization of over 21,000 H.P. on H.M.S. Blenheim on twin- screws, within comparatively moderate limits of draught, has been remarkably efficient. Much greater power (said to attain 30,000 H.P.) chap, xv.] : MARINE PROPELLERS. 579 has been associated with great efficiency on accepted limits of draught in the latest twin-screw steamers belonging to the Cunard Line. Until actual experience has been gained on the triple-screw ships, it is not possible to say whether equal efficiency will be obtained. The French experiments on the model vessel do not settle this point, for reasons above stated. The Italian experience seems adverse. It is certain that there is a danger of decreasing efficiency by the mutual inter- ference of triple-screws. The matter will no doubt be dealt with satisfactorily on the basis of experience, and it is now being in- vestigated experimentally. Much light will be thrown upon these problems by the performances of the triple-screw ships now approach- ing completion in France, Germany, and the United States. It will be of great interest to ascertain if the anticipated economies at low cruising speeds will be realized. Careful trials, made in twin-screw ships of all classes, have proved it to be advantageous, as a rule, to use both engines and screws, even at very low powers, rather than to stop one engine and drag the corresponding screw. In that case some small angle of helm must be used to keep a straight course, and this tells against economy. But when ample allowance has been made for the drag of the rudder, greater economy is still found to result from using both engines. With two idle screws the case will be less favourable than with one. It may be added that marine engineers are fully alive to the importance of economy in cruising speeds, and plans are under consideration which aim at increasing economy by modifications in engine design, while retaining twin- screws. For war-ships, with their necessities for convenient stowage of magazines, shell-rooms, etc., in relation to the disposition of the armament, the use of three sets of machinery and triple-screws in- volves many disadvantages. Were important gains to be certainly realized in propulsion, these other considerations would have to give way, and the best arrangements possible in association with triple-screws accepted. Up to the present time, however, there is no evidence that this step need be taken, or fighting efficiency diminished, in order to obtain more economical propulsion. In their manoeuvring power, twin-screw ships of good form have proved entirely satisfactory. This is dealt with at some length in Chapter XVIII. The screw-turbine propeller devised by Mr. Thornycroft has hitherto been used almost exclusively in vessels of light draught and moderate dimensions. It has features, however, which make it pos- sible that, as speeds are , increased, and greater powers have to be developed on limited draughts of water, this form of propeller may be more extensively used. A brief . description of its principal 580 NAVAL ARCHITECTURE. [chap. xv. arrangements will be given.* The screw used is of very small diameter and coarse pitch ; the blades are carried by a special form of boss, and there is a gradual increase in their pitch. A cylindrical casing surrounds the screw-blades. At the forward end of the casing the opening between the casing and the boss is of considerable cross- sectional area ; this is gradually contracted by the enlargement of the boss, the varying area of the channel being adjusted to suit the gradual acceleration impressed upon the water by the action of the screw-blades, in order that losses of efficiency incidental to sudden changes of motion may be avoided. Abaft the revolving blades, and attached to the casing and the after part of the boss, which is also fixed, are numerous fixed " guide-blades " of contrary flexure to the screw-blades. The coarse pitch of the revolving blades causes the water to be delivered from them with considerable rotary and sternward motion. The guide-blades direct this water into a stem- ward stream, and in doing so sustain a forward reaction which is a virtual increase of thrust available for propulsion. It is stated that this increase, when measured in a model experiment, amounted to one-third of the total thrust, and that the [efficiency realized was equal to that of a common screw. The last claim was practically established by a trial made in a torpedo-boat of the Koyal Navy. Originally she was fitted with an ordinary screw 5 feet 10 inches in diameter. This was removed, and a screw-turbine 3 feet in diameter substituted. The engines and boiler remained unaltered, and equally good results were obtained on trial as with the original propeller. One drawback must be mentioned ; the screw-turbine, from the nature of the case, cannot be efficient when going astern, all its details being devised to give efficiency when moving ahead. Proposals have been made for meeting this objection to some extent, but it is understood they are only in the experimental stage. In extremely shallow-draught vessels, with the screw-turbine fitted in suitably shaped tunnels, of which the tops rise above still-water level, very good results have been obtained. Quick-running engines can be adopted with this propeller, and weight saved on the propelling apparatus. Fundamental Principles of the Action of Propellers. Before considering the actual and relative efficiencies of the three classes of propellers which have been used in steamships, it is proposed to sketch briefly the fundamental principles governing the action of * For fuller details, see papers by 1883-85. Also Mr. S. Barnaby's " Marine Mr. Thornycroft in the Transactions of Propellers." the Institution of Naval Architects for chap, xv.] MARINE PROPELLERS. 5^1. all propellers.* When a ship has acquired uniform motion, the thrust of the propeller is equal and opposite to the resistance of the water to her motion. Both thrust and resistance may be considered to be forces acting parallel to the keel of the ship. The thrust of the propeller is measured by the sternward momentum communicated in each unit of time to the column of water on which it acts. Some propellers communicate other than sternward motion to the water they act upon, but only the sternward momentum can be reckoned into the thrust. As the simplest case, take first a direct-acting propeller com- municating only sternward motion to the water. Let C = the cubic feet of water acted upon by the propeller per second. w = the weight in pounds of each cubic foot of water. v = the sternward velocity (in feet per second) relatively to still water impressed upon the column of water (C) by the action of the propeller ; v measures the " true slip " of the propeller. V = the speed of advance of the ship relatively to still water, and of the propeller carried in the ship. Vi = the sternward speed of the column relatively to the propeller at the point of passage through the pro- peller. B = reaction of the column, corresponding to the accelera- tion v. Then, in accordance with principles previously explained — Beaction (B) v Weight of water acted upon per second ff where g is the acceleration corresponding to the force of gravity, or 32-2 feet per second. Hence — * The following authorities may be Nos. 2 and 3, and in the Transactions of consulted by readers desirous of follow- the Institution of Naval Architects for ing out the theoretical investigations on 1879 and 1887 ; by Professor Greenhill this subject : Papers by the late Pro- in the same Transactions for 1888 ; by fessor Bankine in the Transactions of the late Sir Francis Knowles in the the Institution of Naval Architects for Proceedings of the Institution of Civil 1865, and in his "Miscellaneous Scientific Engineers for 1871; by Professor Fitz- Papers ; " by the late Mr. Froude in the gerald in the Proceedings of the Belfast same Transactions for 1865 and 1878 ; Philosophical Society for 1890 ; and by by Mr. B.3S. Froude in the same Trans- MM. Pollard, Dudebout, and Drzewiecki actions for 1883, 1886, 1889, and 1892 ; in the Bulletin del' Association Technique by Professor Cotterill in the Annual of Maritime for 1892. the Royal School of Naval Architecture, 5^2 XAVAL ARCHITECTURE. [chap. xv. R (in pounds) = - x weight of water acted upon per second = - x C . w (1) 9 For sea-water w = 64 lbs. ; so that — E =_^- x C x 64 = 2C . v (nearly). The " total work " expended in giving the sternward momentum to the water acted upon, is expressed by the change in vis viva involved in passing from the speed V to the speed V + v. In symbqls — Total work = W(foot-pounds) =^-i^{(Y + vf - V 8 } %9 ■ t0V (2Y + v). . . (2) 2<7 = *.(Y + !) The " useful work " of propulsion is measured by the product of the reaction R into the distance V per second. Or — Useful work = R . V (3) The excess of the " total " above the " useful " work measures the " waste " work. Hence — Waste work = R(v + ^) - R . V = R . | Also — useful work R . V 2V Efficiency = total work K f V + - 1 2 "V + v The " total work " expended may also be expressed in the form — Total work = R,.V 1 . . . . (4) Equating the values for the same quantity given in (2) and (4) — B.V,-B.(V + |) v Vx-V-J (5) Hence it appears that, under these assumed conditions, the pro- peller may be regarded as producing half the acceleration (v) before the water reaches the propeller, and the remaining half when the water is passing through the propeller. This analysis is due to Mr. R E. Froude, the ordinary assumption having been that the whole chap, xv.] . MARINE PROPELLERS. 5^3 acceleration was produced with comparative suddenness at the pro- peller. In practice, no doubt, other conditions tend to modify the theoretical result indicated by Equation (5) ; but it has great interest, and the fact that a certain part of the acceleration is pro- duced before water passes through a propeller tends to increase .efficiency. So far as the thrust (E) is concerned, it will be obvious, from Equation (1), that so long as the final acceleration reaches v the thrust remains unaltered. From that equation it will be seen also that, so long as the product C . v remains constant, the thrust remains constant. On the other hand, if C is diminished, and v cor- respondingly increased to maintain the constant thrust, then the waste work is increased, and the efficiency diminished. Consequently, for a given thrust, so far as these mathematical expressions are a guide, it is advantageous to increase the quantity of water (C) acted upon, and to dimmish the sternward acceleration v. In prac- tice, as will be shown hereafter, this broad conclusion requires modification. In dealing with large quantities of water, a serious increase may arise in the waste work on propelling apparatus. Thus it may happen that the desire to obtain the best combined efficiency of propulsion puts a limit upon the quantity of water acted upon. Again, with special forms of propellers and arrangements for utiliz- ing the momentum of the " race " delivered by the propellers, good efficiency may be obtained with considerable sternward acceleration. As a second case, take a propeller which is set obliquely to the keel line, and communicates transverse as well as sternward motion to the water.* Let T = the transverse component of the reaction. E = the longitudinal „ „ „ v 1 = the transverse component of the acceleration. v 2 = the longitudinal „ „ „ Then— *]v? + v 2 2 = the oblique acceleration. . . (6) Then, according to the results obtained in the first case — EC . w ,_. = . v 2 (7) 9 t = 9e. Vi (8) c w Oblique reaction = v'E 2 + T 2 = — — ■ vV + v?. Also after the water has passed through the propeller it has the * This and the following case are re- in the Transactions of the Institution of produced from Mr. E. E. JTroude's paper Naval .Architects for 1892. 5^4 NAVAL ARCHITECTURE. [chap. xv. longitudinal speed Y + V& and the transverse speed v x . Compound- ing these velocities — Oblique velocity after passing) .-==— — ^- — -„ through the propeller. \~ ^ + ^ + ^ < 9 > elocity before being ac upon by the propeller Velocity before being actedl Y /in\ Total wort = — {(V -f- r..)- + t-, 9 - V' 2 } -9 Civ ( v , v.,\ . Cu< v x = E(Y + J) + T.| . (11) As a third case, take a propeller which produces rotary as well as sternward acceleration in the water acted upon ; for example, a strip or annulus on a screw-propeller blade situated at a radial distance d from the axis about which it turns. The annuhis is supposed to be very narrow measured radially from the axis, but to have the full breadth of the propeller blade. Let v = the sternward component of acceleration imparted, o = the angular component „ „ E = the longitudinal component of reaction. M = the rotary component of reaction expressed as a mo- ment about the axis. Here the linear motion in a transverse plane is d . a, corresponding to V! in the preceding case ; also M = T . d. Making these substi- tutions in Equations (7), (8), and (11) — K = ^.r (12) 9 M = 9l v .d'.a (13) 9 Total work = r(v + * ) + M." . . . (14) The three cases of direct-acting, oblique, and spiral propellers, above considered, have been dealt with under certain hypothetical conditions, which hold good for elementary propellers of small area, but which are known not to apply absolutely to actual propellers. For instance, paddle-wheels in practice have floats of large area spaced at certain distances apart ; these act more or less obliquely on the water, waste work in various ways, and cause changes of level and pressure in the race as well as changes of velocity. Screw pro- pellers also cannot be considered simply as an aggregation of annular elements such as that considered in the third case. For chap, xv.] WATER-JET PROPELLERS. 5^5 such an annular element, it may be supposed that the acceleration, or spiral speed, impressed on the water forms a hollow cylindrical column of water which has practically the same pressure as the un- disturbed water surrounding it. When a screw acts on the whole column of water which forms its race, this condition does not hold good, and there is a change of pressure as well as of velocity to be considered. Moreover, in the hypothetical cases no attempt has been made to define the manner in which the acceleration is pro- duced, nor to evaluate the waste work which in practice has to be done in overcoming frictional and other resistances to the motion of the propellers through the water. This waste work is tantamount to a decrease in thrust, or to an increase in the total work to be done in obtaining a certain thrust, and therefore to a decrease in efficiency. Another difference to be noted between the hypothetical cases and the conditions of practice is that the equations framed for the former assume that the propellers act upon water which is undis- turbed except by the action of the propellers. In practice, propellers have to act upon water which has impressed upon it independent stream-line motions, due to the advance of the ship, and upon frictional wakes of the character previously described. The action of the propellers is necessarily affected by this circum- stance, and the point will receive further illustration when dealing with paddle-wheels and screws. Speaking broadly, all conditions which affect the flow of water relatively to propellers must also influence their efficiency. Amongst these conditions may be men- tioned the kind of propeller used, its dimensions, its position in relation to the hull, and its immersion. The forms of ships, especially in the neighbourhood of the propellers and the degree of roughness of their bottoms, are also important factors in determining efficiency. The Water-jet Propeller. This form of propeller is exceedingly simple in its action. Water is permitted to enter the ship through inlets in the sides or bottom. The motion of the ship is necessarily impressed upon the water which enters. It then passes, in most cases, into a turbine or centrifugal pump driven by the main engines, and is expelled with considerable velocity through passages leading to an outlet or nozzle placed on each side of the ship. The re- action of the streams issuing from the nozzles constitutes the pro- pelling force; and this remains practically constant, whether the nozzles are above or under water, so long as the velocity of outflow and the speed of the ship remain the same. If the nozzles are 586 NAVAL ARCHITECTURE. [chap. xv. placed below water, their projection beyond the sides of the ship causes additional resistance. If they are placed above water, the turbine has to do some additional work in raising the issuing jets to this higher level. Experience shows, however, that the balance of advantage is obtained by placing the nozzles a little above the water- line. In most cases arrangements have been made by which, while the engines and turbines continue to run in one direction, the issuing streams can be diverted, at the will of the commanding officer, from the sternward direction of outflow to the reverse. By this means the movement of a vessel can be rapidly checked or reversed. By making one jet deliver ahead, and the other astern, the vessel can be turned within a very small space, practically on the centre of her length. In order to secure the greatest efficiency with this form of pro- peller, the following points require to be carefully considered : First, the arrangement of inlets, so that the water on entering may be given the motion of the ship gradually and without shock, and the mini'mum of waste work done in giving motion to water which does not enter the ship. Second, the arrangements of the passages by which the water is conducted to the turbine, and from the turbine to the outlets, so as to minimize the resistances and waste work due to friction, sharp bends in pipes, etc. Third, the quantity of water employed, and the character of the turbine. As explained above, this quantity of water involves the consideration of the velocity of outflow and the sectional area of inlets, passages, and outlets. Fourth, the design of the engine which drives the turbine. The total efficiency of the propelling apparatus depends, therefore, upon the individual efficiencies of the engines, the turbine (including the inflow and delivery of water), and the jets.* Using the same notation as on p. 581, let A = the joint area of the outlets in square feet. Then — Cubic feet of water (C) delivered per \ _ . y second 5 ~~ * * x Weight of seawater (W lbs.) delivered } _ .,, . y per second (nearly) . . . .5 • ~ i Sternward velocity of jets (v) in relation ? _ y _ y to still water .... 5 Beaction (B lbs.) in sea-water (nearly) = 2 . Cv = 2AV!(Vi — Y) Useful work of propulsion = E . V = 2AV 1 (Y 1 - V) . V Energy in " race " = C . i? = AV^Vx - V) 2 . * See papers by Signer Brin in the Bamaby in the Proceedings of the In- Transactions of the Institution of Naval stitution of Civil Engineers for 1884. Architects for 1871; and by Mr. S. chap, xv.] WATER-JET PROPELLERS. 5 8 7 Neglecting waste work involved in the admission of water and its movements while being accelerated up to the velocity of discharge — Total work of propulsion = useful work + energy in race = AV^V^ - V 2 ) Efficiency of jet » useM TOrk = 2AY ^ - V ) V 3 total work AVxCVV-V*) 2V This limiting efficiency is not attained in practice, and could only he reached supposing the inlets and passages were so arranged that the water entered the turbine at the speed V, and was gradually accelerated up to the speed Vi. The total energy of the "feed- water " under these hypothetical conditions would be represented by the expression — Energy of feed-water = A . V! . V 2 and in practice this energy is more or less lost. Supposing it to be -entirely lost, then the total work done in propulsion becomes increased by the lost energy. In symbols — Total work = useful work + energy in race + energy of feed = 2AVi . (V X -V)V + AVxCVj - V) 2 + AVi . V 2 = AV 1 (2VV 1 - 2V 2 + Vx 2 - 2VV! + V 2 + V 2 ) Efficiency of jet I ^M™* = 2AY 1 (V 1 - V)Y total work AVi 3 _ 2(V X - VJV _ 2v . V V x 2 Yf The extent to which the energy of feed is lost varies with the character of the inlets and of the passages leading to the turbine, as well as the design of the turbine. In cases where it is desired to preserve the power of steaming equally well ahead or astern, the whole energy of feed is practically lost. If this quality is sacrificed, and motion ahead made as efficient as possible, then a consider- able part of the energy of the feed can be utilized by suitably forming the inlets and passages. In the Watermtch the inlets were placed under the bottom, nearly amidships, and the water passed almost vertically into the centrifugal pump, whence it was delivered through nozzles placed at the water-line. By simple; arrangements the streams ■could be ejected either ahead or astern, without altering the motion •of the engines and pump. The vessel was a " double-ender," so as to be capable of steaming equally well with either end foremost. The joint sectional areas of the nozzles amounted to 5£ square feet. On her full-speed trial, at a displacement of 1160 tons, the ship attained 588 NAVAL ARCHITECTURE. [chap. xv. a speed of 9-3 knots with 760 H.P. The velocity of discharge (Vj) was 29 feet per second ; the speed of ship (V) was 15*7 feet per second ; the speed of discharge (v) relatively to still water was therefore 13*3 feet per second, and 154§ cubic feet of water were discharged per second. In this case nearly the whole energy of feed-water was lost, and consequently by the preceding formula — Efficiency of jet = 2x_13j3x_157 = Q . 5 ( nearly ). The total efficiency of the propelling apparatus is given by the expression — Total efficiency = useM work _ 2 x 154§ x 13-3 x 157 I.H.P x 550 760 x 550 = 0-16 (nearly). This final residt expresses the losses resulting from waste work on the engines, and from waste work on the pump. It has been estimated that fully 23 per cent, of the indicated horse-power would be absorbed by frictional and other resistances in the engine, and that the efficiency of the pump would have been only about 40 per cent, of the power delivered to it ; the net power represented by the jets being, there- fore, only about 30 per cent, of the indicated horse-power.* If it be assumed that the jet propeller practically causes no considerable augment of resistance, then the expression for the total efficiency would correspond to the propulsive coefficients above described, and its value will be seen to be very low as compared with the propulsive coefficients of screw-steamers given on p. 540. The Waterwitch was actually tried against two twin-screw vessels, the Viper and Vixen, of equal length and beam, and approximately the same displacement. These two vessels were similar in form to the Waterwitch in the fore body, 'but in the after part they were not nearly so well shaped. The twin-screws were carried by double dead- woods, with a tunnel-shaped cavity between them ; and the resist- ances were thus increased to a considerable but unknown extent as compared with the Waterwitch, while the efficiency of the propellers was probably diminished as compared with that of ordinary twin- screws. Notwithstanding these disadvantages, the Viper attained a speed of 9 - 6 knots at a displacement of 1180 tons with 696 I.H.P.. which was a sensibly better performance than that of the Waterwitch. Experiments were made in the Waterwitch with reduced sectional areas of the nozzles. The results indicated a decreased efficiency, as * See the detailed calculations for In that paper the sectional area of noz- efficiency of Waterwitch and other ves- zles is taken at 6'28 square feet, instead! sels in Mr. Barnaby's paper above cited, of the 5J square feet used in the text. chap, xv.] WATER-JET PROPELLERS. 5 8 9 might be expected from the formulae given above. In order to maintain the thrust requisite to drive the ship at a given speed, if the sectional area of discharge (A) is diminished, the velocity of the discharge V, and the sternward speed of the jets relatively to still water, must be increased. On the other hand, increase in the sec- tional area of discharge enables the velocity of discharge and waste work in the race to be diminished. There are, of course, practical limits to increase in sectional area of discharge and the quantities of water dealt with, and what has to be sought for is that combina- tion which will give the highest total efficiency for the whole propelling apparatus. In 1878, twelve years after the trials of the Waterwitch, another very interesting comparative trial was made in Sweden on two torpedo- boats, 58 feet long, and of about 20 tons displacement, identical in form, with boilers of the same size and type. One of these boats was driven by twin-screws, the other by water jets delivered by two centrifugal pumps. The inlets were placed amidships under the bottom, and the outlet pipes were carried some distance forward and abaft of the pumps in order to avoid sharp bends. The jets could be discharged either towards the bow or the stern, and as first fitted it was intended to be able to steam equally well in either direction. Subsequently the inlets were altered in form, so as to favour the admission of water without shock and the utilization of the energy of the feed-water when moving ahead. The results were strikingly in favour of the twin-screw boat. She attained 10 knots with 90 I.H.P., while the jet-propelled boat, in her best trials after altera- tion, attained 842 knots with 78 I.H.P. Allowing for difference in speed, this indicates a superiority of nearly 60 per cent, in the expenditure of power in the twin-screw boat. In 1881, the Admiralty instructed Messrs. Thornycroft to con- struct a second-class torpedo-boat, which should be fitted with a jet propeller, and compared with another boat of practically the same dimensions driven by a single screw. Both boats were fitted with boilers of the same size and type. The screw boat was 63 feet long, 1\ feet broad, and of nearly 13 tons displacement ; her rival was over 66 feet in length, 7J feet broad, and of nearly 14^ tons dis- placement. Every endeavour was made to increase the efficiency of the jet propeller when the boat was moving ahead. The inlet was placed at the bottom, and formed as a " scoop," so that the energy of the feed-water should be utilized as much as possible.* The turbine was designed to accelerate the water gradually, and the outlets were of short length with easy bends. The nozzles could be readily For full details and drawings, see Mr. Barnaby's paper above cited. 59° NAVAL ARCHITECTURE. [chap. xv. turned, and the jets delivered astern or ahead as desired. A con- siderable loss of efficiency when moving astern was accepted as a consequence of the "scoop" form of inlet. The total sectional area of discharge was rather under 1 square foot; the velocity of discharge was 37 - 25 feet per second, about 1 ton of water being dis- charged per second. Under these conditions, with nearly 170 I.H.P., this boat attained a speed of 12-6 knots per hour. The screw boat, with practically identical power, attained 17'3 knots per hour. An analysis of the efficiencies made by Mr. S. Barnaby gave the following results : — In the screw boat the efficiencies were : engine, 077 ; screw pro- peller, 0-65 ; total, 0-5. In the hydraulic boat the differences were : engine, 077 ; jet pro- peller, 0-71 ; pump, 0-46 ; total, 0-254. The jet-propelled boat, therefore, was only about half as efficient as the screw boat, and the principal cause of loss was in the pump. The efficiency of the pump and jet in this boat was 033, as against 0-234 in the Waterwiteh, showing a gain of 40 per cent., due to the xitilization of the energy of the feed-water. This is the latest comparative experiment made in this country, and its results do not encourage the further use of the jet propeller except in special cases, such as the lifeboat above mentioned. A jet-propelled vessel, with turbine, has also been built for the German Navy. She is said to have been about 170 tons displace- ment, and to have attained a speed of 7 knots with 292 I.H.P. In this case we are unable to give a comparison with a screw ship of similar form and power. A novel experiment in jet propulsion was made (in 1879) in Germany by Dr. Fleischer, in a vessel named the Hydromotor, 110 feet long, 17 feet beam, with a mean draught of 6£ feet, her dis- placement being 105 tons.* It is claimed for this vessel that with 100 I.H.P. she attained a speed of 9 knots ; but particulars of the conditions under which the speed trials were made were not given, and these conditions may have differed from those usual in English Admiralty measured-mile trials, where all possible care is taken to determine accurately the true mean speed, and to eliminate the influence of wind and tide. Apart from the reported performance, there were, however, features of great interest in this vessel. There was no centrifugal pump, but the steam acted directly upon the water in two reservoir cylinders placed above two large pipes leading * For particulars see the two pain- Fleischer. Kiel, 1881. See also En- phlets entitled " Der Hydromotor " and gineei'ing of September 9, 1881. " Die Physik des Hydromotoxs," by Dr. chap, xv.] WATER-JET PROPELLERS. 59 1 to the nozzles, which were situated nearly amidships on either side of the keel. In each cylinder there was a "float" or piston of nearly the same diameter as the cylinder, and with a closed spherical top. When the cylinder was full of water, this float was at the upper part of the cylinder ; when steam was admitted into the top of the cylinder, it pressed the float down and expelled the water at a high mean velocity. After a certain portion of the stroke had been made, the admission of steam was shut off automatically, and the rest of the stroke was performed by the expansion of the steam, the Telocity of ejection decreasing as the float approached the bottom of the cylinder. The exhaust valve to the condenser was then opened, and as the steam rushed out from above the float a vacuum was formed, and the water entered the cylinder partly through the ejecting nozzle and partly from a separate valve communicating with the water-space of the surface condenser. The float was thus raised again to the top of the cylinder, after which the operations described were repeated. In the Sydromotor there were two cylinders working alternately ; Dr. Fleischer proposed in larger or swifter vessels to use a larger number of similar cylinders. The cylinders were placed as high as possible in the vessel, so that the vacuum produced by the exhaustion of the steam might be utilized in raising a column of water above the sea-level, thus adding an effective " head " of water to the steam pressure during the down stroke. In the Hydroniotor, rather less than 12 cubic feet of water were expelled per second at a mean velocity of 66 feet per second. The efficiency of the jets must have been low, therefore, even if the speed of 9 knots was reached. Dr. Fleischer supposed that considerable economies would be obtained by abolishing centrifugal pumps, and simplifying the mechanism by which motion was given to the jets ; and it may be admitted that this was possible. On the other hand, there were unavoidable losses. Although the cylinders were wood-lined, con- densation of steam must have taken place in the cylinders. The velocity of ejection was variable as well as high, and two or more cylinders were essential to approximately continuous delivery. Dr. Fleischer claimed an efficiency of 34 per cent, at full speed ; but the grounds on which this claim was based were not specified. The system does not appear to have been applied in any other vessel. The theoretical investigations given above indicate the un- desirability of using small quantities of water and high velocities of discharge; yet many recommendations and some experiments have been made in that direction, with unsatisfactory results. One of the latest of which public mention has been made, but not in a detailed or authoritative manner, is that of a vessel said to have been tried in America. The dimensions reported are : length, 106 59 2 NAVAL ARCHITECTURE. [chap. xv. feet ; breadth, 23 feet : draught, 3 feet ; and displacement, 100 tons. The water jets are said to have been only £ inch in diameter, and the velocity of discharge over 600 feet per second, about 1000 gallons (160 cubic feet) being discharged per minute. With these con- ditions it is not surprising that the results as regards speed were not satisfactory. Apart from their relative efficiency, the use of jet propellers has been advocated for war-ships and in special cases, because they have the following advantages : greater freedom from damage in action, or fouling by wreckage or grounding ; greater control by the command- ing officer from the deck of the movements of the vessel ahead, astern, or in turning, without change in the motion of the engines ; the possibility of applying the centrifugal pumps, fitted primarily for propulsion, to clearing rapidly large masses of water which niay enter a ship whose skin is perforated. The first and second claims must be admitted, subject to the reservation that twin-screws also give great mobility (Chap. XVIII.). But the efficient realization of the idea that the centrifugal pumps should be available for pumping the hold spaces involves the necessity of a very serious i interference with watertight subdivision. By common consent the maintenance of that subdivision is admitted to be of greater importance to the safety of ships than any possible increase in pumping power.* In view of their very inferior efficiency as propellers, therefore, the use of water jets is now confined to special vessels, such as floating fire- engines or lifeboats. Paddle-wheels. Paddle-wheels, like jet propellers, give direct sternward momentum to streams of water, the reaction of which constitutes the thrust or propelling force. These streams form what is termed the " paddle- race ; " and their cross-sectional areas depend upon the area and immersion of the paddle-floats. " Feathering " paddle-floats are now generally employed ; in earlier practice the paddle-floats were often fixed radially upon the wheels. The speed of the floats depends upon their radial distance from the centre of the wheel and the number of revolutions of the wheel in a unit of time. Suppose the centre of the floats to be 16 feet from the centre of the wheel, and the wheel to make 16 revolutions per minute, then speed of floats in feet per second (Vj) would be given by , 7 2 x 3-1416 x 16 x 16 OP Q * A / , n Vi = = 26-8 feet (nearly). 60 \ JJ * See a paper by the author " On the ships," in the Journal of the Royal Piunping Arrangements of Modern War- United Service Institution for 1881. chap, xv.] PADDLE-WHEELS. 593 If the speed of the ship is called V, the difference (V t — V) between that speed and the speed of the paddle-floats is termed the apparent slip of the paddles, and is usually expressed as a fraction of V! or— Slip (per cent.) = Vl ~ V x 100. Suppose, in the example chosen — which is taken from an actual ship — that the speed V ig 224 feet per second (about 13 knots per hour) — Slip (per cent.) = 26 ' 8 ~ 22 ' 4 x 100 = 16£ (nearly). 26*8 From 20 to 30 per cent, appears to be a fair average for the slip of paddle-wheels when working under favourable conditions ; in some cases a greater slip occurs. The real slip of the paddle may differ sensibly from this apparent slip, because the water upon which the paddle-floats act has been set in motion by the advance of the vessel, and the cha- racter as well as the velocity of that motion varies at different positions. Ordinarily paddle-wheels are placed nearly amidships, where the " streams " surrounding a ship have their maximum stern- ward velocity relatively to the ship. The presence of the factional wake may modify this relative motion near to the side of the ship, and the effective thrust may also be increased by an "elevation (due to an increase of pressure) of the paddle-race above the normal water level.* Experience shows, however, that the wave phenomena accompanying the advance of ships moving at high speeds has a very important influence on the efficiency of paddle-wheels. Hollows frequently occur nearly amidships in the wave series, the water surface being lower than in still water, while the orbital motions of the particles of water involve an addition to their relative sternward velocities. All these circumstances may affect the efficiency of paddle-wheels placed amidships, and in some in- stances have greatly reduced that efficiency. In paddle-steamers of very shallow draught the paddles are commonly placed at the stern, where they act upon water having its least sternward motion, and where wave crests appear in the wave series at certain speeds. These conditions are more favourable to efficiency ; but, on the other hand, the " augment " of resistance is likely to be greater than with paddles placed amidships and outside the main breadth of the vessels. Even in the latter case a considerable augmentation of resistance, as * See on this point Professor Cotterill's paper in $ne Transactions of the Institu- tion of Naval Architects for 1887. . , ; , . .; 2Q ' 594 NAVAL ARCHITECTURE. [chap. xv. compared with the condition when towed, is likely to be produced by the action of paddles. The water in the paddle-race is driven astern with considerable velocity, and the stream-line system is disturbed in a manner involving increased resistance. The paddle-floats rarely dip more than one-third to one-half of the draught of water ; but while they do not affect the whole mass of water in the stream-line system, they act directly upon that portion which flows round the upper and fuller portion of the stern, and consequently produce a sensible augmentation. The late Dr. Tideman made some model experiments on this subject, using model paddle-wheels mounted in models of ships. The published results indicate considerable variations in the augmentation, and are hardly to be taken as conclusive. In one series paddles, a single screw, and twin-screws were tried, and the former caused the greatest augmentation.* More recent experiments have been made with models in connection with the designs of very fast Channel steamers, propelled by paddles. The results have not been published, but it is stated that the use of models has been of considerable advantage in arranging the sizes, positions, and character of the paddle-wheels. Paddle-wheels necessarily do a considerable amount of work besides that which is effective in propelling a ship. This waste work includes that done in overcoming the resistance offered by the water to the entry and exit of the floats, in "churning" the water, driving it in other than the sternward direction, and in sudden increases in velocity of the water acted upon. Various devices for reducing waste work have been tried, including feathering floats, special forms of floats, differences in the breadth and depth of floats, and in the diameter of wheels. From the explanations given above, it will be obvious that the minimum amount of waste work must be considerable, since the " race " of the paddles must have a consider- able sternward velocity and energy. If the paddles be assumed to act upon water which is undisturbed by the passage of the ship, and the other causes of waste work just mentioned are neglected, it is possible to express their thrust in a simple form. Let A = the cross-sectional area of the paddle race on both sides. Then, using the previous notation — Cubic feet of water acted \ „ upon per second . • J "~ * x (V —V) Thrust of paddles (pounds) = — x AV! x w = 2A YjiYt — V) nearly for sea-water. * See the record of the experiments in the Memorial van de Marine (9° Afle- vering) : Amsterdam, 1878. CHAP, xv.] PADDLE-WHEELS. 595 With the common (or " radial ") float A is generally assumed to equal the transverse measurement (or length) of the floats into their maximum depth of immersion ; with feathering floats A is assumed equal to the area of the floats. In the practical work of designing paddle-steamers, two of the most important governing conditions are the number of revolutions per minute proposed for the engines and the intended speeds of the vessels. Experience in other vessels is necessarily the best guide as regards probable " slip " of the paddles at full speed, with suitably designed wheels and areas of floats. Assuming a certain percentage of slip, the circumferential speed of the floats can be estimated, and hence the diameter of the wheels ascertained, which, with the given number of revolutions of engines and speed of vessel, will give this slip. There is a great range of practice in relation to revolutions, and it is necessary to proceed with caution in any new design when fixing on the rate of revolution. In a large number of high-speed paddle-steamers the revolutions have been from 20 to 30 per minute ; in certain cases they have risen to 40 or 50, and in special vessels to 70. Increase in the rate of revolutions, of course, secures greater lightness in the engines for a given indicated horse-power. On the other hand, if the " slip " is supposed to remain unchanged, as well as the augmentation of resistance, while revolutions are varied — assumptions not likely to hold absolutely true in practice — a smaller diameter of Avheel must be employed. The following symbolical expressions are useful only in making comparisons between ships which have been tried, and new designs fairly close to them. Let N" = number of revolutions of engines per minute. D = diameter of wheel (to centre of feathering floats). s = assumed percentage of slip. Then- circumferential velocity ") it „ , T ,„ , ,. .,, V i = { at centre of floats *} = ^ • ^ • N (feet per second) (1) s = Vl ~ V x 10 °; whenc e Vi = , A »°° • V . . (2) V x 100 — s w Equating these two values of V! — 100 IT 100- S - Y = 60- D - N • • ■ ( 3 ) If the speed of the vessel is given in knots, it can be converted into feet per second by multiplying it by T688. Further, it will be seen that — 596 NAVAL ARCHITECTURE. [chap. xv. Thrust (fori _ 2A yy _ y) _ 2X 100 y x s y sea-water) ;- 2A - N ^ N * ~ X ' "^ "lOO - « " N X 100-s" V _ 200 . A . s . Y 2 (100 - s) 2 Taking 25 per cent, as a fair average value for the slip, these expressions may be reduced to simpler forms as follows : — D . N = 25 . V (roughly) . . . (4) A . V*= | X thrust (in pounds) . . (5) While fornmke of this kind are useful for purposes of comparison, practical rules based on experience are generally preferred for guid- ance. These may be briefly summarized : * The size of the wheel must be determined by comparison on the basis of intended speed, revolutions, and slip. The height of paddle-shaft must be so regu- lated that, at the deepest draught of the ship, not more than one- third to one-half of the radius of the wheel shall be immersed ; while in the light condition the upper edges of the paddle-floats shall be a few inches under water when they are vertical. In vessels where the variation of draught is small, it is usual to follow the rule named for the light condition. The transverse measurement (or length) of the floats should, as a rule, not exceed one-third to one-half the breadth of the ship. In special vessels a greater length may be used. In a common paddle-wheel with radial floats, the number of floats should about equal the number of feet in the diameter, and the breadth is usually about f inch to 1 inch for each foot in the diameter. With feathering floats, about half the number of floats should be used as with common paddle-wheels, and they should be individually about twice as large. Shallow-draught vessels require to be specially treated. * Chiefly taken from the late Mr. Scott Russell's work on "Naval Archi- tecture." ( 597 ) CHAPTER XVI. THE SCREW PROPELLER. Before proceeding with the discussion of the special features of screw propellers, it will be desirable to explain a few of the terms that will be frequently employed. The diameter of a screw is measured from the circle swept by the tips of its blades during their revolution; the area of this circle measures the serew-dise. The pitch of a screw is the length of a complete turn measured parallel to the axis; in other words, it is the distance which the screw would advance in one revolution if it worked in a solid nut. The speed oi a screw is the distance it would advance in a unit of time if it worked in such a nut, and is clearly equal to the product of the number of its revolutions, in that unit of time, by the pitch. Screws usually have two, three, or four blades, united by a central " boss " which fits upon the after end of the propeller shaft. Each blade may be regarded as a slice or section of a helical surface cut off by planes at right angles to the axis of the cylinder on which the helix is generated ; the distance between these planes of section is known as the " length " of the blade. The number of helical surfaces (corresponding to the number of " threads " on a common screw) from which the blades are cut is equal to the number of blades. The sum of the areas of all the blades is known as the " blade-area," or " developed area," and this excludes the boss. This must be distinguished from, the " projected blade-area," which repre- sents the sum of the areas of projections of the blades on one of the planes of section. The edge of the blade which first meets the water when a ship is moving ahead is known as the " leading " edge ; the other is called the " following " edge. The after surface of the blades is termed the " driving " surface or " face ; " and the other surface is known as the "back" of the blades. The back of the blades is usually well rounded (sections of the driving face by cylinders of different radii giving approximately straight lines), so that^strength may be secured in association with sharp edges. It is now recog- nized that great attention should be given to the condition of 598 NAVAL ARCHITECTURE. [chap. xvi. surface, and to the sectional forms of blades, in order to minimize waste work on frictional and edgewise resistance to the motion of the screws, especially in ships of high speed, and with screws making a large number of revolutions per minute. In some cases the blades, instead of being portions of true helical surfaces with " uniform " pitch, are made with " varying " or in- creasing pitch from the leading to the following edges. The " mean " pitch is then ascertained by measurement, and used in all estimates of performance. The ratio of the pitch to the diameter is termed the " pitch ratio ; " the ratio of the length of the blade to the pitch is termed the " fraction of the pitch " in comparing different screws. Suppose a screw propeller to be carried forward through undis- turbed water at the speed of V feet per second, being mounted ahead of a suitably designed framework. As it advances let it be rotated N times per second ; if the mean pitch be p feet — Speed of advance of the screw = V Speed of screw, corresponding to revolutions 1 _ y _ to- and pitch j " 1— ' P Slip of screw = V x — V V, - V " Slip-ratio " of screw = — — — V — V Slip of screw (per cent, of its speed) = — ^= — x 100. For example, take a screw making 72 revolutions per minute with a pitch of 14 feet, the speed of advance being 8-2 knots. Speed of advance = V = 8-2 x 1-688 = 13-8 feet per second (v), therefore, of the " phantom ship," the thrust of the screw for a See Transactions of the Institution of Naval Architects for 1883 and 1886. 602 NAVAL ARCHITECTURE. [chap. xvi. given number of revolutions, would be identical with that of the screw propelling the model at a speed V, the revolutions of the screw being the same in both cases. Let T = thrust of screw in pounds, which equals the tow-rope resistance of the model at the speed v. Then — Thrust horse-power = T . v . . . ■ ■ ■ (4) Let E = tow-rope resistance of the model ship at speed V. Effective horse-power = E . V (5) Also if at the speed V the indicated horse-power be called I.H.P., and the waste work of engines on friction, etc., be supposed pro- portional to the indicated horse-power (see p. 542) ; then if e be a constant depending on the proportion of the indicated horse-power delivered at the end of the screw shaft — Tjl TT p e t = Efficiency of screw when propelling actual ship = c (6) T H P e 2 = Efficiency of screw when propelling phantom ship = e ' * * (7) e x E.H.P. . T.H.P. E.H.P. E V (8) e 2 ~ I.H.P. " I.H.P. T.H.P. T v This ratio of the efficiencies Mr. E. E. Froude terms the "hull efficiency," and remarks that there are two factors influencing it. The first, E -^ T, expresses the amount by which the resistance is less than the thrust for the speed of advance V. The second, Y-~-v, repre- sents the excess in the speed of advance of the screw over its speed through the water in which it works. " Concerning these two factors " of the hull efficiency," he adds, " they appear to be to a great extent " inter-dependent ; the conditions which increase the wake-gain tend " generally to increase the thrust-deduction loss ; and the product " (the ' hull efficiency ') is therefore, roughly speaking, constant. It " is, in fact, roughly equal to unity in all cases. Such variations as " do exist in the value of hull efficiency appear to mainly accompany " differences in shape of hull, or in position of screw in reference to " it, rather than differences in size or proportion of screws with the " same hull." This most important conclusion rests upon such a basis of experimental facts that it may be accepted as practically correct. Its main value is found in the circumstance that, by adopting it, all questions of screw efficiency can be experimentally investigated in undisturbed water, and the deductions applied to ship propulsion. It is assumed, in the foregoing remarks, that the forms of the after parts of screw-steamers are such as to permit of the free flow of water to the screws. Fineness in the run, and the avoidance of CHAP, xvi.] THE SCREW PROPELLER. 603 blunt forms behind which " dead water " could accumulate, are now universally recognized as essentials to efficiency of propulsion, and are of the greatest importance in single-screw ships. In the earlier periods of screw propulsion, this was not so well understood, and great waste of power resulted. Many of the " converted " ships in the Eoyal Navy, built for sailing only, and afterwards altered into screw-steamers, had the screw apertures formed in the after- deadwoods, with flat-ended recesses. Other vessels were built with full sterns, and the existence of thick wood stern-posts and rudder posts also involved considerable waste of power. Experience very soon proved the necessity for finer forms. As an example, the screw- frigate Dauntless, built in 1848, may be mentioned. Her stern was at first very full, and her performance so unsatisfactory that she was lengthened aft about 10 feet, and given a much finer run. With the same propelling machinery and screw as before, a much better performance was secured. In the earlier trials, with 836 I.H.P., she attained 7"3 knots ; after alteration she attained about 10 knots with 1388 H.P. The alteration in the stern not merely increased screw efficiency, but diminished resistance, and effected a saving in power of fully 30 per cent, at the maximum speed. Screw efficiency also depends upon a proper immersion. The upper blades should not be allowed to break the surface of the water, or draw down air, if full efficiency is to be secured.* So long as the surface is not broken or air drawn down, the atmospheric pressure supplies a " head " equivalent to about 33 feet of water, and effective for causing the water to follow up the movements of the propeller blades. When this " head " is lost, the flow of water to the pro- peller must be affected, and efficiency decreased. Moreover, the splashing and churning of the water at the surface represents waste work and diminished thrust. Partial emersion of screws may result from vessels being at a lighter draught, as when cargo-steamers are without full cargoes, or from " pitching " at sea. In no case, how- ever, can it fail to be accompanied by reduced efficiency. Trials have been made of plans to secure deeper immersion, and freedom from " racing " when pitching. One of the most important experi- ments was that made in the White Star steamer Britannic, where the screw and after portion of the shafting could be lowered when in deep water. The results were not satisfactory, and the plan has not been continued in use. Twin-screws have an advantage over single screws as regards possible depth of immersion and its consequent gains. * See Professor Osborne Keynolds' the remarkable illustration of the effect paper in the Transactions of the Insti- of " splashing " given by Mr. S. Barnaby tution of Naval Architects for 1873 ; and in his " Marine Propellers." 604 NAVAL ARCHITECTURE. [chap. xvi. Theories of the Screw Propeller. — Many attempts have been made to establish a theory for screw propellers, and to frame mathematical formulae for deciding on the best forms and dimensions. These theoretical investigations have been of considerable service in ad- vancing conceptions of the phenomena of screw propulsion, and the causes contributing to efficiency. In assisting and guiding experi- mental work they have also been of value. But it is still true that we are chiefly dependent upon experience and experiment, aided by mathematical analysis, in determining the most suitable screw propellers for individual ships. A short account of these theoretical investigations must suffice, therefore, and readers desirous of following them up may refer to the original publications. The late Professor Eankine laid the foundation on which all subsequent investigators have proceeded, to some extent, in dealing with the mechanical principles of the action of propellers.* For screws, he assumed that the number and surface of the blades would be adjusted, on the basis of past experience, so as to give sternward motion to the whole of the water in which the screws revolved. The race was assumed to consist of a cylindrical column of water, having for its cross-section the disc area of the screw, less the sectional area of the boss. It was made a condition that the flow of water to the screw should be ample. Little was said respecting the method in which sternward and rotary acceleration were supposed to be im- pressed on the water, but it would appear that this was assumed to happen in the short interval occupied by the water in passing through the propeller. The motions of the particles in the race, after passing through the propeller, were supposed to be of a spiral character, including both sternward and rotary movements. At a given radial distance from the axis of a screw, particles were assumed to have identical motions impressed upon them by the action of those annular elements of the screw blades which would be cut off by a cylinder, having the given radial distance as its radius, and a very small thickness. The race was conceived to be made up of a series of concentric hollow cylinders, "each having a rotatory motion and " a sternward motion ; these motions being, in general, different for " each cylinder, so that they would slide through each other and rotate "within each other." On these assumptions, approximations were made to — (1) the quantity of water acted upon by the screw in a unit of time ; (2) the sternward momentum generated in a unit of time ; (3) the waste work expended in overcoming the friction of the blades ; (4) the change in efficiency produced by the action of the blades on water which had been previously disturbed by the advance of the ship. Mathematical formulae were framed for all * See Transactions of the Institution of Naval Architects for 1865. chap, xvi.] THE SCREW PROPELLER. 605 these quantities, and practical applications made to the determination of the dimensions of screws suitable for various ships moving at assigned speeds. For any ship the resistance corresponding to the intended speed was first approximated to ; and so was the mean speed of the wake in which the screw would work. It was assumed that a certain apparent slip of the screw would be accepted ; con- sequently the speed of the screw, and its real slip relatively to the water it worked upon, were known. Hence, by means of mathematical formulae, the disc area and diameter of the screw considered most suitable were determined. The numbers, areas, and forms of the screw blades were left to be determined from experience with other vessels. Eankine's formulas assumed certain values for coefficients of friction, and other particulars which cannot be accepted in view of later experiments. His rules rested, however, on scientific prin- ciples, and were framed in a manner worthy of his high reputation. The fact that they have but little influenced practice indicates that the method suggested required to be so far supplemented by experi- ence, that most naval architects and engineers have preferred to depend upon direct comparisons with vessels of which the perform- ances had been recorded. Another purely theoretical presentation of the action of the screw propeller has been made by Professor Greenhill.* It is unnecessary to do more than summarize the principal steps of this investigation. First, the rotation of the race was calculated from the velocity of the water as it leaves the propeller, on the assumption that particles move in planes perpendicular to the axis, and at constant angular velocity. Then the angular momentum was estimated, and the turning couple of the engines deduced from it. By the principle of virtual velocities the thrust of the propeller was deduced from the turning moment, and the conditions of pressure accompanying the rotation of the race were investigated. In Professor Greenhill's words, " The " change of momentum and the change of pressure are the two causes " at work in obtaining propulsion. ... It is instructive to discuss a " case in which the second question only operated, and to compare it " with the theory of Kankine in which the first cause alone is con- " sidered." Professor Greenhill, therefore, deals with an ideal case in supposing the propeller to impart a purely rotary motion to the race ; and while his investigation has considerable interest and suggestive- ness, it does not profess to represent the actual conditions in the race of a screw, where particles necessarily have sternward as well as rotary motions imparted to them in passing through the propeller. * See his paper in the Transactions thereon in the same Transactions for of the Institution Of Naval Architects for 1889. 1888, and Mr. R. E. Froude's remarks 606 NAVAL ARCHITECTURE. [chap. xvi. The late Mr. Froude added much to existing knowledge of the action of screw propellers, both by experimental and by mathematical investigation. One of his latest contributions to the subject was in some respects the most important, and requires to be noticed at some length. Mr. Froude desired to demonstrate the fact that increase in the diameter and surface of screw propellers, while it enabled a larger quantity of water to be acted upon, might be accompanied by such an increase in waste work on the blades — representing frictional resistance, or edgewise resistance — as would make it advantageous to use screws of less diameter and surface, but with greater pitch. At the time the lesson was much needed.* In order to bring the problem into a form admitting of readier solution, Mr. Froude assumed the screw to work in undisturbed water, making no correction for wake. It is necessary to remark, howeTer, that in other papers he had completely sketched the principal features of wake motion, and their influence upon screw efficiency. For the special purpose in view, Mr. Froude desired to show how the sternward momentum was imparted to the water by a screw, and what waste work was involved in the operation. He therefore framed equations for the action of an annular element of the area of a propeller blade, situated at a given radial distance from the axis, and having a known angle of obliquity to an athwartship plane standing at right angles to the axis. This elementary propeller would have a certain speed of advance (that of the ship) and a certain athwartship motion (due to rotation). Its actual motion relatively to the water would be compounded of these two motions ; and thus its actual motion and obliquity could be ascertained. Mr. Froude treated this elementary propeller as a plate moving obliquely (the case discussed at p. 438). He estimated the normal pressure on the plate, and the frictional resistance involved in its passage through the water. These forces were resolved into their longitudinal and transverse com- ponents. The difference between the longitudinal components of the normal pressure and the frictional resistance measured the effec- tive thrust ; the product of this into the speed of advance measured the useful work. The sum of the transverse components of the two forces multiplied by the distance the centre of the elementary area travelled in its circular path in the unit of time, measured the total work. Hence an expression for the efficiency — the quotient of the useful work by the total work — was obtained for the elementary propeller. Applying differential methods to this expression, it was possible to show how the efficiency varied with changes in the pitch * See the Transactions of the Insti- The trials of H.M.S. Iris (mentioned tution of Naval Architects for 1878. hereafter) were then of recent occurrence. chap, xvi.] THE SCREW PROPELLER. 607 (or obliquity), slip, and area for a given speed, and what combination gave maximum efficiency. Passing from the element to the whole propeller blade, Mr. Froude assumed that it might be converted into a plane area with an equivalent or mean angle of obliquity ; he thus applied to the. propeller as a whole deductions made from the investigations for an element. This step is open to question, for reasons which will be apparent from preceding remarks. Differences of behaviour must arise when a large and continuous area of varying obliquity is sub- stituted for a series of independent and individually small elements of that surface. Questions of variation of pressure in the race necessarily have to be considered, as well as the disturbance of the water by the action of certain blades or portions of blades before it comes under the influence of the other blades or portions of blades. These considerations could not have been absent from the mind of Mr. Froude when he framed the following deductions, and they must not be overlooked when considering the practical value of his suggestions and conclusions, which may be summarized as follows : First, for maximum efficiency, the mean effective angle of the screw blade, measured from an athwartship plane, or " pitch-angle," should be 45 degrees, which is obtained when the pitch is about twice the extreme diameter. Second, for maximum efficiency, the slip-angle must vary directly as the square root of the coefficient of friction, and inversely as the square root of the coefficient of normal pressure, which gives a slip' of about 12^ per cent., with the values of the coefficients adopted in the investigation. This is the real slip ; the apparent slip will usually be less, and will vary according to the amount and character of the disturbance of the water in which the screw works. Third, that, for maximum efficiency, the area of the screw-blades may be expressed approximately by the formula — Area (in square feet) = 8'9x- 2 ; where E = the resistance of the vessel (in pounds) at her maximum speed v (in feet per second). Fourth, that since at moderate speed the resistance of a ship varies as the square of her speed, the same propeller should, within those limits of speed, drive a ship with the same percentage of slip ; but that above those limits of speed the percentage of slip should increase.* Fifth, that for moderate speeds, if the blade areas of the * In the case of torpedo-vessels, when ance varies at a less rate than the square driven at very high speeds in proportion of the speed, and it is found that the slip to their lengths (see p. 470), the resist- decreases. 608 NAVAL ARCHITECTURE. [chap. xvi. screws of two similar ships have the ratio of the squares of the respective dimensions, the percentage of slip should be the same. Sixth, that, if two ships have the same resistance at different speeds, the area of screw blades which will overcome the resistance while maintaining a given slip will be less, in the ratio of the squares of the speeds, for the ship which has the higher speed. The last three deductions are obtained from the formula for blade area. Seventh, that the maximum efficiency which can be realized under the most favourable conditions is about 77 per cent. ; but that the percentage of slip might be increased considerably (even as high as 30 per cent, with the screw working in undisturbed water) without any serious decrease of efficiency in screws of ordinary proportion. An attempt has been made by Mr. Calvert to calculate the thrust and turning moment for screw propellers on the lines followed by Mr. Froude in the investigation just described.* The quantitative results for normal pressure and frictional resistance of an element of blade area are based by Mr. Calvert on the special series of experi- ments he conducted for that purpose, to which experiments allusion is made at p. 439. Allowance is made in this calculation for the varying obliquity of different annular elements of the blades, for the forward movement relatively to undisturbed water of the wake in which the screw works, for the " real " as distinguished from the apparent slip, and for the velocity of the element through the water. In a specimen calculation for a screw with four blades, 10 feet in diameter and 15 feet pitch, the efficiency was found to be - 679, which is probably not far from correct. On the other hand, the remarks made above, as to the difference between the behaviour of an elemen- tary propeller, or series of such propellers, and a screw blade, apply here also. Professor Cotterill followed up the investigation of the late Mr. Froude by another, in which he indicated how the two methods of inquiry pursued by Eankine and Froude were related to one another ; as well as the form of blade area which would be required to fulfil the condition laid down by Eankine, viz. that the whole column of water having the screw disc for its cross-section shall be given stern- ward acceleration. In this and a subsequent paper Professor Cotterill has done much valuable work, particularly in regard to the conditions of velocity and pressure which exist in the water surrounding ships in motion, or acted upon by propellers.! The contributions of Mr. * For details see the Transactions of tution of Naval Architects for 1879 and the Institution of Naval Architects for 1887; as well as remarks on Mr. E. E. 1887. ' Froude's papers of 1889 in the same t See the Transactions of the Insti- Transactions. CHAP. XVI.] THE SCREW PROPELLER. 609 Thornycroft to this and other branches of the theory of screw pro- pulsion have also been valuable. Some of them have already been mentioned, and his experimental investigations are referred to hereafter. Professor Maurice Fitzgerald has attacked the problem of screw propulsion in another way. He endeavours to assign reasonable values to the longitudinal and circumferential velocities of the water in the screw race, such that they " would make the resistance to rotation (due to the inertia of the water like that of a heavy friction- less nut on a screw) the thrust (due to the same nut), and the head or pressure in the stream lines which depends on both the circum- ferential and longitudinal velocities, consistent with one another." Having obtained such values for these velocities, he then ascertains what form of vortex would agree with the movements of the race, and estimates the power expended in producing such a vortex. Applying the method to a number of cases, Professor Fitzgerald found a fair agreement between this estimated power and the power actually delivered to the screws. His intention was to design the screw blades suitably so as to produce the longitudinal and circumferential veloci- ties, and it is stated that the blades fulfilling this condition did not differ greatly from ordinary forms.* The last investigator of the theory of the screw propeller to whom reference will be made is Mr. E. E. Froude. To him are due the most valuable and extensive additions to the literature of the subject made in recent years, including many original conceptions in regard to the action of propellers upon water. Besides this work, Mr. Froude has done much towards harmonizing and contrasting apparently conflicting theories, such as those of Eankine and Grreenhill ; clearing up branches of the subject which were previously obscure ; and putting into a quantitative form various features of propulsion of which the relative importance had not been ascertained, although their exist- ence and qualitative effects had been recognized. He has also continued and greatly extended, on behalf of the Admiralty, the ex- periments on model screws which were commenced by the late Mr. Froude. Eepeated references have been made in preceding pages to his investigations, and they have already had a great influence upon practice in the designing of screw propellers. The Determination, of Dimensions for Screw Propellers. — In the design of screw-steamers the selection of a suitable propeller is of great importance in relation to economical propulsion. From the foregoing sketch of the theory of screw propellers, it will be seen that * For details see the discussion on of the Institution of Civil Engineers for " Screw Propellers " in the Proceedings 1890, vol. cii. 2k 6lO XAVAL ARCHITECTURE. [chap. xvi. there are no complete or accepted rules for guidance in making the selection. Experience and experiment of necessity exercise great influence, and the recorded results of trials are invaluable when dealing with new designs. These trials may be arranged in two classes. First, what may be termed " full-scale " experiments made on ships or boats which are actually propelled by different screws. Second, " model " experiments made with small screws, in order to obtain information which can be used in the design of actual screw propellers. Again, these full-scale experiments may be subdivided into (1) trials made in ships on ordinary service ; and (2) trials made on measured distances, special care being taken to ascertain accurately the speeds attained and the corresponding expenditures of power, in order to determine the relative efficiencies of different screws in the same ship. Sea trials, on ordinary service, while they are of undoubted value, have to be made under very various conditions of wind and sea, and often with different degrees of foulness of bottom, different lading, and variations in the quality of coal used, or in the state of engines and boilers. All of these circumstances, of course, affect efficiency, and must be reckoned in the aggregate result. Usually the com- parison is made in the simple form of average speed on a voyage, average power indicated, and average rate of coal expenditure. It may, and does happen, therefore, that the results obtained in many cases afford no fair or conclusive evidence of the relative efficiencies of the screws employed. To this fact is due, no doubt, many of the opinions expressed respecting the gains in speed and coal consump- tion supposed to have been realized by special and patented pro- pellers. In order to obtain trustworthy results, which must neces- sarily be of a general character, sea trials of rival screws must be continued over long periods, and proper records kept of the loading, weather, condition of bottom, and working of machinery and boilers- Cases occur where the improvement or deterioration in performance accompanying a change of screw is so marked on actual service as to leave no doubt of relative merits. In general, however, the economies or losses resulting from such a change are not so strongly marked, and experience must be gained under varying conditions of service and of weather, over a long period, before it can be decided which screw is, on the whole, most advantageous. For smooth-water steaming one screw may have the advantage over another ; and the conditions may be reversed in rough water. The latter case involves an increased resistance for a given speed, and a considerable effect on screw efficiency in consequence of pitching motions, both of which circumstances require to be recognized in fixing upon the diameter and blade area of screws. CHAP. XVI.] THE SCREW PROPELLER. 6ll Progressive Trials. — But while regard must be had to these con- ditions of sea service, it must be admitted that a much more exact measurement of screw efficiency, as influenced by changes in dimen- sions, form, and pitch, is possible when the trials are made in smooth water, under fairly exact and ascertainable conditions of speed and power. For this purpose it is necessary to have " progressive " trials at various speeds on the measured distance. At each speed a number of runs must be made with and against the tide or current, in order to eliminate its influence, the horse-power, revolutions, and mean speed being ascertained for each set of runs. This process, repeated for each screw tried at a considerable number of speeds, enables diagrams to be constructed, showing the expenditures of powers with each screw over the whole range of speed. Much has been done in this way during recent years, and particularly in con- nection with the construction of swift torpedo-boats running at unprecedented speeds. As an example take Pig. 158, which re- FIG. 158. presents results obtained by Mr. Yarrow in a torpedo-boat which was tried progressively, with no less than twenty-five different screws. The diagram shows two extreme cases. The curve AAA records the ascertained performance of a two-bladed screw of 5 feet 6 inches diameter, 4 feeV-e. inches pitch, having a blade area of 496 square inches. With 56 s 0*"fe4{ i p. ) this screw drove the boat 20£ knots per hour. The curve Efcst belongs to a two-bladed screw 4 feet 4 inches diameter, 5 feet pitch, ha*^ 540 square inches of blade area. With 520 I.H.P., this screw drovSN^ e boat at the 6l2 NAVAL ARCHITECTURE. [chap, xvi remarkable speed of 23 knots per hour, 20£ knots being attained with. 430 H.P. With 500 H.P., the first screw gave the boat a speed of about 19J knots, and the other screw gave 22J knots. Some doubt attaches to the accuracy of the determination of the horse-power in torpedo-boats, on account of the very rapid move- ments of the indicators, but the comparative expenditure of power with these two screws is not likely to be affected by any such inaccuracy. Another most extensive and valuable series of experiments was that made by Mr. Isherwood on the steam-launch mentioned on p. 540. Eight different screws were tried in this vessel. The highest speeds attained were only about 8J knots, but, having regard to the moderate length of the launch (54 feet), this corre- ponded to high speeds in ships of similar form and large dimensions. In these trials dynamometric results were obtained giving the thrusts of the screws at different speeds, while independent experiments were made to determine the nett-resistance (tow-rope) for the same speed. The results were analyzed in great detail, and the conclusions reached respecting many of the phenomena affecting screw efficiency were of very considerable value. To some of these reference will be made hereafter. Sir. Yarrow, in his trials with a first-class torpedo- boat described above, followed a similar method. More recent experiments of this kind, presenting many inte- resting features, were conducted by Mr. W. G. Walker, of Bristol, in 1891, on a single-screw yacht 55 feet in length. Seven screws were tried, including screws with two, three, four, and six blades, with several variations in the relative positions of the four and six blades.* Mr. Walker has presented the results in full detail, and has analyzed them on the lines laid down by Mr. Isherwood. Trials of this nature necessarily involve the expenditure of much time and labour, even when they are carried out on small steam- yachts or launches. For large ships driven by engines of considerable power the difficulties and laboriousness of the task are much greater : and it is only under special circumstances that it is attempted. One of the most notable instances is found in the experiments made with various screws on H.M.S. Iris in 1878. The results are recorded in Fig. 159. On her first trials she was fitted with twin four-bladed screws 18 feet 6J inches in diameter, with a mean pitch of 18 feet 2 inches, and a blade area of 194 square feet. The curve of indicated horse-power with these screws is rnarkecLA^A in the diagram. The results were very disappointing, a**'** Wft s decided to remove two * See an account o£> ! "'' e ^P e " ment8 *^ e Proceedings of the Institution of and an interestkj^ "^* 011 = seoo =loL On the measured mile, with a displacement of 9190 tons, the ship steamed 11-91 knots with 3400 H.P., the displacement coefficient being 218 ; and at full speed she realized 13-84 knots with 6650 H.P., the corresponding coefficient being 175. Had the estimated power — 5600 H.P. — been realized, the vessel would have steamed about 13 knots, that is, about £ knot faster than the estimated speed. Or, had she steamed 12£ knots, the indicated horse-power required would have been 4000 H.P., instead of 5600 H.P., as estimated. When the Devastation had been tried, and her coefficients deter- mined, it was an easy matter to determine the appropriate engine- power for the succeeding deep-draught ships with twin-screws ; and the superior performances of twin as compared with single screws rendered it possible to economize engine power. This was done ; and in the Alexandra, Temeraire, and other vessels, the engines were made less powerful and weighty than they would have been with single screws. Subsequent trials fully justified this procedure. Take, for example, the Alexandra. It was estimated that 8000 H.P. would suffice to drive the ship about 14£ knots, when fully laden and weigh- ing 9500 tons. On the measured mile the speed of 15 knots was attained, and the engines exerted 8600 H.P., 600 H.P. more than the guaranteed power. When allowance is made for this excess of power, it appears from calculation that the fully laden ship would chap, xvii.] ESTIMATES FOR HORSE-POWER. 627 have exceeded the upper limit of her intended speed with 8000 H.P. Had she been fitted with a single screw, instead of twin-screws, at least 500 or 600 H.P. additional would have been required to attain the same speed. Another method of approximation which has been largely used consists in the determination of the ratio of the indicated horse-power to the wetted surface in the exemplar ship or ships at the trial speeds ; and the estimate from this ratio of the probable value of the corre- sponding ratio for the new ship at her designed speed. This method of procedure will be seen to correspond to that described for sailing ships on p. 512. It can be safely used when the speeds considered are moderate in proportion to the dimensions ; for which speeds the resistance of the new ship, as well as those of the exemplar ships, vary nearly as surfaces and the squares of the speeds. From the remarks made on the surface friction of ship-shaped forms on p. 449, it will appear that larger differences of form, within the stated limits of speed, can probably be dealt with by this method than by the use of the " Admiralty coefficients." For higher speeds where wave- making resistance assumes relative importance, neither the wetted surface ratio nor the Admiralty coefficients can be applied without correction of the kind indicated above. The late Professor Rankine proposed a method for computing the probable speed and power of steamships closely resembling that just described. Assuming that the speeds were kept within the limits for which the resistance varied sensibly as the square of the speed, Rankine approximated to the resistance by means of the " augmented surface" described on p. 450. The nett resistance of the hull in well-formed ships with clean bottoms he thought might be expressed in the form — Nett resistance .(in pounds) = augmented surface (in square feet) X speed of ship (in knots) 4- 100. The ratio of the " effective horse-power " (estimated from the nett resistance) to the indicated horse-power, he assumed to be 1 : 1-63 ; and thence obtained as a final approximate rule for practice : — P v, 1,1 T TT P — au g men t e( l surface x (speed in knots) 3 r ° a 6 ' ' " ~~ 20,000 This divisor was termed the " coefficient of propulsion," and its value might vary considerably in different ships with differences in the roughness of the bottom, the efficiency of the engines and pro- pellers, or defects of form. In some cases it was found to be as low as 16,000. The remarks made above as to the use of the wetted surface apply here also. Either method, depending as it does upon 628 NAVAL ARCHITECTURE. [chap. xvn. the assumption that the resistance varies as the square of the speed, fails to include a very large number of the cases occurring in practice ; and Rankine's coefficient of propulsion, like the Admiralty coefficients, rarely has a constant value for a large range of speed in the same ship. Moreover, on the basis of the experiments made by Mr. Froude, it may be questioned whether the computation of the augmented surface is to be preferred to that of the wetted surface, even for estimates of surface friction. As a provisional theory, this of Eankine's was valuable ; but subsequent experiments with ships and models have practically superseded it. Attention must next be directed to the very valuable assistance in speed-calculations derivable from proffi-essive steam-trials ; that is to say, the trial of the same ship at several different speeds, and the determination of the horse-power, and other particulars for each speed. Trials of this kind have been made occasionally with ships of the Royal Navy for a long time past, and in recent years examples of most of the types introduced have been tried progressively. As early examples of progressive trials, made for special purposes, we may refer to the trials made with the Flying Fish in 1856, to test different kinds of propellers and forms of bow ; those made on her Majesty's yacht Victoria and Albert in 1855-56 ; and those made on the Warrior in 1861. In the case of the Victoria and Albert, the trials were very exhaustive, and the curve of horse-power corre- sponding to various speeds (see Fig. 161) was constructed. Out- side the Royal Navy also such trials were occasionally made. Mr. Isherwood, in 1869, tried the steam launch, to which many refer- ences have been made, progressively; and determined the power, revolutions and slip of screw, mean pressure, etc., for a large number of speeds, in order that he might construct curves for all these features of the performance. Mr. Thornycroft did very similar work at an early date for some of the small swift vessels' built by him.* These progressive trials were, however, exceptional, up to 1870 ; since which date they have been commonly carried out for merchant ships and war-ships with great advantage. This change of practice and development of progressive trials is to be attributed largely to the action of the late Mr. W. Denny (of Dumbarton), whose firm took the lead in this movement, and greatly assisted its progress by the publication of a large amount of valuable information obtained on trials of ships built by them.f An example of the ordinary method * See Transactions of the Institution Institution of Engineers and Ship- of Naval Architects for 1869 and 1872. builders in Scotland for 1875 ; and to t See papers by Mr. W. Denny con- the British Association for the same tributed to the Proceedings of the year. chap, xvii.] ESTIMATES FOR HORSE-POWER. 629 of recording these trials is given in Fig. 160, and represents the performance of a very successful steamer built by Messrs. A. and J. Inglis of Glasgow. Abscissae measurements on the base-line represent speeds in knots per hour. The curve AAA represents, by FIG. 160. Spteiin inotr per Tump References. AAA — Curve of indicated horse-poyrer. BBB — „ thrust. CCC — revolutions of screw. EEE — jj slip of screw (apparent). FFF — 11 slip of screw, expressed as percentage of its speed. GGG — j> coefficients of performance. its ordinate measurements, the variation of the indicated horse-power with the speed ; it was drawn through points determined by trials made at a series of four or five speeds between 8 knots and 15 j knots. The curve BBB represents, by its ordinates, the variation of the "indicated thrust" with variations of the speed. The curve is obtained from the curve A A A taken in connection with the curve C C which represents, by its ordinates, the variation of the revolu- tions of the screw with the speed, these revolutions being counted for each trial speed, and the curve CCC being drawn through the points thus obtained. Since the indicated thrust equals the fraction 33,000 x I.H.P. pitch of screw x revolutions per minute while the indicated horse-power is expressed by the product (see p. 536). Mean piston pressure x stroke X revolutions, it is obvious that the curve BBB, by its ordinates, represents " mean piston pressure " for. any speed as well as " indicated thrust," the scales being different in the two cases. At the zero of speed there is an ordinate value for the curve BBB; this represents ; the 630 NAVAL ARCHITECTURE. [chap. xvii. " constant friction " (see p. 542). The curve E E E represents the apparent slip of the screw in knots, and F F F the percentage of slip ; these are obtained from the curve C C 0, the pitch of the screw being given. Another curve G- G- Gr also appears, its ordinates being proportional to the quotient of the cube of the speed by the indicated horse-power ; it is derived from curve AAA. This curve G G- G- is termed the " curve of coefficients," and its ordinates can obviously be made to represent, by suitable scales, both the Admiralty coefficients and Kankine's coefficient of propulsion. Were these coefficients really "constants," the curve of coefficients would become a straight line parallel to the base-line. With graphic records of progressive trials before him, the designer of new ships of similar form and type can proceed with greater assurance of success than is attainable with less extensive informa- tion. If a ship of practically identical form and size, but less speed, is to be built, his task is simply one of measurement from the curves, with some slight correction for difference in constant friction. If the speed of such a ship is to be greater than that of her predecessor, it is also possible to make a close approximation — provided that the excess in speed is not very considerable — from an inspection of the curves of indicated horse-power and coefficients. When the sizes and speeds of ships are both varied, but approximately similar forms are maintained, the problem is more complicated, but still it can be dealt with approximately, by an application of Mr. Froude's law of " corre- sponding speeds " explained on p. 478.* Supposing that from the graphic record of the results obtained on a progressive trial, the constant friction of the engines has been deter- mined, and then eliminated from the indicated thrust by drawing a line parallel to the base-line through the point where the original curve of indicated thrust (B B B, Fig. 160) cuts the ordinate of the zero speed. The line so drawn forms a new base-line giving the indicated thrusts and mean piston pressures, excluding constant friction ; and the corresponding corrected indicated horse-power curve can be con- * The late Mr. Froude indicated this Froude's writings, and contributed a application in a paper on " Useful Dis- valuable paper on the subject to the placement" contributed to the Transac- Transactions of the Institution of Naval tions of the Institution of Naval Archi- Architects in 1877. An interesting tects in 1874. The author had also graphic method of dealing with the applied it commonly in his professional subject will be found in a paper con- work for some time before the publication tributed by Mr. Young to the Transac- of the first edition of this book (1877), tions of the North-Bast Coast Institution and therein gave an illustration of the of Engineers and Shipbuilders for 1892- method. Mr. John Inglis was led to 93 (vol. ix.). the same practice by a study of Mr. CHAP, xvii.] ESTIMATES FOR HORSE-POWER. 63 1 structed. In what follows we shall speak of these corrected curves, and of the derived curve of coefficients. Next let it be assumed, although not strictly nor necessarily true, that the corrected indicated thrust bears a constant ratio to the nett resistance at any speed. For any speed V^of a ship that has been tried, let T 1 = the corrected thrust (or mean pressure) and Pj = the corresponding horse-power. Then, with the foregoing assumptions, if we increased the lineal dimensions of the ship D times, and towed the larger ship at a speed of Vxa/D, her resistance at that speed (or indicated thrust) would be expressible in the form — T 2 = T x . D», ■and the corresponding horse-power would be — P 2 = T 2 x V^D X a constant, while Pi = Tj x Vi X the same constant. Hence — Pi""^ This is an expression from which the horse-power for the larger ship can be found for a speed V^D, when that for the exemplar ship has been ascertained from the progressive trials at speed V x . To the value of P 2 , thus determined, must be added the assigned percentage for constant friction, of which particulars are given on p. 542, in order to find the indicated horse-power required for the speed (V^C). In this manner not merely the power for full speed can be estimated approximately, but that for any other speed, and so a new curve of indicated horse-power can be drawn for the new ship. This could not be done, it will be seen, unless curves such as those in Fig. 160 were available; and they are therefore of great value. If the difference in size is considerable between the two ships, it may be necessary to deal with the frictional resistance separately, and to apply the foregoing rules to the wave-making resistance only; but this kind of correction is not usually made. Using the same notation as before, another deduction may be made from the foregoing investigation. Suppose the coefficient of performance curve for the exemplar vessel to be drawn from the equation — speed 3 x area of midship section Coefficient = : — r. — . -, , ' indicated horse-power Let Ai = area of midship section in smaller vessel ; A 2 = correspond- ing area in larger vessel ; then obviously A 2 = D 2 . A x . 032 NAVAL ARCHITECTURE. [chap. : XVII. Also, the following values will hold good : — Cx = : coefficient for smaller vessel at speed V = V 3 x Pi A, C 2 = = coefficient for larger vessel at speed WD = . d A 1 P 2 1 A! PlBI. "C 2 ~A 2 P 1 " D f~D"A 1 "p^jji _ Y 3 = 1 P 2 A 2 That is to say, with the preceding assumptions, the coefficients of performance for two similar vessels steaming at "corresponding speeds " are identical. This statement holds good for the Admiralty coefficients as well as for Eankine's coefficient of propulsion. In practice it may be modified by some departure from the assumptions ; but the broad deduction is useful for practical purposes in comparing efficiencies of vessels similar in form and method of propulsion, but unequal in size. From this investigation it follows that for two ships of unequal size, but similar form and similarly propelled, driven at the same speed, the larger will have the higher coefficient of performance; the indicated horse-powers usually increasing at a more rapid rate than the cube of the speed. In applying the results of progressive trials to speed calculations, care is required to secure, if possible, similar conditions in the exemplar ship and the new design as regards not merely form, but type of engine and propeller, and equal smoothness of bottom. Differences in the coefficient of friction, arising either from different degrees of roughness or greatly different lengths of ships (see p. 441), must be allowed for; and this can be done without difficulty, if desired, in comparing small ships with large. In fact, to secure the closest approximation to the horse-power in a new ship, every part of the work requires to be done with scrupulous care and intelligence. For rough estimates, on the other hand, some of the foregoing correc- tions may be omitted ; and more especially the correction for constant friction of engines when approximating to the indicated horse-power for full speeds. One example may be given of the approximate formulae based on corresponding speeds. We will choose her Majesty's ships Hercules and Greyhound, which are very similar in form, but different in size, speed, and character of bottom. The similarity of the forms will appear from comparing the ratios of the lengths, breadths, draughts, and cube roots of the displace- chap, xvii.] ESTIMATES FOR HORSE-POWER. 633 ments given in the Table below. Using the letter D to express this ratio, we have — D=v 7 ^ 6 = 1-957; v 1157 VD = Vl-957 = 14 (nearly). On trial, the Hercules attained a speed of 14-69 knots. Corresponding speed } U^9 14j69 = knotg tor Greyhound j Jj) 14 v J/ On trial, the Greyhound attained a maximum speed of 10-04 knots with 786 I.H.P. ; at that speed her resistance was varying about as the cube of the velocity, and therefore the horse-power would vary as the fourth power. Hence- Indicated horse-power for 1 / 10-5 speed of 10-5 knots = 786 X U(M)4/ 940 H.P. Ships. Length. Breadth. Mean draught. J Displacement on trial. Hercules . Greyhound feet. 325 172J feet. 59 33£ feet. 24-6 13-7 tons. 8676 1157 The thrust of the propeller in the Greyhound at 10-5 knots might therefore be considered proportional to the quotient 940 -^ 10-5 ; if for the Hercules at 14-69 knots a corresponding assumption is made, and the thrust considered to be the same proportion of the quotient of the required indicated horse-power (P, say) -r- 14-69. In both ships the engines would be working at full speed ; and for our present purpose it may be assumed that the thrusts would be proportioned to the resistances of the two ships. Using the law of comparison proposed by Mr. Froude — (resistance for Greyhound Eesistance for Hercules^ = C 1 * 957 ) 3 * ] at 10-5 knots, at 14-69 knots . . I _ n . n ^ (resistance for Greyhound 7-5 at 10-5 knots. Hence, approximately — I.H.P. for Hercules at 14-69 knots 7-5 x 940 14-69 10-5 I.H.P. for Hercules at 14-69 knots = 9870 H.P. This power is largely in excess of that actually developed in the Hercules, when she attained a speed of 14-69 knots ; but it must 634 NAVAL ARCHITECTURE. [chap. xvii. be remembered that in the calculation the same coefficient of friction has been assumed for the Hercules as for the Greyhound ; whereas the Hercules was tried with a cleanly coated iron bottom, and the Greyhound with a copper bottom somewhat deteriorated by age. A correction is therefore necessary, and it may be simply made. It has been estimated that for a speed of 600 feet per minute the coefficient of friction for the bottom of the Greyhound was about 0-325 lb. per square foot of surface, as against 0-25 lb. for a cleanly painted iron bottom ; and this difference would involve an increase of between one-seventh and one-eighth in the total resistance and indicated horse-power for the speed of 10-5 knots. In other words, if the Greyhound, instead of being tried with her worn copper, had been tried with a cleanly coated iron bottom, like that of the Hercules, the speed of 10-5 knots would probably have been attained with about 830 H.P., instead of 940 H.P. Making this correction in the foregoing equation, we have, approximately — TTjn „ d- 7 . -,, on , 7'5x 14-69 x 830 I.H.P. for Hercules at 14-69 knots = 10-5 = 8715 H.P. This is a close approximation to the actual power (8529 H.P.) which was developed on the measured-mile trial of the Hercules; but the same degree of accm-acy may not always be secured iu estimates made in this manner. The foregoing methods of approximation are all in common use by shipbuilders and marine engineers, and there are others of undoubted value to which limits of space prevent even a passing reference.* Valuable as these methods are in ordinary practice, they do not compare in accuracy or trustworthiness with the method of model experiment devised by the late Mr. Froude. Twenty years' experience in the designing of ships for the Eoyal Navy, covering a period during which unprecedented speeds have been attained, and many new types of ships and machinery have been introduced, have placed the value of this method beyond doubt. Less extended experience of the model-experimental system outside the Admiralty fnTT;i ^° th at h ° me and abroad ' has con &'med this conclusion. Ine full descriptions given in preceding pages have indicated how the problems of nett resistance, screw efficiency, augmentation of _* Seethe reports of the British As- Architects for 1869 and 1880; and sociation Committee on Steamship Per- numerous papers by Mr. Robert Mansel formance; papers by Mr. Thornycroft in the Proceeding, of the Institution of and the late Mr Kirk in the Trans- Engineers and Shipbuilders in Scotland, actions of the Institution of Naval as well as in other publications. chap, xvn.] STEAMSHIP EFFICIENCY. 635 resistance, and propulsive coefficients have been dealt with experi- mentally by means of models and the trials of actual ships ; while the efficiency of the mechanism in marine engines has also received investigation. When novel problems in propulsion have to be solved, or unusual forms of ships built for special services, or speeds attempted which lie much outside experience, the designer, aided by model experiments made at small cost, can proceed with greater certainty of success. As specimen cases, reference may be made to the imperial Russian yacht Livadia, the form of which was quite novel. The late Dr. Tideman made trials on the tow-rope resistances of a model ; these were supplemented by an interesting series of trials on a large scale model, propelled by its own screws ; and in the actual ship the performances under steam substantially confirmed the estimates based on the models. Again, in the Inflexible of the Royal Navy, where the form was of a novel character, and the breadth extreme was unusually large in relation to length and draught, the estimates for engine-power based on model experiments were closely verified on the measured-mile trials. Many other striking examples might be given, but they are scarcely required. Steamship Efficiency. The subject of steamship efficiency has occupied much attention, and several standards of comparison have been \ proposed. None of these standards can be employed universally, however, in the com- parison of different types of ships ; because in many types, and more especially in ships of war, the choice of forms and proportions is largely influenced by other considerations than those relating to economical propulsion. It is unnecessary to repeat the remarks already made on this point, although their importance is frequently overlooked ; no distinction being made between the ideal conditions of forms of least resistance, propellers of maximum efficiency, and engines of perfect construction, and the conditions of practice with all their limitations or restrictions. Bearing this distinction in mind, we now proceed to summarize the circumstances which chiefly influence economy of steam-power. For any selected form and type of ship, economical propulsion is favoured by increase in size. This is readily illustrated if the speeds are assumed to fall within the limit where the resistance varies as the square of the speed. Suppose two similar ships to be compared, the weight of one being W x and that of the other W 2 . Let D be the ratio which the length or any other dimension in the larger ship bears to the cor- responding dimension in the other. Then it must follow that — W x = D 3 . W 2 , 636 NA VAL ARCHITECTURE. [chap. xvii. the weight increasing with the cube of the ratio of corresponding dimensions. On the other hand (as explained at p. 478), the resistances will bear to one another the ratio of the two-thirds power of the displacement ; and if E^ Ea represent the resistances — the resistance increasing only with the square of the ratio of corre- sponding dimensions. For instance, a ship twice as long, twice as broad, and twice as deep as another will hare eight times as great displacement, but, when moving at the same speed, will experience only four times the resistance, and require only four times the engine-power. The longer ship would require to have heavier scantlings than the smaller ; and consequently the hull might be somewhat^heavier in proportion to the displacement. But even sup- posing this greater proportionate weight of hull were incurred, the larger ship would be far more economical of steam-power in propor- tion to the dead weights carried. Irrespective of any assumed law of resistance, it is possible in general terms to ■ indicate the economy of propulsion obtained by increase in size. Using the same notation as before, let the two ships compared be supposed moving at the speed V, their resistances, excluding the frictional resistances on the bottoms, being E x and B 2 . Let E be the resistance of the smaller vessel when moving at the speed V — VD ; and let it be supposed that between this speed and the speed V the resistance varies with some unknown power (2») of the speed. Then — — = ( — - J X — = — ; whence E = — * R 2 VD^ V 2 " D" D" Also, by the law of comparison — Ei (for large ship) = D 3 x E = D 3 -" . Rj, 5i = a = D 3 -"; R 2 and, as before — W t (for large ship) = D 3 . W 2 ; whence — * = b = D 3 ; W a so that finally, for equal speeds of two similar ships — D""W»~B»' ° l b ~D" The greater the value of n for a certain value of D, the less will be the ratio a : b measuring the ratio of the increased resistance, chap, xvii.] STEAMSHIP EFFICIENCY. 6 37 involved in enlarging the ship, to the corresponding increase in displacement and carrying power. If the resistance between the speeds V and V -f- ^D varies as the square of the speed, n = 1, and the final equation assumes the form — 1_ w 1b b, D ' W E 2 agreeing with the result previously obtained for that law of variation. But if the resistance between the speeds V and V ■— VlT varied as the fourth power of the speed, then n = 2, and we have — D 2 ' W 2 E 2 If the resistance of the smaller vessel between the speeds V and V 4- v D varies as the sixth power of the speed, then n = 3 : and D 3 ' W 2 E a that is to say, the small ship would experience as great a resistance at the speed V as the larger ship of similar form if the foregoing assumptions held good. As a matter of fact, however, whatever may be the law of variation in the wave-making resistance in terms of the speed, the frictional resistance does not vary more rapidly than the square of the speed, and this would make the resistance of the smaller vessel less than that of the larger.* It is easy to make the necessary correction for friction in the manner explained on p. 449. The comparison of the Merkara and Greyhound types will furnish a good illustration of the foregoing equations. At 12 knots, for thp Merkara, n may be taken as unity, and for the Greyhound as 2 nearly ; in both ships E = 20,000 lbs. Suppose both vessels to have their lengths and other dimensions increased by one-third ; then D = 1 J. The Merkara has a displacement of 8980 tons ; the Greyhound one of 1160 tons ; the enlarged Merkara would weigh 9430 tons, the enlarged Greyhound about 2750 tons. For enlarged Merkara, Ej = 20,000 x f - V = 35,555 lbs. For enlarged Greyhound, B, = 20,000 x - = 26,666 lbs. The Greyhound type, therefore, gains more in economy of propulsion * For interesting graphic illustrations Mr. Biles in the Transactions of the In- of the above equations, see a paper by stitution of Naval Architects for 1881. 638 NAVAL ARCHITECTURE. [chap. xvii. by enlargement than does the Merkara ; although the latter type benefits considerably by the same process, and would have much greater carrying power in proportion to the expenditure of fuel as the size increased. To the foregoing considerations, which have had regard only to smooth-water performances, it is necessary to add one remark. In ocean steaming, the longer, larger, heavier ship is far more likely to maintain her speed under varying circumstances of wind and sea than is the smaller vessel. These two sources of gain in larger ships fully explain the general adoption of the policy which has resulted in very large increase of the sizes of ocean steamers. Increase in size and variation in proportion may, as explained in Chapter X., affect the ratio which the weight of hull bears to the displacement. No general law can be stated for this ratio ; but for purposes of illustration let it be supposed that the longer, larger vessel has a relatively heavier hull. This increase in weight of hull must be set against the proportionate saving on propelling apparatus and coal. But the balance of advantage in a commercial sense on long voyages would still remain with the larger ship when the difference in size is considerable. As an example take the Mer- kara and the enlarged Merkara mentioned above. If 1600 H.P. was required to drive the Merkara 12 knots, about 2800 H.P. would suffice for the latter. For voyages of equal length at that speed the weights of coal burnt would bear to one another the same ratio as the horse-powers. Take 400 tons for the weight of engines, etc., for the smaller ship; then 700 tons will be about the corresponding weight for the larger ship ; if the Merkara be credited with a coal supply of 500 tons, the larger ship should carry about 880 tons. Suppose, further, that in the Merkara the hull weighed about 33 per cent, of the displacement, whereas in the larger ship it was increased to 40 per cent. ; then in the Merkara there would remain 1800 tons available for cargo and equipment, which could be propelled over a certain distance by an expenditure of 500 tons of coal, as against 4100 tons in the large ship, which would require an expenditure of less than 900 tons of coal for an equal distance. In the former case the expenditure of 1 ton of coal would carry 3*6 tons of cargo over the distance, and in the larger ship an equal consumption would carry about 4-5 tons, or an increase of 25 per cent. From the commercial side the gain' in dead-weight capacity would represent a large increase in earning power, accompanied of course by a considerably increased first cost, and greater working expenses. Into these matters it is not proposed to enter here ; but the fact that the balance of advantage lies considerably on the side of the larger vessel is undoubted. The figures given above, it will be chap, xvn.] STEAMSHIP EFFICIENCY. 639 understood, are simply for purposes of illustration ; but they do not err on the side of favouring the larger vessel. Increase in size is found to be accompanied by equal economy in power when war-ships are compared. For example, a vessel of the Admiral class, 325 feet long, 68 feet broad, with a displacement of 10,000 tons, requires about 5000 H.P. for a speed of 14 knots in smooth water, whereas for the same speed about 6400 H.P. suffices to drive the Boyal Sovereign, of 14,200 tons displacement, 380 feet in length, and 75 feet in beam. In both cases the ships are well formed, the engines are vertical and applied to twin-screws. Although the Boyal Sovereign has triple-expansion engines, while the Admiral has compound engines, the losses on friction are probably nearly the same in both cases. At higher speeds the larger ship gains upon the smaller. For example, about 12,000 H.P. would be required for 17 knots in the Admiral, whereas the Boyal Sovereign attained 16'77 knots on the measured mile with 9760 H.P., and would require less than 10,500 H.P. for 17 knots, or absolutely less power than the shorter and smaller ship. Weight of propelling machinery and rate of coal expenditure being dependent upon the indicated horse-power, it will be obvious how great is the gain in weight disposable in armour, armament, and equipment by adopting larger dimensions. Economical propulsion is also greatly promoted by the adoption of forms and proportions, in association with a given displacement, which lead to diminished resistance. This may seem a mere truism, but it is desirable to give one or two illustrations of the extent to which economy may be carried. For this purpose recourse may be had to the steam trials of ships, although it is necessary to observe that in these results the relative efficiencies of propellers and machinery are influential as well as differences of form. The table on p. 640 is of interest, as indicating the horse-power required to give a smooth- water speed of 14 knots to certain typical war-ships of approximately the same displacement but varying dimensions and forms. The first two vessels are single screw, and their maximum speeds were between 14 and 15 knots, so that their engines were working under very favourable conditions near their maximum powers at 14 knots. The other two are twin-screw, and their engines were only developing about one-third and one-fifth respectively of the maximum powers when the ships were steaming 14 knots. Consequently they were not working under such advantageous conditions. The table furnishes an illustration of what may be done, with a practically constant length and draught, in the direction of economizing power by changes in form. Comparing, for example, the Warrior and Blake, a decrease in power of 20 per cent, is associated with an increase in beam of 7 feet, and a slight decrease 640 NAVAL ARCHITECTURE. [chap. xvii. in draught. Again, as between the Hercules and ship of the Admiral class, there is an economy of about 38 per cent., associated with an increase in beam of 9 feet and in draught of a few inches. The greater breadths in the later ships are only amidships, and at ■ Indicated Ship. Length. Breadth. Mean draught. Displace- ment. horse-power for 14 knots. ft. . ft. ft. in. Warrior .... 380 58 26 8850 5000 Hercules . 325 59 24 8 8675 7250 Admiral class . 325 68 25 3 8900 4500 Blake .... 375 65 25 9 9100 4000 the extremities finer forms are thus made possible. At p. 462 the gain in economy of power resulting from this change of form has been explained. Twin-screws in the modern vessels have also favoured economical propulsion. As between war-ships and merchant ships, built as they are to fulfil widely different conditions of service, and having radically different vertical distributions of their weights, comparisons of the expenditures of power at equal speeds have little practical value. Speaking broadly, the merchant steamer is longer and narrower for a given displacement than the war-ship. Her length is greater in relation to the maximum speed attained. As a rule, therefore, for equal speeds and displacements the merchant ship requires a less expenditure of power for reasons which have been explained above. It is unnecessary to repeat those explanations, or to dwell upon the much greater importance of handiness and manoeuvring power in the war-ship. The question of protection has an important influence on the most suitable forms and proportions in war-ships. The designer has to consider not only what expenditure of power will be required with given dimensions at the intended speed, but what weight of protective material — vertical or deck armour — will be needed with those dimensions. It may, and does often, happen that the best results in point of cost and efficiency are obtained by choosing dimensions and forms less economical in engine-power and coal consumption, but which tend to minimize the weight and cost of armour. In the earlier periods of the armour-clad construction, when the whole length at the water-line was protected, either by a belt of considerable depth or by armour carried to the height of the upper deck, this matter was of great importance. Sir Edward Keed CHAP. XVII.] STEAMSHIP EFFICIENCY. 641 discussed it exhaustively when Chief Constructor of the Navy, and one case may be taken as an illustration. Taking the ironclad frigate Hercules as a type, an estimate was ^ made of the dimensions and cost of a vessel which should carry the same battery and guns, the same armour protection on the water-line belt, have the same speed and coal supply, and be built on the same system ; the new ship was to have the same proportion of length to breadth as the Minotaur, and to be equally economical of steam-power. The follow- ing tabular statement shows the result of careful calculations : — Particulars. Length (in feet) Breadth (in feet) Displacement (tons) . Weight (in tons) of — Hull Armour and backing on belt . „ „ ,, on batteries Engines, boilers, and coals . Equipment and armament Indicated horse-power for speed of 14 "69 knots First cost of— Hull \ at average prices for ironclads Engines J built prior to 1869 . New ship (as estimated). 385 9088 4574 1518 398 1460 1138 6585 £ 326,500 55,500 Hercules. 325 59 8676 4022 1292 398 1826 1138 8529 £ 287,400 72,000 After crediting the long ship with less powerful and costly engines, it appears that the total cost of the Hercules for hull and engines would be about £22,000 less. The more powerful engines of the Hercules would undoubtedly be more expensive to keep at work, owing to their greater consumption of fuel ; but " the interest at a low rate on the difference of prime cost would quite make up for the additional cost of fuel in the Hercules, supposing her to be in com- mission and on general service." The longer and larger ship, more- over, would be more costly to man and maintain in repair ; and her rate of turning would be slower as compared with the Hercules. When the " central-citadel " system was introduced in the Inflexible, another consideration had an important influence upon form and proportions : viz. the provision of stability when the ends were riddled (see p. 134). A less ratio of length to breadth was adopted than in any preceding ironclads of equal speed, and much greater fineness was given to the extremities. These changes in form, as a matter of fact, proved aids to economical propulsion, and the measured-mile performances of the Inflexible with her ratio of length to breadth (4£ to 1) compared favourably with those of other vessels of equal length, greater draught, and having ratios of length 2t 642 NAVAL ARCHITECTURE. [chap. xvii. to breadth of 5 or 5J to 1. At 14 knots the "displacement coefficient" of the Inflexible was nearly 190, which is about the same as that obtained with the Alexandra of equal length, over 11 feet less beam, and nearly 2 feet greater draught, with 2000 tons less displacement. It is possible, of course, to carry too far restriction in length and increased fulness of form. In economizing on weight of hull and protective material, forms and proportions may be adopted which most seriously and to an unwise extent cripple efficiency of propul- sion. The extreme case of the Eussian circular ironclads will illustrate this statement. They were designed for coast-defence service in the shallow waters of the Black Sea, and the circular form was chosen because it gave the least surface and the greatest carrying power in proportion to displacement. If the vessels had been mere floating forts, this view would have been correct. But passing from stationary flotation to the case of locomotion at moderate speeds, the circular form is found to be most unsuitable. Model experiments and the actual performances of the ships show that a circular ship of the cross-sectional form adopted by the Russian designers experienced about five times as great resistance as a ship like the Devastation when moving at equal speed. It is probable that by changes in cross-sectional form the resistance might be reduced ; but for purposes of illustration we will take the Russian form, and show what would be its influence upon size if a circular ship were built to steam as fast and as far as the Devastation, both ships being fitted with the same types of machinery and boilers — say the compound type used about 1870 (see p. 562), and carrying the same dead weight of armour, armament, and equipment. Using for the Devastation the ascertained weights for the ship as built, with suitable changes on account of compound engines instead of the low-pressure surface condenser type with which she was originally fitted, and using for the circular ship data furnished by the advocates of that type, the comparative results for the Devastation's maximum speed of about 13| knots are given in the table on the following page.* If the proportions of the existing ships were followed, this vessel would be about 230 feet in diameter, and 19J feet draught. The oircumference at the water-line would be about 720 feet ; whereas the total length of the water-line requiring to be armoured in the Devastation would not exceed 640 feet ; and consequently an armour belt of equal depth and thickness on the two ships would weigh * For an able defence of the circular Transactions of the Institution of Naval type, see Captain GoulaefFs paper in the Architects for 1876. CHAP. XVII.] STEAMSHIP EFFICIENCY. 643 •about one-eighth more for the circular ship than for the Devastation. The deck area of the circular ship would be about 41,000 square feet; the corresponding area in the Devastation would not exceed ■one-third that for the circular ship ; and here, for equal protection, Devastation. Circular ship. Horse-power for 13 j knots . Weight of propelling machinery . „ coal .... hull ... . Dead weight .... Total displacement . I.H.P. 6600 tons. 1150 1200 . 2880 4070 I.H.P. 34,000 tons. 6,000 6,100 4,000 4,070 9300 20,170 the Devastation would be at a great advantage. On the upper and breastwork decks of the Devastation, the mean thickness of the plating may be taken at 2£ inches ; the total weight is about 500 tons. On the circular ship, 2J-inch plating over the whole area of the deck would weigh about 1600 tons. These figures sufficiently indicate the unsuitability of the circular form for armoured vessels moving at moderate speeds. The existing vessels are reported to have steamed at very low speeds, and at these to have required an abnormal power. For example, the Novgorod, with 2490 tons displacement and 2200 H.P. (indicated), is said to have steamed 1\ knots only. In contrast with this, the performance of the coast-defence monitor Abyssinia may be mentioned. With a displacement of 2800 tons, she attained practically the same speed with 560 H.P. The model experiments made by the late Mr. Froude disclosed another curious characteristic of the Kussian circular ships. As the speed increased the models tended to " dive " below their normal draught, and this fact alone renders it doubtful if, apart from the extravagant expenditure of power, such vessels could be driven at high speeds without danger. These remarks now have only an historical interest, but at no remote period there were many advocates of the circular form or approximations thereto. In the Livadia the Eussian designers made a departure from the circular form, and the experiment was sufficiently interesting to justify a brief summary of the results. Although built as an imperial yacht, it was understood that the vessel was regarded also as a model for an armoured ship it was then contemplated to build, of similar form, but much larger dimensions. The Livadia was 235 feet long, 153 feet broad, and under trial conditions had a dis- 644 NAVAL ARCHITECTURE. [chap. xvir. FIG. 161 placement of about 4400 tons on a draught of 7 to 8 feet. With 12,350 I.H.P. she is said to have attained a speed of 15-725 knots per hour; with about 4800 H.P., 13 knots ; and with 3000 H.P., 11 knots. In Fig. 161, the curve AAA shows the curve of indicated horse-power based on these figures. For purposes of comparison there also appear the corresponding curve BBB for her Majesty's ship Iris, the curve COC for the Merhwa cargo and passenger steamer built by Messrs. Denny ; the curve DDD for Eoyal yacht Victoria and Albert ; and the curve EEE for the fast passenger steamer Charles Quint, built by Messrs. II 000 3000 I 2 3 4 5 6 7 8 9 10 II 12 13 1* 15 IG Scale of speed in, Taiots per hour. Inglis. The principal particulars of the vessels thus compared are given in the following table : — Ships. Length. Breadth (extreme). Measured-mile condition. Mean draught. Displace- ment. Livadia .... Iris Merkara .... Victoria and Albert . Charles Quint . feet. 235 300 370 300 315 feet. 153 46 37* 40| 33| feet. 7£ 18 17 14 14f tons. 4400 3290 3980 2000 2480 The Livadia form had very great advantages as compared with the circular form. Model experiments showed that at speeds varying from 13 to 7 knots the Livadia form experienced only 60 per cent, of the resistance of the circular form with equal displacement. Her three screws were more favourably placed than the multiple screws of the circular ships ; a better supply of water to the propellers was secured, and the augmentation of resistance must have been much less. On the other hand, the diagram shows how very large was the expenditure of power as compared with well-formed ships of ordinary CHAP. XVII.] STEAMSHIP EFFICIENCY. 645 proportions. When compared also with short bluff-ended armoured ships designed for low speeds, the Livadia does not show so badly. For example, the Hotspur ram turret-ship of the Eoyal Navy is 235 feet long and 50 feet broad, and on trial drew 20J feet, with a dis- placement of 4180 tons. She attained 11-3 knots with less than 2000 I.H.P., or about two-thirds the power required by the Livadia for that speed. Allowing for the greater weight of the Livadia, and the greater constant friction of her more powerful engines, probably the Livadia's performance is • about 40 per cent, worse than that of the Hotspur, measuring by the ratio of horse-power ito weight driven. The most interesting deduction from these trials is the possibility, when necessity arises, in vessels of moderate speed, with a given length and displacement, of exchanging ordinary forms of midship section (where the draught of water is from 40 to •50 per cent, of the extreme breadth) for a very broad, shallow section of equal area. By means of suitable changes in other cross-sections, accompanied by a considerable amount of fineness in the longitudinal sections (buttock and bow-lines), a given speed can be obtained in the broader, shallower vessel with about 40 per cent, more power than in the ship of ordinary form.* For armoured or protected ships, the Livadia form may be regarded ■as distinctly inferior to the Hotspur form. The length along the side at the water-line must be greater than in the Hotspur, so that belt protection, if adopted, would be more costly and heavier. The deck area would be very much greater in the Livadia form, and for a given thickness of protective plating the weight would be much increased. In the following table a comparison is made between the Alexandra and an enlarged Livadia of equal displacement : — Alexandra. Enlarged Livadia. Length .... Breadth .... Draught (mean) Displacement (tons) . Indicated horse-power Speed .... 325 feet 63 feet 10 inches 26 feet 6 inches 9500 8600 15 knots 300 feet 200 feet 11 to 12 feet 9500 12,500 to 13,000 15 knots This increase in engine-power would necessitate a proportionate increase to weight of machinery and coals ; there would be practically the same length of water-line to protect, and the area of deck requir- * See papers on the Livadia by €aptain Goulaeff and Sir E. J. Keed in the Transactions of the Institution of Naval Architects for 1881. 646 NAVAL ARCHITECTURE. [chap. xvii. ing horizontal armour would be about double that of the Alexandra. Hence it follows that on the Livadia form the association of speed, coal endurance, armour, and armament actually existing in the Alex- andra could not be repeated. It might be possible, of course, to adopt the Livadia form in connection with some entirely new dis- position of the armament or the protective material, but it is unneces- sary to pursue the subject further. Economical propulsion demands (as explained on p. 457) a due relation between the lengths of ships and their maximum speeds. As speeds have increased, therefore, lengths have been increased in both mercantile and war-ships. For a long time the lengths of war- ships were kept within moderate limits in order to increase handiness when making or avoiding attacks with the ram. It still remains true that, other things being equal, the space and time in turning are increased by increase of length. On the other hand, the develop- ment of mechanical appliances for readily operating rudders of large size have greatly increased the power of control, and the introduction of torpedo armaments has made ram-attacks more dangerous than formerly to the ship which tries to ram. The balance of naval opinion in recent years has, therefore, been in favour of greater length, with its consequent advantages of more economical propulsion and better maintenance of speed in rough water. It will be noted that, whereas with maximum measured-mile speeds of 14 to 15 knots armoured ships up to 1885 rarely exceeded 330 feet in length, the corresponding speeds at the present time are 17 to 18 knots, and the lengths 380 to 400 feet. In relation to these speeds, the greater lengths now used are really more moderate than were the less lengths in relation to the speeds formerly accepted. Similar remarks apply to merchant steamers. Lengths of 450 feet were accepted for sea speeds of 15 knots. With the present sea speeds of 20 to 22 knots, the maximum lengths of 525 to 600 feet are relatively moderate. It is unnecessary to repeat the explanations previously given, as to the advantages of length in relation to expenditure of power and dead-weight capacity at moderate speeds, or the distinction necessary between the influence of absolute length and the effect of variations in the proportion of beam to length. Narrowness is not a necessary condition of economical propulsion, and may make against it when there is a long "middle body." The increase in dimensions and speeds of seagoing steamships made in recent years has been achieved without sensible increase in the draught of water, the upper limit of draught being fixed by the depths available at the ports and docks frequented by ships. From the remarks made on p. 476, it will be understood that if increased draughts were permissible, higher speeds and greater carrying power CHAP. XVII.] STEAMSHIP EFFICIENCY. 647 might be attained with less relative lengths than are necessary under present conditions. The great influence of increased length on weights of hull has also been discussed on p. 410. This matter has been pressed upon the authorities of harbours, canals, and docks ; there is now a fuller recognition of the advantages obtainable with greater draughts ; and in many instances steps have been taken to provide greater depths of water.* During the last thirty years, side by side with the development of the sizes and speeds of ocean steamers there has been in progress the construction of small vessels possessing higher smooth-water speeds for short periods than the larger vessels. Vessels of from 50 to 200 feet in length have been driven at smooth-water speeds of 15 to 27 knots, and have furnished remarkably suggestive facts as to the phenomena accompanying propulsion at very high speeds. The principal characteristics of their machinery and boilers, and of their behaviour, have been dealt with in previous pages. It has been shown that the expenditure of power in proportion to the weight driven is very great, and that the key of all the designs is to be found in the lightness of the propelling apparatus in relation to the power it develops, and in the association of extreme lightness of hull structure with sufficient strength for the special service. The following tabular statement may be of interest as summarizing the relative expenditure of power in propelling these small craft and other vessels of different types and dimensions at the same speeds : — t lst-class cruiser. Atlantic Torpedo- boat. Torpedo- gunboat. 3rd-class cruiser. 2nd-class cruiser. passenger- steamer Edgar. Blenheim. (light). Length .... 135 ft. 230 ft. 265 ft. 300 ft. 360 ft. 375 ft. 625 ft. Breadth . lift. 27 ft. 41ft. 43 ft. ■ 60 ft. 65 ft. 63 ft. Trial draught 5 ft. 1 in. 8 ft. 3 in. 16 ft. 6 in. 16 ft. 2 in. 23 ft. 9 in. 25 ft. 9 in. 21ft. 3 in. Trial displacement 100 tons 735 tons 2800 tons 3330 tons 7390 tons 9100 tons 11,550 tons Indicated horse-power— For 10 knots . 110 450 700 800 1,000 1,500 2,000 ,. H „ 260 1100 2,100 2400 3,000 4,000 4,600 .. 18 „ 870 2500 6,400 6000 7,500 9,000 10,000 „ 20 „ 1130 3500 10,000 9000 11,000 12,500 14,500 Notb. — The figures for horse-power are " round." The 3rd-class cruiser was run at 20 knots in the shallow water at Stokes' Bay, while the powers for the other ships at that speed correspond to deep water. Applying the law of corresponding speeds to the performances of the torpedo-boat in this table, some interesting deductions may be made. These speeds, it will be remembered, bear to one another the ratio of the sixth roots of the displacements. Comparing the second- * See the Proceedings of the Inter- national Maritime Congress. London, 1893. t This table is taken from a paper contributed by the author to the Trans- actions of the Institution of Naval Architects for 1892. 648 NAVAL ARCHITECTURE. [chap. xvh. class cruiser with the torpedo-boat, the corresponding speeds are as 1-79 : 1 ; for the first-class cruiser, Blenheim type, the corresponding speeds are as 2*12 : 1. For the Atlantic steamer the corresponding speeds are as 2-2 : 1. In other words, to 20 knots in the torpedo- boat would correspond speeds of about 36 knots for the second-class cruiser, 42'5 knots for the first-class cruiser, and 44 knots for the Atlantic steamer. The torpedo-boat, therefore, if used as a model for the larger vessels at these respective speeds, would by an analysis of its performance furnish many useful and fruitful sug- gestions for guidance in dealing with these ships. It will be noted, for example, that the very advantageous conditions of resistance attained by torpedo-boats at their maximum speeds would not be reached by the larger vessels until their speeds were very much greater than any yet attained, or even contemplated at the present time. In view of progress already made, however, it would be unwise to limit future developments, or to assume that the great engine powers necessarily required with increased speeds will not be obtained hereafter with relatively lighter machinery than any yet in use, as well as with greater economy in fuel, and lighter hulls. ( 6 4 9 ). CHAPTEE XVIII. THE STEEKING OF SHIPS. Ships are ordinarily manoeuvred by means of rudders, sails, or pro- pellers driven by steam-power. Steering by sail-power alone may be accomplished by the skilful seaman, if his ship has been well designed. Steering by the action of the propellers alone is also a possibility in certain classes of steamships, and may be a great advantage under certain circumstances. Eudders are fitted, how- ever, in all classes of ships, and form the most important means of controlling their movements under ordinary conditions of service. In this chapter attention will be chiefly directed to the principles upon which the action of rudders depends. A brief notice will suffice respecting manoeuvring by the use of propellers ; but nothing will be said respecting manoeuvring under sails alone, as that is peculiarly a matter of seamanship. The rudder is almost always placed at the stern of a ship, which is its most advantageous position for controlling her movements when she has headway. In what follows it will be understood therefore, that, unless the contrary should be stated, we are dealing with stern rudders. After discussing their action, a few remarks will be made respecting the use of bow rudders, auxiliary rudders, and other supplementary methods of increasing the turning power of ships. Two kinds of rudders require to be noticed. First, the ordinary rudder, which rotates about an axis near its foremost edge, and is hung to the sternpost of the ship. Fig. 162 shows the common arrangement in a single-screw ship. AA is the axis of the rudder, the line passing through the centre of the pintles by which the rudder is hung to the after sternpost, or rudder-post. In the plan, AB represents the rudder put over to port, the helm being a-star- board. In sailing ships, paddle steamers, jet-propelled vessels, and twin-screw ships, the ordinary rudder is hung to the after end of the ship, there being only one sternpost in such vessels. Fig. 163 shows 650 NAVAL ARCHITECTURE. [chap. xvhi. the common arrangement in twin-screw ships ; and, apart from the propellers, the drawing will also serve for the other classes named. A few ships have had the rudders placed before the single-screw FIG. 162. Profile propellers, but this is not a common plan ; when it is adopted, the rudder is generally of the ordinary kind, and is placed in the after deadwood below the screw-shaft. The second form to be noticed is the balanced rudder, which differs from the ordinary form in having a part of its area — usually about one-third — before the axis about which it rotates. This kind of rudder has been used in many steamships of the mercantile marine and the Royal Navy. Fig. 164 illustrates a common arrangement : AA is the axis. There is no rudder-post, the weight of the rudder being taken inboard, and the lower bearing at the after end of the keel is made use of simply to steady the rudder. In some cases balanced rudders have been fitted without the lower bearing, the rudder-head being made exceptionally strong; but this plan has considerable disadvantages in large ships, especially as regards liability to derangement by shocks or blows of the seaj Usually the balanced rudder is made in one piece, and, when put over, occupies a position similar to that indicated (in plan) by Fig. 165, the part AC before the axis A being rigidly attached to the part AB abaft it. When the rudder is thus made in one piece, it is termed a " simple " balanced rudder. In a few war-ships having auxiliary sail-power as well as steam, so-called "compound" balanced rudders have been fitted in the manner illustrated by Figs. 164-166. The part before the axis is attached to a hollow annular head, up through which passes the rudder-head which carries the after part of the rudder; and the two parts are hinged to one another along the axis. When CHAP. XVIII.] THE STEERING OF SHIPS. 651 the ship is tinder steam, the two parts can be locked together and made to act as a simple balanced rudder ; when she is under sail, the forepart of the rudder can be locked fast in the line of the keel (as shown by AC, Fig. 166), occu- pying a position resembling that of the rudder-post in ordi- nary screw steamers, and the after part alone (AB) is used -=S^M^3iT" = 3^HSS^ FIG. 164. to steer the ship. This more complicated arrangement was devised because, in some of the ships first fitted with large balanced rudders, complaints were made that evolutions under sail were hindered by the "drag" of these rudders, as compared with ordinary rudders of less area. As experience was gained, however, less helm angles were used with the large balanced rudders when FIG. 165. FIG. 166. FIG. 167. Profile. under sail, and the difficulty in manoeuvring disappeared. Some of the compound rudders, in fact, have had their two parts rigidly secured to one another, and are now worked as simple balanced rudders. Another form of rudder is illustrated by Fig. 167. It resembles an ordinary rudder in its mode of suspension, by pintles, to the body- post. The deadwood of the ship is cut away, and the lower part of the rudder extends forward below the ship. In this way a comparatively small proportion of the total rudder area can be made to balance, or nearly balance, the remaining part abaft the axis. The lower forward portion of the rudder is exceptionally well placed for steerage. Eudders of this kind have been fitted to torpedo- boats built by Mr. Yarrow, and also to torpedo-gunboats of the Eoyal Navy. Kudders identical in principle, but differing in details, have been fitted by Messrs. Thomson to some very large and swift merchant steamers, as well as to cruisers. In all cases these rudders have proved efficient both for headway and for sternway. Plan. 652 NAVAL ARCHITECTURE. [chap, xviii. In a considerable number of small vessels and torpedo-boats an arrangement of balanced rudders has been fitted similar to that illus- trated in Fig. 168. Mr. J. S. White has chiefly developed this arrangement, which is known as the " turn-about " system. A modi- fication of the plan has been carried out in torpedo-gunboats of the Eoyal Navy. One of the two rudders is before and the other abaft the athwartship vertical plane passing through the centre of the screw propeller or propellers. The deadwood is cut away to a con- siderable extent to facilitate turning. Both rudders are controlled by the same steering gear, and act together. Excellent manoeuvring FIG. 168. Profile. FIG. 169. Profile. Plan. End View. power is thus obtained, not merely when a vessel is going ahead, but also when she is moving astern. The plan is applicable both to single and to twin screw ships. Mr. Thornycroft has introduced a plan, illustrated in Fig. 169, of "twin " balanced rudders in torpedo-boats. This has answered admirably. Instead of a single balanced rudder at the middle line, one is fitted on each quarter abreast of and outside the screws. The rudder heads are carried inboard and strongly held; there is no bearing at the heels of the rudders. When the helm is amidships, the blades of the rudders and the suitably shaped stern between them form a "tunnel" in which the propeller works, and it is considered that greater efficiency in propulsion is thus obtained, while the "race " of the screw is utilized for steering either ahead or astern. Both ordinary and balanced rudders may be regarded simply as plane surfaces which, by means of suitable mechanism, can be placed at an angle with the keel-line. It is customary to speak of the chap, xviii.] THE STEERING OF SHIPS. 653 " angle of helm " rather than the rudder angle. " Helm a-starboard " means that the rudder has been put over to port, and that the head of the ship moves to port. " Helm a-port " means that the rudder has been put over to starboard, and that the head of the ship moves to starboard. A sailing ship has " weather-helm " when the rudder has been put over to the leeward side, in order to make the head of the ship fall off from the wind. When the helm is " a-lee," the rudder has been put over to the windward side, in order to bring the head of the ship up to the wind. In discussing the action of the rudder, it will be convenient to consider separately the following features : — 1. The causes which produce, and govern the amount of, the pressure on the rudder, making it effective in turning a ship. 2. The relation which exists between the pressure on the rudder and the force required at the tiller end to hold the helm at any angle desired ; as well as the work to be done in putting the helm over. 3. The turning effect on a ship produced by the pressure on the rudder. The first and second of these subdivisions are very closely con- nected. In discussing the third, it will be necessary to distinguish between, what may be termed, the initial motion of a ship when her helm is put over, and her subsequent motion when the speed of rota- tion has become approximately uniform. Causes of Pressure on Rudders. — When a rudder is placed obliquely to the keel-line of a ship, and streams of water impinge upon its surface in consequence of the motion of the ship, or the action of her propeller, the motions of these streams must be more or less checked or diverted, and a change of momentum is produced, which reacts upon the rudder and causes a normal pressure upon its surface. If all these streams were moving with uniform velocity and with parallel lines before they impinged on the rudder, the normal pressure upon it could be estimated approximately by the rules stated for thin plates on p. 438. Since rudders are commonly not wholly submerged, these rules would give somewhat less than the true pressure. In practice the streams impinging upon a rudder do not move in parallel lines or with uniform velocity ; and to estimate strictly the normal pressure on a rudder it would be necessary to take account of the velocity and direction of motion of the water in each elementary stream, in order to determine the change of momentum. Approxi- mate estimates suffice, however, for practical purposes, and in making such estimates it is customary to express the speed of approach of the streams to the rudder either in terms of the speed of the ship or that of her propeller, assuming the same speed for all the streams. 654 NAVAL ARCHITECTURE. [chap. xvm. If the vessel is moving ahead in a straight course and her helm is put over, it is usual to assume that the streams are flowing parallel to the keel, and that the angle of obliquity to be used in estimating the effective pressure on the rudder is the angle which it makes with the keel. As soon as the turning effect of the rudder begins to be felt by a ship, and she acquires angular motion as well as translatory motion, the conditions are altered, and the effective angle of obliquity of the rudder is usually made less than its angle with the keel. This has been proved experimentally, and will be made the subject of further remark when considering the phenomena attending the turn- ing of ships. In making approximate estimates of the rudder pressure, it is, usual, however, to take the helm angle with the keel as the effective angle of obliquity. Although these assumptions are commonly made in calculations for the sizes and strengths of rudders and steering gear, no one supposes them to strictly represent the facts, even in the simplest case, such as that of a sailing ship running dead before the wind. From the explanations given on p. 453, as to the stream-line motions at the stern of a sailing ship thus circumstanced, it will appear that the speeds and directions with which the streams impinge upon the rudder will vary with the headway, the form of the stern, the rough- ness of the bottom, and the helm angle. When a ship is not running before the wind, she has leeway as well as headway, and is inclined to the upright, all of which circumstances affect the stream-line motions, and the normal pressure on the rudder ; but their influence cannot be exactly estimated, and is of little practical importance. The rudder pressure which is effective for turning a ship obviously has no connection with the hydrostatical pressure which would be acting upon the surface, if the rudder were put over to any angle when the ship was at rest in still water. This distinction is men- tioned because some persons have confused hydrostatical pressure with the pressure or reaction due to the relative motion of the streams and the rudders, and have proposed to shape the rudder according to laws based upon this wrong assumption. The mistake made is similar to that referred to at p. 436, as to the relative resistances of a plane surface wholly or partly submerged ; but there can be no question that without motion of the ship, or of the water past the rudder, the rudder can have no steering power. Paddle-wheel steamers and jet-propelled vessels differ somewhat from sailing ships in their steerage power. The latter require to be in motion if the water is still — to have " steerage way " — before the rudder can act ; but the former may acquire steerage power with little or no headway by means of the action of their propellers. If the wheels of a paddle steamer are started, for example, when she is at chap, xviii. J THE STEERING OF SHIPS. 655 rest in still water, a paddle race is driven astern at considerable speed on each side ; and it is a matter of common experience that this motion of the race relatively to the rudder will develop an effective pressure and bring the ship under control by her rudder, before she has gathered much headway. Similar conditions probably hold good in jet-propelled vessels, although experience with them is limited. In both these classes of vessels, when their speed has been increased by the continued action of the propellers, and approximately uniform motion has been attained, the influence of the propeller race becomes far less, and the steering power of the rudder is governed mainly by the speed of the vessel, the fineness of the run, and other conditions closely agreeing with those described for sailing ships. The steerage of screw-steamers presents certain special features deserving careful consideration. In single-screw ships as ordinarily constructed, the propeller is situated immediately before the rudder ; when a vessel is moving ahead the race is driven aft more or less directly upon the fore side of the rudder, and when she is moving astern the action of the propeller induces a forward pressure on the after side of the rudder. The particles of water in the propeller race have rotary as well as sternward motion communicated to them, and, moving in more or less spiral paths, impinge upon the rudder in directions which may depart widely from parallelism with the keel- line. Experiments have been made to determine the " position of zero-pressure" for rudders placed behind single screws, and they indicate clearly the obliquity of the motion of the streams in the race. Herr Schlick, for example, divided an ordinary rudder into two equal parts, in the steamer Vimodol ; the line of section being horizontal. When the screw was at work, the lower half found its position of rest at an inclination of rather less than 10 degrees on one side of the keel-line, while the upper half rested at nearly an ■equal inclination on the other side of the keel-line. In other cases the helm has been left free while the screw was at work, and the rudder has been found to rest at a sensible angle to the keel-line, the effective pressure of the streams delivered by the lower blades being predominant over that of the streams delivered by the upper blades. This position of rest or zero pressure is clearly that from which the effective rudder angle should be reckoned, and not from the keel-line, in estimating the initial pressure on a rudder put over when a single- screw ship is proceeding on a straight course. Further, it will be noted that, to obtain equal pressures on opposite sides of the keel, the helm must be brought to a greater angle with the keel-line on one side than on the other. This has been considered disadvantageous, and various proposals have been made to remedy the supposed loss of efficiency, but they have not found favour in practice. 656 NAVAL ARCHITECTURE. [chap. xvm. The influence of the propeller upon the steerage of single-screw ships is illustrated by the well-known practice of " slewing " ships completely round in a very limited space. Suppose a vessel to be at rest in still water, and that her screw is started ahead ; it delivers a race having considerable sternward velocity and thus gives good steerage power before the vessel has gathered headway. The head of the ship begins to turn, say to starboard, the helm being a-port ; and when headway is becoming sensible the engines are reversed, the hebn put a-starboard, and by the action of the screw a pressure is developed on the aft side of the rudder tending to augment the previous motion of the head of the ship to starboard. In this manner, by suitable manipulation of engines and rudder, the ship can be turned completely round in a very small space, if that manoeuvre should be thought necessary. The time occupied in turning would, of course, be considerable as compared with that needed for turning under way. Twin screws, placed in the manner indicated in Fig. 163, are not so favourably situated as single screws for influencing the effective rudder pressure by the motion of the race. But the same kind of influence is exerted to some extent ; and to give it marked effect, rudders of large longitudinal dimensions have been fitted in many twin-screw war-ships. These broad rudders sweep out to a con- siderable distance from the keel-line, even for moderate helm angles, and their after parts, at least, come fully under the influence of the screw race. Experience shows this simple expedient to be very effective; for example, in the Inflexible, an addition fitted to the after part of the rudder caused a sensible improvement in the steering. No serious difficulty is encountered in the steering of twin-screw ships when proper care is bestowed upon the rudder and steering gear, as will be seen from the facts given at the end of this chapter. So far as the action of the rudder is concerned, therefore, the form of the after part of either single or twin screw steamers is not so im- portant as it is in sailing, paddle, or jet-propelled vessels ; but it has been shown (on p. 603) how necessary to the efficiency of screws as propellers is fineness of form in the after body. Broadly speaking, it may be said that, when a screw-steamer is moving ahead, the velocity with which the streams impinge upon her rudder, if placed abaft the screw, equals the speed of the screw, and therefore equals the sum of the speed of the ship and slip of the screw. When the slip is considerable, as it may be in some cases, the increase in rudder pressure and steering effect above that due to the headway of the ship may be a most valuable element in her handiness. Similar reasoning applies to the case where the propeller is driving a ship astern at a steady speed. But the most important chap, xviii.] THE STEERING OF SHIPS. 657 case of screw-ship steerage is that when, to avoid a collision or any other danger, the engines of a screw steamer are suddenly reversed, say from full speed ahead to full speed astern. The vessel will then maintain headway for a short time, but the effect of the propeller race upon the rudder may more than counterbalance the effect of headway, and the vessel may steer as if she were moving astern, the resultant pressure being delivered upon the after surface of the rudder. This feature of screw-ship steerage has long been known. An analogous experiment was made with the Great Britain in 1845 ; and it was found that, when the vessel was going astern at the rate of 9 or 10 knots, if the engines were rapidly reversed, she steered imme- diately as if she were going ahead. Similar experience appears to have been gained with the Archimedes and other early screw-steamers. Experiments of a more detailed character made by a Committee of the British Association, appointed in consequence of action taken by Professor Osborne Eeynolds, have added valuable information. The main purpose of the inquiry was to discover the best rules for the guidance of ships' captains in endeavouring to avoid collisions ; and the following extracts from the final Report summarize the principal conclusions reached. " It appears both from the experiments made by the Committee, "and from other evidence, that the distance required by a screw- " steamer to bring herself to rest from full speed by the reversal "of her screw, is independent, or nearly so, of the power of her "engines, but depends upon the size and build of the ship, and "generally lies between four and six times the ship's length. It " is to be borne in mind that it is to the behaviour of the ship during " this interval that the following remarks apply. " The main point the Committee have had in view has been to "ascertain how far the reversing of the screw in order to stop a " ship did, or did not, interfere with the action of the rudder during "the interval of stopping; and it is as regards this point that the " most important light has been thrown on the question of handling " ships. It is found an invariable rule that, during the interval in " which a ship is stopping herself by the reversal of her screw, the " rudder produces none of its usual effects to turn the ship ; but that "under these circumstances the effect of the rudder, such as it is, is "to turn the ship in the opposite direction from that in which she "would turn if the screw were going ahead. The magnitude of "this reverse effect of the rudder is always feeble, and is different "for different ships, and even for the same ship under different " conditions of lading. " It also appears from the trials that, owing to the feeble influence 2 u 658 NAVAL ARCHITECTURE. [chap. xvni. "of the rudder over the ship during the interval in which she is " stopping, she is then at the mercy of any other influences that may " act upon her. Thus the wind, which always exerts an influence to " turn the stem (or forward end) of the ship into the wind, but which " influence is usually well under control of the rudder, may, when the " screw is reversed, become paramount, and cause the ship to turn in " a direction the very opposite of that which is desired. Also the "reversed screw will exercise an influence which increases as the " ship's way is diminished to turn the ship to starboard or port, accor- " ding as it is right or left handed ; this being particularly the case " when the ships are in light draught. " These several influences, the reversed effect of the rudder, the " effect of the wind, and the action of the screw, will determine '• the course the ship takes during the interval of stopping. They *■ may balance, in which case the ship will go straight on ; or any " one of the three may predominate and determine the course of the *' ship. The utmost effect of these influences when they all act in *• conjunction — as when the screw lis right-handed, the helm star- " boarded, and the wind on the starboard side — is small as compared " with the influence of the rudder as it acts when the ship is steaming " ahead. In no instance has a ship tried by the Committee been able " to turn with the screw reversed on a circle of less than double the " radius of that on which she would turn when steaming ahead. So '• that even if those in charge could govern the direction in which the " ship will turn while stopping, she turns but slowly ; whereas, in point " of fact, those in charge have little or no control over this direction, ■" and unless they are exceptionally well acquainted with their ship, " they will be unable even to predict the direction." Similar trials have been made in ships of the Eoyal Navy, in order to determine their behaviour as regards stopping and turning when the screws have been reversed. In comparing the results with those obtained by the British Association for merchant ships, it is necessary to bear in mind certain facts. War-ships differ from mer- chant ships in their forms, the proportion of engine-power to dis- placement, the area of their rudders and other features influencing their behaviour under the experimental conditions. Allowing for these differences, and recognizing the necessarily approximate cha- racter of the results obtained in such trials, the following summary will be of general interest. First, as to the distances traversed after war-ships have their «ngines reversed. If ships are moving full speed ahead, they can usually be stopped in from 2£ to 4£ times their length. In some few cases they were stopped in from 1J to 2 lengths. If ships are moving at slow speed, but with a large command of steam, so that the chap, xviii.] THE STEERING OF SHIPS. 659 engines can be worked full speed astern quickly, the distances travelled before stopping are much reduced, varying in many instances from 40 to 70 per cent, of the distances traversed when reversing from full speed ahead. Second, as to the steerage of single-screw war-ships with engines moving astern. This is the case comparing with the British Associa- tion experiments, which were made on single-screw merchant ships. While there is a general agreement between the two sets of trials, there are some differences. When the helm was put over, and a ship had begun to answer her helm, before the engines were reversed, she usually continued to turn in the same direction, but at a gradually decreasing rate, after the screw was reversed up to the moment when she ceased to have headway. Some ships turned in the original direction for a short time only after the engines were reversed, the propeller race overpowering the influence of headway on the rudder very soon, and causing the ships to swing round in the opposite direction to that in which they were turning before the engines were reversed, just as the single-screw merchant ships did. When the engines of single-screw war-ships were reversed at the same instant as the helm was put over, they behaved in an uncertain fashion, much as described above for single-screw merchant ships. In most cases the war-ships were found, when headway ceased, to have their heads turned slightly from their original course to the side where the rudder would have turned them under the influence of headway. Twin-screw ships usually continue to have headway when one screw is reversed and the other continues to turn ahead ; the reason for this will be found on p. 576. Consequently the reversal of one screw did not, in the course of the trials, bring the ships to rest, or make them turn on their centres ; but caused them to reverse their course or turn a complete circle in a smaller space than when both screws were moving ahead and the same amount of helm was used. This was true, whether the helm was put over before, or simultaneously with, the reversal of the engines. It will be explained hereafter that, when required, by suitably adjusting the revolutions and directions of movement of the screws, a twin-screw ship may be turned practically on her centre. Summing up these remarks on the causes which govern the pressure on the rudders of different classes of ships, it may be said generally that without motion of a ship through the water, or of the water past the rudder, it can have no steering power. A ship or boat anchored in a tidal current or river may be turned to some extent from the line of flow by the action of her rudder, because the water has motion relatively to the rudder. A ship almost destitute of 660 XAVAL ARCHITECTURE. [chap. xvm. headway may be under command, if her propeller is at work and delivering a race which flows past the rudder. But for a ship at rest in still and undisturbed water the rudder is powerless. The hydro- statical pressure sustained by the sides of the rudder, if held at any angle, balance one another, and are quite distinct from the reaction due to change of momentum in streams having motion relatively to the rudder. In all cases of relative motion of water and rudder, the normal pressure depends iipon the area of the immersed part of the rudder : the angle of its obliquity to the position of zero pressure, or, roughly speaking, to the keel-line ; and the speeds and directions with which the streams impinge upon the rudder surface. In sailing ships the motions of the streams depend principally upon the motions of the ships, and the forms of the after body. In paddle-steamers and jet- propelled vessels similar considerations are most influential, although the action of the propellers may influence the steerage of ships start- ing from rest, or reversing their course. In screw-steamers the action of the propellers is very important, especially when the slip is con- siderable, and the velocity of the race is high. "When ordinary rudders are employed, and hung either to a broad rudder post abaft the screw, as in Fig. 162. or to the body of the ship, as in Fig. 163, the check put upon the motion of the streams by the rudder must produce a reaction and pressure not merely upon the rudder itself, but upon the portion of the stern-post or deadwood adjacent to the rudder. This additional pressure will be delivered on the side towards which the rudder is put over, and there is good reason for believing that it considerably assists the rudder pressure in steer- ing a ship, being most valuable in cases where the rudder is hung to the body of the ship. With simple balanced rudders placed as in Fig. 165, there is no corresponding pressure on the deadwood, but instead of it a normal pressure on the additional rudder area placed before the axis. Compound balanced rudders, with the forward part locked fast (as in Fig. 166), resemble the ease illustrated in Fig. 162 for an ordinary rudder. Besides these normal pressures on the rudder, stern-post, and dead- wood, there will be a certain amount of frictional resistance on the rudder surface when placed obliquely ; but this is of little importance as compared with the normal pressures; except for very small angles of helm. So far as it produces any effect on the steering, this frictional resistance acts against the normal pressures. It has been shown in Chapter XI. that surface disturbance may become an important factor in fluid resistance. As rudders in most classes of ships extend above the water-level, some surface disturbance occurs when the helm is put over, and this increases the reaction on chap, xviii.] THE STEERING OF SHIPS. 66 1 the rudder. In war-ships, both armoured and protected, it is usual to keep the rudders and steering gear well below the water-line, and consequently there is little or no surface disturbance. For smooth- water work, this point has but small practical importance. In rough water at sea, however, the upper portions of rudders as ordinarily fitted are exposed to blows of the sea, which sometimes involve heavy shocks on rudders and steering gear. These blows are avoided to a considerable extent in rudders completely submerged. In a few of the largest and swiftest Trans- Atlantic steamers such xudders have been fitted, no doubt chiefly because of the advantages that would be gained if the vessels were employed in war, but partly in order to reduce the risks above mentioned. Forces required on Tillers. — Reference will next be made to the force required at the tiller end to hold the rudder at any angle. This will, of course, depend upon the F | G 17 _ length of the tiller and the mode of applying the force ; but it may be assumed that both these conditions are given. In Fig. 170 an ordinary rudder • is shown. The resultant pressure upon it is P, acting through the centre of effort C of the immersed rudder area. AT represents the tiller, Q the force required at its end, if applied normally to the tiller, in order to hold the rudder over. Apart from friction ■of the pintles, rudder bearings, collar, etc., we should have — P x AC = Q x AT. These frictional resistances vary considerably in different vessels, but may be made comparatively small by means of careful arrangements ; in most cases they probably act with the force Q in resisting the motion of the rudder back towards the keel-line. Neglecting friction, and supposing the other conditions fixed, the force Q at the tiller end will vary with the distance AC of the centre of effort from the axis of the rudder. On the same assumption the force Q may be determined approximately for any helm angle, if the distance AC is known, since the normal pressure P can be estimated roughly in the manner described on p. 438. In practice the maximum helm angle varies from 30 to 45 degrees ; so that inquiries as to the variation in the value of AC need not be carried beyond 45 degrees except it be done for scientific purposes. Formerly it was assumed that the centre of effort coincided with the centre of gravity of the immersed area of the rudder, and that the pressure due to the reaction of the 662 JVA VAL ARCHITECTURE. [chap. xvm. streams was uniformly distributed over that area. Experience and investigation have proved this view to In? incorrect for a thin plate set obliquely to the line of motion, and for actual rudders. In the case of balanced rudders, for example, it has been ascertained that, when the area before the axis was about one-half as great as the area abaft the axis, a dynamometer attached to the tiller end when at 40 degrees indicated little or no strain, showing that the centre of effort was then practically coincident with the axis. With ordinary rudders a similar excess of pressure probably exists on the forward part : although it is conceivable that in twin-screw ships the more direct action of the race on the after part of the rudder may tend to modify the position of the centre of effort. If the rudder be treated as a rectangular plate advancing obliquely, its leading edge (cor- responding to the fore edge of a rudder) may be regarded as continually entering water which was comparatively little disturbed by the previous motion, and which, therefore, reacts more powerfully on that part of the area than does the water which impinges upon the after part, and which had been previously disturbed by the motion of the plate. This matter has been dealt with mathematically by Lord Eayleigh and experimentally by M. Joessel. the late Mr. Froude, and others. For a rectangular plane of breadth b, the distance d of the centre of pressure from the forward edge has been expressed by the following formulas a being the angle made by the plane with its line of motion : — Lord Kavleigh . . d = - - !? 6 . , - 1 ' 09 n '2 4 4 + it sin a M. Joessel . . . d = 0-1956 + Q-SQob . sin a. Herr Hagen, after numerous experiments on comparatively small plates, proposed the following approximate formula : —

degrees in li minutes, while turning the circle occupied about 7§ minutes. With steam steering-gear two men put the helin over to 35 degrees in 16 seconds, the circle was turned in about 5£ minutes, and its diameter was less than two-thirds that on the former trial. In a few of the largest mercantile steamers hand steering-gear has been dispensed with, and a second steering-engine fitted with independent driving-gear, as an alternative mode of steering in case of accident, or the need of repair to the engine ordinarily at work. Turning Effect of Rudders. — Attention will next be directed to the effect of rudders in turning ships. This is the purpose for which rudders are fitted, but the preceding remarks have been necessary in order to clear the way for the description that will now be attempted. Suppose a ship to be advancing on a straight course and with uniform speed, the stream-line motions on either side being perfectly symmetrical ; then it is known, as the result of model experiments, that the least disturbing cause will produce a departure from this balance of the stream-line motions, and cause the vessel to swerve from her original course. Immediately after the helm begins to move over, such a disturbing cause is de- V-^ — ^ fe- j^>\ veloped in the pressure on the rudder, the magnitude of which increases as the helm angle becomes larger. Fig. 171 shows the plan of a ship, with the rudder (AB) put over to the angle BAD ; the arrow indicates the line of action of the resultant pressure P. Let G indicate a vertical axis passing through the centre of gravity of the ship ; through G draw the line HL parallel to the line of action FC of the resultant pressure on the rudder, and along HL suppose two equal and opposite forces P, P to be applied. These forces will balance one another, and therefore will not produce any change in the conditions to which the ship is subjected independently of them. By this means the single force P on the rudder is replaced by a single force P acting along HG-, and a couple formed by the pressure Y on the rudder and chap, xviii.] THE STEERING OF SHIPS. 669 an equal force acting along LG- ; the arm of this couple is G-F, and it evidently tends to turn the vessel in the direction indicated by the arrows at the bow and stern. The single force P acting along HG- tends to produce a simultaneous motion of translation of the vessel along its line of action. This force P may be resolved into two components : if G\H represents P, HK will be its component acting parallel to the keel, and KGr the component acting perpen- dicularly to the keel. The transverse component is usually larger than the longitudinal ; but it is not so important, because at each instant it has opposed to it the great force of lateral resistance (see p. 504), and therefore can cause but a very small speed of drift. The longitudinal component, on the contrary, may exercise a sensible effect in checking the speed of a ship while she is turning. As the rudder is put over, the value as well as the direction of P changes, and the absolute and relative values of these component forces will change ; but at each instant conditions similar to those described will be in operation. It becomes important, therefore, to trace the consequent motion of ^the ship, and for the sake of simplicity it will be assumed that she is a steamer, the propelling force being delivered parallel to the keel-line. Ultimately, when the rudder has been held at a steady angle for some time, the ship will turn in a path which is very nearly circular, and is usually treated as if it were a circle. Her speed will be less than it would be if she were steaming on a straight course with the same eugine-power, and her ends will be turning about the vertical axis passing through the centre of gravity, with a nearly uniform motion, or angular velocity. Before this condition could have been reached, however, there must have been a period during which the angular velocity was gradually accelerated up to its uniform value, while the headway was being checked, and before the lateral drift had supplied Ja resistance balancing the component of the rudder pressure and the centrifugal force. It will be well, therefore, to glance at this period of change before considering the case of uniform motion. As soon as the rudder is put over, an unbalanced couple will be brought into operation, and the ship will begin to acquire angular velocity. At first this velocity will be very small ; and as the resistance offered by the water to rotation varies very nearly as the square of the angular velocity,* that resistance is of little importance in - the earliest stages of the motion. The initial values of the * Analyses of numerous turning trials velocity almost identical with that de- made with the Warrior enable us to duced from the experiments made by state that in her case the resistance Mr. Froude on frictional resistance, varied with a power of the angular 6/0 NAVAL ARCHITECTURE. [chap. xvm. angular acceleration will therefore chiefly depend upon the ratio which the moment of the couple bears to the moment of inertia of the ship about a vertical axis passing through the centre of gravity (G, in Fig. 171). That moment of inertia is determined by multi- plying the weight of every part of the ship by the square of its distance from the axis of rotation ; and the moment of inertia would evidently be much increased if heavy weights were carried near the extremities instead of being concentrated amidships. Hence, with a certain rudder area put over to the same angle iu the same time, in two ships similar to another in outside form and immersion, but differing in their moments of inertia, the ship having the less moment of inertia will acquire angular velocity more quickly than her rival. Moreover, it will be evident that a ship of which the rudder can be put over quickly to its extreme angle will acquire angular velocity more rapidly than she would with the same rudder put over slowly. As the angular velocity is accelerated, the moment of the resistance increases, exercising an appreciable effect upon the acceleration ; and finally a rate of motion is reached for which the moment of the resistance balances the moment of the couple due to the corresponding pressure on the rudder, the angular velocity then becoming constant. Simultaneously with this acquisition of angular velocity, a retardation of headway will have taken place, and carried with it some change in the pressure on the rudder, which will also be affected by the considerations mentioned above ; the balance between the lateral resistance and the other forces named above will also have been established. Four featiues, therefore, chiefly affect the readiness of a ship to answer her helm : (1) the time occupied in putting the helm hard over ; (2) the rudder pressure corresponding to that position ; (3) the moment of inertia of the ship about the vertical axis passing through the centre of gravity ; (4) the moment of the resistance to rotation. Only the first and second of these can be much influenced by the naval architect ; their importance has already been illustrated from the turning trials of the Minotaur. The moment of inertia is principally governed by the longitudinal distribution of the weights in the ship ; in arranging these weights, considerations of trim, con- venience, and accommodation are paramount. The moment of resistance depends upon the form and size of the immersed part of the hull, and is especially influenced by the fine parts of the extremities. In merchant steamers of great length the deadwood forward is often cut away to a considerable extent, in order to saA r e weight at the extremities, simplify construction, and assist in turn- ing the vessels at low speeds. The after deadwood in such cases is usually retained. In certain torpedo vessels and cruisers — the chap, xviii.] THE STEERING OF SHIPS. 67 1 Polyphemus being a notable example — the deadwood both forward and aft is cut away, and the vessels have proved very handy. In torpedo-boats and torpedo-gunboats it is usual to leave the forward deadwood, but to cut the after away, as illustrated in Figs. 168 and 169. This is advantageous, no doubt, in swift vessels of shallow draught, especially in the reduction of the space required for turning when going ahead at full speed. Experiments have been made which prove that the retention of the forward deadwood, or additions thereto, will effect such a reduction. On the other hand, when going astern the conditions are reversed, as might be expected, and a boat with large forward deadwood is less handy than one with a less area of flat surface forward. A very interesting experiment made by Lieutenant Hovgaard on two Danish torpedo-boats (mentioned at p. 180) illustrates this. The boats were 137 feet long, and of 110 tons displacement ; alike in all respects, except that one of them was fitted with an external vertical keel, or "ventral fin," placed well forward, having an area of about 60 square feet. At 18 knots speed, the boat so fitted turned in a circle of 500 feet diameter, 60 feet less than the diameter for the sister boat. When going full speed astern, the boat fitted with the " fin " forward turned in a circle of 790 feet diameter, and her sister boat in one of 420 feet diameter. Under these circumstances the balance of advantage was clearly in favour of the latter boat, and the experiment is conclusive against the proposal to add to the forward deadwood in order to increase handiness in war-ships. Power of command ahead is no doubt of the greatest importance, but steerage with sternway is also important. Another consideration which must not be overlooked is, that when the finer portions of the deadwood are cut away to a considerable extent the resistance to rolling motions is diminished. In sailing vessels the lateral resistance would also be reduced, and leeway increased. Modern types of yachts have the deadwoods cut away greatly, c but they are also of very deep draught, and thus combine" considerable lateral resistance with great handiness under sail. Closely associated with this readiness to answer the helm, or to acquire angular velocity, are the conditions which control the decrease of that velocity when a vessel has had her head brought round to a new course upon which it is desired to keep her. The greater the ratio of the- moment of resistance to the moment of inertia, the more rapid will be the rate of extinction of the rotation ; and, conversely, the greater the ratio of the moment of inertia to the moment of resistance, the slower will be the rate of extinction. Both moment of inertia and moment of resistance must be considered ; and possibly the helm may be brought into action to assist in keep- ing the ship on her new course. Deep draught, considerable length, 672 NAVAL ARCHITECTURE. [chap. xvm. fine entrance and ran, deep keels, and other features which lead to an increased resistance to rotation, are not, therefore, altogether dis- advantageous. They make a vessel slower in acquiring angular velocity, but they enable her to be kept well under control. Shallow- draught vessels are not unfrequently less manageable by the helm than deep-draught vessels; they quickly acquire angular velocity, and turn rapidly, but have comparatively small resistance in propor- tion to the moment of inertia, and are not easily kept on a new course, •' steering wildly " in some cases, as a sailor would say. In such cases the addition of a deep keel and consequent increase of resistance to rotation and drift often greatly improves the steerage. Vessels of the circular form possess considerable moment of inertia, whereas nearly the whole resistance to rotation must be due to skin friction, and can be but of moderate amount. It might, therefore, be expected that these vessels would be difficult to check and keep on any desired course if they had been turned through a considerable angle and acquired a good angular velocity. It has, in fact, been asserted that the vessels are "ungovernable" under the action of their rudders ; and their designer, Admiral Popoff, in replying to these criticisms, dwelt upon the manoeuvring power obtained by the unusual number of their propellers, not claiming for them great handiness under the action of the rudders alone.* It is a matter of common experience that ships which are perfectly under control in deep water steer wildly and require careful watching when they are navigating in very shallow water, and have their keels only a few feet clear of the bottom. In view of the remarks made in Chapter XI., on the influence of depth of water on resistance, it will be readily understood why the manoeuvring qualities should also be affected. Moreover, under these circumstances vessels usually proceed at very slow speeds. For example, when passing through the Suez Canal, a low speed is insisted upon. The turning power of the rudder for a given helm angle is then reduced, and consequently the management of a ship is made more difficult than at higher speeds, while the shallowness of the water and the limited size of the channel increase the difficulty of management. Experienced seamen declare that, when a steamer has headway, and the helm is put over, " the head appears to turn comparatively " slowly, while the stern swerves suddenly to the right or the left." f This is quite in accordance with theoretical considerations. Professor Eankine many years ago published an investigation for the instan- * See a lecture delivered at Nicolaieft' t See an interesting article, " On in 1875, of which a translation appeared Sternway," by Captain Allen, R.N., in in Naval Science. Naval Science for 1875. chap, xviii.] THE STEERING OF SHIPS. 673 taneous axis about which a ship should begin to turn when the rudder was first put over, on the supposition that the first action of the rudder might be regarded as an impulse. His construction for this instantaneous axis is shown in Pig. 171. The length G-L represents the " radius of gyration " of the ship about the vertical axis passing through the centre of gravity G; and is measured on the line HL drawn perpendicular to the arm FG- of the couple.* Join FL, and produce FG to M ; draw ML perpendicular to FL, meeting FM in the point M ; that point will be the " instantaneous axis " about which the first movement of the ship takes place, and M may lie considerably before the centre of gravity. To determine the instantaneous motion of any point in the ship, it is only necessary to join that point with M, and to describe a small circular arc with M as centre. It will be understood that this construction only applies to the motion of the ship at the first moment after the rudder is put over. Purely theoretical investigation does not enable one to lay down the path traversed by the centre of gravity of a ship in turning from a straight course under the action of her rudder. The equations of motion can be framed in general terms ; but our knowledge respect- ing the resistance offered by the water to the motion of the ship is not sufficient to enable all the quantities to be expressed, and a complete solution reached. Hence it becomes necessary that the problem should be attacked by actual experiment,, and that careful observations should be made of successive positions occupied by a ship so that the path traversed might be subsequently plotted. In such determinations of the path of a ship it is convenient (1) to take the original straight course as the line of reference, from which to measure the angles turned through by the keel-line of the ship in specified times ; (2) to take as an origin of co-ordinates the position of the centre of gravity of the ship on her straight course at the instant when the helm begins to move over ; (3) to note the path of the centre of gravity while the ship turns. This centre in most ships is situated very near the middle of the length ; so that the path of the latter point will serve for all practical purposes, as the path of the centre of gravity. With these means of reference, if the place of the centre of gravity is fixed at frequent intervals of time, a curve can be drawn through the points obtained, and will be the path required. If simultaneous observations are made of the angles through which the head of the ship has turned from her original course, the instantaneous positions of the keel-line are known for a series of positions, and its instantaneous inclination to the cor- * See p. 150 for an explanation of the term " radius of gyration." 2x 674 XAVAL ARCHITECTURE. [chap. xvhi. responding tangents to the path of the centre of gravity can be ascertained. Until questions of steam tactics for war-ships became important, and the employment of ships as rams occupied attention, no attempts appear to have been made to determine accurately the path traversed. In recent years, however, many such observations have been made both in the Eoyal Navy and in foreign navies ; their great practical value is now generally recognized, and additions are rapidly being made to our knowledge. The French experimental squadrons of 1864r-66 were subjected to very exhaustive turning trials, and the observations made would have sufficed to determine the complete motions of the ships from their straight course ; but this was not done, attention being chiefly de- voted to the determination of the circular path in which each ship turned after her motion had become uniform. Since then it has been recognized that for tactical purposes it is more important to know what is the nature of the path traversed immediately after the helm is put over, and where the ship will be placed when she has turned through the first 90 degrees, as well as her position when she has turned through 180 degrees and reversed her course. One of the earliest proposals for determining accurately the motion of a ship in turning was made by M. Eisbec of the French Navy, and applied by him to a small vessel, the Elorn, at Brest, in November, 1875., This method is, we believe, still generally used in the French Navy, and is exceedingly well adapted for its purpose.* In its main features it resembles methods of observation previously known, and occasionally ap- plied, and a brief account of it may be of interest. Two observers are stationed at a considerable distance apart on a line parallel to the keel-line of the ship, as in- dicated by the points A and B, Fig. 172. They are each furnished with a simple sighting instrument (or azimuth instrument), and at frequent intervals of time, at a given signal, observe simultaneously, and record the angles a and /3 made with the line AB by their respective lines, of sight to a floating object, O, placed within the path traversed by See vol. xlix. of the Revue Maritime for further particulars. chap, xvm.] THE STEERING OF SHIPS. 675 the vessel. This object may be anchored if there is no tide or current, but otherwise may be a simple buoy or boat with a flagstaff. A large number of observations being made, a series of triangles, such as AOB, can be constructed, the length AB being constant, and the errors of observation can be eliminated by a careful comparison and analysis of the results. To complete the plotting of the path of the ship, it is necessary to fix the position of any such triangle as AOB ; this is done by a third observer, C, who notes and records the bearings of a fixed and distant object, with reference to the keel-line, each time that the signal is given for the first two observers to note the bearing of from their stations. The angle LCD is that which he has to determine in each case, and this may be done in other ways than that named above. Another very excellent series of trials was made on the Thunderer at Portland in 1877. The details of the observations and their prin- cipal results will be found in the Appendix to the Beport of the Inflexible Committee. In some respects these trials were more ex- haustive than any previously made, and the utmost care was taken to check the several observations and eliminate errors. They well deserve the study of all who are interested in the turning trials of ships, and have been issued to H.M. ships by the Admiralty for the information and guidance of officers in the Boyal Navy. Since the completion and publication of the results of these turning trials in the Thunderer, very many similar trials have been carried out in H.M. ships. Admiralty instructions have been issued for guidance in making the necessary observations.* More exact information has thus been obtained and recorded respecting the paths traversed by ships in turning through the first quadrant and reversing their course than was formerly available. Before these observations were systematized it was the established practice to make turning trials of all new ships, primarily for the purpose of thoroughly testing the efficiency of the rudders and steering gear. Measurements' were also made of the diameters of the " circles " in which ships turned, in order to obtain a rough idea of their relative handiness. These trials were made in smooth water and light winds, with helms hard over to port and starboard, and with ships running at full or half power. Careful note was taken of the times occupied in putting the helms over, in reversing the course, and completing * These instructions embody methods respecting results of turning trials, in a of observation agreeing in principle with paper published in the Transactions of those above described. They ,' were the Institution of Naval Architects for chiefly based on work done by Admiral 1886. See also a paper by the author, Colomb, who has fully described them, published in the Journal of the Royal and given much interesting information United Service Institution for 1879. 676 NA VAL ARCHITECTURE. [chap, xviii. the circles. For twin-screw ships, or other ships with duplicate pro- pellers, additional trials were made with one propeller only at work, and with one propeller turning ahead and the other astern. Some- times the turning trials were extended to other speeds, or to angles of helm ranging from " hard-over " to very small angles. M\ich informa- tion was thus gained, but the actual path of a ship in turning was not determined, and the assumption that she turned in a circle was known to be inaccurate. These preliminary (or constructors') trials are still continued, and necessarily so ; but they no longer stand alone as records. Continued experience in the management of ships during service at sea has always enabled commanding officers to obtain an intimate knowledge of the turning powers of their ships under varying circumstances of wind, sea, speed, and helm angle. Fleet manoeuvres necessarily require a knowledge of the manoeuvring powers of the individual vessels which have to work together. In all these ways information is acquired, and under the regulations the facts are recorded in the " Ship's Books " issued to H.M. ships, for the informa- tion of officers who may succeed to the command. For many ships, diagrams are also inserted in the " Ship's Books," showing the paths traversed in turning, or the critical points on those paths, giving the positions of the ships when they have turned 90 and 180 degrees respectively from their original course, or completed 360 degrees and resumed that course. The case of the Thunderer may be taken as fairly representative of war-ships possessing good manoeuvring power, and it will be in- teresting to trace her movements from the moment the helm is put over, until she settles into uniform motion. Fig. 178 will enable this to be done. The path of the ship when she begins to turn away from her straight course will be seen to be spiral, and not circular; con- sequently when she has turned through 360 degrees she is found (at E) somewhat within the line AC of her original course. As she acquires angular velocity, so her bow turns inwards from the tangent to the path of her centre of gravity, and the angle between this tangent and the keel-line, or " drift-angle," (angle de dSrive) as it is termed, gradually increases. Owing to the existence of this drift- angle, the thrust of the propellers, when a ship is turning, is delivered at each instant athwart her course ; and to this must be mainly attributed the loss of speed which takes place, and which is com- monly attributed to the " drag " of the rudder. Her angular velocity meanwhile undergoes rapid acceleration ; and, as she turns, centrifugal force comes into operation, and the ship heels from the upright. By degrees these transitory conditions give place to uniform conditions, if the helm is kept at a oonstant angle and the engines at a nearly CHAP. XVIII.] THE STEERING OF SHIPS. 677 •constant speed ; and ultimately the ship moves in a practically circular path, with a constant drift angle, and a steady angle of heel. The time occupied in attaining this state of uniform motion varies in different ships; the time occupied in putting the helm hard over must largely influence the time occupied in acquiring uniform c/ References. AC, original straight course of ship. A, her position when helm begins to move over. B, „ she has turned 90°. D, „ » ?> „ 180°. E, „ 5) )> „ 360°. F, „ )» » „ 540°. G, „ J? •>■) „ 720°. angular velocity, and other considerations must affect the periods occupied by different ships in passing through the various changes sketched above. In the following table appears a summary of facts for the earlier portions of the turning of the Thunderer which will lender further explanation unnecessary : — 678 NAVAL ARCHITECTURE. [chap, xviii. Turxing Trials of Tbuvbebsr. Time. At end of time. Speed of ship. Angalar Telocity per second. To put helm over 31° . To turn ship's head 45° 90° . . . ,. 135° . . . 180° . . . 360* . . . seconds. 19 56 89 123 159 320 knots. 10-4 9-25 8-3 7-75 7-5 7-14 0° 20' 1° 18' 1° 18' 1° 15' 1° 12' 1° 6£ At 360 degrees the turning motion had become practically uni- form. It appears that with steam steering gear similar conditions of uniform motion are usually reached as soon as, or sooner than, they were reached in the Tliunderer. With manual power only, similar conditions are sometimes not reached until a vessel has made two or more circuits. When a ship has turned through 90 degrees, her motion will not be uniform, and her path is still spiral. Hence it is desirable that a commanding officer of a war-ship shoidd determine by actual observation, at different speeds and with different helm angles, how the ship would be placed, in relation to her course and position at the instant when the helm was put down, after she has turned through 90 degrees. When the motion of a ship in still water has become uniform, her centre of gravity will move in a circular path, and all other points in her will move in concentric paths. The fore end of the keel-line of the ship will be turned within the tangent to the path of the centre of gravity, making a drift-angle with it of greater or less amount. In Fig. 174, O represents the centre of the circle ; GjGGa the path of the centre of gravity ; G the instantaneous position of that point, and TGTj the tangent at G; AB is the keel-line; BGTj is the drift-angle for G. From O a perpendicular OP is let fall on AB. Then the tangent to the circular path described by the point P coincides with the keel-line ; consequently there is no drift-angle at P, and it is sometimes termed the " pivoting point," because, to an observer on board, the ship seems to be turning about it. It will be understood, of course, that O is the true centre of motion for the ship in turning. In the Thunderer the pivoting point P varied from 67 to 103 feet before the centre of gravity, or from 80 to 40 feet abaft the bow. As the speed and drift-angle increased, the point P moved forward. Cases may occur where the drift-angle at the centre of gravity is so considerable that the pivoting point lies before the bow, and is found on the keel-line produced. By means CHAP. XVIII.] THE STEERING OF SHIPS. 679 of a construction similar to that shown for the centre of gravity G, the drift-angle can be determined for any other point on the keel- line. Take, for example, the extreme after-end B : join OB, draw QB perpendicular to OB, and the angle DBQ is the drift-angle at B. FIG. 174. The angle DBQ is greater than the drift-angle BGrT, for the centre of gravity ; and it will be obvious that, for all points lying between B and the pivoting point P, the drift-angle will remain of the same sign, but decrease in value as the distance of the point under con- sideration from P diminishes. At P the drift-angle has a zero value, in passing through which it changes sign, and for all points lying before P the drift-angles have negative values, as compared with the angle BGTj. That is to say, if a point such as A is taken, lying on the fore side of P, and OA is joined, the line drawn through A per- pendicularly to OA, representing the tangent to the circular path of the point A, will lie on the other side of the keel-line AB, from that on which the tangent GrTj is situated. The value of the drift-angle measured at the centre of gravity varies in different vessels, and also varies in the same vessel under different conditions of speed and helm-angle. In the Thunderer experiments with a constant helm-angle, and practically a constant time for putting the helm hard over, the drift-angle varied from 5f degrees at 8 knots to 9 \ degrees at 11 knots. In the Iris, under similar conditions, the variation in drift-angle was only from 6J degrees at 9 knots to 7 degrees at 16J knots. In some of the experiments made with French ships, drift-angles from 16 degrees to 18 degrees have been reached. Further experiments are needed in order to determine the law of variation, but so far as can be seen at present, the drift-angle becomes greater as the area of rudder and the angle of helm (up to 45 degrees) are increased, speed being con- <58o NAVAL ARCHITECTURE. [chap, xviii. stent; and also sometimes increases with increase in speed, other things remaining the same. As a consequence of the drift-angle, the bow and stern of a ship revolve in circles of different diameters when the motion has become imiform. In the TJiunderer this difference varied from 60 to 100 feet on a mean diameter of 1800 feet, the stern, of course, moving in the larger circle. In the French ironclad Solferino. the diameter of the circle swept by the stern exceeded that swept by the bow as much as 40 metres on 900 metres. The larger the drift-angle the greater is this difference. Another consequence of the drift-angle, to which allusion has already been made, is the reduction iu speed sustained by a ship in turning. In several cases where the loss of speed has been accurately measured, it has been found to reach two-tenths to three-tenths of the speed on the straight course before the helm was put over. In experimental trials with small vessels, fitted with rudders of very large proportionate area, the loss of speed has been much greater, amounting it is said to 40 or 50 per cent, of the speed on the straight In the Delight gunboat, the late Admiral Sir Cooper Key ascertained that when the balanced rudder was very large and it was put over to 40 or 45 degrees, the first quadrant was turned through in about 31 seconds, and the diameter of the circle was 205 feet, or only twice the length of the vessel ; but the loss of speed was so considerable, due to the large drift-angle and the drag of the large rudder, that the whole circle took 2 minutes 46 seconds to perform. With an ordinary rudder of small area put over to equal angles, and about the same speed on a straight course, the first quadrant took 33$ seconds. The diameter of the circle was 225 feet, and yet the loss of speed was so much less in turning that the whole of the larger circle was completed in 2 minutes 38 seconds. This example illus- strates a well-known fact in screw-ship steerage; viz. that a very large rudder-area will increase the drift-angle, and diminish the time during which the angular velocity is becoming uniform, as well as the space required for turning, but may lengthen the time. On consideration of the facts above stated it will be seen that the motion of a ship in turning resembles that of a ship sailing on a wind, except that in the latter case the path of the centre of gravity is straight instead of being curved. At each instant the vessel moves obliquely to her keel-line. To the " angle of leeway" in the sailing ship (see p. 504) the " drift-angle " of the ship which is turning may be considered to correspond : but whereas in the first case all points in the ship are moving in parallel lines, and the angle of leeway has a constant value ; in the second case (as explained above) the drift-angles for different points have different values, and chap, xviii.] THE STEERTNG OF SHIPS. 68 1 possibly different signs. This variation in the drift-angle complicates the problem, rendering difficult any general statement of the condi- tions which govern the flow of water relatively to different parts of the immersed surface of a ship which is turning, or the distribution of the fluid pressures. There can be no question but that, on the side of the ship most distant from the centre of her path, there will be an ■excess of pressure, usually styled the force of the lateral resistance. Nor can it be doubted that cases occur, wherein the pivoting point P lies before the bow, and there is a considerable accumulation of pressure on the outer or lee bow, which pressure not merely checks the speed, but assists the rudder in turning the ship. If the pivot point P lies (as in Fig. 174) between the bow and the middle of the length — &s it very frequently does — the case is less simple. For points on the keel-line abaft P, there are positive drift-angles ; and if small "" drop-rudders," hinged at their fore ends, were let down below the keel and left free, they would probably find their positions of rest At some angle of inclination to the starboard side of the keel-line AB. BQ in Fig. 174 may be taken as an indication of the position of rest for one such rudder. For points on the keel before P the positions ■are reversed: similar drop-rudders placed at any of these points would find their position of rest at some inclination to the port side of AB. These rudder-indications simply show that, in the case of which Fig. 174 is an illustration, the flow of water for points abaft P is inwards, and that there is an excess of pressure on the outer side ; whereas for points before P the flow is outwards, and the excess of pressure is on the inner side of the bow. The last-mentioned excess clearly acts against the rudder ; but it extends over only a small portion of the length from the bow. The excess of pressure on the outer side acts upon a more considerable portion of the length, and is probably so distributed in many cases, with reference to the centre of gravity, that its movement assists that of the rudder in turning the ship. An increase in the drift-angle, and consequent movement of the pivot point towards the bow, is likely to be accompanied by an increase in the turning power of a ship. The same circumstances sensibly affect the flow of water at the stern, even of screw steamers, and reduce the effective helm-angle. Turning to Fig. 174, let BR represent the rudder, and BD the middle line of the ship produced. Then RBD represents the angle made by the rudder with the keel, and for motion on a straight course this would be taken as the effective helm-angle. For a ship turning rapidly, however, the angular motion of the stern causes the flow of water to take place very differently ; and, if for an instant the helm were left free, while the angular motion of the ship continued, it would find its position of rest (or zero-pressure) at some line, such 682 NAVAL ARCHITECTURE. [chap. xvm. as BQ. inclined more or less to the keel-line. The ordinary assump- tion is that, if OB is joined and BQ drawn perpendicular to it, BQ will be approximately the position of rest ; and it has been shown that the angle DBQ is the drift-angle for B. On this assumption, therefore, the effective helm-angle is the difference between the angle made with the keel-line by the rudder and the drift-angle at the stern. This reduction may be very considerable, amounting to one- half of the apparent helm-angle. French experimentalists have endeavoured to determine the reduction exactly in some cases, and assert that it commonly reaches one-half of the apparent helm-angle ; therefore practically reducing the turning effect of the rudder by nearly one-half, as compared with what the same angle of rudder with the keel would give at the first instant the helm is hard over, and before a ship has acquired much angular velocity. Further observations are needed in order to decide this matter ; but it is evident that, in ships where the greatest angle of helm with the keel-line cannot be made to exceed 30 degrees a possible reduction of 10 or 15 degrees involves a very serious loss of efficiency. Supposing the effective helm-angle and the corresponding normal pressure on the rudder to have been determined, then, when the turning motion of a steamship has become uniform, the forces acting upon her are as follows ; (1) the propelling force delivered parallel to the line of keel ; (2) the pressure delivered perpendicularly to the surface of the rudder ; (3) the centrifugal force acting at each instant along the radius of the circular path traversed by the centre of gravity ; (4) the resistance of the water to the motion of the ship. Of these the first and third, acting through the vertical axis passing through the centre of gravity of the ship, do not tend to produce rotation about that axis. The pressure on the rudder and the lateral resistance, each exercise a powerful turning moment, and the sum of these moments must be balanced by the moment of the resistance to rotation. But while these general considerations may be stated, it is not possible, at present, to express definitely the values of either the moments of the lateral resistance or of the resistance to rotation. Heeling of Sliips in Turning. — In this connection it may be well to refer to the heeling which accompanies turning. The forces which tend to produce heeling are as follows : — 1. The centrifugal force acting outwards through the centre of gravity of the ship, and tending to make her heel away from the centre of the circle. 2. The lateral component of the rudder pressure, acting through the centre of pressure of the rudder and usually at some depth below the centre of gravity of the ship, tending to make her heel inwards towards the centre of the circle. CHAP. XVIII.] THE STEERING OF SHIPS. 68 3 3. The lateral component of the fluid resistance on the outer side of the ship, which equals in magnitude the resultant of the centrifugal force and the rudder pressure, and acts through the centre of lateral resistance. Fig. 175 shows the distribution of these forces in the Thunderer, determined from the turning trials made at Portland. Here again it is common to find the rudder pressure credited with the heeling FIG. 175. Side must distant ±ram centre o£ circle. effect; whereas it may, in most cases, be neglected in comparison with the centrifugal force. A fair approximation to the angle of heel for a ship in turning is given by the following equation : — . „ 1 d & sm0 = 32 X m X E where 6 = angle of heel, v = speed of ship in feet per second, E = radius of circle turned (in feet), m = « metacentric height ; " the height of transverse meta- centre above centre of gravity, d = distance of centre of gravity above centre of lateral resistance. This expression for sin should strictly be multiplied by cos , where # is the drift-angle for the centre of gravity; but this correction may be neglected if falls below 10 degrees, as it fre- quently does. In the Thunderer, the centre of lateral resistance was found to be from 043 to 049 of the mean draught below the water-line ; pro- bably a fair approximation for war-ships of ordinary form would be from 0-45 to 0-5 of the mean draught. From the foregoing equation it will be seen that — The angle of heel varies — (1) Directly as the square of the speed of ship ; (2) Inversely with the metacentric height ; (3) Inversely with the radius of the circle. 684 NAVAL ARCHITECTURE. [chap. XVIII. Hence it is obvious that ships of high speed, fitted with steam steering gear, capable of turning in circles of comparatively small diameter, are those in which heeling may be expected to be greatest. Moderate values of the metacentric height further tend to increase the heeling. If the speed be doubled, the angle of heel will be about quadrupled, if the radius of the circle turned and the meta- centric heights remain constant. In order to maintain the same angle of heel under these altered conditions of speed, the meta- centric height would also have to be quadrupled ; but such an increase in stiffness is clearly undesirable even if it were practicable. The following figures may be interesting : — Speed on Diameter Draught. Metacen- Angle of straight. of circle. tric height. heel. knots. feet. It. in. feet. deg. min. f 8-2 1340 •26 3 ] f 52 3%underer 9-4 1250 26 1 3-12 1 11 ( 10-4 1240 •26 1 J ( 1 14 TottrviUe (French). 15-0 2030 3 30 Victorieuse (French) 10-0 1290 2 It is important to notice that, in taking observations of the angle of heel for a ship in turning, allowance must be made for the effect of the centrifugal force upon the indications of pendulums or clino- meters. The error of indication is usually in excess, and the correction is very easily made when the diameter of the circle and time of turning have been ascertained. Although it is the rule in large ships to heel outwards in turning, after a sensible angular velocity has been attained, the first effect of putting a large rudder over quickly may be to cause the ship to heel inwards under the influence of the rudder pressure, and this heel may be the greater because of the comparatively sudden application of the force (see p. 185). This condition was actually illustrated in the Thunderer — the initial heeling took place inwards ; it was of small magnitude, and was quickly succeeded by a considerable heel outwards as the ship acquired angular velocity. Cases are also conceivable, and have occurred, where the heeling has taken place inwards throughout the motion. If the circle turned has a very large diameter, if the distance d is small (as in light- draught vessels such as torpedo-boats) the inclining moment of the centrifugal force will be small, and the inclination may take place as supposed, especially if the rudder is placed low clown. It is also possible, though not likely to occur in ordinary forms of ships, that the centre of gravity may fall so low down as to be below the centre chap, xviii.] THE STEERING OF SHIPS. 685 of lateral resistance ; in which case, of course, the inclination would he inwards. If bow-rudders are fitted, their tendency is to make a vessel heel outwards from the centre of the circle. For large ships this question of heeling when turning rapidly usually has only a scientific interest. It may, however, become very important in small craft, such as torpedo-boats, when turning under the action of powerful rudders in a seaway. Cases of this kind have occurred, and the circumstances may be briefly explained. Suppose a torpedo-boat with a moderate metacentric height and a high position of the centre of gravity to be turning at speed in a circle of comparatively small diameter, this great handiness being secured by large rudders placed low under the stern of the boat. If the manoeuvre takes place in smooth water, the boat heels outward under the action of centrifugal force, and the actual angle of heel will be moderated greatly by the fact that the rudder pressure acts against the centrifugal force. Conceive that the helmsman either acciden- tally or intentionally suddenly allows the rudder to right itself; the steadying effect of the rudder pressure is suddenly withdrawn, while for the moment the boat continues to turn on practically the same path as before. Consequently the centrifugal force continues to act as before, and, having no rudder pressure acting against it, must produce an increased angle of heel. Moreover, the sudden withdrawal of the rudder pressure must cause the boat to lurch outward beyond the steady angle of heel due to the centrifugal force. It may happen, therefore, that if circumstances of this kind occur when a boat is turning among waves, whose action has set her rolling through considerable angles, they may so increase the angle of roll as to cause the boat to capsize. Such accidents have actually occurred, or been avoided with difficulty. One obvious precaution, which is now commonly adopted, is to fit simple mechanical arrangements on the steering gear by means of which the rudder can only be righted intentionally and very gradually. When this is done there can be no sudden loss of the steadying effect of the rudder pressure. Further, the gradual " easing-up " of the helm necessitates a reduction in the angular velocity, and a corresponding decrease in the centri- fugal force. In this way serious lurching outward can be avoided. Ships may obviously change trim when turning under the action of their rudders. Such changes are, however, scarcely appreciable in most cases, and never have any practical importance. Deductions from Turning Trials of Ships. — From the records of turning trials of war-ships many interesting deductions may be made. The following are amongst the more important and practically useful : — 686 NAVAL ARCHITECTURE. [CHAP. xvm. 1. The path traversed by the centre of gravity of a ship while she turns from a straight course through ISO degrees — that is, reverses her course — is usually more or less spiral, and not a circular arc. Allusion has already been made to the principal circumstances which influence the form of this part of the path. For tactical purposes two points on it are of the greatest importance : viz. the position of the ship when she has turned through 90 degrees, and her position when she has reversed her course. The perpendicular distance between this reversed course and the original course is termed the "tactical diameter" (diet met re d'evolution). But its determination does not fix the space required for turning ; because it leaves unknown the distance which the ship advances parallel to her original course from the instant when her helm is put over to that when her head has • swung through 90 degrees. In Fig. 173, for instance, let A be the position of the ship when the helm began to move ; B her position when 90 degrees have been turned through. Draw AC as a prolon- gation of the original straight course, and BC perpendicular to AC ; then AC is the distance required, or, as it has been termed, the " advance " of the ship. This may become very considerable under some circumstances, in proportion to the tactical diameter, or to the simultaneous movement, sometimes termed the "transfer," in a direction at right angles to the original course.* For example, in the Tlmnderer the tactical diameter was 1320 feet, the " advance " to the 90 degrees position was 1000 feet, and she was then at 700 feet perpendicular distance from her original course. In the Iris, at 10 knots the tactical diameter was 2300 feet, the advance for 90 degrees was about 1470 feet, and she was then 1040 feet distant from her original course. It will be noted that when the head of a ship has swung through 90 degrees, the tangent to the path of the centre of gravity will have only turned through 90 degrees less the drift-angle at that instant, which will have different values in different ships, and under varying circumstances in the same ship. The ratio of the advance to the transfer at the 90 degrees position will also vary greatly in different ships. In shallow-draught vessels, and more especially in those of high speed, such as torpedo-boats, the momentum in the direction of the original course, which the vessels have at the instant when the helms are put down, is not quickly destroyed by the lateral resistance, and they " sheer off" in turning, the advance having a considerable relative value. 2. After the turning motion of a ship has become uniform, the * These terms — advance and transfer be styled the " co-ordinates " of the — were suggested by Admiral Colomb. centre of gravity at any time,, referred They express very simply measurements to the axes CA and CB. which in mathematical language would chap, xviii.] THE STEERING OF SHIPS. 687 path of her centre of gravity is practically a circle having a diameter somewhat smaller than the tactical diameter. The French use the term diametre de giration, for this circle ; jmal diameter has been proposed as the English equivalent. In the Thunderer trials, the mean ratio of the final to the tactical diameter was about 100 : 105. In trials with the Iris, at speeds from 9 to 14 knots, nearly the same mean ratio held good. In trials with the French armoured corvette Victorieuse, the ratio was about 100 : 117. 3. Most of the turning trials hitherto made on new ships — the constructors' trials as they have been termed above — may be supposed to give approximations to the tactical diameters of the ships. For war-ships, the following results have been obtained.* With manual power and ordinary rudders the diameter of the circle for large ships has been found to vary between six and eight times the length of the ships. For small ships, wherein manual power suffices to put the helm over rapidly and the speed is low, the diameter falls to three or five times the length. For swift torpedo-boats, with ordinary rudders, manual power only at the helm, and very small angles of helm, the diameter of the circle for full speed has reached about twelve times the length, and for half speed about four or six times the length. With manual power and balanced rudders, the diameter for large ships has been reduced to four or five times the length, and nearly equal results have been obtained with ordinary rudders worked by steam or hydraulic steering gear. About three times the length is the minimum diameter attained in large war-ships turning under the action of their rudders. In the despatch-vessel Iris, with steam steering gear, the diameter of the circle was from eight to nine times the length, which is to be explained by her relatively small rudder, and extremely fine form. In the Shah swift frigate with steam steering and a larger rudder-area, the diameter of the circle varied from five to six times the length. Corresponding facts as to merchant ships are not numerous ; but it would appear that diameters from seven to eight times the length are not un- common with steam steering gear and good helm-angles. In these ships great handiness is not sought for, moderate rudder-areas are common, and it is chiefly desired to have the vessels well under control. Larger rudder-areas might be advantageously adopted, no doubt, now that steam steering gear is so extensively used. 4. The propellers of the ships were working at full speed when the * For details see Admiral Boutakoff's Navales, Admiral Colomb's paper in the Tactiques Navales, M. Dislere's Marine Transactions of the Institution of Naval Cuirassee, Admiral Bourgois' Etudes sur Architects for 1886, and the author's les Manoeuvres des Combats sur Met, paper, "On the Turning Powers of M. . Lewal's Principes des Evolutions Ships," mentioned above. 688 XAVAL ARCHITECTURE. [chap, xviii. preceding results were obtained. But it appeal's that differences of speed do not greatly affect the diameters of the circles, although they affect the- time of turning, so long as the helm-angle remains constant, and about the same time is occupied in putting the helm over. With steam steering or with balanced rudders these conditions may be fulfilled, and the diameter remains nearly constant in smooth water and light winds. In the Thunderer, for example, at speeds from 8 to 10 knots, the diameter only varied from 1400 to 1320 feet. In the Iris, for speeds varying from 9 to 14 knots, the diameter varied only from 2300 to 2400 feet ; at the still higher speed of 16J lcnots it was nearly 2700 feet, but this was a single trial. In the Bellerophon, with balanced rudder and manual power, the diameter of the circle at 14 knots was 1680 feet, and at 12 knots 1650 feet. In large ships, with manual power only available at the steering wheels, a shorter time suffices to put the helm over, or larger angles can be reached, at lower speeds, and then the diameters of the circles are decreased. In the Warrior, for example, while the diameter of the circle at 14 knots was 2340 feet, at 12 knots it was 1580 feet only. 5. The time occupied in putting the helm hard over exercises a considerable influence on both the time occupied in turning the circle and upon its diameter; but more particularly affects the latter. The case of the Minotaur, mentioned on p. 668, is a good illustration of this, and as another the trials of the sister ships Hercules and Sultan may be cited. The latter had steam-power applied to her balanced rudder, which could be put over in about half the time occupied by manual power in the Hercules. The diameter of the circle in the Hercules was nearly twice as great as that for the Sultan ; the time of turning for the Sultan was rather less than that for the Hercules, although the speed was half a knot less. It will be evident that the distance traversed by a ship in turning will depend upon the rapidity with which her uniform angular velocity is acquired, the rate of that velocity, and the check to her headway, all of which will be affected by the time occupied in putting the helm up. By means of balanced rudders or steam steering, the mean angular velocity, or speed with which the ends of a ship turn relatively to the middle, has in some cases been almost doubled as compared with the results obtained with ordinary rudders and manual power. 6. Other things remaining unchanged, an increase in the rudder area is most influential in diminishing the space traversed in turning ; and this diminution may be of the greatest value to a war-ship intended to act as a ram. This point has been illustrated by the performances of the Sultan and Hercules with their rudders acting as simple CHAP. XVIII.] THE STEERING OF SHIPS. 689 balanced rudders, and with the after parts of the rudder alone at work. Further, it appears that increased rudder-area and helm-angle may, in some cases, check the headway so much as to produce no greater turning effect than, if so great as, would be produced by smaller rudders and less helm-angles. In the experiments on the gunboat Delight, with balanced rudders of different sizes, mentioned on p. 680, it was found that the largest rudders diminished the space traversed in turning, made the time of turning the first quadrant less (that is, enabled the full angular velocity to be more quickly attained), but somewhat increased the time of com- pleting the circle, in consequence of the greater check to the headway. 7. For the same ship, with the same angle of helm and about the same time occupied in putting the helm over, the time occupied in turning the circle appears to vary nearly inversely as the speed. Take, for example, the following results for the Warrior and Hercules : — Warrior. Hercules. Times Products of Times Products of Speeds. of turning speeds Speeds. of turning speeds circle. by times. circle. by times. knots. mill. sec. knots. min. sec. 3 28 46 86-3 6 9 32 57-2 6 15 30 93-0 8 7 21 58-8 9 10 40 96-0 10 6 22 63-6 12 8 45 105-0 12J 4 28 54-2 14* 7 21 104-1 14-7 4 58-8 The following results for the Thunderer are also interesting ; they relate to the second circle turned when the motion had become uniform : — Times Products of Speeds. of turning speeds circle. by times. knots. min. sec. 5-83 7 6 41-4 6-87 5 38 38-7 7-14 5 24 38-5 7-24 5 16 38-1 This approximate rule will be seen to rest upon the facts that 2t 6go XA VAL ARCHITECTURE. [CHAP. xvih. the diameters of the circles at different speeds are practically equal under the assumed conditions, and that the loss of speed in turning bears a fairly constant ratio to the speed on a straight course. It may be of some service in estimating the time that will be occupied in turning at any selected speed, when the performance of a ship at some other speed is known ; but it clearly cannot be used with safety except the fundamental assump- tions are fulfilled. S. Up to helm-angles of 40 degrees, the turning power of the rudder has been found to increase with increase in the helm-angle. Theoretically, if the streams impinged upon the rudder parallel to the keel-line, and the effective pressure on the rudder varied with the sine of the angle of inclination, 45 degrees would be the angle of maximum turning effect. This may be seen very easily. Using the notation of p. 668, the moment of the pressure (P) on the rudder will vary very nearly as the product P x GA cos a (Fig. 171) ; the distance AC from the axis to the centre of effort of the rudder being very small as compared with AG. Also (as explained on p. 663) the pressure (P) equals the product of the normal pressure (P x ) by the sine of the angle a. Hence, approxi- mately — Moment of pressure on rudder about G . . = P X GA cos a = P t sin a x GA cos a = p\ sin 2a x GA. This will have its maximum value when sin 2a = 1 and a = 45 degrees. Balanced rudders are usually arranged so that they can be put over to 40 degrees ; ordinary rudders are seldom put over beyond 35 degrees, and with manual power only, the angle seldom exceeds 25 degrees in large screw steamers. Experience fully confirms these conclusions, as will be seen from the following examples. The Delight gunboat behaved as under, when the helm-angle alone was varied : — Helm-angle. Times of turning full circle. Diameter of circle. degrees. 10 20 30 40 mln. eeo. 3 52 3 18 2 57 2 47 feet. 615 405 275 205 CHAP. XVIII.] THE STEERING OF SHIPS. 691 In trials conducted with the floating battery Terror the results were no less striking — Helm -angle. Times of turning fall circle. degrees. 10 20 30 40 min. sec. 6 19 5 28 5 1 4 42 Lieutenant Coumes, of the French Navy, gives the following results for the ironclad corvette Victorieuse for an initial speed of about 12£ knots : — Helm-angle. Times of turning full circle. Diameter of circle. degrees. min. sec. metres. 7 9 48 1060 14 6 50 933 21 5 50 750 27 5 20 572 32J 5 20 465 In practice, as has been shown above, it may happen that, with large rudder-areas, the least time in turning through the complete circle does not occur with the largest angle of helm, although the least diameter of circle does then occur. But for tactical purposes the first quadrant or first half-circle is more important usually than the complete circle, and within these limits large rudders at large angles economize both space and time. Moreover, in such a case the commanding officer can use his large rudder at a somewhat less angle if he wishes to turn completely round in the least time, or at the full angle, if economy of space is more important. Determination of Rudder-Areas. — Attention will next be directed to some matters of practical interest relating to the determination of the areas and forms of rudders, and the helm-angle to be adopted in new ships. It will be convenient if the last-named problem is taken first. From the remarks made above it will be evident that, so far as the steering effect is concerned, a possible helm-angle of 40 to 45 degrees would be advantageous, or even a greater angle, if regard is to be had to the reduction of the effective helm-angle which takes place in turning (see p. 681). Other considerations come in, how- ever, and affect the decision. It may be very difficult with certain 692 NAVAL ARCHITECTURE. [chap, xviii. forms of stern to secure a large angle of helm, eTen when all care is taken and recourse had to various mechanical devices. When manual power only was used in the great majority of ships with ordinary rudders, it became important to decide between the relative advantages of area and helm-angle which were possible with a certain power available at the tiller-end. Mr. Barnes drew attention to this matter some years ago, basing his investigation on the old law, that the effective pressure on the rudder varied as the square of the sine of the angle of inclination.* Adopting the law of the sine, it may be interesting to make a similar comparison between a narrow rudder held at a certain angle by a given force at the tiller-end, and a broader rudder of equal depth held at a smaller angle by the same force. Let it be supposed that the rudders are of similar form, so that their areas and the distances of their centres of effort (C, Fig. 170) from the axis will be proportional to the extreme breadths, B! and B2 ; then for the narrow rudder we may write — Area of rudder = S x = depth of rudder x B x x / = / . d . B^ where /is some fraction of the breadth applicable to both rudders. Using the notation previously adopted, c^ being the helm-angle — Pressure on rudder = Pi . Sj . V 3 sin a t = P x . fd . Y 1 . Bj sin ^ = C\ . B x sin a,. Moment of pressure about! (P ressi ™ * AC axis of rudder . . .J = = ^ . B, tan «, x r . ^ { = }• . d X Bi sin a v If S 2 be the area of the broad rudder, a 2 its angle, B 2 its breadth, similar expressions will hold for it, the constants C^ and r being identical. Hence, in order that the moments of pressure about the axes of the rudders may be equal, we must have — C^ . B^ sin a t = C^- . B 2 2 sin a 2 whence — sin a x B 2 3 sin a 3 ~~ Bj 2 The last equation succinctly expresses the relation which must hold when the force applied at the tiller-end is the same in both cases. For the turning effect of either rudder, we may take — Turning effect = pressure x AG- x cos of helm-angle ; and, since AG is the same for both rudders — Turning effect of narrow rudder _ B[ sin a x cos a, _ B 2 cos a x Turning effect of broad rudder B 2 sin n a cos a 2 B t cos a 2 * See his paper in the Transactions of the Institution of Naval Architects for 1864. -chap, xviii.] THE STEERING OF SHIPS. 6 93 Suppose, as an example, the narrow rudder put over to 40 degrees -and the broad to 20 degrees by the same force on the tiller-end — T* _ T5 * / Sin 4 °° - tt A /°' 643 1 -qV-R Turning effec t of narrow rudder _ cos 40° Turning effect of broad rudder cos 20° = 1-37 x ^ = 1* (nearly). 0-94 The broad rudder, with an area 37 per cent, greater than the narrow one, has therefore less turning effect by about 11 per cent. If the ship had sail-power as well as steam, the smaller area of the narrow rudder would have the further advantage of checking the headway less when the ship was manoeuvring under sail alone. It will be seen, on reference to p. 664, that in his multiple- Jbladed rudders, M. Joessel endeavoured tQ associate large effective rudder-area with comparatively small longitudinal dimensions in order to reduce the force required at the tiller-end, and he based his procedure on reasoning similar to that above. Various rules have been used for determining the area of the rudder for a new ship. For sailing ships of former types, having lengths about 3J to 4 times the beam, the extreme breadth of the rudder was commonly made one-thirtieth of the length, or one-eighth of the breadth of the ship. The mean breadth of a rudder commonly varied between seven-tenths and nine-tenths of the extreme breadth. JW steamships a similar rule is used, the extreme breadth of the rudder being made from one-fortieth to one-sixtieth of the length. Mr. Scott Russell proposed to make a slight modification of this rule, the extreme breadth of the rudder being one-fiftieth of the length plus 1 foot. Another mode, commonly used for English and foreign ships of war, is that by which the area of the immersed part of the rudder is proportioned to the area of that part of the longitudinal middle-line section of the ship situated below the load-line ; the same area which is made use of in determining the " centre of lateral resistance " for sailing . ships (see_ p. 518). As the area of this section depends upon the product of the length of the ship into the mean draught, while the rudder-area depends upon the product of its breadth into the draught of water aft, it will be seen that this rule agrees in principle with the old rule. In sailing ships, the rudder area was often about one-thirtieth or one-fortieth of the area of the middle-line plane; in the screw line-of-battle ships and frigates, similar values were common ; from one-fortieth to one-fiftieth are common values in ironclad ships of moderate length with ordinary 694 NAVAL ARCHITECTURE. [chap. xvm. rudders. In the long ironclads of the Warrior and Minotaur classes, the rudder-area Taries between one-fiftieth and one-sixtieth of the area of the middle-line plane ; whereas in the ironclads fitted with balanced rudders it rises to one-thirtieth, and in some recent types in the French Navy and in the Russian circular ironclads has been made one-twentieth. One-fortieth would probably be a fair average for steamships of war. In merchant ships much smaller rudders are used, and values as low as one-hundredth have been met with. None of these rules can be regarded as entirely satisfactory; because they take no cognisance of the law of variation of the resistance to rotation. "When the angular velocity has become constant, that resistance varies nearly as the square of the angular velocity ; and the moment of the pressure on the rudder should be proportioned thereto. In fact, it appears on investigation that the pressure on the rudder, which — other things being equal— depends upon the rudder-area, should in similar ships vary, not with the area of the middle-line plane, but with the product of that area into the square of the length, if the speed of turning is to be equal, after the motion has become uniform. In this statement it is assumed, of course, that the ships compared are of similar form ; the limitations, explained on p. 505, for lateral resistance in sailing ships, being similar to those which will hold here. If regard is had to the initial motions of the ships under the action of their rudders, the moments of the pressure on the rudder should be made proportional to the moments of inertia of the ships. In other words, the products of the rudder-areas into the lengths of similar ships should be pro- portional to the moments of inertia, which will involve the product of the displacements into the squares of the lengths. The displace- ments will vary as the cubes of the lengths ; the moments of inertia will therefore vary as the fifth powers ; the area of the middle-line plane will vary as the square; and therefore, under this mode of viewing the question, the rudder-areas should be proportional to the products of the areas of the middle-line planes into the squares of the lengths. Expressed algebraically, if Ai and A 2 are the areas of the middle-line planes of two similar ships ; a x and a^ the rudder areas ; ^ and Z 2 the lengths : the rule would be — This would give a much larger area to the rudders of long ships than is commonly adopted; and, as a matter of fact, long ships usually turn more slowly than short ships, in consequence of their proportionately small rudders. Great differences of opinion have been expressed respecting the CHAP. XVIII.] THE STEERING OF SHIPS. 695 best form for rudders. In Fig. 176 a few of the commoner forms are illustrated. The balanced rudder a has been previously described ; b is a form much in vogue for the older classes of sailing ships and unarmoured screw-ships of the Eoyal Navy, the broader part being near the heel of the rudder, and the narrower part near the water-line ; e is a form now com- monly used in the steamships of the Eoyal Navy ; d is the oppo- site extreme to b, the broadest part of the rudder being placed near the water-line : this form is much favoured in the mercantile marine, especially for sailing ships, and is recommended on the ground that the lower part of a rudder is less useful than the upper part ; but this is a misconception of the real facts of the case. From the remarks made on p. 452 as to the unequal motion of the currents in the Wake of a ship, it appears that the fineness of the run near the keel should make the lower part of the rudder the most effective ; and this has been verified experimentally.* Hence it seems probable that, with the form of rudder d, the nar- rower, lower part does quite as much work in steering as the broader, upper part : whereas, by tapering the rudder, the power required to put the helm over is made considerably less than it would be if the breadth were uniform. These considerations would not have equal force in screw steamers where the rudder is placed abaft the screws ; and then the form e is to be preferred, as the broadest part of the rudder is much less likely to be emerged by pitching than with the form d. In war-ships having under-water protective decks at the extremities, the rudder-head and steering gear are placed under those decks, six or seven feet below water. It then becomes necessary to use very broad rudders in order to gain sufficient area, and this form is advantageous also, because it enables the rudder to sweep out into the race of the twin-screws. With steam steering gear these broad rudders can be easily manipulated. In some vessels, to obtain greater command over their movements, the keel has been deepened aft, and the rudder thus made to extend below the body * See the account of an experiment made by Mr. Froude, cited by Dr. Woolley, in a paper " On Steering Ships," read at the British Association in 1875. A model was fitted with a rudder of uniform breadth, divided into two equal parts at the middle of the depth, and the lower half, when fixed at 10 degrees only, balanced the upper half fixed at 20 degrees when the model was towed ahead. 696 NAVAL ARCHITECTURE. [chap. xvm. of the skip into less disturbed water. The case of Chinese junks also bears out the advantages obtained by placing rudders in water which has a maximum sternward velocity relatively to a ship. In the floating batteries built during the Eussian war, " drop-pieces " were fitted at the bottom of the rudder, and hinged to the heel, so that, when the rudder was put over, they might drop down below the keel and increase the steerage. The results in this case were not entirely satisfactory, but the circumstances of these vessels were peculiar. To assist the steerage of large steamers when passing at low speed through the shallow waters of the Suez Canal, temporary enlargements are sometimes fitted to the permanent rudders, with beneficial results. A few special forms of rudders may be mentioned. One proposed by Professor Eankine for screw-steamers was to be on the balanced principle, but to have curved sides, in order that the propeller-race in passing might communicate a pressure which should have a forward component and help the ship ahead to a small extent. Herr Schlick proposed a very similar rudder, the surface of which was twisted, so that the currents driven obliquely from the screw- propeller, might move freely past the rudder when it was amidships, and not impinge upon its surface as they do upon that of an ordinary rudder. By this change it was supposed that two advantages would be gained : (1) there would be little or no check to the headway of a ship when the helm was amidships ; (2) steering power would be obtained from all parts of the rudder surface immediately the helni was put over to either side, whereas with plane-surfaced rudders, placed behind screw-propellers, this is not the case. Experiments made at Fiume with small vessels are said to have demonstrated the great superiority of the new rudder in both these particulars. The following particulars have been furnished to the author by Herr Schlick. The Vinodol was 1,40 feet long, 19 feet broad, and 8J feet mean draught. She was first fitted with an ordinary rudder of 2ti square feet area (immersed). With 89 to 90 revolutions of the screw per minute she traversed a distance of 2^ knots in 14JJ minutes, and turned a circle of about 1000 feet diameter in -if minutes. Subse- quently a twisted rudder, having an immersed area of 17^ square feet, was fitted. With the same steam-pressure and cut-oft" as before, 91 revolutions were made per minute, and the measured distance was run in 14 minutes 6 seconds, showing a gain in speed of about 4 per cent. ; the circle turned had a diameter of 900 feet and was com- pleted in 4 minutes 55 seconds. The vibration at the stern was also reduced. Another novel and ingenious rudder has been patented by Mr. Gumpel. It is a balanced rudder as to suspension, but is carried on chap, xviii.] THE STEERING OF SHIPS. &97 crank-arms ; and the fore edge has attached to it a vertical pintle, which works freely in a fore-and-aft slot cut in the counter of the ship. When the helm is put over, therefore, the fore edge of the rudder is constrained to remain at the middle line, the rudder being moved bodily over to one side of the keel by means of its crank- arms. This movement would be especially useful in the case of a twin-screw ship, since it would bring the rudder more into the race. The force required at the tiller-end to hold the rudder at any angle is less than that for an ordinary rudder ; and the crank-arms can be so proportioned that, when the rudder is hard over, little or no force is required at the tiller to hold it there. Mr. Gumpel tried the rudder in a small steam yacht with great success ; but it has not been tested on a large scale. There are obviously greater risks of damage and derangement with this rudder than with balanced rudders fitted in the usual manner. Mr. Lumley proposed to make ordinary rudders in two parts, hinging the after part to the fore part, which was attached in the usual way to the stern-post. When the helm was put over to any angle, it moved the fore part of the rudder through an equal angle ; but the after part was made to move over to a greater angle by means of a simple arrangement of chains or rods, and thus a greater pressure on the rudder was obtained. Several ships were fitted on this plan, and it was favourably reported upon in some cases, but has now fallen into disuse, at least in the Royal Navy. Auxiliary Appliances for Steering. — Of the auxiliary appliances fitted to increase the steering power of ships, the most important are bow rudders. These rudders are rarely fitted except in vessels which are required to steam with either end foremost; to avoid the necessity for turning, or to be capable of service in rivers or narrow waters where there is little room for turning, or to meet some other special requirement. In nearly all cases arrangements are made by which such rudders can be locked fast in their amid- ship position when the ship is steaming ahead. Few ships of the Eoyal Navy are thus fitted. The jet-propelled Waterwitch, intended to steam indifferently with either end foremost, had rudders at both ends. Many coast-defence and river-service gunboats have rudders hinged to their upright stems for use when steaming astern in narrow waters. The cable ship Faraday had a bow rudder for use when steaming astern; when steaming ahead it was locked fast amidships, and similar arrangements are not un- common in double-bowed river or ferry steamers which do not turn when reversing their course. Ordinarily, bow-rudders have been hinged at their after edge either to the stem or to an axis situated a 698 NAVAL ARCHITECTURE. [chap, xviii. little abaft the stem, a recess being formed to shelter the rudder when locked amidships. Several obvious objections arise to this mode of fitting, especially in war-ships, and for use when steaming ahead. Rudders so placed are very liable to damage or derangement from collision or blows of the sea. If put over to a good angle they must cause a considerable increase of resistance and disturbance of the flow of water relatively to the ship. Moreover, if hinged at their after edges to the body of a ship, these bow-rudders have a further disadvantage, if used when going ahead, because the accunmlation of pressure which then takes place on the fine part of the bow, on the side to which the rudder is put over, acts against the rudder-pressure and diminishes its turning effect.* This additional pressure resem- bles that described on p. 668 as acting on the deadwood or stern- post before an ordinary stern-rudder when a ship is going ahead; only in that case it increases the turning effect of the rudder. Hence it appears that, if bow-rudders have to be used as auxiliaries to stern- rudders when a ship is moving ahead, they should be so placed that the streams flowing past them should not subsequently impinge directly upon the hull and reduce the speed of turning. This can be done either by using balanced rudders, placed in large recesses in the bow, or by fitting the rudders so that they can be dropped into clear water under the bow, somewhat as has been mentioned for the drop-rudders of Chinese junks. The latter plan has been used in many torpedo-boats, in associa- tion with rudders at the stern. They were found useful in diminish- ing both the time and space required for turning when the boats were going ahead, and in keeping the boats under control when going astern, and when the stem rudders on the ordinary plan were in- effective. In some of the smaller boats the heeling effect of these bow-rudders under the bow was found objectionable, especially if the helm was put down quickly, and as other means have been found for increasing the manoeuvring power when going both ahead and astern, bow rudders have ceased to be employed. In the Polyphemus torpedo-ram of the Royal Navy a balanced two-bladed bow-rudder was fitted, and arranged so that it could be drawn up into recesses when desired, or dropped under the keel when in use. Careful observations were made on the turning powers of the vessel at various speeds, with the ordinary stern rudder only, as well as with both stern and bow rudders working together. It was found that when the ship was moving ahead at various speeds, the use of the bow-rudder reduced the " tactical diameter " and the time of reversing the course (completing the first half-circle) by about twelve * This effect may often be observed senger-Bteamer when turning astern with in the slow motion of a Thames pas- helm hard over to swing clear of a pier. CHAP, xviii.] THE STEERING OF SHIPS. 699 per cent. Going astern at 11 knots, with the stern rudder only at work, the vessel was not well under control, and under many cir- cumstances of wind and sea did not obey her helm. With the bow rudder also at work she was perfectly under control, and turned astern in a circle of which the diameter was little greater than that for an equal speed ahead. One serious objection to bow rudders is that their action depends entirely on the relative movements of the ship and the water ; and that the action of the propeller-race does not give steerage, as it does with a rudder near the propeller, before the ship gathers way. This is not true with the arrangements illustrated in Figs. 167-169, and their successful application has practically caused the disuse of bow- rudders. Vessels fitted with these plans have proved very handy, both when moving ahead and going astern. A very interesting series of trials has been made by the Admiralty on three torpedo-gunboats. One of these (Rattlesnake class) had a straight keel and an ordinary rudder ; a second was identical with the first, except that the after deadwood had been cut away, and the " turn-about " system applied (Fig. 168) ; a third and larger vessel (Sharpshooter class) was fitted with the rudder illus- trated by Fig. 167, and had her deadwood cut away to a smaller extent. It was found that the first vessel behaved similarly to torpedo-boats built with straight keels and ordinary rudders, as was anticipated from the great ratio of length to draught. With 33 degrees of helm the tactical diameter was about 1\ times the length, and over 4 minutes was occupied in turning the circle at full speed. In the sister ship, fitted on the " turn-about " system, the tactical diameter for the same helm-angle was about 5 times the length, and the time for the circle was under 3 minutes. These greatly superior results were due to two causes : the large increase in rudder-area, and the removal of the deadwood. Going astern, the first vessel was not under control of her rudder ; the second was perfectly under control, and the tactical diameter was about 9J times the length, while the time for the circle was from 1\ to 8£ minutes. The vessel of the Sharpshooter class fitted with the rudder illus- trated in Fig. 167 r was one-sixth longer and nearly 2 knots faster than the others, while her draught of water was rather less. Her maximum helm-angle was 35 degrees. At full speed ahead the tactical diameter was about 6 J lengths, and the time for the circle 3£ minutes. Going astern, the tactical diameter was about 82 lengths, and the time for turning the circle 8 minutes 50 seconds. These results indicated great manoeuvring power, although not so great as those obtained with the " turn-about " system, and the latter plan has been generally used in the later torpedo-gunboats. /OO NAVAL ARCHITECTURE. [chap. xvm. Steering screws have also been suggested as a means of con- siderably increasing the speed of turning, or of enabling a single- screw steamship to turn without headway. The principle of most of these proposals is to fit a screw of moderate size in the deadwood either forward or aft, in such a manner that, when set in motion by suitable mechanism, its thrust shall be delivered at right angles to the keel-line. Small manoeuvring screws, driven by manual power, had been previously proposed and tried in sailing ships ; but Sir N. Barnaby, we believe, first suggested the use of similar and larger screws, driven by steam-power, for the Warrior and Minotaur classes of the Koyal Navy : proposing to fit the steering screws at the bows of these ships, in apertures cut in the deadwood for the purpose.* Subsequently the late Astronomer Royal, Sir George Airy, proposed a similar screw, but suggested that it should be placed in the after deadwood below the main propeller-shaft. Other proposals of a similar character have also been made ; but we are unaware of any trials having been made on actual ships. There can be no doubt as to the manoeuvring power that might thus be obtained ; but con- siderable practical difficulties would have to be overcome in carrying the plan into practice and communicating driving power to the steering screws. The use of water-jets expelled athwartships from orifices near the bow and stern has also been repeatedly suggested ; not merely for jet-propelled vessels, but for screw steamers. Trials were made of this principle on a gunboat belonging to the Royal Navy in 1863, but they were not so successful as to lead to an adoption of the plan. For a given amount of engine-power much better results might be hoped for from the employment of a steering screw, such as is described above, than from the use of water-jets. A special form of steering screw proposed by Herr Lutschaunig deserves to be mentioned.t It consists of a small screw carried by the rudder, and put over by the helm to the same angle as the rudder. By means of a simple train of mechanism, the steering screw is made to revolve by the motion of the main propeller-shaft ; and its thrust is always delivered at an angle with the keel when the rudder is put over. A very similar arrangement was subsequently patented, and fitted to several boats and small vessels by Mr. Kundstadter. Trials made with these vessels were said to have given satisfactory results both as regards speed and turning power. Prior to the actual trial of this principle, it was anticipated that considerable * See the Transactions of the Insti- t See the Tmnsactions of the Insti- tution of Naval Architects for 18G3 and tution of Naval Architects for 1874. 1864. chap, xviii.] THE STEERING OF SHIPS. 7 or steering power might thus be obtained if the steering screw was suitably arranged for working in the race of the main propelled. It is clear, however, that the mechanism of the steering screw is of a character and occupies a position which renders it liable to derange- ment, while damage to it might interfere seriously with the efficiency of the main screw propeller. ~No extended use has been made of the plan. The difficulties experienced in the steerage of high-speed torpedo- boats have given rise to various devices for increasing the manoeuvring power. To some of these attention has been directed above. One of the most ingenious mechanical arrangements made for this purpose is the " steering paddle " patented by Mr. Thornycroft. It consists of a broad-bladed paddle placed near the stern of the boat, and operated by steam-power somewhat in the manner in which a " scull " over the stern is operated by hand. In the small boat to which it was fitted it answered perfectly, and enabled her to be " slewed " without headway. On a larger scale it would be practicable ; but it would require a considerable engine-power in a ship of large size to produce results at all comparable with those obtained in the experimental boat. A twin passenger-steamer, the Alliance, designed by Mr. George Mills, had manoeuvring paddle-wheels fitted at the bow and stern, the axes of the wheels lying fore and aft, and their thrust being delivered athwartships. No reports of the performances of this vessel are recorded, but we are informed that the plan was adopted chiefly to enable the vessel to " cant off " from the piers on the Clyde. Auxiliary rudders of various kinds have been tried, but none have proved so successful as to pass beyond the experimental stage, or to be used apart from the special circumstances for which they were devised. In some of the floating batteries built during the Crimean War, in which the shallow draught and peculiar form made steering very difficult, auxiliary rudders were fitted on each side at some distance before the stern, and arranged so that they could be put over to an angle of about 60 degrees. No sensible improvement in the steering appears to have resulted from these additions. Another form of auxiliary rudder was proposed by Mr. Mulley, and tried at Plymouth in 1863. It consisted of a rudder fitted on each side of the after deadwood, at a short distance before the screw aperture ; it was hinged at the fore edge, and, when not in use, could be hauled up close against the side, but, when required, could be put over to 38 degrees from the keel-line. When applied to a paddle-wheel tug, it answered admirably, steering her by its sole action, and making her turn more rapidly when acting in conjunction with the main /02 iVA VAL ARCHITECTURE. [chap. xvih. rudder. It completely failed, however, when tried on a screw ship, and produced a distinct turning effect on the ship in the direction opposite to that in which it was expected to act. The explanation of the failure suggested by the inventor is probably correct: the action of the screw propeller may have produced a negative pressure on the side of the deadwood abaft the auxiliary rudder when it was put over ; and the turning effect of the negative pressure more than counterbalanced the effect of the auxiliary rudder. Possibly, if the latter had been placed further before the screw, it might have suc- ceeded, as it did in the paddle-wheel vessel. Another kind of auxiliary rudder was tried in her Majesty's ship Sultan. She was fitted with sliding rudders, one on each side, arranged so as to counterbalance one another ; when one was allowed to project under the counter, the other was drawn up into a casing within the ship, and both could be "' housed " when desired. The area of each of these auxiliaries, when fully immersed, was about one-sixth of the area of the main balanced rudder, and it was set about 50 degrees from the keel-line. On trial it was found that the small area and the position of the auxiliary rudder rendered its steering effect practically unimportant. Another plan of auxiliary rudders was tried in the corvettes of the Comus class of the Royal Navy. It was desired to give these unarmoured vessels the advantage of a submerged rudder in addition to the ordinary rudder, for use in case of damage to the latter in action. For this purpose a recess was formed in the deadwood under the shaft, and before the single screw propeller. The auxiliary rudder was placed in this recess, hinged at the fore end, and when housed amidships it nearly made good the recess in the deadwood, com- pleting the shape of the ship. It could be put over to about 30 degrees, but as manual power only was available, the time occupied in putting the helm over was very long. On trial it appeared that, although the- area of the auxiliary rudder approached equality to that of the ordinary rudder, it possessed little steering power. It was then decided to fit side-blades on the Joessel principle as a further experiment, and when this was done the auxiliary rudder proved capable of turning the ship in about three times the period which sufficed for a complete circle with the ordinary rudder, the diameter of the circle being increased about four times. This result was not satisfactory, and, as it involved a sensible loss of speed, when the auxiliary rudder was locked amidships, it was finally decided to remove the side-blades, and to leave the single-bladed rudders as first fitted, simply as a reserve in case of damage. In subsequent vessels of the class similar rudders were not fitted. These experi- ments incidentally furnished remarkable evidence of the gain in •chap, xviii.] THE STEERING OF SHIPS. 7°3 steering effect, for the case of headway, generally obtained by placing the rudder abaft the screw.* Steering blades or boards somewhat similar in principle to those tried in the Sultan have been used successfully in vessels designed for shallow-water service. These blades were set at an angle of about 45 degrees from the keel-line on either side, and could be pushed out from the stern or dropped down into the water on the side towards which the head of the ship was to be turned. The idea is an old one, and has been made use of on some occasions to steer seagoing ships which have lost their main rudders. Of the very numerous plans of " jury rudders " which have been proposed, we can say nothing in the space at our disposal. They are all based upon the principles explained above for the ordinary rudder, and are more or less satisfactory expedients for taking the place of the rudder properly belonging to any ship. Steering by Propellers. — Various methods have been devised for steering steamships by means of their propellers, independently of the action of the rudder. Single-screw ships, as ordinarily fitted, do not possess this power. As explained on p. 656, they can be slewed without headway by using the rudder and the screw. It is also a matter of common experience that, with the helm amidships and screw in motion a single-screw ship can be turned completely round in smooth water, and in a calm or light winds. In most cases turning under these circumstances is performed slowly and in circles of large diameter. In fiat-bottomed ships with full sterns it may be otherwise. The commanding officer has little or no command over the direction in which the vessel turns, and in practice the action of the wind or sea may counterbalance or overcome the steering effect of the screw. Even in smooth water and calms the steering effect varies as certain conditions change. Many interesting facts bearing on this subject will be found in the Eeports of the British Association Committee mentioned on p. 657. f The broad conclusions from experience may be summarized as follows : — (a) When a ship is moving ahead at good speed with screws well immersed and helm amidships, then, with ordinary forms of * M. Normand has discussed the the screws, is sufficiently distant to relative efficiencies of rudders placed permit the water deflected by the rudder before and abaft the screws in two in- to resume its normal direction of flow teresting papers, published in vols. 1 before reaching the propellers, and 4 of the Bulletin de V Association t See also a paper by Professor Technigue Maritime. From experience Osborne Reynolds in the Transactions with torpedo-boats, he considers that of the Institution of Naval Architects for •equal steering power may be obtained 1873; and one by Mr. Maginnis in the provided the rudder, if placed before Transactions for 1879. 704 iXAVAL ARCHITECTURE. [chap, xviii. stern, the water in the upper portion of the wake has a greater forward motion than that in the lower portion. Consequently the thrust on the upper blades of the screw is greater than that on the lower blades, and the excess in the transverse components of the thrusts produces a steering effect. The bow of the ship tends to turn towards the side on which the screw descends. If the screw be right-handed, the head will tend to turn to starboard: if it be left-handed, the head will tend to turn to port. If the helm is left free, the rudder will rest in a position inclined to the keel-line on that side towards which the particles of water in the race are driven by the lower blades of the propeller. (i) If the screw is not well immersed, if the ship is just starting from rest, if she is moving very slowly ahead, or if the engines are suddenly reversed when the ship is moving at good speed ahead, then the thrust of the lower blades may be iu excess of that on the upper blades, and the steering effect will be the opposite of that described in the first case. (c) When the vessel has sternway. the lower blades are likely to have a greater thrust than the upper, and the steering effect will be similar to that described for the first case. These rules necessarily have many exceptions in practice, as the circumstances may vary in a great many ways. No general rules can be laid down, but commanding officers soon become familiar with the general tendency in individual ships. A single-screw ship can be turned more qxiickly in one direction than in the other, because of this steering effect of the screw. In some cases the difference in times of turning is greater than in others. For example, the Bellerophon completed a circle turning to starboard in 4 minutes, but required 4 minutes 20 seconds to complete a circle of the same diameter turning to port. The floating battery Terror was built with a very full stern, causing a great excess of thrust on the upper blades of the propellers. The circle with starboard helm occupied 5 minutes 12 seconds, and that with port helm 6 minutes 18 seconds. With the helm left free she turned to port and com- pleted a circle in 5 minutes 52 seconds, or less time than she turned to starboard (with port helm) under the action of her rudder hard over. On consideration it will be seen that, when the rudder is used in a ship with her screw well immersed, the streams delivered by the lower blades impinge more directly upon the lower part of the rudder when it is put over to the side on which the blades descend when the ship is going ahead, than they do when the rudder is put over to the other side. This circumstance further assists the steering to one side as compared with the other. Pilots always allow for the steering effect of the screw in entering rivers, harbours, or docks. chap, xvm.] THE STEERING OF SHIPS. 705 Various proposals have been made for the purpose of gaining steering power from the direct thrust of single screws. One of the earliest plans was that proposed by Mr. Curtis, in which the screw was attached to the shaft by means of a suitable joint, and was carried by a frame hinged like a rudder to the stern. The frame, carrying the propeller, could be put over with the helm to any angle desired ; and the thrust of the screw, driven by the main engines, was then delivered at an angle with the keel-line, exercising a powerful turning effect on the ship. On trial it was found that this turning effect was very powerful, and the motions of the small vessel so fitted were very rapid ; but there was far less control over the motion than with the rudder, and this fact, together with the difficulties and risk of derangement to the propelling apparatus which would attend the adoption of the plan on a large scale, has prevented its use. An ingenious plan for effecting the same object has been patented by an American, Colonel Mallory, who devised a method for rotating the screw through a complete circle, and meanwhile keeping the main engines running continuously in one direction. A boat fitted with the Mallory propeller can be turned almost on her centre, stopped very rapidly, and kept thoroughly under control by the action of the screw alone, no rudder being fitted. The American torpedo vessel Alarm (of 140 feet length and 750 tons displacement) was fitted with this propeller, and the Eeport of the Board of Naval Engineers who conducted the trials was very favourable. It was asserted that, without any loss in efficiency as a propeller when com- pared with single or twin-screws, there was an enormous gain in manoeuvring power. The only drawbacks were considered to be "increased cost and complexity of mechanism and necessarily decreased reliability and durability ; " but for torpedo-boats, small rams and gunboats, the Board considered the advantages of the Mallory system to far outweigh its disadvantages. Notwithstanding this favourable report, the system has not found favour or been widely used. Another very ingenious method of increasing manoeuvring power in single-screw ships has been fitted by Mr. Thornycroft to a large torpedo-boat, in connection with the novel form of propeller described on p. 580. The " guide-blades " behind the screw are enclosed by a casing, and abaft this casing is another casing carried by the rudder. When the helm is put over, the water from the screw is therefore delivered into the after casing, which is set obliquely to the keel-line, and the manoeuvring power thus obtained when the boat is moving ahead has proved to be most remarkable on trial ; the boat which previously traversed a large circle in turning could be slewed almost without headway, the bow remaining nearly at rest. For sternway the plan is not well adapted. 2z 706 NAVAL ARCHITECTURE. [chap, xviii. A manoeuvring propeller was invented some years ago by Mr. Moody, and applied to a few barges on the Clyde. It was subsequently proposed by Mr. Fowler, who does not appear to have been aware of the other invention, and fitted to the American torpedo-vessel Alarm, as well as to a few small vessels. This propeller consists of a feather- ing paddle-wheel placed at the stern, the axis of the wheel being vertical. By means of a suitable mechanism the paddle-floats can be made to " feather " at any point in their revolution ; and in this way the maximum thrust can be delivered in different directions, and made either to propel the vessel ahead or astern, or to steer her on any desired course. The apparatus was said to have answered well in the Alarm, as regards handiness, but not to have been favourable to speed. It was removed, and a Mallory propeller substituted, with a considerable gain in speed and greater handiness. Another American invention of a very similar kind consisted of two feathering wheels placed on opposite sides of the stern-post and made to revolve in opposite directions when the ship is turning. All such devices are obviously more liable to derangement, damage, and fouling than screws, nor can they be so efficient as propellers. Yessels fitted with duplicate propellers, such as disconnecting paddle-wheels, water-jets, or twin-screws, can be manoeuvred more or less successfully by the propellers alone. By making one propeller deliver its thrust ahead and the other astern, a ship can be made to turn nearly on her centre without headway ; if only one propeller is used, she will describe a circle of more or less considerable diameter ; and if the rudder is used in association with either of these conditions it is possible to increase the speed of turning or lessen the space traversed. The principle is the same for all three propellers, but the distance between the lines of thrust of twin-screws is com- monly less than one-half the extreme breadth of a ship, whereas, with disconnecting paddles, the corresponding distance would commonly be four-thirds the extreme breadth ; and with water-jets the distance somewhat exceeds the breadth. Notwithstanding this advantage, twin- screws compared favourably with water-jets on the only occasion on which we know their turning powers to have been tried in competition. No similar competitive trials appear to have been made with twin- screws and disconnecting paddles ; but the restricted use of paddle- wheels makes it unnecessary to inquire into their relative merits. Nearly all twin-screw vessels are fitted with single rudders at the after end, as shown in Figs. 163-165, and such rudders, as already explained, are not so directly under the influence of the propeller- race as are the corresponding rudders in single-screw ships. Con- sequently, it is desirable to make the rudders of twin-screw ships of great breadth, in order that they may sweep out into the race chap, xviii.] THE STEERING OF SHIPS. 7°7 of one or other of the screws. On this account ordinary rudders have been very commonly adopted with twin-screws, and for a time there was a general disinclination to use balanced rudders in these vessels. Possibly this opinion was partly based upon the unsatis- factory manoeuvring of some twin-screw vessels, built primarily for coast defence, in which the under-water form was very full, and the want of control was due to that fact fully as much as to the balanced rudders. Even at that period there were facts pointing in the direction of the efficiency of balanced rudders in twin-screw ships of good form. The Iron Duke, for instance, with twin-screws and an ordinary rudder, occupied about 4 minutes 38 seconds in turning a circle 505 yards in diameter ; whereas sister ships fitted with balanced rudders occupied only 4£ minutes in turning circles of 325 to 400 yards diameter. It must be admitted that during the first movements of the propellers ahead or astern in a twin-screw ship, the rudder has not as great steerage power as in a single-screw ship. On the other (hand, in the twin-screw ship there is the enormous advantage that the screws can be worked in opposite directions and the ship turned on her centre. Extended experience has also placed it beyond question that under all the ordinary circumstances of navigation twin-screw ships fitted with either ordinary or balanced rudders can be made practically as handy and manageable as single- screw ships. Recent types of swift cruisers with fine under-water forms, twin-screws, and balanced rudders have been proved to possess manoeuvring powers of the most remarkable character. Where difficulties have occurred in the steerage of twin-screw ships, they have usually been traceable to singularities of form under water or at the stern, to ill-considered arrangements of rudders, or to improper relative positions of propellers and rudders. It will not be over- looked that, from the necessities of the case, twin-screws are commonly fitted in vessels of shallow draught and full form ; and there is a danger of attributing to twin-screws features of performance which would be the same if single screws had been fitted. The remarks made above as to the floating batteries built during the Crimean War bear this out. One remarkable case deserves brief notice. In the twin-screw armoured ships Ajax and Agamemnon,, of full form and shallow draught, considerable difficulties were experienced in steering. The movements of the vessels were erratic and uncertain under the action of the helms. It was recognized that their flat floors and blunt ends made them " unsteady " on a course. But this did not explain their behaviour entirely. Careful observations and experiments with models showed that the peculiar form of the stern in the neighbour- hood of the water-line was the chief cause of trouble. Behind this 7°8 XAVAL ARCHITECTURE. [chap. xvm. blunt termination a mass of dead-water accumulated and practically travelled for a time with the vessel. At intervals this mass of dead- water fell off the stern, sometimes on one side and sometimes on the opposite side, thus causing unbalanced reactions on one or other side at the stern, and making the vessel "yaw." By a simple alteration in the shape of the stern, which gave it a fine termination, the accumulation of dead-water was prevented, and the consequent disturbance avoided. Subsequent experience proved that the control of the ships had been very greatly improved, and their manoeuvring is now as good as can be obtained with vessels so full and fiat in form. Speaking broadly, extended experience with twin-screw vessels has established the following conclusions : — 1. That with both screws working ahead at all speeds used in practice, except dead-slow, twin-screw ships are as well under control with the helm as single-screw ships, turning as quickly and in as small space for the same dimensions and speeds. 2. That with helm amidships, one screw working ahead and the other astern at properly adjusted rates, such vessels can be turned nearly upon their own centres, but the time of turning is considerably greater than when both screws are working ahead and the rudder is used. It will be remarked that, when the screws are thus worked, that which is turning ahead delivers its race aft, and tends to diminish the pressure on that side of the deadwood to which it is adjacent : whereas that which is turning astern delivers its race forward and tends to increase the pressure on its side of the dead- wood. The head of the ship turns towards that side where the screw is working astern, and consequently the excess of pressure on the same side of the deadwood aft helps the thrusts of the propellers in turning the ship. This fact tells sensibly in favour of the manoeuvring power of twin-screws. Another circumstance worth noting is the difference which exists between the effective thrusts of the two screws; that which is working ahead has the greater thrust, and the excess in thrust constitutes a force tending to propel the vessel ahead, increasing the space she requires in turning. If the ship is of fine form and easily moved at moderate speeds, she may therefore traverse a considerable space in turning under the assumed conditions; if she is of large size and full form, the difference in the thrusts may only suffice to give her a small speed when she will occupy little space. To illustrate this statement we may take the cases of her Majesty's ships Iris and the ill-fated Captain, which have nearly equal lengths. With one screw ahead and one astern, the Iris traversed a circle of about 500 yards diameter, say 5 times her length ; whereas the Captain traversed a chap, xvni.] THE STEERING OF SHIPS. 7°9 circle of 150 yards mean diameter, or about \\ times her length. By suitably adjusting the revolutions of the engines, a twin-screw ship may, of course, be turned upon her centre. 3. That when the screws are working in opposite directions, as in the preceding case, if the helm is put over, the time of turning is usually greater than when both screws are working ahead and the rudder is used. For example, the Captain took 5 minutes 24 seconds to complete a circle of 750 yards diameter with both screws full speed ahead and helm hard over ; as against 6 minutes 52 seconds in the other condition, when she turned nearly on her centre. The explanation of the difference is to be found in the diminished efficiency of the rudder produced by the absence of headway, as well as by the action of the screw which is working full speed astern on the side towards which the rudder is put over. It is worthy of remark, however, that the rudder does some work under these circumstances ; for the time of turning has been found to be less than when the same vessel was turned by the action of the screws alone. In one instance the times for the two conditions were respectively 4 minutes 15 seconds and 6 minutes 55 seconds. A possible explanation of this circumstance may be found in the turning effect of the accumulated pressure that will act on the side of the deadwood before the rudder, and will assist the screws in turning the ship. 4. That when one screw is stopped and the other worked full speed ahead, with the rudder hard over, vessels can be turned some- what more slowly than when both screws are working ahead. As to the relative diameters of the circles described under these two con- ditions, there is less agreement. In one case a twin-screw ship completed the circle in 3 minutes 48 seconds with both screws working ahead ; and in 3 minutes 58 seconds with one screw stopped ; the diameter of the circle in the latter case being one-third less than in the former. In the Captain, the corresponding results were 5 minutes 24 seconds to complete a circle 750 yards in diameter, when both screws were worked ahead, and 7 minutes 50 seconds to complete a circle 874 yards in diameter, when one screw was stopped. In the Iris the corresponding results were 8 minutes 14 seconds to complete a circle of 767 yards diameter at a speed of 10 knots with both screws, and 10 minutes to complete a circle of 613 yards diameter with one screw stopped. 5. That with one screw only at work and the helm amidships, the ship can be turned completely round ; but the time of turning is considerable, and the diameter of the circle large as compared with the other modes of turning. In the Captain, about 9f minutes were occupied in turning a circle nearly 1100 yards in diameter. 7IO XAVAL ARCHITECTURE. [chap. xvm. Even this turning power might be of service, however, to a vessel of which the rudder and one screw had been damaged. 6. That with one screw at work ahead, the other being stopped, or allowed to revolve freely, the ship can be kept on a straight course by the use of the helm. The angle of helm required varies in different ships, and possibly at different speeds in a given ship. In the Iris at speeds of 7 to 8 knots, about S degrees to 10 degrees of helm sufficed. In the Nelson, at 10 knots. 16 degrees of helm were required. Other cases have come under notice where the helm hard over did not keep a ship straight ; but the fact simply proved that either the maximum helm-angle available was too small, or that a form and area of rudder had been adopted which were not suited to the ships. For effectiveness under these conditions the rudder should clearly be made broad, in order to sweep out into the race of the screw at work. It is usual in twin-screw ships to place the shafts parallel to one another and to the keel ; but more than once it has been suggested that advantage in steering might result from making shafts diverge from one another, in order to increase the leverage of the thrust of either propeller about the centre of gravity. This plan has been applied in the Faraday, a ship built for the special purpose of laying submarine telegraph cables, and therefore requiring great handiness under all conditions of wind and sea. It is said to have proved very successful ; and with the rudder locked amidships, some of the most delicate operations connected with laying and splicing cables were performed in a rough sea and strong wind, the ship being manoeuvred by the screws alone. The shafts in this vessel diverge from parallelism with the keel-line by being at a greater distance from it at their fore ends than at the after ends ; abreast of the centre of gravity the distance between the shaft lines is about 40 feet, near the propellers the distance is about half as great. Another interesting fact in the management of this exceptional vessel is that, in order to maintain her position with wind or sea on the beam, the two propellers were frequently worked at different speeds and sometimes in opposite directions. She furnished, in fact, one of the most remarkable illustrations of the manceuvring power obtainable by the use of twin-screws. Vessels propelled by three screws, one on each side and one at the middle line, will obviously possess the advantages in manoeuvring both of single and twin-screw ships. The middle-line screw will deliver its race upon the rudder, just as happens in a single-screw ship, and so give steerage with little or no headway or sternway. The side screws are capable of being manoeuvred like those of a twin-screw ship. It is probable that these considerations CHAP, xvm.] THE STEERING OF SHIPS. 7 l 1 have had some influence on the decision to construct triple-screw vessels; although the governing condition has been the desire to secure economical propulsion at low cruising speeds. Jet-propelled vessels, when moving ahead at full speed, derive their steering power from the reaction of the water in the wake upon the rudder ; and, as previously explained, this is likely to be less than that on a rudder placed in the race of a screw. In the trials made with the twin-screw ship Viper and the jet-propelled Waterwiteh, there was practical identity of length and draught, as well as approximate equality of displacement and speed; but the Viper was constructed with two deadwoods, and had a rudder on each, while the Waterwiteh had only one rudder at work, the rudder at the fore end being locked. Hence any exact comparison between the manoeuvring powers of the two systems of propulsion can scarcely be made from the trials of these ships ; but the following facts may be interesting. When steaming full speed ahead, the Viper turned a circle in 3 minutes 17 seconds, as compared with 4 minutes 10 seconds for the Waterwiteh ; a saving of time in the twin-screw ship of about 20 per cent. With one screw reversed, the other full speed ahead, and the rudders hard over, the Viper turned on her centre in rather less time than with both screws working full speed ahead (3 minutes 6^ seconds, mean of trials in opposite directions).* The Waterwiteh, under similar conditions, with one nozzle reversed, also turned on her centre, but occupied more than twice the time of the Viper (6 \ minutes), and half as long again as she took when steaming full speed ahead. Making allow- ance for the additional rudder of the Viper, and the additional resistance to turning which her peculiar form of stern involved, it appears that the twin-screws possess some advantages over the jets in manoeuvring ; but further trials would be required to settle this point conclusively. It is, however, certain that ample manoeuvring power can be secured with twin-screws in association with greater propelling efficiency than has yet been obtained, or is likely to be secured with water-jets. In conclusion, it may be remarked that, throughout the preceding discussion, it has been assumed that the manoeuvres of ships are performed in smooth water, in order that the principles of the action of the rudder, or of auxiliary appliances for steering, might be more * It will be observed that this is an always remained thoroughly efficient in exception to the deduction marked No. 3 assisting to turn the ship, although the on p. 709 ; but the explanation of the other rudder, placed behind the screw, difference is simple. As the Viper has which was driving the ship astern, was two rudders, that placed behind the less efficient, screw, which was driving the ship ahead, 7 12 NAVAL ARCHITECTURE. [chap. xvm. simply explained. When ships are manoeuvred in rivers, currents, or a seaway, or in stormy weather with high winds, their perform- ances necessarily differ from those in still water ; but all the varying conditions of practice can scarcely be brought within the scope of exact investigation ; and the foregoing statement of principles will probably enable the conditions of any selected case to be intelli- gently treated. INDEX. Admiralty :^ Coefficients for steamship performance, 623 Eegulations for preservation of iron and steel ships, 425 Agincourt, grounding of, 35 Air blast, 558 Air resistance to motion of ships, 485 Aluminium for bottoms, 433 American : — River steamers, special construction of, 332, 375 Wood-built ships, rapid decay of, 418 Angle of leeway, 504 Angular velocity of ships : — When rolling, 149, 172 When turning, 668 Arc of oscillation, 147 Ardency of sailing ships, 507 Armour : — Contribution of, to structural strength of ships, 360 Atwood's formula for statical stability, 127 Augment of resistance due to screw pro- peller, 544 Augmented surface, 450 Automatic instruments for measuring and recording rolling, 288, 290 Auxiliary appliances for steering, 697 Awning deck vessels, 15 Axis of rotation of a ship : — When rolling, 151 When turning, 673 Balanced rudders : their advantages and disadvantages, 666 Barques : — Plain sail of> 511 Barques {continued) : — Position of centre of effort of sail, 520 Stations of masts and base of sail, 521 Batten instruments for observing rolling and pitching, 285, 286 Beam of ships : — Effect upon metacentric stability, 88 „ range of stability, 129 „ the resistance and pro- pulsion, 462, 475 Ratio to length in sailing ships, 528 „ „ in unarmoured war- ships, 472 Ratio to length in ironclads, 473 Beams :— Approximate rules for strength, 404 Calculations of bending moments due to loads on, 299 Knees of, 389 Methods of scarphing wood, 406 Principles of strength, 349 Sectional forms in iron or steel, 403 To decks : as transverse strengtheners of ships, 322, 335, 387 Bearers, longitudinal, contribute to local and general strength of ships, 332 Behaviour of ships at sea. See Rolling and Pitching Bellerophon in collision, 35 Bending moments : — Longitudinal, for ships, 297, 314, 315, 381 Methods of estimating, for beams, 299 Resistance of beams and girders, 349 „ ships to longitudinal, 355 „ „ transverse, 383 Transverse for ships, 321, 324, 327 7H INDEX. Bilge-keels : — Means of increasing fluid resistance to rolling, 176, 179 Means of increasing steadiness in a seaway, 252 Boilers : — Forced draught, 558, 561 Induced draught, 558 Locomotive, 553, 500 Types of, 552 Water-tube, 554 Bottom (see also Double Bottom) : — Corrosion of iron and steel bottoms, 420 Of wood ships, strong against ground- ing, 334 Penetration of, 333 Bow rudders, 697 Bows of ships : — Construction of, for ramming, 337 Influence of form upon pitching, 269 Influence of form upon resistance, 461 Bowsprits, steeve of, 522 Bracket frame : system of construction for iron ships, 367, 370, 385 Brass skins, 433 Brigs: — Loss of older classes by swamping, 21 Plain sail, and position of centre of effort, 511, 520 Stations of masts and base of sail, 521 Buckling, special danger of, in iron or steel ships, 333, 345, 366, 400 Builders' old measurement tonnage : — Antiquity of rule, 47 Examples of calculation, 49 Objections to, and abolition of, 50 Rationale of rule, 49 Bulkheads, as watertight subdivisions : — Arrangement of transverse, 23, 32 „ „ longitudinal, 29, 32 Means of maintaining stability, 110, 115 Use of transverse, 332, 383 „ partial, 384 „ longitudinal, 354 Bulkheads committee, 41 Buoyanoy : — Centre of, 80, 126 Definition of, 2 Loss of, causes ships to founder, 21 Buoyancy {continued) : — Beserve of, in different classes of ships, 9, 15 Strains due to unequal distribution of weight, 7, 297, 302 Butt-joints : — In wood ships, 347, 407 In iron ships, 408 C^XPAyiA, dimensions of, 417 Captain, her Majesty's ship (late) : — Curve of stability and principal dimensions, 132, 133 Safety under sail in still water, 186 Upsetting angle, amongst waves, 259 Cargoes : — Dangers of shifting, 110 Stowage of, checked by rolling ex- periments, 170 Causes of pressure on rudders, 653 „ foundering, 21 Cellular construction for iron ships, 32, 43, 367, 370, 385 Cellulose packing, 38 Central-citadel ironclads : — Forms and proportions of, 473 Ram bows of, 337 Centre boards of sailing vessels, 505 Centre of buoyancy : — Approximate rules for position of, 87 Defined, SO Motion of, as ship heels, 126 Centre of effort of sails : — Longitudinal position of, 520 Method of estimating position, 519 Vertical position of, 524, 526 Centre of flotation, 152 Centre of gravity : — Effect of vertical position of, upon range of stability, 133, 144 Effect of position of, relatively to centre of effort of sails, 523 Height of metacentre above, in various classes of ships, 90, 97, 100, 104 Inclining experiments to determine vertical position of, 103 Motion of, when weights are shifted, 103, 106 Weight may be supposed concen- trated at, in ships at rest, 80 INDEX. 715 Centre of lateral resistance, 518 „ pressure on rudder, 662 Centrifugal pumps as a means of clearing water out of ships, 592 Change of trim due to bilging, 27 Estimates for, 119 Cigar ships : — Conditions of stability for, 94 Curve of stability, 127 Still- water oscillations of, 153 Circular ironclads, Russian : — Behaviour at sea, 246 Rudder arrangements and steerage, 672 Steaming capabilities of, 642 Weights of hull for, 412, 643 Clipper ships, proportions and perform- ances, 528 Coal consumption, rates of, for various types of engines, 562 Rates of, for merchant ships, 564 Coefficients of: — Augmentation (Rankine's), 450 Fineness, for displacement, 3 Friction (skin), 441 Moment of inertia of plane of flotation, 87,88 Steamship performance, 540, 623 Collision : — Construction of ram-bows to withstand, 337 Examples of accidental, 35, 37 Local strains produced by, 337 Committee on bulkheads, 41 „ „ load line, 13 Comparative weights of wood, iron, and steel ships, 409 Comparative durability of wood, iron, and steel ships, 417 Compartments, watertight : — Methods of forming, 23, 29 Of war-ships, 31, 33 Composite ships : — Arrangements of decks, 363 „ ,, framing, 365 „ „ skins, 373 „ „ beam end connec- tions, 338 Freedom from fouling of the bottom, 430 Compound engines : — Economy of fuel with, 562 Weights of, 562 Compressive strengths of wood and iron, 397, 398 Conditions of equilibrium, 1, 80 Copper sheathing : — Anti-fouling properties of, 426 For iron ships, 430, 431 Insulation of, in Inconstant class, 430 Protected by zinc bands, 427 Corinthian Yacht Club, rule for tonnage, 76 Cork packing, 38 Corrosion of iron ships : — Causes of, 420 Experiments on rate of, 422 Means of preventing, 425 Cross curves of stability, 143 . Curves of : — Displacement, 5 Extinction, for colling in still water, 167, 184 Flotation, 152 Loads and bending moment, 302, 306, 309 Metacentres and centres of buoyancy, 89,93 Progressive speed trials, 613, 629, 644 Resistance for models and full-sized ships, 479 Rolling motion of a ship under sail, 249, 262 Stability, tl29, 132, 135, 138, 142, 145 Tons per inch of immersion, 6 Turning for steamers, 677 Wind pressure at oblique angles, 496 Cutters : — Plain sail for, 511 Position of centre of effort, 520 Station of mast and base of sail, 521 Danube rule for tonnage, 63 Dead weight tonnage for merchant ships, 68, 70 Deck erections, 17, 57 Deck beams, planking, plating, and pillars, 387 Decks : — Contributories to longitudinal strength, 352, 362 716 INDEX. Decks {continued) : — Local strains on, 335 Resistance of, to rolling and pitching with low freeboard, 184, 269 Utilized as watertight partitions, 23, 27, 29, 32 Deductions from turning trials of ships, 678, 685 Delight gunboat : — steering trials of, 690 Design, general condition of, 640 Detachable ballast, 39 Determination of rudder areas, 691 Devastation : — Compared with circular ironclads, 643 Inclination under wind pressure, 188 Mr. Froude's rolling experiments with model, 177, 253 Performances at sea, 237, 240, 255, 266 Developments in dimensions and speeds, 416 Diagonal riders : — For composite ships, 373 For ordinary wood ships, 372 Framing for iron ships, 375 Not necessary for iron ships, 374 Planking for wood and composite ships, 374 Dimensions for screw-propellers, deter- mination of, 609 Dipping oscillations of ships, 162 Disc area of screw-propellers, 597-615 Dismasting of merchant sailing ships, 341 Displacement : — Approximate rules for, 3 Compared with B.O.M. tonnage, 49 „ „ gross register tonnage. 70 Curves of, 5 Definition of, 1 Most suitable tonnage for war-ships, 73 Tonnage, 73 „ for yachts, 77 Double bottoms : — Cellular construction of, 367, 370, 385 Effect upon stability of water ballast in, 111, 117 Facilitate preservation of skins, 425 Uses of, in iron ships, 31 Draught of water : — Changes in, by altered density of water, 7 Changes in, by addition or removal of weight, 7 Displacement for any, 5 Effect upon, of entry of water into hold, 23, 30 With changes of trim, 122 Ductility, 398 Durability of wood and iron ships com- pared, 417 Dynamical ^stability (see also Stability), 158 Economical propulsion of steamships, 455, 462, 469, 646 Cannot be exclusively considered, 635 Favoured by increase in size, 635 „ certain types of machi- nery, 543, 578 Favoured by suitable propellers, 612 Narrowness not a necessity for, 646 Not of paramount importance in all cases, 472, 475, 640 Eddy-making resistance of ships, 451 Effective horse-power, 535 Efficiency of marine engines, 541 „ propellers, 582, 587, 599 „ steamships, 635 Elastic limit, 396 Worn, experiments in, 155, 177 Engine design, influence of, upon ship design, 567 Engines, marine : — Measures of power, 535 / Of swift steam-launches and torpedo- boats, 562, 647 Types in common use, 550 Weights per indicated ^horse-power and rate of coal consumption, 562 Entrance of ships, connection between speed and length of, 457 Equilibrium of ships : — Instantaneous position of, among waves, 227, 231 Stable, unstable, and indifferent, 82 When floating in still water, 1, 80, 82 Equivalent girders for ships, 346, 353 Experiments : — On air resistance, 485, 491, 496 INDEX. 717 Experiments (continued) : — On deck resistance to rolling, 183 On rate of corrosion of iron, 420, 422 On resistance of ships, 451, 453, 464, 473, 477 On resistance of wood and iron to penetration, 334 On screw propulsion, 573, 578, 613 On screws and paddle-wheels, [594, 601 On screws and water-jets, 588 On steerage of single-screw ships, 657 On steerage of twin-screw ships, 659 On steerage of jet-propelled ships, 655 On still-water rolling, 155, 167 On strengths of iron and steel, 398, 399 On strengths of timber, 397 On the effect of bilge-keels, 176, 253 On waste of metals in sea-water, 422 To determine vertical position of centre of gravity of ships, 102 To determine "quiescent point" or point tranquille of ships, 155, 168 With model screws, 614 Factors of safety for wood and iron, 401, 404 Fan-draught : open stoke-holds, 561 Fastenings in ships : — Importance of proper, 344 Metal bolts in wood ships, 407 Fillings between frames of wood ships very useful, 363 Flanged forms of beams and girders very advantageous, 352, 403 Flush-deck vessels, 15 Forced draught, 557 Forces required on tillers, 661 Formula? : — Admiralty, for steamship performance, 623 Atwood's, for statical stability, 127 Centre of pressure on rudder, 662 Expressing relative economy of steam power in large and small steamers, 636 For augmented surface of a ship, 450 For observing waves, 206 Heeling force when steering, 683 Formulae {continued) : — Maximum angle of heel in unresisted rolling among waves, 236 Moseley's, for dynamical stability, 160 Normal pressure on a plane advancing obliquely in water, 438, 439 Period of unresisted rolling in still water, 150 Sail-carrying power, 526 Trochoidal waves, 202 Fouling of bottom : — Effect on resistance of ships, 426 Especial disadvantages of iron ships, 428 Proposals for preventing, 429 Foundering of ships, causes of, 21 Framing of ships : — Diagonal, for iron ships, 375 Longitudinal for iron ships, 366, 370 Subordinate to skins, 368 Transverse, in ironand composite ships, 362, 365 Transverse, in wood ships, 361, 384 Freeboard : — Effect of, upon the stability, 129 Various rules for, 10, 12 Free water in a ship, effect on stability, 112 Freight tonnage, 72 French : — Experiments on still-water oscillations, 155, 177 Observations of deep-sea waves, 213, 219, 222 Rule for nominal horse-power, 539 Fresh water, weight of, 7 Frictional and eddy-making resistance of ships, 448 Frictional resistance : — Constant, of engines, 542 Generally, 440 To motion of ships, 449, 464 To rolling of ships, 175, 248 Froude, the late Mr. W., F.R.S. :— Disadvantages of large screws, 606 Investigations on resistance to oscilla- tion of ships, 166,225,231 Modern theory for rolling among waves, 225,231 Report on behaviour of Devastation, 240 7i8 INDEX. Froude, the late Mr. W., F.B.S. («m- Experiments : — On usefulness of bilge-keels, 177, 253 On resistance of ships and models, 477, 481 On relative efficiencies of upper and lower parts of rudders, 695 On frictional resistance, 441 On wave-making resistance, 454, 460 On air resistance, 491 On ratio of effective to indicated horse-power, 541 On screw-propulsion, 597, 613 On circular ships, 643 On planes and rudders, 662 Galvanic action : — Accelerates corrosion of iron skins, 421 Assists in preventing fouling of zinc sheathing, 433 Means of preventing, 423 Special danger in iron ships copper- sheathed, 431 Girders : — Equivalent for longitudinal strength of ships, 346, 355 Comparison of ribs and adjacent parts of skin to, 384 Lattice, used as strengtheners to shallow ships, 377 Principles of strength, 349 Graphic integration, 249 Great Britain dimensions, 417 Great Eastern dimensions, 416 „ „ ashore, 34 „ „ framing of, 332 Great Western dimensions, 417 Greyhound, H.M.S. :— Model experiments on resistance, 473 478 Boiling experiments in still water, 175 Boiling experiments in a seaway, 253 Used as basis for calculations of performance under steam of large ships, 633 Grounding, local strains produced by, 333 Grosser Kurfurst, loss of, 37 Gunboats, unarmoured : — Engine-power and speeds, 647 Head resistance to motion of bodies through water, 436 Headway, advantage of, to ships in turn- ing, 654 Heaving oscillations, 201, 258, 271 Heeling produced by : — Action of wind on sails, 82, 185, 327, 496, 502, 525 Entry of water into hold, 29 Shifting weights athwartships, 103 Heeling of ships in turning, 682 Hercules in collision, 35 Helm :— Angle of greatest efficiency, 690 Importance of quick motion, 688 Power to put it over, 661 Starboard and port, weather and lee, 653 Hog frame in shallow-draught vessels, 307, 375, 377 Hogging :— Causes of, in still water, 298 „ on wave crest, 311 Conditions of strain incidental to, 315, 381 Holyhead packets, steaming capabilities of, 572 Horse-power of marine engines : — Effective, 535 Indicated, 535 Lloyd's rule, 539 Measures of, 534 Nominal, 537 Normal, 539 Hulls of ships : — Advantages of iron as compared with wood, 409, 417 Becent use of steel, 413 Should combine lightness with strength, 3 Hydromotor propeller, experiments with, 590 Inclining experiment, 103 Indicated horse-power, 535 INDEX. 719 Iron as a material for shipbuilding : — Compared with wood, 393, 397, 401 Modulus of elasticity, 398 Resistance to bending strain, 404 „ „ perforation, 334 Simple combinations possible with, 408 Tensile and compressive strength of (see also Corrosion, Fouling, and Wood), 398 Ironclads : — Behaviour at sea, 243, 255 Expenditure of engine-power, 639, 640 Local requirements in structures, 380 Long and short types compared, 641 Longitudinal strains of, 315, 381 Rapid decay of wood-built, 418 Rudder areas of, 694 Sailing capabilities of, 516 Speeds under steam, 639 Structural arrangements of, 367 Watertight subdivision of, 32 Weights of hull for, 415 Iron Duke ramming Vanguard, 36 Iron ships : — Beam end connections, 367, 388 Causes of corrosion, 420 Compared with steel ships, 413 Construction of decks, 387 „ ,, ram-bows, 337 Copper and zinc sheathing for, 430 Features of superiority to wood ships, 32, 321, 324, 337, 347, 374, 408 Fouling of bottoms, 426 Great durability of, 419 Methods of framing, ordinary and special, 362, 367, 370 Penetrability of bottom, 334 Progress in construction and sizes, 416 Skins of, 359 Strains of, compared with those on a bridge, 387 International tonnage, 65 Isochronism of oscillations of ships in still water, 166 Jet-pbopelled vessels : — Steaming capabilities of, 588 Steerage of, 655 Joessel rudders, 663 Jury rudders, 703 Keels : — Bilge (see Bilge-keels) Methods of scarphing in wood ships, 406 Sliding, to diminish leeway, 505 Keelsons : — Longitudinal strengthened, 331, 364 Knees to beams, methods of fitting, 367, 388 Lap-joints for iron plates and bars, 408 Lateral resistance. See Resistance Launches : — Of Royal Navy, diagonal planking, 374 Swift steam, engines and speeds of, 552, 561, 647 Launching, curves of stability for, 142 „ severe strains due to accidents in, 321 Leaks, rate of inflow of water through, 24 Leaks, usefulness of stoppers, 24 Lee-boards, use of, in shallow-draught vessels, 505 Lee-helm, 508 Leeway : — Angle of, 504 Causes of, in ships sailing on a wind, 506 Liquid fuel, 566, 568 Livadia, behaviour at sea, 246 „ propulsion of, 643 Lloyd's register, investigations on mast- ing, 341 Lloyd's rule for freeboard, 10 Load-line legislation for merchant ships, 12 Local strains, 330 Longitudinal : — Bending moments (also see Bending), 315 Bending moments among waves, 310 „ „ as affected by wave structure, 317 Bending moments in ships ashore, 320 „ „ in still water, 297 Bulkheads (also see Bulkheads), 32 Framing adapted for iron ships, 331 Oscillations (also see Pitching), 263 Strength. See Strength 720 INDEX. Lucania, dimensions of, 417 Lurching, strains consequent upon, 324 Marine boilers, types of, 552 „ engineering, progress in, 546 Mast and guy system, 332 Masts : — Height of, 526 Number of, 522 Proportion of sail carried by each of the, 523 Bake of, 522 Stations of, in sailing vessels, 521 Supported by tripods in turret ships, 342 Materials for shipbuilding. See Wood, Iron, and Steel Megcera, H.M.S., rate of corrosion of skin and loss of, 423 Merchant ships : — Cellular construction of, 370 Check upon stowage of cargoes, 170 Dead-weight tonnage for, 68, 70 Longitudinal bending moments ex- perienced by, 315 Longitudinal strains on, 381 Nominal horse-power for engines of, 537 Parallelopipedon tonnage for, 71 Eatios of length to breadth, 417, 460, 475 Register tonnage for British, 59 Reserve of buoyancy, 9 Rules for freeboard, 10, 12 Rudder areas for, 694 Sailing capabilities of, 529 Stability under different conditions, 92, 110, 112 Steaming capabilities of, 569 Suez Canal tonnage for, 59, 65 Water-logged vessels, 22 Metacentre for transverse inclinations: Approximate rules for estimating position of, 87, 88 Change of position due to entry of water into the interior, 112 Definition of, 83 Effect of metacentric height upon period of still -water oscillations, 154 Metacentric for Transverse inclinations (continued) :-— Height above centre of buoyancy, 86 » ,. » gravity, 97, 100, 104 In a submerged vessel, 95 Metacentre for longitudinal inclina- tions : — Height above centre of gravity in various classes, 119, 120 Use in estimating change of trim, 122 Metacentric diagrams, 89, 93 „ stability, practical applica- tions of, 102 Metals, rates of waste in sea- water, 421 „ galvanic action on iron, 422 Miantonomoh, behaviour in Atlantic, 246 Minotaur in collision, 35 Model experiments : — On efficiency of bilge keels, 177, 253 On resistances of ships, 479 On resistance, 477 On screw-propellers, 614 Modern sailing ships, dimensions and proportions of, 528 Moduli of elasticity : — Method for estimating, 396 Values for iron and timbers, 397, 398, Moment : — Longitudinal bending, 298, 302, 315 Of inertia : explanation of term, 86, 150 Of inertia, its effect on rolling, 154, 246 Of inertia, its effect on turning , 670 Of resistance of girders and' ships to bending, 349, 355 Righting, for transverse inclinations, 81, 228 To change trim, 122 Transverse bending, 323, 324, 327 Muntz metal for sheathing ships, 430 Naval brass, 427, 431 Neutral axis and neutral surface of beams, 349 Nickel steel for bottoms, 433 Nominal horse-power, 537 Normal horse-power, 539 Northumberland in collision, 35 INDEX. 721 Observations : — Of dimensions and periods of waves, 208, 211 Of rolling and pitching by : — Automatic instruments, 283, 290 Batten instruments, 285 Gyroscopic instruments, 281, 283 Pendulums, 275 Photography, 288 Spirit-levels, 279 Tower's steady platform, 292 Wheel-pendulums, 292 Oscillations of ships. See also Rolling, Pitching, and Dipping Paddle-wheels : — Disadvantages of, in seagoing steamers, 571 For manoeuvring, 654, 706 High speed obtained in ships driven by, 572 Practical rules for, 596 Principles of propulsion by, 592 Panting produced by ^ transverse com- pression on ends of ships, 324 Pendulums : — Comparison of oscillations with those of ships, 147 Departure from isochronism with large angles of swing, 235 Discussion of motion of simple and bar, 149 Errors of, when used to measure rolling motion of ships, 277 Use of, for measuring rolling and pitching, 275, 279, 290 Use of, to illustrate behaviour of ships at sea, 238 Wheel, 290, 292 Periods of ocean waves :— Facts respecting, 209, 211, 221 Formulae for, 202 Methods of observing, 205, 208 Periods of oscillation, definition of, 147 Periods of pitching for ships, 263 „ „ rolling for ships in still water, 154, 165 Pillars, contribution of, to structural, strength, 387 Pitch of screw-propellers, 597 Pitching and 'scending : — Bertin's automatic records, 267 Causes of, 263 Governing conditions, 265 Influence of form of bow and stern, and longitudinal distribution of weights, 268, 269 Of low-ended ships, 269 Periods for, 263 Pitting of iron and steel skins, 424 Planking of wood ships. See Skins Platforms : — As watertight partitions, 23, 30 Effect on maintenance of stability, 116 Plating of iron ships. See Skins Portage of ships. See Tonnage Progressive trials, 611, 619 Propellers : — Fundamental principles of, 580 Guide-blades, 580 Mallory, 705 Paddle-wheels, 592 Screw, 597 Under steam and sail, 530 Use of, for manoeuvring, 655, 706 Water-jet, 585 Propulsion : — By sails, 489 By steam power, 532 Strains incidental to, 327, 339 Proportions of yachts, 531 Propulsive coefficients, 540 Pumps cannot cope with a large leak/ 24, 592 Racking strains on ships , Incidental to propulsion, 327, 339 Mode of resisting, 372 Produced by rolling, 324 Radius of gyration : — Defined, 150 Effect upon period of pitching, 263 „ „ rolling, 155 „ turning, 670 Rake of masts, 522 „ sternposts in yachts and ships, 48 Rate of inflow through hole in bottom, 24 Ram attacks : — Best met by watertight subdivision, 33,37 3A 722 INDEX. Ram attacks (continued) : — Construction of bows to meet strains of, 337 Register tonnage : — Allowances to steamships, 60 Compared with displacement (also see Tonnage), 70 Law of 1854 and approximate rules, 56,59 Relative strengths and weights of single pieces of wood, iron, and steel, 395 Reserve of buoyancy for various types of ships, 9 Reserve of dynamical stability, 186 Resistance of water (to advance of ships ) : — Augment of resistance due to screw propeller, 544 Early theories of, 434, 442 Frictional, direct and eddy-making, 436, 438, 441, 449, 451 Largely independent of area of mid- ship section, 463, 476 Stream-line theory of, 443 Summary of results, 464 Values of, for certain ships, 469 Resistance, wave-making, 454 In a seaway, 488 To pitching and Vending, 268 To planes moving obliquely, 438 To rolling of ships, 172, 175, 247 When motion is not uniform, 487 Resistance, lateral : — To ships sailing on a wind, 503 To turning of ships, 669 Resistance of air to motion of ships, 485 Resisted rolling among waves, 247 „ „ in still water, 163 Results of calculation of longitudinal strength, 378 Revolutions and piston speed, increase m, 550 Ribs. See Framing, Transverse, Riders, diagonal, for wood aud composite ships, 372, 373 Rigging:— Air resistance to, 485 Spread of, 327 River steamers, shallow-draught, special features of, 332, 377 Rolling of ships in still water : — Coefficients of extinction, 172 Rolling ot ships in still water (con- tinued) : — Dipping oscillations which accompany, 162 Effect of changes in stiffness and dis- tribution of weights, 154 Effect of moment of inertia upon, 155 „ resistance upon, 157 Extinction of rolling, 167 Hypothetical case of unresisted rolling, 148 Instantaneous axis of rotation, 152, 168 Isochronous rolling, 157 Oscillations resemble those of pendu- lums, 147 Periods of, 154, 169 Resistance due to keels and bilge keels, surface friction, and surface disturbance, 175, 177 Resistance due to internal free water, 180, 184 Resistance in a seaway compared with resistance in still water, 174 Under action of suddenly applied forces, 184 Rolling of sailing ships, 266 Rolling of ships among waves : — As influenced by size, 227 Behaviour of quick-moving ships, 226, 237 Behaviour of slow-moving ships, 237, 239 Bertin's formulse, 251 Circular ironclads, Russian, 246 Causes of, 224, 225 Dangers of synchronism of periods of ships and waves, 233, 240, 252 Devastation, trials of, 229, 241 Early theories of, 224 Effect of bilge keels, 252 Effects of changes in speed and course of ships, 240, 245 Endymion, as obtained by graphic integration, 249, 262 Governing conditions of, 225 Importance of ratio of wave period to period of ships, 226, 233, 236 In a seaway with sails set, 249, 258 262 Limul in, case of, 246 Miantonomoh, case of, 246 INDEX. 7*3 Rolling of 'ships among waves (con- tinued) : — Mathematical assumption, 231 Methods of measuring angles of. See Observations of Rolling Motion of a small raft, 226 Pendulum illustrations of, 238 Permanent rolling, 236 Phases of oscillation, 238 Records of, 239, 243 Safety due to increased period as angle of swing increases, 235 Sailing ships, 256 Sketch of modern theory, 225 Small rolling of vessels having very short periods, 226, 246 Steadiness secured by bilge keels, 253 Steadying effect of sails, 262 „ ,, a confused sea, 232 Strains on structure due to, 324 Thornycroft apparatus for steadying ships at sea, 182, 256 Rudders : — Auxiliary, 701 Balanced, 663 Bow, 697 Centre of pressure of, 662 Considerations respecting areas of, "693 Effective pressures on, 653, 682 Force required on tiller-end, 661 Joessel's, 663 Lumley's, 697 Mallory,705 Mechanical work done in putting over, 665 Ordinary and balanced, 650 Rankine's and Schlick's, 696 Ruthven's counterbalancing weight applied to, 667 Turning effect of, 668 Rules for freeboard, 10 Run of ships : — Connection between speed of ships and length of, 457 Sagging : — Astride wave hollows, 311 Causes of, in still water, 298 Conditions of strain incidental to, 315, 355 Sail plans for ships, 327, 502, 525 Preparation of, 510 Sailing vessels :— Arrangement of sail, 489, 519 Areas and forms of rudders, 693, 695 Area of sail in terms of wetted sur- face and displacement, 513 Area of sail in terms of under-deck tonnage, 515 . Balance of sail, 518 Base of sail, 521 Centre of effort, position of, in, 519, 524, 526 Determination of aggregate sail area , 514,515 Forms and proportions of, -529, 530 Heel of, under canvas, 81, 185, 258, 327, 502, 525 High speeds of modern, 529 Longitudinal distribution of sail, 518 Plain sail for various styles of rig, 511, 515- Propelling effect of wind on sails, 502 Range of stability necessary for safety, 261 Register tonnage of, 57, 60 Steadying action of sails, 262 Stiffness, or sail-carrying power, 526 Strains due to propulsion, 327 Under action of squalls of wind, 186, 262 Vertical distribution of sail, 524 With more than three masts, 522 Scarphs of various pieces in wood ships, 406 'Scending. See Pitching Schlick's, Herr, experiments on divided rudders, 655 Sea trials of speed, 610 Shoal water, effect of, on resistance, 464,467 • Schooners : — Centre of effort of, 520 Plain sail of, 511, 515 Stations of masts and base of sail, 521 Screw-propellers : — Augment of resistance due to, 544 Conditions for maximum efficiency, 599, 606 Diameter, pitch, disc-area, and slip, 597 Experiments to determine best propel- lers for Iris, 613 . Ditto for torpedo-boats, 611 724 INDEX. Screw-propellers (continued) : — Effect of propeller race upon steerage, 656 Large diameters not always advan- tageous, 606 Mallory, 705 Manoeuvring powers of single and twin, 655, 656 Motion of particles in race, 604 Necessity for free flow of water to, 603 Principles of action, 598 Use of twin and multiple, 577 Virtual increase of resistance produced by, 544 Screws, steering, mode of fitting, 651 Screw turbine propeller, 579 Sea water, weight of, 7 Shallow- draught vessels : — Difficulty of steering, 672 Special structural arrangements, 332, 377 Shearing strains on ships unimportant, 297 Sheer strakes, useful as longitudinal strengtheners, 363 Shift of butts for planting and ribs of wood ships, 347, 361 Shifting cargoes, effect on stability, 110, Ship design as regards forms and resist- ances, 472 Ship rig : — Base of sail, 521 Plain sail of, 511 Position of centre of effort, 520 Stations of masts, 521 Shoal water : — Effect on speed, 464, 467 „ resistance, 464, 467 „ steering, 672 Sinkage due to bilging, 26 Skins of ships : — Arrangements in composite ships, 373 : „ „ iron ships, 374 „ „ wood ships, 347, 361 ' Essential features of all classes, 344 Resistance to penetration of wood and ] iron, 344 j Strains due to water pressure between frames, 333 '• Slackness " of sailing ships, 508 , Slip of paddle-wheels, 593 Slip of screw propellers, 598 Spar-deck vessels, 15 Speeds : — Lengths of entrance and run appro- priate to, 457 Limited by commercial considerations, ■172 Of merchant steamers, 641, 647 Of sailing ships, 529 Of ships, recent advances in, 468 Of unarmoured warships and ironclads, 639, 647 Spirit-levels not trustworthy instruments for measuring rolling, 279 Stability, statical : — Affected by shiftihg cargoes and free water in hold, 110, 112 Amongst waves reckoned from normal to effective slope, 231 Atwood's formula for, 127 Construction and use of curves of, 127 Definition of, 82 Effect of adding or removing weights, 117 Effect of heaving motion on, 201, 258 Less for mastless ships than for rigged ships, 186 Longitudinal, 121 Metacentric method of estimating, 84, 102 Of cigar and cylindrical forms, 94 Of ships partially water-borne, 124 Of ships when launched, 141 Of submarine vessels, 95 Range of, required for safety, 261 Transverse, 83 With liquid cargoes, 111 „ ship bilged, 115 Stability, dynamical :— Definition of, 158 Effect of suddenly applied forces with reference to, 184 Mode of estimating, 161 Moseley's formula for, 160 Reserve of, 186 Steadiness : — Assisted by deep-bilgo-keols, 252 „ sails, 262 Definition of, 84 Increased by lengthening still-water period of ships, 155, 211 Lessons transverso straining, 321 INDEX. 725 Steam blast. 557 Steamships : — Economical propulsion of, 476, 635, 639 Engine power and speeds of various classes, 640, 647 Estimates of speed and engine-power, 623, 633 Measures of engine-power, 534, 539 Ordinary conditions of design, 472, 533 Progress in construction of, 416, 646 Eegister tonnage of, 59 Steerage of, 650 Steam pressure increase in, 546 „ propulsion, 532 Steam-steering gear, advantage of, 667 Steel as a material for ship-building : — Features in which it is superior to iron, 413 Mild steel used in the Eoyal Navy, 415 Precautions against buckling and cor- rosion, 400 Savings, due to use of, 413 Steerage of sailing and steam ships, 649 Steering blades, use of, 703 „ by propellers, 656 Steering gear : — Manual, 666 Steam and hydraulic, 667 Steering screws, proposed use of, 700 Steering trials : — Axis of rotation, 673 Deductions from trial of steamers, 685 Drift angle, 679 Initial motions of ships, 673 Path described by the ship, 677 " Pivoting point," 679 Preliminary or constructor's trials, 687 Slewing when not under way, 656 " Tactical diameter " and " advance " of ship, 686 Steeve of bowsprits, 522 Stern : — Effect of length and form upon resist- ance, 443, 451, 457 Strengthenings of, in wood screw steamers, 340 Sternway, steerage of ships having, 657 Stiffness : — Definition of, 84 Effect of form and stowage of ships upon, 87, 92 Stiffness {continued) : — Effect of variations in, upon periods, of oscillation, 154 Measured by metacentric height, 83 Measure of power to carry sail, 526 Stowage of weights or cargo : — Effect upon stability, 92 „ longitudinal bending mo- ments, 298, 301 Proposal to check by rolling experi- ments, 170 Strains experienced by ships :— Among waves, 311 Classification of principal, 297 Due to collision, 335 „ grounding, 333 „ propulsion, 326, 339 Local, 297 Longitudinal bending: — Among waves, 311 In still water, 297, 315 „ „ when light, 308 Measures of, in mercantile and ironclad ships, 315, 381 When vessel is heeled over, 319 Racking or shearing, 325 Transverse : — Ship aground, 322 „ afloat, 323 „ rolling in a seaway, 324 Values (numerical) of bending, 315 Stream-line theory of resistance, 443 Strength of shipbuilding materials. See Wood, Iron, and Steel Strength of ships : — As influenced by proportions of length, breadth, and depth, 354 Against local strains, 326, 330 „ longitudinal bending, 315 „ transverse strains, 383 Compared with that of a bridge, 382 Considerations governing vertical and longitudinal distribution of the material, 358 General remarks on, 343 Sometimes reduced by increasing the depth, 356 Stringers :— In hold, uses of, 362 On decks, valuable strengthenings, 354, 362 726; INDEX. Subdivision, watertight. See Watertight Subdivision Submarine vessels, 19 Principles of construction, 19 Resistance of, 436, 445 Stability of, 95 Suez Canal, tonnage for dues, 59, 65 Surface vessels, 19 Systems of watertight subdivision, 25 Tables : — Angles of heel as measured correctly, and as given by pendulum clino- meters, 279, 280 Behaviour of ships at sea, observa- tions of, 239, 242, 244 Beaufoy's experiments on oblique re- sistances, 438 Calculation for centre of effort of sail, 519 Calculation for change of trim, 124 Circular ship compared with Devasta- tion, 643 Coal consumption, weights, etc., of marine engines of different types, 562,565 Coefficient : — For tons per inch, 7 For moment of inertia of water- plane, 87, 119 For extinction, 173, 174 Of fineness, for displacement, 3 Comparative weight of iron and steel ships, 413 Corrosion and waste of metals in sea water, 422 Equivalent girder, calculation of, 353, 354 Experimental determination of pres- sure of wind, 491 Froude's experiments on surface fric- tion, 441 Galvanic action, 422 Greyhound,resistaiioea at given speeds, 474 Hercules compared with Greyhound, . '633 . I.H.P. in typical war-ships, 647 Illustrating economy of propulsion in large steamers, 647 Influence of bilge-keels, on range and period of rolling, 177, 253 Tables (continued) : — Influence of freeboard and beam on range of stability, 129 Influence of helm-angle in circle turning, 690 Lengths, speeds, periods, heights, etc., of ocean waves, 212, 214, 220, 222 Livadia compared with other ships, 644 Longitudinal bending moments, 315 Merkara compared with model B, 463 Merkara resistances at given speeds, 474 Metacentric heights of merchant steamships, 100 Metacentric heights of sailing ships, 105 Metacentric heights of war-ships, 97 Modulus of elasticity of iron and timber, 397 Particulars : — Of Hercules and long type of iron- clad, 641 Of indicated horse-power and speeds for various vessels, 647 Of stability for Captain and Mon- arch, 187 Pendulum errors in rolling, 279, 280 Period of rolling as affected by arc of rolling, 235 Period of waves, trochoidal, 203 Principal dimensions, etc. : — Of merchant steamers, and results of inclining experiments, 100 Of sailing vessels and yachts, 104 Of war-ships, 104, 418, 640, 647 Reduction of speed on circle, 669 Reserve of stability, Monarch and Captain, 187 Resistances : — Of Greyhound and Merkara, 474 Of keels, bilge keels, skin, and wave- making, 175, 454 Sail, plain, with various styles of rig, 511, 515 Stability of Inflexible, 134 „ „ ships at various angles (curves of stability), 133, 135, 138, 142 Stations of masts, base of sail, etc., 521 INDEX. 727 Tables (continued) : — Steadying action of water on armour deck of Inflexible, 184 Strengths and weights of iron and shipbuilding timbers, 397, 402 Tensile strains in merchant vessels, 381 Tensile strengths of materials, 397, 402 Thermopylae compared with Pique, 529 Tonnage register of merchant steamers, 57 Turning trials of Thunderer, 677 „ ' „ Warrior and Her- cules, 688 Watertight compartment of ironclads, 33 Weights of hull and carrying power, 415, 416 Tensile strengths of wood and iron, 397, 398 Thames rule for yacht tonnage, 75 Theories of the screw-propeller, 603 Thrust, indicated, 629 Thunderer, as refitted : — Voyage to Madeira and back, 568 Timbers, shipbuilding : — Compressive strengths, 397 Moduli of elasticity, 397 Tensile strengths and weights (see also Wood), 397 Tonnage deck, 54 „ of ships, 45 Act of 1889, 53, 55, 58, 60, 64 Admiralty commissions of, 1821, 1833, 50 Alternative systems of tonnage, 67 , Awning-decked ships, 55 Builders' old measurement, 47 Breadth for tonnage, 48 Cellular-bottomed ships, how measured, 55 Commission of 1849, 52 „ „ 1881, 53, 55 „ „ Danube, 63 „ International, at Con- stantinople, in 1873, 65 Countries using Moorsom system, 67 Danube rule, 63 Dead- weight tonnage, 68, 70 „ cargo a ship can carry, 69 ' > Tonnage of ships (continued) : — Deck-spaces, allowances for closed-in. 58 Deductions for measuring, 60 Displacement tonnage, 70, '73 Earliest English law relating to ' ' keels or coal barges, 47 Early laws, 47 Freight tonnage, 72 German rule, 63 International tonnage, 65 Legal tonnage of coal vessels, 46 Legislation during 1821, 50, 53 Length of keel for tonnage, 48 Merchant Shipping Act of 1854, 52 Moorsom system, 52 New measurement of 1836, 51 Origin of B.O.M. rule, 49 Parallelopipedon tonnage, 71 Parliamentary " tons weight of hull," 74 Register tonnage, 59 Approximate rules for, 56, 57 Gross, 59, 66 Nett, 59, 66 Of sailing ships, 60 Of tugs, 66 Suez Canal rules, 59, 65 War-ship tonnage, 73 Yacht tonnage, 75 Tons per inch immersion, 7 Torpedo attacks, watertight subdivison as a precaution against, 33 Torpedo-boats, 647 Transverse : — Bulkheads. See Bulkheads Oscillations. See Rolling Stability at large angles of inclination-, 125 Strains on ships afloat in still water, 323 „ „ aground, 322 „ „ in a seaway, 324 „ „ under sail, 327 Strength, 383 Trim of ships : — Affected by entry of water, into hold, 27 Change of, in ships under sail, 504 Definition of, 5 Estimates for changes of, 121, 124 How measured, 5 728 INDEX. Triple-expansive engines, 548 Advantages of, in cargo vessels, 569 „ „ in the older war- vessels, 567 Weight of, 562 Triple screws, 577 Tripod supports to masts, 342 Trochoidal theory for waves. See Waves Turbine propellers, 579 Twin screws : — First used in shallow-draught vessels. 573 Good performances of, in deep-draught ships, 574, 640 Steering power of, 708. See aho Pro- pellers and Screw Propellers Uxapmoured war-ships: — Sailing capabilities of, 528 Speeds and dimensions of, 647 Steaming capabilities of, 562, 647 Structural arrangements of, 337, 361, 367 Use of iron hulls for, 418 Weight of hulls for, 416 Useful displacement, 2, 476 „ work of marine engines, 535 Utilization of ocean-wave power, 223 Vanguard, loss of, 35 Vessel with bottom bilged, 23 Vibration of steamships, 328 Wake of ships, characteristics of the, 452 Wake percentage, 454 War-ships (see Ironclads and Unarmoured Ships) tonnage, 72 Waste work and augmentation of resist- ance due to action of propellers, 544 Water :— Draught of. See Draught of Water Not a perfect fluid, 435 Velocity of inflow into damaged ship, 24 Weights per cubic foot of sea and river, 7 Water ballast : — Effect upon stability, 117 Methods of carrying, 32, 111, 367, 370 Water chambers, 180, 255 Water-jet propellers, 585 Water-logged ships, 22 Watertight subdivision : — By decks and platforms, 30 By longitudinal bulkheads, 29 By transverse bulkheads, 26, 27 In merchant ships, 39 Maintenance of stability by, 111 More important than pumping power, 592 Of vessels on Admiralty list, 39 Of war-ships, 31,33, 367 Principles of, 25 Wave-line theory of resistance, 455 Wave-making resistance of water, 454 Defined, 454 Expenditure of force on, 464 Governing conditions of, 457, 460 Importance of, at certain speeds, 402, 479 To rolling of ships, 175 Waves, deep sea : — Advance of form and motion of par- ticles, 194 Construction of profiles, 192 Dimensions corresponding to given forces of wind, 220 Effective slope of, 227 Exaggeration of heights, 210 Fluid pressures in, 196 Heaving motion produced by, 201, 258 Influence of ratio of wave period tu still-water period of ship, 233 Internal structure, 196 Longitudinal strains of ships amongst, 311, 315 Maximum slopes, 201 Methods of observing dimensions, 205, 208 Oscillations of ships amongst. See Pitching and Rolling Ratios of heights to lengths, 212, 221 Speed of wave compared with speed of wind, 220 Summary of observed dimensions, 209 Superposition of series, 215 Theoretical formulte for, 202 Transverse strains of ships amongst, 383 Utilization of power, 223 Viscosity of, 203 INDEX. 729 Weights, per cubic foot :— Of iron, 398 Of principal shipbuilding timbers, 397 Of sea and river water, 7 Weights of hulls in various classes of ships, 413, 415, 416 Weights per indicated horse-power for various types of marine engines, 562 Wind on sails, propulsive effect of, 501 Wind pressure, laws of, 489 Wind pressures on oblique plates, 496 Winds : — Apparent direction of, 501 Condition of ships sailing on a, 503 Connection between force of wind and size of wave, 220 Classification of, 500 Distribution of pressure of, over area, 494 Normal pressure as affected by size, 493 Oblique action on sails, 496 Outstripped by ice yachts, 507 Wing passage bulkheads, 35 Wood as a material for shipbuilding : — Causes of decay in, 418 Compared with iron, 404 Moduli of elasticity, 397 Eesistance of combination to tensile and compressive strains, 407 Resistance to bending strains, 402 „ „ perforation, 334 Tensile and compressive strengths of, 397 Wood ships : — Average durability of, 417 Construction of ram bows, 336 Wood ships {continued) :— Features in which inferior to iron and steel, 418 Metal sheathing on bottoms, 426 Methods of framing, 361 Kapid decay of many, 418 Skin planking of, 347, 361 Stern strengthenings of screw steamers, 340 Strengths of bottoms, 334 Work, mechanical : — Definition of, 158 Done in inclining ships, 160 „ putting rudder over, 665 Useful, of marine engines, 535 Yachts :— Displacement tonnage, 77 Forms and proportions of racing, 531 Her Majesty's, special construction of, 374 Her Majesty's, speed of, 572, 644 Ice, speed of, 507 Power to carry sail, 527 Sail spread of, 517 Time allowance on racing by New York rule, 78 Tonnage measurement : — By Corinthian rule, 76 By sail-spread rule, 77 By Thames rule, 75 Yards, bracing of, when sailing on a wind, 508 Yawing, mode of measuring, 283 Yawls, plain sail of, 51 1 Zinc sheathing for bottoms of wood and iron ships, 428, 432 Zinc protectors to copper sheathing, 427 LONDON : PKIMtED BY WILLIAM CLOWES AND SONS, LIMITED, STAMroRD STREET AND CHARING CROSS.