Cornell University Library The original of tliis book is in tlie Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004663310 Cornell University Library TJ 475.B91 Engine tests and boiler efficiencies 3 1924 004 663 310 ENGINE TESTS AND BOILER EFFICIENCIES ENGINE TESTS AND BOILER EFFICIENCIES BY J. BUCHETTI Sometime Professor at the Central Technical School, Paris. TRANSLATED AND EDITED FROM THE THIRD EDITION BY ALEXANDER RUSSELL, M.I.E.E., Etc. NEW YORK NORMAN W. HENLEY & CO 132 NASSAU STREET 1903 AUTHOR'S PREFACE TO THE THIRD EDITION IN this edition I have made considerable alterations and additions in almost every chapter of the book, especially in those parts which are concerned with the theory of indicators, the analysis of the working of their various parts, the description of new apparatus, such as indicators, with exterior springs for use with high pressure engines or when the steam has been superheated, explosion recorders for gas, petrol or alcohol engines, apparatus for reducing the scale of the reciprocating motion and the methods of setting it up, apparatus for verifying the flexibility of the springs of the indicators, etc. I have also made some additions to the chapter on brakes. In the second edition I had added a chapter on transmission dynamo- meters for use in measuring the work transmitted from the prime mover to the machine which it drives. This chapter, however, grew so large, especially that part of it which dealt with the theory of the dynamo- brake, that it appeared better to make this the subject of a separate book. J. BrCHETTI. PUBLISHER'S NOTE IT has been thought that a translation of Mr. Buchetti's standard work "Guide pour I'essai des moteurs " should prove useful to English and American engineers, as it would enable them to compare the best continental practice with that in use in their own countries. With this end in view the measures and tables have in every instance been converted into English units. The formulae also have been adapted into English measure. It is unnecessary for us to speak of the great value and striking origin- ality of Mr. Buchetti's work. We are indebted to the Hon. C. A. Parsons, F.R.S., for a brief chapter on testing steam turbines, a subject which is not touched upon by the author. Vll TABLE OF CONTENTS PAQB Auttor's Preface to the Third Edition v Publisher's Note ........ vii CHAPTER I INDICATORS Watt, MacNaught, Hopkinson. Figs. 1-4 . . . .1 M. P. Gamier (annuls inertia effects). Figs. 5, G . . .4 Richards' Indicator, Elhott Brothers. Figs. 7, 8 . . .7 Darke's Indicator, for high pressures, Elliott Brothers. Fig. 9 8 Thompson's Indicator ...... 10 P. Garnier's Indicator for high pressures and speeds. Fig. 13 . 10 Martin-Garnier's Indicator (annuls jerking of the drum). Figs. 15-17 11 P. Garnier's Magazine drum (rigidly driven). Figs, 18-21 . 1-3 SchaefEer and Budemberg Indicator. Fig. 22 . . 15 Rosenkranz's Indicator ... . . 16 Dreyer-Rosenkranz and Droop. Fig. 23 . . 16 Crosby's Indicator (double spiral spring). Figs. 24-26 . 16 Indicator with external spring, Elliott Brothers. Figs. 27, 28 18 Rosenkranz's Indicator with exterior spring. Figs. 29, 30 . 19 Kenyon's Indicator (elastic tube). Fig. 31 . . . .21 Prussmann's Differential Indicator, Schaeffer and Budemberg. Fig. 32 22 ix CONTENTS CHAPTEE II CONTINUOUS INDICATORS Guinotte's Indicator and diagrams. Figs. 34-36 PAGE . 25 RECORDING INDICATORS. Astton and Storey's Indicator. Figs. 37-41 . . • .28 Calculation of the diameter of the wheel to give 1,000 foot- pounds per revolution of index . . . . .33 H. Lea's Planimeter Indicator. Figs. 42,43 . . . .34 Theory, Calculation of Work, manipulation. Fig. 44 . .35 Boys' Indicator. Figs. 45-47 .... .38 Mechanism of the Integrator . . . . • .38 Calculation of the Work ... ... 40 CHAPTER III. ON MOUNTING INDICATORS. General Arrangements. Figs. 49, 51, 52, 53, 54, 58, 60, 61 . . 41 TRAVEL REDUCING GEAR. Stanek's Apparatus. Figs. 62, 63 Various Apparatus. Figs. 64-67 . P. Garnier's Apparatus. Figs. 68-70 . Calculating the diameter of the little Pulley Crosby's Eeducing Gear. Fig. 71 Electric control of Pencil (Kovarik's system). Fig Perry's Optical Indicator. Figs. 76-78 . 74 47 49 50 51 52 53 55 CHAITER IV. THEORY OF THE INDICATOR. Plunger Tests — the Scale of the Spring (hot and cold). Figs. 83-85 58 Eelation between the movement of the Plunger and that of the Pencil 63 X CONTENTS PAGE The Pencil or Tracer, vibration of Pencil . . . .65 The Paper Drum. Cord. Drum worked by non-flexible rod. Figs. 94, 95 68 CHAPTER V. THE STUDY OF DIAGRAM. The Diagram. Advance Admission . . . . 71 Eapid action of Steam. Duration of Admission . 74 Expansion. Two-Cylinder Engines . . . . .78 Steam Jacketing. Mariotte's or Boyle's Curve . . 81 Graphical Method. Advance of Exhaust . . 84 Exhaust and Back Pressure. Compression . . . .86 The Compression Curve. Determination of Clearance Space . 89 Expansion in Compound Two-Cylinder Engines . . .90 Diagrams of Compound Engine. Figs. 110-112 . . .91 Diagrams of Woolf Engine. Pig. 113 . . . .93 Diagram of a Triple Expansion Engine. Fig. 114 . . 93 Causes of errors in Diagrams. Various . . 94 Applications of Indicator. Steam Chest. Exhaust Pipe . 95 Use of Indicator in Hydraulic Work .... 98 CHAPTER VI. TESTING GAS AND OIL ENGINES. Ordinary Diagram of a Gas Engine (Otto). Fig. 118 . . 100 Mathot's Registering Indicator, M. Gamier. Figs. 119, 120 101 (1) Testing the Value of the Compression. Fig. 121 . .102 (2) Finding the Resistance to Admission and Exhaust (dia- grams). Figs. 122, 123 . ... 103 (3) Comparing the Mean Power of Explosions by means of Ordinates in juxtaposition. Fig. 124 . . • 105 (4) Analysis of the Cycle by four diagrams representing the four Periods. Fig. 125. . . . • -105 (5) Analysis of the efiectsof inertia on the Recorder. Choice of a suitable Spring (diagram). Fig. 126 .... 1C6 xi CONTENTS CHAPTER VII. MEASUREMENT OF THE INDICATED HORSE POWER. Mean Ordinate. Trapezium Method. Fig. 127 . Graham's Screw (Fig. 128). Another Method. Fig. 129 Simpson's Method (Fig. 130). Observations. Fig. 131 Amsler's Planimeter. Theory. Figs. 132-137 . Revolution Counters. A. Sainte's Counter. Fig. 138 Calculation of the Indicated Power TT Values of the Ratio >? = -rj. . Calculation of the diameter of H the Piston 124 Work on friction. Diagram at no load. Inertia of the Fly-wheel 125 CHAPTER VIII. MEASUREMENT OF THE BRAKE HORSE POWER. PAGE , 109 no 112 , 114 . 120 , 121 § 1. Ordinary Brake. Prony. Fig. 140 Construction. Figs. 145 and 141 ... . Vertical Shaft. Figs. 142, 143 Calculation of the Effective Work .... Calculation of the Dimensions of a Brake — Pulley. Bolts Example. Lever - . . ... Various Constructions. Detachable Brake. Fig. 146 . Brake of the Societe Centrale (water-cooled). Fig. 147 . Thiabaud Brake. Results with this Brake. Pigs. 148, 149 Carpenter's Hydraulic Brake. Figs. 150-152 § 2. Automatic Brakes ...... Brake with Spring Balance. Fig.*53 .... The Creuzot Arrangement. Calculation of Work. Fig. 154 Amos or Appold Brake (Royal Agr. Soc). Figs. 155-157 Balk Brake — mounted on Trolley. Fig. 159 . Brauer Brakes (three arrangements). Figs. 160-162 Beer or Fetu-Deliege Brake. Fig. 163 .... Cadiat Brake. With hanging weights. Fig. 164 . xii 129 130 131 134 136 141 143 144 146 148 148 149 151 154 155 160 161 CONTENTS PAGE Other automatic arrangements. Spring Balance. Figs. 165-167 162 Imray, Deprez and Carpentier Brakes. Figs. 168-170 . . 164 Brake and Indicator Testing . . . . . .169 CHAPTER IX. USE OF A DYNAMO AS A BRAKE. The Dynamo as a Magnetic Brake or Dynamometer . . 171 Arrangement as a Brake (connections). Fig. 172 . 172 Calculation of the Work. Direct Measurement of the Effi- ciency. Fig. 173 173 CHAPTER IX. A. STEAM TURBINES. Hypothetical Indicated Horse Power . . . .175 Marine Steam Turbines . . . . . . .176 CHAPTER X. PROPERTIES OF STEAM. Equivalence of Heat and Work ...... 177 Saturated Steam. Total heat of Evaporation . . .177 Latent Heat. Superheated Steam ..... 179 Saturated Steam. Compression. Adiabatic Expansion . 180 Expansion of Steam (temperature constant). Mariotte's or Boyle's Law . 181 Calculation of the Mean Pressure. Hyperbolic Logarithms (table) ... . . .181 Theoretical Weight of Steam per Horse-power Hour . . 184 Weight of Dry Steam per Horse-power Hour from Warrington's Diagram. Corrections ...... 185 Application to Double Expansion Engines . .188 Direct Measurement. Damp Steam. Priming . . 189 Measurement of Water carried over. Condensation of Steam . 190 xiii CONTENTS CHAPTER XI. §1. EVAPORATION. Calorific Power of Fuels ..... Wood. Densities. Chevandier's Eesults Table A. Charcoal. Efficiency. Mean Composition Tan Bark. Sawdust. Peat .... Peaty Coal. Lignites. Coal .... Non-caking Coal (long flame). Gas Coal. Coking Coal Coking Coal (short flame). Anthracite (short flame) Mean results of tests on the five types of Coal. Table B Evaporation Results (Brickwork Furnaces) Table C . Briquettes. Coke. Anthracite .... Calorific Powers. Table D . . . . PAGE . 193 . 195 . 197 . 199 . 201 . 202 . 203 . 204 . 206 . 206 . 208 § 2. COMBUSTION. Volume of Air necessary for Combustion Combustion in Furnaces. Combustion of Carbon Combustion of Carburetted Hydrogen . Management of the Fire .... . 209 212 . 214 . 215 § 3. STEAM TRIALS. General. Best Fuel . 219 Steam Trials . 221 Condensed Water brought over ; Drainage Water . . 223 Correction. Example. ..... . 224 Control of the Combustion . 228 Orsat's Apparatus . 229 APPENDIX. Weight of Fuel burnt per Hour . ..... 235 Chimneys and Flues. Permissible Power for Given Chimneys . 235 Chimneys at the Paris Exhibition (1878) .... 239 Stability of Chimneys ....... 241 xiv CONTENTS PAGE Example of a Chimney 93 feet high. ..... 243 Furnaces with Ordinary Grates ...... 244 Boilers. Steam per Square Foot ...... 246 Various Types. Volume of Water. Heating Surface per cubic foot of water. Relative Proportion in Varipus Types . 248 Heating Surface per square foot of the Surface of the Water. Safety Valves. Tables of Diameter .... 250 Comparative Table of Pressures . . . . . .251 Efiective Pressures and Temperatures . . . . .251 Saturated Steam. Based on Regnault's and Zeuner's tables . 252 Diameter and Areas from 1 to 1,000 . . . . . 254 XV CHAPTER I. Indioatoes. A BRIEF REVIEW OP THE VARIOUS INDICATORS INVENTED PRIOR TO THAT OF RICHARDS. Watt's Indicator. TBIS apparatus (Figs. 1 and 2) consists of a small bronze cylinder of from 1"5 to 2 inches in diameter in which works a plunger, also of bronze, on the upper surface of which rests a spiral steel spring. The piston rod, passing through the spiral spring and a guide bracket, has a pencil holder attached to the end of it, which holder, by means of a spring, keeps a lead pencil pressed upon a wooden board covered with a sheet of white paper. This board is free to slide to right or left in a frame, being pulled in one direction by means of a counter- weight, and in the other by means of a cord, the pull on which corresponds to the movement of the piston of the engine which is to be tested. Whilst the cock which is fixed between the indicator cylinder and the cylinder of the steam engine is shut off and no steam passes, the pencil will trace a line a-e on the paper, corresponding to the atmospheric 1 B ENGINE TESTS AND BOILER EFFICIENCIES pressure on either side of the piston. On opening the cock the plunger will rise during the admission of steam and compress the spring to an extent cor- responding to the steam pressure behind it ; whilst, Fig. 1. ^^ when the steam is exhaus^ng, and as the sliding board moves back, the plunger will sink below the atmo- spheric line a-e, extending the spiral spring if the engine is a condensing one. For each complete revolution of the engine, the pencil traces a diagram, of which the abscissae are INDICATOES proportional to the crank throw — or travel of the piston — and the ordinates to the steam pressure throughout the forward and return stroke of the piston. This diagram represents the power developed during one revolution of the engine on one side of the piston. MacNaiLCjlht and Hoplcinson Ind,icafnrf<, In the place of Watt's sliding board and counter- weight, MacNaught used a drum with a rotary action (Fig. 3) and an interior spring, the cord in this case passing over a grooved pulley at the base of the drum. The pencil holder is at- tached to an arm connected to the rod of the plunger, and a spring keeps the lead constantly pressed upon a paper fixed round the drum. In this case it is difficidt to regulate the pressure of the pencil or to lift it from the paper. To get over this difBculty, Hopkinson modified MacNaught's pencil holder (Fig. 4). Here the pencil d is carried by a rod, which is free to re- volve round the spindle c and carries at its other extremity another rod h. By means of a lever a the 3 Fig. ENGINE TESTS AND BOILEK EFFICIENCIES pencil may be lifted off the paper at will, whilst the indicator is at work. Adjustment is effected by means of a thumbscrew. The Indicators above mentioned, in which the pencil is rigidly at- tached to the plunger, have long since been abandoned, for they are useless for engines of even moderate pres- sure, owing to the ir- regularity of the dia- grams produced. To get over this diffi- culty, Gamier (Figs. 5 and 6) fixes two collars, i-i, to the rod of the plunger, allowing an amount of play y which represents the throw of the plunger between them and the bracket b. The bracket b is moved forward by means of the bevel wheels M N. Assume the pencil to be lifted off the dnim, the spring to be compressed and the drum in motion — now press the pencil down on to the drum, and it will trace a series of ovall if the movement is steady or of horizontal lines if sudden and intermittent. But, in actually pressing down the pencil, the spring is slackened and its tension rapidly adjusts itself to the pressxire of the steam, the plunger moves to the extent of the space y and the pencil traces at each 4 Fig. 4. INDICATOKS revolution of tlie engine a pattern which is the full extent of the first elements of the diagram. Fig. 5. ENGINE TESTS AND BOILER EFFICIENCIES Continuing this, succeeding elements are traced of which the whole constitutes the diagram of the mean fatter n produced by a definite number of revolutions. This indicator is now out of date. INDICATORS Biclmrds' Iiodioator, manufactured by Elliott Bros. (Figs. 7 and 8). This indicator is an important advance upon those already described, and is applicable to engines of high steam pressure and high speed. Here the travel of the plunger is reduced to about three-quarters of an inch, whilst a lever, whose arms are in the ratio of about 1 to 4, permits the tracing of a diagram with sufficiently long ordinates. A pencil A attached to a parallelogram traces within the limits required of it a practically straight line. The light- ness of the levers carrying the pencil reduces their inertia, which is very small compared with that of the plunger, and hence, notwithstanding the increase of travel of the pencil, the consequent natural ten- dency to exaggerate every oscillation is very slight. The collar a-a which carries the parallelogram, and the link b, are each free to move round the axis, and hence the pencil can be pressed or lifted from the drum, even while the plunger is at work. This move- ment is limited by a stop c. Holes drilled in the cover of the cylinder admit air to the upper side of the plunger and allow of its escape as the plunger rises. The washer / carries two pulleys, seen in the plan, which act as guides to the cord, from whatever direction the pull comes upon it. A movable drum which carries the paper for the cylinder fits over and is attached by a stud to the cylinder, which is fixed to the pulley j; and the barrel containing the counter spring. The drum may be fitted with Darhe's ratchet 7 ENGINE TESTS AND BOILER EFFICIENCIES adjustment, by which means its movement is arrested when a complete movement to and fro has taken place, so that the paper may be changed without dis- connecting the cord. This ratchet is thrown in or out of gear by the movement of a button from to 0'. The Richards' Indicator is the model followed by all subsequent inventors. Darlfe's Indicator, manufactured by Elliott Bros. (Figs. 9-12). This little Indicator is designed for engines of high steam pressure and high speed. The diameter of the plunger is here reduced to half an inch, and its throw to about two or three eighths of an inch ; the diagrams are at most one and a half inches deep by three and a half inches long. The hollow plunger rod has at its upper end two flanges, which hold a socket between them by means of two screw pins. The enlarging lever b passes, an easy fit, through this socket. One end of this lever is attached to a bracket fixed on the collar e, whilst to the other end, which is flattened out, is attached a slide c carrying a pencil which works in a straight groove cut in the plate d which is also attached to the collar e. The pencil is moved on to or away from the paper by means of a small handje which turns the collar e and lifts the lever b and guide plate (/. The drum, provided with the Darke ratchet adjustment, carries the paper. After taking each diagram, the drum must be stopped and a new piece of paper, bent to the diameter 8 INDICATORS of the drum, slipped over it and kept in position by means of two hinged plates provided with teeth on their upper surfaces, on to which each end of the paper is folded back. Nearly all makers of Indicators manufacture two Fig. 9. Figs. 11, 12. types, the one for low, the other for high speeds and steam pressure. ENGINE TESTS AND BOILER EFFICIENCIES Thompson's Tnclicator {American). This Indicator only differs from that of Bichards'- by using a parallelogram which is practically that used by Evans, except that it has a short connecting rod. Evans' parallelogram, which is simpler than that of Richards, has less inertia, and so the irregular movement of the pencil is less. Chapter IV. will describe the conditions to which it is most applicable. P. Gamier' s Indicator (Figs. 13, 14). This little pattern is constructed for high speed Figs. 13, 14. engines with high steam pressure, and is fitted with Evans' parallelogram. The upper surface of the 10 INDICATORS plunger, which is made of steel, is cup-shaped, and is filled with oil which is at each movement to and fro thrown over the inner walls of the cylinder. The lower end of the spring fits into a cap with a ball in the centre. This ball fits in between the plunger and the hollow rod screwed to it. Thus the tension of the spring can be altered by simply unscrewing the piston, when it has been taken out of the cylinder, with- out taking the rod off and without using a spanner. The drum is provided with two grooves, the upper carrying a cord which can work a second indicator. Care has to be taken with the indicator previously dealt with not to bend the parallelogram, as this would alter the spring, for the cover of the cylinder which has been unscrewed and the socket carrying the parallelo- gram are both loose in the hand. In this indicator, however, the upper part of the cylinder to which the cover is screwed and to which the socket carrying the parallelogram is fixed, can be unscrewed and entirely disconnected from the lower part. The Mwrtin-Garuier Indicator (Figs. 15-17). This Indicator is distinguished from the preceding ones in the first place by the fact that the drum is worked by means of a small wooden pulley with the cord wound on it and a pinion and helical toothed wheel. The spindle of this pulley has at the other end a return action spring attached to a fixed band. The pulley can be changed to suit the requirements of the engine under test, and the apparatus suitably reduces the effect of the throw of the crank shaft of the engine, and has the additional advantage of stiffening 11 ENGINE TESTS A.ND BOILER EFFICIENCIES Fic;. Ic Fig. 16. the drum in the case of higli speeds, and thus increas- ing the correctness of the length of the diagram ; on which point we will touch later. 12 INDICATOES In the second place, this indicator is distinguished by having a valve at the base of the cylinder. The inventor claims that this valve is lifted by any sudden steam pressure, and that it then checks the flow of steam into the cylinder ; the plunger is therefore saved from any sudden inflow of the steam to the cylinder, and any tendency to irregularity in its movement is reduced to a minimum. Nevertheless the beneficial effects of this valve are questionable, and the need for it -would only appear to exist in the case of tests of engines of very high speed. P. Garnier's Marjadnc Drum, wWi. Steadijiinj Gear (Figs. 18-21). This steadying gear does away with irregular move- ment of the drum at high speeds as well as those draw- backs attendant upon the vibrations and elasticity of the cord (see Chapter IV^). It is eminently suitable, therefore, for high speed engines. The ratchet a (Figs. 18-19), which has a to and fro motion trans- mitted to it by the engine, gears into a pinion h. This pinion h with its sheave r is loose on its spindle, and the rack can be moved backward and forward through the guides through which it passes. The sheave c (Fig. 20) forms, with the sheave d fixed on its spindle, a clutch, which is thrown in or out of gear by the lever e. The fixed sheave J (Fig. 21) mounted on a squared portion of the spindle, when thrown into gear with c, sets in motion the pinion / with helical teeth, geared to a similar pinion fixed to the spindle of the paper drum Is. The barrel ;/ contains a return action spring, giving 13 ENGINE TESTS AND BOILER EFFICIENCIES the return motion to both the rack a and the drum h. Inside the paper drum h is a spool of paper which is rm. 20. Fig. 18. Tig. 19. 14 INDICATORS reeled off on to the drum as required, and which is held in position by closing down the lever blades. As each diagram is traced, the apparatus is thrown out of gear by the lever e and the paper torn off along the blade ; the blade is then lifted, a new length of paper drawn out and fixed round the drum, the clutch thrown into gear again and a new diagram taken. Schaeffer and Budemherg^ s Indicator (Fig. 22). In this Indicator, the hollow piston rod, which is of steel, works in a guide at the head of the cylinder, and the con- necting rod which con- nects the piston rod to the multiplying lever is also made of steel, and has a ball and socket joint. A cord actuates the paper drum in the usual way. The cap of the barrel containing the return action spiral spring for the drum is loose on the spindle, and is fixed to the inner end of the spring. To stretch the spring H TO. ^Ot to the required extent, all that has to be done is to slacken the upper guard 15 ENGINE TESTS AND BOILER EFFICIENCIES nut, give a turn to the cap of the barrel and tighten down the nnt again. Rosenhranz' s Ivdir.afor (Fig. 23). Here an interior cylinder a steam jacketed to a dejjth equal to the whole travel of the plunger keeps the walls of the cylinder throughout the stroke at an even temperature, and pre- vents any unequal expansion between the plunger and the cylinder. In order that the expansion should have free play throughout the material of the inner cylinder, there is a clearance between its upper portion h and the outer cylinder. With this arrangement, the plunger never jams in the cylinder, even when the latter has not been heated beforehand. The arm d carries the guide rod of the parallelogram. The nut r, is used to draw away any water caused by condensation in the cylinder. Crosby's .hviffafor (Figs. 24, 25). The spring (Fig. 26) is in this case a double spiral, with a ball fitting on to it at the base. The socket which prolongs the piston is split to receive the spring, and the ball is held firmly between the screw placed inside the socket (Fig. 24) and the 16 Fig. 28 INDICATORS piston rod proper, which is screwed into the socket after the spring is inserted. Several holes drilled in the cylinder, above the Fig. 2B. plunger, prevent the air cushioning, and they also allow any water which may have formed by condensa- tion above the piston to escape. The cylinder is 17 c ENGINE TESTS AND BOILER EFEICIENCIES steam jacketed, as in the Indicator last described, in order to secure equal expansion. The parallelogram is of special design, and its functions will be found described in Chapter IV. In this Indicator the lever guide is smaller, and nearer the axis than that of Evans', and its inertia is conse- quently less. The long lever arm has a web which serves to stiffen it. The drum is set in motion in the usual manner ; the spring b is first lifted, then the handle a is pressed down and the elbow of the spring fit- ting into the niche c holds the ratchet The object of this ratchet is, as has already been explained, to stop the drum without disconnecting the cord which works it. Pig. 26. out of gear. Elliott Brothers' FMernnl Spring Indicator (Figs. 27, 28). For use with engines driven by superheated steam of very high temperature, Messrs. Elliott Brothers have constructed an Indicator in which the spring is placed outside the cylinder in order that its hard- ness, and consequeAly its elasticity, shall not be affected. The spring is of special design, shaped like tongs, the two ends being bent round and fitting into sockets. The spring can be taken out and replaced without taking the apparatus to pieces. 18 INDICATORS Fig. 27. Fig. 28. Bosenkravz'-'i Evrtpninl Sprinq Ivrlieafor (Figs. 29, 30). This Indicator, as the last described, is designed for steam engines working at very high temperatures, engines using siiperheated steam, gas engines, etc. The connecting rod E carries above it a ^stirrup B upon which fits the lower sheave (? of a double spiral spring. The turned boss M, B fits into the upper sheave G 1 . The hollow cap A is fitted with a milled and screwed cap N, which presses on B and holds it in place. On the same piece as the hollow boss is a smaller 19 ENGINE TESTS AND BOILER EFFICIENCIES Tra. 29. Fig. 30. one which fits into the hollow steel column F, which is rigidly fitted to the base plate of the whole apparatus, the rigidity being increased by a tie rod Z also attached to the base plate. For the rest, the Indicator resembles those already described. The weight of the stirrup B is of no importance. To change the spring, the screwed cap N must be re- moved after the screws which hold the cap of the cylinder have been taken out. The plunger can then be withdrawn from the cylinder, and the head B from 20 INDICATORS the hollow boss A. There is no difficulty in this, as the external parts keep cool, and as the lever arms are not interfered with, the parallelogram need run no risk of injury. Kenyan's Indicator (Fig. 31). Mr. Bourdon, with his well-known hollow spring Fig. 31. device, constructed an Indicator of which there is a specimen at the Conservatoire. Kenyon, taking up the idea, applied Bourdon's hol- low spring to the Richards' Indicator. The flexibility of the spring is varied to suit the pressure of the steam in the engine under test. This apparatus obviates all difficulties arising from friction between the plunger and the walls of the cylinder, and all discharges of hot 21 ENGINE TESTS AND BOILER EFFICIENCIES water which interfere with the operator and so often wet the paper and cause it to tear. But as the values of the angles of deflection can only be plotted under steam, compressed air or water pressure, the apparatus has been discarded. Pruss7nan's Indicator, manufactwed hij ScJiaeffer and Budenberg (Fig. 32). The diagram traced by all the Indicators above described gives the varying pressure on one side only of the piston of the engine, and it is often taken for granted that the pressure is the same on the other side as well. This is not true, for the slanting stroke of the con- necting rod causes a difference in the distribution and speed of the piston in its backward course. In order to obtain the total work done by the steam on the two faces of the piston, it is^ necessary to take indicator diagrams on both sides of the cyhnder. If 22 Fig. 32. INDICATORS we arrange the indicator diagrams as shown in Fig. 33, and subtract from the ordinate of the curves showing the steam pressure for the forward strokes on each face the simultaneous back pressure on the other face, we get the shaded diagram in Fig. 33. For example, b' equals h, and c' equals c. This shaded diagram may be regarded as the true indicator diagram. Fig. 88. The differential Indicator actually gives this true diagram. One side of the plunger of the Indicator is connected to one end of the engine cylinder, and the other side to the other end. The plunger rises or falls with each stroke of the engine in proportion to the difference of pressure in the cylinder. It will be seen from the drawing that the spring is always in compression, and therefore that the diagram given is that shown (Fig. 33), which is a combination of the true diagrams — back and front — and represents the work given out at each complete revolution of the engine. The ordinates within the curves show the true varying pressure upon the piston of the engine. '23 ENGINE TESTS AND BOILER EFFICIENCIES If the Indicator is connected up separately, first to one side of the piston of the engine and then to the other, the two separate diagrams (Fig. 33) are ob- tained. This Indicator can be altered from a differential to a simple one by stopping the left-hand steam inlet, and by replacing the bottom plug by a pipe and stop- cook, but the diagram now is not so tall as an ordin- ary one, as the lever carrying the pencil is already on the base horizontal line at atmospheric pressure. In our opinion, the true diagram is not as useful as an ordinary one, for one cannot judge of the distribu- tion of steam in the cylinder from it, since the lines indicating admission, cut off, expansion and com- pression, which will be studied later on, are altered in shape by this fusion. The fact that the diagram shows the work expended on both sides of the piston, for each complete revolution of the crank is however of small importance, for if the engine runs smoothly and without change of load ordinary diagrams taken one immediately after the other will suffice. If on the other hand the engine is not running under steady load, it is necessary, even with the double indicator, to take several diagrams in order to arrive at the mean. When acting as a double indicator, the diagrams do not take atmospheric pressure into account. This advantage is really a'l^light one, owing to the very trifling changes in this pressure, and the stronger the spring, the smaller will be the effect of these changes. 24 CHAPTER II INDIGATOBS WITH CONTINUOUS ACTION CONTINUOUS Indicators— that is to say, indica- tors which give a continuous record — have not been adopted as practical. They are more complicated in their construction and more costly than those we have described. More- over, it is but seldom that a continuous record is really of advantage. So long as we can take a simple diagram, once an hour, or even oftener, this is usually sufficient for ascertaining the output of an engine. The simple diagram suffices to show the engine builder how to adjust cut-ofE and expansion — it is all that is required for an ordinary trial ; nevertheless it will be well to describe some of the very ingenious Indicators that have been designed for taking con- tinuous diagrams. Gtdnotte's Indicator (Figs. 34-36). This is an improved form of Clair's continuous Indicator, the improvement consisting in replacing Clair's direct acting pencil arm by that of Richard's. The paper rolled on the drum A, which is fitted with a check B, passes to the drum G, which, by an 25 ENGINE TESTS AND BOILEK EFFICIENCIES rm r^ ^ l l Vg Fig. 34. Fig. 3B. ingenious arrangement due to Clair, receives a steady rotary movement, proportional to the speed of the 26 INDICATORS WITH CONTINUOUS ACTION engine under test. The pulley D is kept in motion by a cord or belt driven by the engine whilst the re- turn action is given by the spring E. The spindle E moves, therefore, alternately from right to left. In order to convert this alternating movement into a con- tinuous one at the drum G, the spindle F has a right and left screw thread cut in it, of which the right- hand thread is in gear with the bevel wheel G and the left with the bevel wheel H. The drum is given a continuous motion, each wheel driving it in turn by means of three friction clutches I, I, I, inside it, which by means of springs press on the inner periphery of the wheels only when these revolve in one direction. Fig. 35 shows the upper bevel wheel removed, and shows the friction clutches inside the lower one. In the early designs, the curves were traced on the drum G, and some inconvenience resulted owing to its increasing diameter as more and more paper was wound on to it. To get over this difl&culty the paper was passed over a fixed blade K. As the drum G in- creased in diameter the diagrams lengthened, and Fig. 36 shows that given at each revolution, indicated by Fig. 36. dotted lines 1, 2, 3, traced by the pencil /. This pencil I is worked by means of two bolts m, n, clamped into a flange of the wheel H (Fig. 34), and so placed 27 ENGINE TESTS AND BOILER EFFICIENCIES that at each end of the stroke of the piston each bolt alternately strikes one of the bevelled sides (o o) of the lever P, and sharply presses down the spindle q, which carries the pencil I, which pencil is during the rest of the time kept off the paper by means of a spring. In the diagram shown, Fig. 36, the compression curve follows the pressure curve ; if we fold the one back upon the other we obtain the ordinary self-contained diagram. The pencil r traces the line a-c at the same time that the curves are being traced, but we can trace this line after taking the diagrams, by loosening the screw bolt 8 which attaches the drum G to its spindle, re- leasing the check B and winding the paper back on to drum A by hand. Recoeding Indicatoes. Ashton and Storey', i Indicator (Fig. 37). In this Indicator each end of the cylinder A is connected to a different end of the cylinder of the engine under test by means of cocks fitted with blow-off valves. The plunger A, the rod of which carries loose upon it the little wheel a, attached in its turn to the cylin- drical pinion b, moves up and down in proportion to the difference of steam pressure on either side of it. This pressure is balanced by = the work of the low pressure cylinder. Then a. + ^ = the total work. Fig. 38. 31 ENGINE TESTS AND BOILER EFFICIENCIES Take another reading of the high, pressure cylinder a\ then the total output x = x a' *• a In Fig. 38 the movement of the engine piston is transmitted to the indicator by means of a square rod twisted in the form of a spiral, or else by a system of levers (indicated by dotted lines). Fig. 39. Fig. 40. Fig. 41. Figs. 39-41 show the method of driving the wheel a (1) by a cord ; (2) by a rack B ; (3) by a wheel a', a cylinder or roller a" ikid a sliding bar c, acting by friction, and kept pressing upon a" by d. A paper drum and a pencil holder may be fitted to the indicator for taking ordinary or differential dia- grams. 32 INDICATORS WITH CONTINUOUS ACTION Galculatioib of the diameter of the luheel d iu order to give 1,000 foot-pounds for each revolution of the pointer (Fig. 37). Let i> be the pressure whicli compresses the spring by one inch. d the diameter of the plunger of the indicator in inches. ([ the diameter of the little wheel a. k the number of teeth on the cylindrical pinion. I the number of teeth in the wheel. ■lit. the umnber of teeth in the worm wheel. /( the number of teeth on the first clock wheel. D the diameter, in feet, of the pulley which it is desired to find. -f\ the pressure per circular inch to give a deflection of one inch. Let us assume that the little wheel a. is one inch from the centre of the disc e ; one turn of the disc 2 will make the little wheel revolve - times. Therefore, for one turn of the disc the pointer will revolve 2 h m , . _ X - X — times. q I li But, for each revolution of the disc or the pulley the work per circular inch on the engine piston is i-^ X TT X) in foot-pounds. Therefore, for each revolution of the pointer, that is for every 1,000 foot pounds : , r^r^r^ V 7 1 Q X I X 11 1,000 = i^^ ttjUx I — ^ d 2x kx m 33 D ENGINE TESTS AND BOILER. EFFICIENCIES from which we obtain ,, 2000 hmd'. . 6\4 = the diameter of the engine piston in inches, K = the variable coefficient of the springs used. A = the coefficieiit for each indicator. To find the total horse power, therefore, it suffices to calculate the value of the expression shown in the brackets and to multiply it by n. The indicator can be constructed so as to trace either a true diagram or an ordinary diagram. 40 CHAPTER III The Mounting of Indioatoes THE indicator should be fitted in such a position — either vertical or horizontal — as to be most readily handled. In the case of high speed engines, in particular, it should be connected directly to the cylinder. The stop and blow-off cocks permit of its being dismantled without stopping the engine. Fig. 49 shows the stop-cock B with three pijjes in order that diagrams may be taken one after another at each end of the cylinder. This stop-cock (Fig. 50) Fig. 49. is fitted with an outlet a to drain the cylinder of the indicator, and the opening of which enables us to trace the atmospheric line. The pipes, which should have rounded elbows, should also be from a half to five-eighths of an inch in diameter. 41 ENGINE TESTS AND BOILER EFFICIENCIES The pipes leading from the cylinder must be so placed that the piston does not close them at the end of the stroke. The indicator must not be mounted on a steam pipe, because, owing to the rapid flow of steam in the pipe, there would be a tendency to depress the plunger and give an unreliable diagram. Joints should be made with cotton yarn, tallowed, but without red lead, for the smallest particles of this Fig. 50. in the pipes or the indicator itself would affect its accuracy. There are various w*ys of connecting the paper drum with the engine piston. One of the simplest (Fig. 51) consists of two levers, both carried on one spindle, of which the longer is connected at its other end with the sliding crosshead of the engine, and the shorter with a semicircular pulley. 42 THE MOUNTING OF INDICATORS It is essential that the oscillations of the levers should be tangential to the paper drum, in order ^J U- PlG. 51. that the abscissEe in the diagram may be proportional to the travel of the engine piston. If the sliding crosshead is not accessible, as in the case of enclosed engines, an eccentric wheel must be fixed to the end of the shaft. ■ — Fig. 52. Fig. 52 shows the case in which the cord is attached toabar Jf and the indicator itself is fitted with reduction gear. Fig. 53 shows two indicators, 43 ENGINE TESTS AND BOILER EFFICIENCIES the first actuating the second, with reducing gear D B fixed to the frame of the engine. The cord is Fig. 53. attached to the bar M, which is fixed to the piston rod by means of the collar V. Figs. 54, 55, 56 and 57 show amethod employed when the cylinder is of considerable diameter. A bolt a is THE MOUNTING OF INDICATORS Cr3 Pigs. 68, 59. 46 ENGINE TESTS AND BOILER EFFICIENCIES fixed to the sliding crosshead and a hook h connected to the cord catches into one or other of its grooves in such a position that the cord is parallel to the piston rod. Bolt G fixed to the framework of the engine carries two reducing pulleys. The cords starting over these pulleys pass over the pulleys e, and each is then con- ducted to an indicator. For Figs. 52-54 we are indebted to Messrs. Dreyer & Co. Figs. 58, 59 show another way of mounting two indicators. The bolt a screwed to the cross- head carries an endless cord which passes over the pulleys cl and e carried on axles fixed to the framework of the engine. The tension on the cord is ad- justed by means of the screw sleeve h. The pulley d, by means of the inter- nal screw thread, moves sideways at each revolution to Fig. 60. and fro, so that the coils of the cord alway^lie flat on the face of the pulley. The two small pulleys / on which the in- dicator winds and unwinds are attached to (/. In the case, of a vertical engine (Fig. 60) the lever a is fixed at one end of the crosshead and at the other to the fixed bolt c. The cord attached to a leads to 46 THE MOUNTING OF INDICATORS the indicator, which is here of the Martin Gamier pattern. To stop the indicator it is only necessary to hook h into the stationary bolt c. In the case of an oscillating engine (Fig. 61) two methods may be employed, both of which are shown in our illustration. On the right-hand side of the diagram the cord attached to the crosshead passes over the larger reducing pulley and the smaller actuates the indicator A. On the left-hand side the crosshead carries a socket of square internal section which as it moves to and fro causes a twisted square rod to which is affixed the pulley / to revolve. The indicator cord is worked by this pulley. Pig. 61. Fig. 62. Travel Reducing Gear. Stanek's Gear (Figs. 62, 63). The large pulley 47 ENGINE TESTS AND BOILER EFFICIENCIES fitted with an Internal return action spring, and the little pulley which may be changed at will so as to obtain any desired ratio between the crank throw and the movement of the paper drum, are mounted on one and the same screwed bolt and may be adjusted to any desired position on a bolt shown upright in the Fig. 63. illustration by means of a set screw. This bolt, which may be straight or bent as desired, is screwed into a collar, fitted with three fixing screws so that it can be attached to any hexagonal nut on the cylinder or such other suitable support. An arm, also movable*)n the bolt, carries the pulleys over which the cords pass to the engine cross-head and to the indicator. These pulleys have a side movement as in Figs. 58, 59, in order that the cord may be flat upon them. Figs. 64-66 show another method. 48 THE MOUNTING OF INDICATORS Fius. 64, 65. ENGINE TESTS AND BOILER EFFICIENCIES The bolt K (Fig. 64), which may be either vertical or horizontal as desired, is screwed to the angle iron b, which is in turn attached to the frame of the engine. Fig. 67. c is the cord that connects the piston to the indicator. Fig. 66 shows the return action spring inside the large pulley. Fig. 67 shows the apparatus as titted to the base of the paper drum itself. P. Garnier's Apparatus (Figs. 68-70). The cord from the engine is wound on the wooden pulley a. 6 on the same spindle receives the cord from the cylinder c, within which is a return action spring. The cord on pulley d works the indicator. A second pulley e may be used to work a second indicator. The whole is carried on the bolt / attached to the framework of the engine as described above. 50 THE MOUNTING OF INDICATORS Fias. 68-70. To Calculate the Diameter of the small Pulley. Let L = the stroke of the engine. / = the breadth of the diagram. I) = the diameter of the lai'ge pulley. d = the diameter of the small pulley. These diameters include the thickness of the string, which is generally about one-tenth of an inch. We have : D 51 I L ENGINE TESTS AND BOILER EFFICIENCIES •. d^D- Suppose we have D equal to six inches, and I equal to five inches, then d = 30 where L and d are in inches. The following table gives the yalues of d for various values of L : — Piston stroke in inches 24 36 48 60 72 Diam. of winding d 1-25 0-88 0-63 0-50 0-42 Diam. of pulley (d — Q-l) 1-15 0'73 0-53 0-40 0-32 With these five pulleys the length of the diagram for any stroke will be less than five inches, and will be given by d ] = L D Groshy's Iiediicimj Pulleys (Fig. 71). Here the reducing pulleys are mounted on the same frame as the indicator itself. The large pulley, receiving its impulse from the engine, drives the little pulley by means of bevel gearing. The return action spring is fixed to the spindle of the little pulley ; it is helical in form, and contained in a cylindrical covering. 62 THE MOUNTING OF TNDTrATORS Elccfrlr Coiiti-ol of fhe I'l-nc'iL Tlie object of this is to enable diagrams to l^e taken on a nnnil)er of different cylinders at tlie same moment. Tilt' fnll lines in Fi''s. I'l, 7-5 show tlie electric Fic. 71. connections applied to tlu> Rosfmkranz indicator. The stt'el plate A is attached to the cap which carries the parallelogram by a fork-shaped piece of steel // fixcMl to the boss 7'l)y two screws. An electro magnet Vj is attached to the body of the indicator by a strap T'. The distance between J and ENGINE TESTS AND BOILER EFFICIENCIES the electro magnet is adjusted by the screw d and a spring F. Pir,. 72. ^' IMzv: Tig. 73. i «r* 1 K K are terminals of the electric circuit. On closing circuit the electro magnet attracts A and gives such a moverrfint to the parallelogram as to bring the point of the pencil into contact with the paper on the drum ; on breaking circuit the spring pushes back A and lifts the pencil. Fig. 75 shows the connections for a circuit to two or four indicators, the switch being indicated by 1. 54 THE MOUNTING OF INDICATORS f: n- ,1 I ; 1 1 r |V t-, I O I '-\ .-J ;,. ■ ^- -^ Battery Fig. 7B. Professor John Perry's Optical Indicator (Figs. 76- 78). Indicators with springs become erratic in tlieir Pigs. 76, 77. action when the engines under test are of the highest speed class. Only when the period of oscillation of 65 ENGINE TESTS AND BOTLEE EFFICIENCIES the indicator is less than yV that of a revohuion of the engine is the diagram satisfactory. At -^V the diagram is unsatisfactoiy, at ~~ it is defective. The optical indicator consists of a fixed portion a (Figs 70, 77) carrying a l)ox // ):)y means of two pivots ; r is the steam inlet. The Iwx h is closed by a slieet of steel d, which, being thin and elastic, yields somewhat nnder the pref^nre of steam. Upon this steel diapln-agm, aljout halfway between the centre and the edge, is fixed a mirror e. A lever f connected with the crosshead of the engine causes /' to oscillate from side to side at each stroke. 56 THE MOUNTING OF INDICATOES The rapidity of the oscillations of the diaphragm may easily be 500 per second or even more, so that correct diagrams may be obtained at the highest speeds. Fig. 78 shows the indicator fixed to an engine. A ray of light is thrown by a lamp through A on to the mirror, and is projected back on to a piece of ground glass, on which the diagram is shown. Fig. 79. Even at a speed of only 100 revolutions the impres- sion is clear enough to trace the diagram by hand with a pencil either on the ground glass itself or on tracing paper fixed over, the glass. To trace the atmospheric line, open c to the air ; when this has been done, admit steam, and a second line will be traced ; the distance between the two will give the pressure scale of the diagram. Fig. 70 shows two diagrams taken, one at 200 revolutions- of the engine, the other at 500 revo- lutions. 57 B CHAPTER IV The Theory of the Indicator Y theory is understood the part played by each portion of the indicator. The Plunger. See that in pushing the plunger to and fro by hand there is no appreciable friction between it and the inside of the cylinder. A loose plunger allows an escape of steam, of little importance in the case of non-condensing engines ; but in the case of a condensing engine air passes and destroys the vacuum under the plunger, especially if the pipes to the indicator are long or of small diameter. If the indicator is not in good order, the spring under compression may press sideways, and so cause friction on the plunger and plunger rod. To prevent this Mr. Lyne attaches the spring to the plunger-rod by means of a ball-and-sfcket joint (Figs. 80, 81). Tests — the Scale of the Spring. Turn the apparatus upside down and fit it in a vice ; then compress the spring by means of weights affixed to the plunger-rod. 68 THE THEORY OF THE INDICATOR Turn the paper drum by hand, and the various deflections will be recorded by the pencil. The indicator may also be fixed to a bracket or Fig. Fig. 81. such a device as shown in Fig. 83, where the rod carrying the weights is connected to the plunger-rod by means of the stirrup Z, and passes at its lower extremity through the guide hole B. If the spring has to be tested for expansion, in order to measure pressures below the atmospheric line, the indicator must be fixed upright and above the cross piece B. Let q denote the pressure in pounds for every tenth of an inch of deflection. -s the surface of the plunger per square inch. „, q _ _ fload per square inch for every s [tenth of an inch deflection. The scale of the spring e = -= ~ V ? The flexibility of a helical spring, within the limits for which it is designed, is proportional to the pressure upon it. If (Fig. 82) the abscissae repre- 59 ENGINE TESTS AND BOILEK EFFICIENCIES sent the pressures, and the ordinates their corres- ponding deflections, it will be found that the line y ! -■ - — ,, / ::^ / : __ / \ i -?- i / I a a -'■■ j X 1 J/. — ;3 Tig. 82. the indicating the relation of the one to the other is for all practical piirposes a straight line. The same is the case if we consider the effect of vacua as negative pressures and continue the line from in the direction o ». If pressures have been applied successively to 15, 30, 45 pounds per square inch on the pis- ton surface, and the corresponding deflections 15 8U 45 ' scale of the spring. In the arrangement (Fig. 84) the spring alone is placed in a cylinder IL (Fig. 85) built up of two sections and bolted together. The parallelogram D traces the deflections on the scale T. In these tests the weight of the rod K must be taken into account. To test the spring under expansion, the glands at 60 measured //' /", we still have i THE THEORY OF THE iNDlL'ATOK the two L'lids of the cylindL-r must \)c oxchaugcd, alid the .spiiug- must hang from the upj)ci- one. The Uol IWf. The indicator SDi'inii' l)eini'' in connection with the o[)en air, it is always at a lower temperature than tliat of tlie steam in tlie engine cylinder, and as moie- over the temperatvu'e of the steam varies from the time of admission to that at which it exhausts, we may assume that the working- temperature of the spring is but little more than 21 'J de- grees Fahrenheit. In order to test under work- ing conditions, a little boiler heated by gas or oil is con- nected u]) to the apparatus (Figs. 60, ST). In Fig. .s;3 tlie steam is ad)nitt(_'(_l l)y the cock r. lu Figs, yd, .S.~) the steam enters the cylinder at ^1 through the pipe //, and the condensed water escapes at p. In comparing the deflections shown on the diagram (Fig. y2) with those oljtained with the a.pparatirs shown at Fig. S^f, allowance must l)e made fVjr friction, and afsn, what- is more im[Mjrtant still, the rat in between the altei'ed positions (31 ENGINE TESTS AND BOILER EFFICIENCIES of the plunger and the pencih (This point will be dealt with later on.) In the preceding tests, when the full pressure has been reached, the steam cock must be closed ; and the steam gradually condensing, the pressure falls through P Pi Fig. 84. Fig. 85. the same scale as in risii%, and the pencil should give the same readings during the fall of pressure as it recorded when steam was being admitted. These tests may be applied equally well to the testing of vacua. 62 THE THEORY OF THE INDICATOR Relation behueen the Movement of the Plunger and that of the Pencil. The parallelogram must work freely, but there must not be any unnecessary play. In order to see that it works freely, compress the spring and let it expand again and trace a line on the drum which may be turned by hand. Then extend the spring, and as it returns to the normal position let it trace another line. These two lines ought to be identical. Be sure that the movement of the pencil throughout is proportional to the movement of the plunger. Fig. 86. In the case of Darke's Indicator, of which Fig. 86 is the diagram, the line 6-6' traced by the pencil is straight owing to the guide through which the pencil runs. The ratio of the travel of the plunger to that of the pencil is maintained constant, for in all the triangles formed by the points o ft 6 we have, a a' : hh' : : o a : oh:: a' : oh'. In the case of the Evans' parallelogram (Fig. 87) the 63 ENGINE TESTS AND BOILER EFFICIENCIES best form, and the one in which the pencil traces the straight line, is his first design in which the connecting rod e d = ^ b c. When e d is smaller, the line traced by Fig. 87. the pencil is not so straight. The ratio of the dis- placement of the plunger a to the pencil b is found by Fm. y«. taking a point a on o b ; o being the fixed point on 64 THE THEORY OF THE INDICATOR which the rod o r moves ; the piston rod n f being parallel to o c. (t rj equal and parallel to / c may take the place of e d\ af,c g,fr, a g then form a lozenge pattern and the whole constitutes a pantograph, the points o ah being always in the sanie straight line. This applies equally to Crosby's Indicator (Fig. 88). The Pencil or Tracer. The pencil used is sometimes of hard lead, but as a Tig. 89. rule a rounded metal point is used which traces a grey line on paper specially prepared. The pencil should press on the paper without scratching it. It should be light, for its speed being greater than that of the arms its inertia must tend to set up vibration. The friction of the pencil on the paper reduces these vibrations, but at the cost of some want of 65 F ENaiNE TESTS AND BOILEK EFFICIENCIES accuracy in the diagram. Fig. 89 taken with a Kenyon Indicator from a Corliss engine shows this very clearly. It shows that during the admission of steam the line Fig. 90. of admission is either too high or too low, depending upon whether the vibration of the pencil stops on a down stroke (heavy line) or an up stroke (dotted line). The friction raises the line of expansion as well as that of exhaust. "When there is frictioi in the various parts and especially the plunger, in addition to that of the pencil, the curve shows sudden jumps (Fig. 90) due to the jerky movement of the pencil owing to the difference in the coefficients of friction when starting and when in motion. 66 THE THEOEY OF THE INDICATOR This Vibration of the Pencil. is due to the rapid movement of the mechanism set up by the sudden action of the steam and the resistance of the spring. Acted upon in turn by tliese the plunger moves now to one side, now to the other, of its position of equilibrium and the pencil traces wavy lines. During expansion the state of equilibrium is best maintained, but during exhaust the oscillations are less marked because the pressure on the plunger is so much smaller. That the duration of the oscillations is independent of their magnitude is shown by Fig. 91.^ Fig. 91. The more rapid the oscillations the quicker they exhaust themselves, and there is less fear of them dis- torting the diagram. This is the reason why in- dicators in which the compression and expansion of the spring is reduced to a minimum have taken the place of the older forms. ' We have to thank M. de Manpeon for the use of the diagrams, 88 to 91. 67 ENGINE TESTS AND BOILER EFFICIENCIES Formerly endeavours were made to attain the same resnlt by making the sectional area of the steam inlet pipe Toth that of the cylinder, but in this case the effect of the vacuum is interfered with. Seeing that compression diminishes the jerky action of the steam behind the plunger, it is obvious that to decrease these oscillations springs of greater stiffness should be used in proportion as the com- pression is less. The Paper Drum. The drum should be perfectly round, and the paper laid smoothly on it. Its movement is transmitted to it by a cord made of hemp, catgut or wire, all more or less elastic. At the- commencement of a stroke, the / 105 r. p.m. ^65.^3^ -^' y 'fi ..-- / ^' 60*!;-''-" '"' !,l"*-- .'■• ^rarlr.^— — .-._-- -jrr. - --".T.r r.'S'z'.— •-- --r^ Fig. 92. cord, in overcoming the inertia of the drum, the reducing 2Dulleys and ^e tension of the springs, stretches somewhat and the drum is a little behind- hand in starting until the cord returning to its normal length ends by giving the drum a movement pro- portional to the stroke of the engine. There must therefore be a shrinkage in the diagram and a reduction of its area, greater or less in degree as the 68 THE THEORY OF THE INDICATORS speed of the engine is fast or slow or the elasticity of the cord considerable or the reverse. But in the indicating of high speed engines there is often a lengthening of the diagram caused by the impetus of the drum, as shown in Fig. 92. In any given case this can be overcome by reducing the travel of the drum and increasing the tension of the return action spring in proportion to the speed of the engine. The Cord. The cord should be flexible, but should have as little elasticity as possible. It is not infrequently made of ^^"^'^"^'>w^ff.\"> FiCi. 93. hemp or catgut, but it is sometimes made of metal threads or steel strips. A method of connecting the hook to the cord is illustrated in Fig. 93. A hempen cord should be well stretched before use ; it should be dry — for damp increases elasticity — and as short as possible; the pull should be straight and regular without shaking or vibration. Fid. 94. Fig. 9B. 69 ENGINE TESTS AND BOILEE EFFICIENCIES Brum worhed by Non-flexible Bod. The two figures shown above illustrate the difference between diagrams obtained when the drum is actu- ated with a cord and with a non-flexible medium. Fig. 94, which was obtained with a cord susceptible to vibrations and somewhat elastic, gives a less regular curve than Fig. 95 taken with the rigid methods shown on page 14, Figs. 18 to 21. 70 B CHAPTER V The Study of Diacjrams The Diagram.. EFORB taking a diagram, admit steam to the indicator for a short time in order that it may become heated to the same temperature as the steam, then shut the steam cock, which action opens the indicator to the atmosphere, and trace the atmospheric line. Then open the cock again, admitting steam, and if the object is to ascertain the effect of the cut- off and expansion in the cyKnder trace one diagram ; but if it is to ascertain the mean horse power take several. At each test note — 1. The constant factors, such as the dimensions of the cylinder of the valves and steam and exhaust pipes and clearance spaces; the scale of the spring and the length of the diagram, and if it has been traced at slow speed. 2. The variable factors, as they exist at the moment when the diagram is taken, namely, the steam pressure at the boilers, the vacuum, the number of revolutions of the engine ; indeed all the conditions under which the engine is working and the test made. 71 ENGINE TESTS AND BOILER EFFICIENCIES In all the following diagrams, a e (Fig. 96) is the atmospheric line traced by the pencil before admission of steam ; o x the line of absolute vacuum, traced below the atmospheric line at a distance equal to 15 lbs. on Notify' y-^eTTHvi Fig. 96. the scale of the spring. Strictly speaking this should be 14-7 lbs. for a barometric height of 29'9 inches. The line o 7/ at right angles to o .(; lies at a distance v' from the origin and represents the waste spaces in the cylinder which are filled with steam, and which do no useful work. « Each diagram is divided into six periods, namely : Forward travel. 1. Advance admission. 2. Admission. 3. Expansion. 4. Advance exhaust. 72 THE STUDY OF DIAGRAMS -r, , T , ■■ ( 5. Exhaust or vacuum. xJackward. travel. { „ ^ I 6. Compression. In actual practice the diagram shown theoretically hj A B D ef g (Fig. 96) is much modified, following more closely the shaded outline, the reason for which we wall proceed to explain. Advance Admission. This is the extent to which the valve is open and admits steam when the piston is at the end of the stroke, its effect being : 1. To take up the play in the connecting rod bearings at the commencement of each Fig. 97. stroke. 2. To allow of the full pressure of steam acting on the piston at the commencement of the stroke. Compression has the same effect; therefore when there is considerable compression there need be less advance of admission and vice versa. If the advance admission is well designed the line of the diagram and a coincide at the commencement of the stroke. The small oscillations which are almost always apparent at the top of this line are caused by the impulse of the piston, and vary in greater or less degree as the spring 73 ENGINE TESTS AND BOILER EFFICIENCIES is flexible or the reverse. The advance admission is too great in the case of A (Fig. 97) and there is none in that oi B ; it is insufficient in the case of C (Fig. Fig. 98. 98) ; and in that of D admission is late. The dotted line shows the late admission after compression. Compression partly counteracts a late advance admission and the indicator diagram is the only way in which one can see whether the advance admission is suitably adjusted. Ba;pid Action of the Steam. The time taken by the steam to attain its maximum pressure within the cylinder can be found by cutting \ -, ',' . k ^ ^ V > ^^^-r^X^r ^',^^-v\ \^ S'.^VV^\\' Fig. 99. off all advance admission and giving the paper drum a movement proportional to that of the crank. In this way Mr, Vidmann obtained Fig. 99 on a Oor- 74 THE STUDY OF DIAGEAMS liss Engine running at a speed of 60 revolutions "with no advance admission, from which we see that Tm = Ts = 0'055 second, the time taken by the steam in this case to reach its maximum pressure. Duration of Admission. If the full pressure of steam is on the piston from the commencement of the stroke, and if the area of the pipes leading to the indicator is sufficiently large, the admission line will be practically horizontal and identical with A B (Fig. 96). The pressure in the cylinder is less than that at the boiler. The fall in pressure increases with each de- gree of moisture in the steam. It is less marked when the steam pipes are short and straight, and the lower the speed of the steam in the pipes. The size of the pipes is usually calculated for a movement of steam along them at the rate of 100 feet per second. The amount of condensation on admission depends upon the extent of the walls of the cylinder, their tendency to conduct heat and the difference between their temperature and that of the steam. Where the valves and piston rub on the walls of the cylinder their natural conductivity is lessened owing to the lubricant upon them. And the same is the case with other parts where the grease or oil finds a bed. Condensation goes on until the walls of the cylinder have attained the same heat as the steam ; and is least in the case of non-condensing engines and those working without expansion. To show the amount of condensation arising from extreme differences of temperature, let us take the 76 ENGINE TESTS AND BOILER EFFICIENCIES case of steam at 6 atmospheres, where t = 320° F. If the free exhaust takes place at 1'2 atmosphere, for instance, then t' = 222°, t-t' = 98°. Suppose that it is a question of heating 50 lbs. of cast iron having a specific heat of 0'14. The heat needed will be 98 X 50 X 0-14 = 686 B. T. U. But 1 lb. of steam at 6 atmospheres contains latent heat equal to 888 B. T. U. The weight of condensed steam will therefore be Ml = 0-76 lb. nearly. For any given engine the proportion of steam con- densed to that used effectively decreases with increased admission and number of revolutions. Speed is here an important factor. Enormous waste takes place in the case of low speed engines without lagging, and the waste is often greater in such cases where there is expansion than where there is none. In his book on screw-propelled steamships. Admiral Paris relates that the Roland, steaming without ex- pansion, developed 550 HP. with a coal consumption of 7"98 lb. per HP. hour, whereas with a 0*4 cut-off the same engines only developed 201 HP. with a con- sumption of 8'8 lb. of coal per HP. hour. With con- densing engines showing the same defects it has even been found more difficult*to obtain a vacuum when working with expansion than without. Clark, in his experiments with locomotive engines, has shown that with cut-offs equal to 12%, 30% and 74% the condensation has amounted to 42%, 24% and 11% of the weight of steam admitted to the cylinder. 76 THE STUDY OF DIAGRAMS Condensation is reduced by lagging and specially by- steam jacketing. The speed of the piston increasing from the com- mencement to half stroke, if the area of the inlet is not large enough, the line of admission falls (Fig. 100). Fig. 100. This is called wiredrawing. Slide valves gradually closing the ports cause wiredrawing towards the end of the period of admission ; and the line of the dia- gram takes the form shown at 1 and 11 (Fig. 101), FiC4. 101. where it is seen that admission only completely comes to an end at 2 and 22. At the highest speed (14 revolutions), and with ports wide open the pressure falls on admission and rises 77 ENGINE TESTS AND BOILER EFFICIENCIES when exhausting (owing to insufficient area), and the effective work is only equivalent to that part of the diagram which is shaded. The loss from wiredrawing with ports wide open and gradually closing is shown for a similar cut-off by the triangle A B n (Fig. 96), which represents the difference between the theoretical and actual diagram. The work done per pound of steam is independent of wiredrawing. Steam pressure practically varies inversely in proportion to its density, and the power given out at full pressure being equal to the volume multiplied by the pressure, that of 1 lb. of steam is, for an equal degree of expansion, independent of the initial pressure. This would be truly the case if there were no compression, but the power given out in effecting compression is part of the total power, and is greater in proportion as the initial pressure at ad- mission is less. It is therefore important to have the pressure high on admission and to vary the power by altering the cut-off. In accordance with the proper- ties of saturated steam, the pressure decreased by wiredrawing sets free a certain quantity of heat which produces superheated steam. Thus partial evaporation of such water as has found its way from the boiler may be effected by the steam being wire- drawn. Expansion. In the theoretical diagram (Fig. 96) expansion com- mences at B, but in practice expansion begins with the first narrowing of steam inlet, and this is termed for- 78 THE STUDY OF DIAGRAMS ward expansion, the full expansion only commencing at n when the steam pressure has become reduced by wiredrawing. There is, therefore, during the closing of the valve a loss of horse power over and beyond that shown hj A B n. It is often difficult to ascertain where n, the commencement of expansion, is really situated ; for it is the turning point between the curve of wiredrawing and that of expansion. After n. As the piston moves forward, the pressure falls, following a different law for each engine, and de- pendent upon its structure and the nature of work it is doing. Mariotte's (or Boyle's) theoretical pressure curve Fig. 102. is in the form of a hyperbola, which as a general principle may be taken to be fairly correct. After the steam is cut off it still condenses in the cylinder if the walls are not hot enough and the curve follows more or less the form of a hyperbola, but soon, owing to partial re-evaporation, the curve rises and continues at a higher level than that of Mari- 79 ENGINE TESTS AND BOILER EFFICIENCIES otte to tlie end of the stroke. The diagrams (Fig. 102) taken on the engines of the Miclidr/riv, at different speeds, show very clearly the value of this re-evapora- tion. Sometimes the actual curve rises apparently from the very commencement of the cut-off. At first, as Mariotte's law was considered to give the exact expression for the expansion of steam, this rise in the diagram was attributed to leakage of high pressure steam into the cylinder ; but as no accuracy in the construction of the valves made any difference, it was gradually recognised that some of the water condensed on the admission of steam becomes re-eva- porated during the fall of temperature under expansion, owing to its own latent heat and the heat transmitted to the cylinder walls during the admission of steam. Re-evaporation ceases before all the condensed water has been turned to steam again, and the curve falls in consequence, showing a fall in pressure. Re-evapora- tion is never complete. A certain amount of water remains in the cylinder, and being driven back by the return stroke whilst the steam exhausts, tends to decrease the heat of the steam admitted at the next stroke. ~ In the case of locomotive engines, the curve of the forward end of the cylinder is always lower than that of the back end, owing to the cooling of the cylinder end, which meets the wAd. Only by study of the diagram can one fix upon the most economical cut-off for any given engine, namely that which shows at the end of the stroke the minimum pressure which is able to overcome the friction of the engine. 80 THE STUDY OF DIAGRAMS Expansion in the Case of Two-Gylinder Engines. The work given out by steam is tlie same for two cylinders as for one, but it is more economical to use two, for then the high pressure cylinder is not in direct connection with either the outer air or the condenser, and high pressure steam does not pass direct into the second cylinder ; the extremes of temperature are less, therefore, in each of the two cylinders than in the one, and the amount of steam condensed on admission and during expansion is less. This is more noticeable in a compound engine fitted with a steam reservoir. In the case of an ordinary compound engine, there is pressure of steam on both pistons at the end of the stroke ; whereas in the case of the compound engine fitted with a steam reservoir, the steam exhausts into this reservoir from the high pressure cylinder and is re-admitted to the low press- ure cylinder again as though direct from a boiler; with the result that, assuming a constant pressure in the reservoir, the back pressure on the exhaust steam from the high pressure cylinder will be constant, so that all things being in other respects equal, the difference of pressure, and therefore extremes of tem- perature and consequent condensation in the high pressure cylinder, is, where a steam reservoir is used, less than in the case of a high and low pressure cylin- der directly connected with one another. Steam Jaclceting. The steam jacket was invented by James "Watt. Its efficiency has often been questioned, but the best engine builders have recognised its value. 81 G ENGINE TESTS AND BOILER EFFICIENCIES The steam jacket which encloses the whole cylinder has the effect of keeping the internal walls of the cylinder as nearly As possible at the same temperature as the steam admitted to the cylinder; condensation is therefore reduced to a minimum and the curve closely follows that of Mariotte. The jacket is only kept hot in effect by the con- densation, within the jacket, of a certain amount of Fig. 103. steam. This water must constantly be discharged by means of blow-off cocks, or better still, pumped back into the boiler. This water does not re-evaporate and does not therefore rob the walls of the cylinder of any other heat. Care must be taken that none of the water from the jacket can get into the cylinder through the steam pipes. The greater the extremes of temperature of the steam the more important it is to steam jacket the engine. Steam jacketing is of great importance in 82 THE STUDY OF DIAGRAMS the case of condensing engines, and in cases where there is a wide range of expansion within one cylinder. It is of less importance in the case of two cylinder engines with little expansion — especially as regards the high pressure cylinder. Steam should be able to circulate in the jacket. Air will be driven out of the jacket equally well by blow-off cocks below the cylin- der, as the density of air is at all temperatures greater than that of steam ; but all air must be driven out in order that the hot steam may everywhere be in direct contact with the cylinder. Fig. 105. Mariotte's Curve (Fig. 104). Mariotte's law,^ which states that the pressure of steam varies in inverse ratio to its volume, may be graphically represented by a hyperbola. This law states that : P F= constant. ^ Generally called Boyle's law in this country. 83 ENGINE TESTS AND BOILER EFFICIENCIES Let V represent waste spaces, then G being the space traversed by the piston, + V is the volume at the end of the stroke (F). F„ (Fig. 96), the volume of steam on admission, includes V. From the above, it follows that, if we take the abscissae as representing volumes equal to 2, 3 and 4 times V^, the corresponding ordinates will be equal to I, ^ and ^ the initial pressure p at the commencement of expansion — and in this way as many points as desired may be found and a curve drawn. Diagrammatic Representation, From G (Fig. 104) representing the pressure G c=p at the commencement of expansion, draw the hori- zontal line G D parallel to o x. If, at a point F, corresponding to volume V, we rule a vertical line Fj and a diagonal F o, this latter cuts C c at a point g, which, carried to join F f at h, gives a position on the curve, for we have g e _o c P/ _ V The extreme point of the curve K may be found in the same way : -^ . ^ i G V p E x = i c=p, and jy^ = ^ = ~ • In this way any number of pomts on the curve may be determined. Again, if G (Fig. 105), the point at which the original volume V^ begins to expand, has a pressure j), draw the line o a = o ij=p andai=F^. The diagonal G b passes through o and forms two similar right-angled triangles. From b draw a line b h, 84 THE STUDY OF DIAGKAMS cutting a at cl and o x at g. Make g h = h d and h will be a point on the hyperbola. Moreover draw h h' parallel to o a; and g i and /t m perpendicular to o ,v. Clearly h' d=p and ^—j i h Th' or P V o v Advance of ExJmusL This should increase in proportion as the final steam pressure is high and the speed of the engine considerable, in order to insure the depression at the return stroke and the compression on the other side of the piston. In Fig. 106 the shaded parts oi A, B, and G represent Fig. 106. loss of work. In the case of^ the advance is too great — in that of B the exhaust is actually delayed, and the dotted line shows what the diagram would be if there were no advance of exhaust. G shows the least loss, and therefore the best degree of advance exhaust. The expansion curve often continues without show- ing any appreciable fall in pressure, even after the commencement of the exhaust, owing to the rapid re-evaporation of the water carried in with the steam, which may be suspended in minute particles or lie on the walls of the cylinder. 85 'ENGINE TESTS AND BOILEK EFFICIENCIES Exhaust and Bach Pressure. At the commencement of the back stroke of the piston the pressure falls in proportion to the con- densation, or the extent to which the steam is free to exhaust into the open air. This back pressure is greater when the escape ports are not of sufficient area or when the exhaust steam is employed to heat the feed water. At the commencement of exhaust, the water which is held in suspension in the steam, or lies on the walls of the cylinder, evaporates rapidly, especially in the case of condensation, as it takes up the heat from the walls of the cylinder. The pressure is therefore higher than it would be if it were merely the pressure to which the steam had fallen by expansion. But if the temperature of the water of the cylinder has already fallen owing to a long period of expansion and small admission of high pressure steam, all the water cannot re-evaporate, and a certain quantity accumulates in the cylinder at each stroke. This is the cause of the knocking which happens in many cylinders, and which can only be got rid of by keeping the blow-off cocks constantly open, and is one reason why it is a good thing to have the exhaust valve chamber underneath the cylinder. It also shows the disadvantage of having much expansion in the case of locomotive engines. In the case of condensing engines, the back pressure is from 0"10 to 0'15 of an atmosphere — equal to 3 to 4"o inches of mercury, whilst in non-condensing engines it reaches from I'lO to 1*20 of an atmosphere. 86 THE STUDY OF DIAGRAMS Back pressure is greater when the steam is wet. According to Clark, with constant piston speeds it is proportional to the pressures at the end of expansion, and with constant pressures it is proportional to the squares of the speed of the piston. Gompressioii. As soon as the exhaust ports close (Fig. 107) the steam which remains in the cylinder is compressed Fig. 107. by the piston ; its pressure rises, following a regular law as in expansion, owing to the exchange of heat between the steam which becomes heated by com- pression and the water and walls of the cylinder, and the exact reverse takes place to what happens under expansion. It seems, therefore, that the curve of the diagram should lie below that of Mariotte. The work taken up during compression is given out 87 ENGINE TESTS AND BOILER EFFICIENCIES again on the return stroke either in power or in heat. For any given horse power, therefore, the diameter of the piston should be a little larger if there is com- pression than if there is none. But the advantages of compression outweigh this disadvantage. In the first place, the temperature of the steam, rising under compression, causes the water in suspen- sion and that on the walls of the cylinder to re- evaporate, and so decreases the condensation on the next admission of steam. Secondly, the steam compressed in ' the neutral ' space beyond the travel of the piston actually effects an economy in the expenditure of steam, as the in- coming steam has not to fill this amount of space, but only that through which the piston travels. Thirdly, the gradual resistance offered to the piston by this compression forms a buffer, and by keeping the moving parts of the connecting rod, etc., always pressed together, counteracts their natural inertia, and lessens the shock at the change of stroke from one direction to another. With compression the advance admission may be reduced. The larger the amount of waste space in the cylinder, the sooner should compression begin. This is adjusted by the slide valve. It is difl&cult to determine what degree of compression is the most economical. If it is admitted that the work given out in compression is equally restored during the return stroke or in heat, the highest economy will be effected when the pressure of the compressed steam is equal to the pressure of the fresh steam from the boiler. THE STUDY OF DIAGRAMS Let V be the waste space and ^ the compression at the end of the stroke ; F„ the volume of steam and p' the amount of compression at the moment when com- pression begins ; then according to Mariotte's law v+v p=p v If ]) be greater than p' the slide valve will be lifted ofE its face, and to prevent this the clearance space must be increased. The most economical amount of compi-ession can be judged better from a diagram than from any number of calculations. The Compression Curve. Accepting Mariotte's law and knowing the point a (Fig. 108) where compres- sion begins, draw the hori- zontal line a b and the ver- tical line a c. If from any point m on a c we draw the horizontal line m n and the diagonal m 0, the last will cut a b at a point d, a vertical line through which will cut m n in the point e, which lies on the required curve ; and the bisector of the angle y o x is the axis of the hyperbola on which all the points like e lie. To find the Amount of the Clearance Space. Draw any line, cutting the curve (Fig. 109) at two points ft b, and suppose that it cuts o a; at c. 89 Fig. 108. ENGINE TESTS AND BOILER EFFICIENCIES If we make b d = a c, the point d will fix the position of the ordinate o y, the distance of which from the diagram nb=m c=V' the waste space. and ^^=!!L^« or ^'=^?^ b q q c p q c but the right-angled triangles d n b and a m c are Fig. 109. equal, therefore n b = m c=V' the volume after com- pression, and q G = o m= Fthe volume before compres- sion ; therefore ^^ = _^ 2? F From this we arrive at another method of tracing the curve. When we know o x, o y and the point a where compression begins, we have only then to rule oblique lines through a, and, starting from o y, make them the following lengtl^ : d b = a c, d' b' = a c', d" b" = a c", etc. Expansion in Compound Ttuo Cylinder Engines. The amount of horse power given out in these engines is the same as in the single cylinder engine, 90 THE STUDY OF DIAGRAMS but the economy in steam is greater. As the high pressure cylinder is neither open to the air nor to the condenser, and as steam cannot enter the low pressure cylinder direct from the boiler, the extreme differences of temperature in the cylinders is less, and consequently condensation on admission and expansion is reduced to a minimum. Diagrams tahen from a Compound Engine (Figs. 110- 112). These are taken from the high pressure cylinder and the low pressure cylinder of a compound engine with a steam receiver between the cylinders — the indicator being fitted with different and suitable springs. In order to compare the expansion with that which would take place in a single cylinder, following Mariotte's law, the volume and steam pressure in each must be reduced to the same scale. The important dimensions in this case are as follows : Diameter of high pressure piston =11*2 inches. „ low „ „ = 18-9 „ „ piston rod in both cylinders = 2'2 „ Travel of each piston = 18'9 „ Ratio of high to low pressure cylinder ... ... 1 to 2-84 The baseJines of the diagrams (Figs. 110 and 111) are divided into ten equal parts. Draw the line of volumes X (Fig. 112) and the line of pressures Y. From mark off distances to re- present to scale the volumes of the low and high 91 ENGINE TESTS AND BOILER EFFICIENCIES pressure cylinders, and on these new bases replot the two diagrams (Figs. 110, 111), using the same scale of pressures for both curves. Then trace Mariotte's curve, starting from the point ^ .9 ^ o a \ h. S\ ^ i \ 6 \ / 1 £ \ /4I / - / \ M ' M i ' i ^/^ * « rr^ i yi So r« where expansion commences in the high pressure cylinder. The piece of the high pressure diagram which over- 92 THE STUDY OF DIAGEAMS laps Mariotte's curve represents the work done by re-evaporation. The fall of pressure between the two cylinders is found by measuring the difference between the ordinates at the half exhaust of the H.p. cylinder and the admission to the L.p., the crank being at 90 degrees. Diagram talcenfor a Gompound Engine without Intermediate Steam Receiver. If the diagrams of a compound engine without intermediate steam receiver are reduced to one scale of Pig. 113. volume and pressure as in the preceding case, the diagrams obtained are as shown in Fig. 113. Diagram taken with a Triple Expansion Engine. Proceeding as in the above case, we get the diagram Fig. 114 93 ENGINE TESTS AND BOILER EFFICIENCIES r Fig. 114 Causes of Errors in Diagrams. ' One cause of error arises from the paper drum ; for instance, if the tracings are not in true proportion to the piston travel, or if the impulse imparted to it causes an elongated diagram. Another fact to be remembered is that it is essential to take diagrams at each side of the piston. On one side the diagram is sure to show better results than on the other. Duplicates of diagrams, traced by hand, should never be trusted. The exact position of the atmospheric line can only be made sure of when it has been traced by the indicator itself. 94 THE STUDY OF DIAGRAMS Vakious Applications oi? the Indicator. To Fix the Point of Admission. Mr. Glraham has emjDloyed the indicator to trace diagrams of which the ordinates are proportional to the steam pressure, but of which the abscissae are proportional to the travel of the slide valve. Having taken the diagram A G (Fig. 115) on one Fig. 115. side of the cylinder, the drum was connected to the slide valve rod, and the diagram a bed e was obtained. Point a is where admission begins, and corresponds to A. Pressure rises up to b at the same height as B, then on the return travel of the valve it falls as the ports close. Point c is on a vertical line drawn from a, where the ports close ; it fixes definitely G as the point where expansion begins. The length d'd = s represents, on a definite scale, the travel S of the valve, and on the same scale the maximum amount of opening of the port. The actual opening of the port to admit steam is then —x 8. s 96 ENGINE TESTS AND BOILER EFFICIENCIES The dotted diagrams are similar ones taken on the other side of the piston. The distance a a' is equal to double the external lap supposed to be equal on each side. The vertical line drawn midway between a and a' will give the points m and m', which, if there is no internal lap, will determine at once the points n and n' which mark the commencement of the exhaust. If the valve has internal laps r and /, and external laps B and B', we can determine the points m and m! by drawing a vertical line distant from a' by a length B + r, and another vertical line distant from a' by the length B' + /. The indicator may be fixed on any portion of the steam system where the pressure varies during the stroke. 1. On the boiler if the position of the engine allows of it. In this case the indicator drum is worked by a brass wire. The changes in pressure in the boiler, at each stroke of the engine, can be noted. When these variations are considerable the result frequently is that water is forced into the steam pipes. Such variations in pressure are generally found in the cases of boilers whose steam-raising capacity is too small for the requirements of the engine which they feed. 2. On the Steam Chest.-gin comparing the pressures shown by the indicator, first at the boiler and then at the cylinder during admission of steam, the fall of pressure caused by the fiow through the steam pipes and the valves into the cylinder can be determined. Diagrams 1, 2, 3, 4 (Fig. 116), borrowed from Mr. Porter's work, were taken from the steam chest of an 96 THE STUDY OF DIAGRAMS Allen engine running at a speed of 200 revolutions per minute. From the moment when the ports open at the dead points a, the pressure falls more or less to h, where they close. The pressure then rises owing to the inertia of the moving column of steam, and falls again towards a. In diagram 2 the admission is shorter, and N'12 pj?* Fig. 116. the pressure rises less than in the former case after the closing at h. The reverse is the case in diagram 3 : the pressure falls from a to & in proportion as the speed of the engine increases. At h the flow of steam is most rapid, and the pressure rises rapidly. The result of this is a marked fall in pressure at a. The variations in pressure resulting from the inertia of the column of steam increase with th@ revolutions 97 s ENGINE TESTS AND BOILER EFFICIENCIES of the engine and the speed at which the valves close. If the steam pipes from the boiler are long, or if a pressure regulator is used between the boiler and the engine, it is advisable, in order to lessen the loss of pressure, to fix a steam reservoir close to the engine of an area equal to that of the cylinder itself. Diagram 4 shows how the changes in pressure are lessened by the use of a steam reservoir. 3. On the Exhaust Pipe. — The indicator shows, especially in the case of non-condensing engines, how much of the back pressure is due to cushioning and how much to the exhaust pipe by comparing the pressures obtained with those inside the cylinder. 4. On the Condenser and on the Air Pump. — The in- dicator shows the amount of vacuum in the one case and the horse power used in the other. The Indicator Applied to Hydraulic Machinery. The indicator has been applied to pumps, to high pressure water pipes serving hydraulic lifts, etc., and to hydraulic riveting machines. "We can only here indicate the modifications neces- sary for very high pressures. The springs for these high pressures are difi&cult to make, and it is preferable ti proportion the area of the piston to the pressure which it is desired to measure, whilst using any springs one may select. In the indicator shown in Fig. 117 (made by Dreyer, Rosenkranz & Droop) the lower portion, P, forms the cylinder of reduced area, the plunger K and the spring 98 THE STUDY OF DIAC4RAMS are mounted on a specially constructed rod. In some cases the small cylinder E is used as shown. If four springs are used to cover a range of pressure of from 2 to 1-5 atmospheres on a plunger of 0'8 inch, the pressures which can be measured will vary inversely Fig. ll"; with the areas. The following tal)]e gives these pressures in the case of two pistons of 0'5 inch and 0'35 inch diameter : — Diameter of pistons in inches. 0-8 0-5 0-35 Ratio of Areas. 1 f- i Limit of pressures in lbs. per 30 75 180 square inch. 75 187-5 450 120 300 720 225 655 1350 99 CHAPTER VI. The Testing op Gas and Oil Engines. A SIMILAR diagram to that given by the steam engine may be taken from a gas engine, the diagram showing the force of the explosion, varying as it does with the degree of air in combination with the gas, petroleum, benzoline, etc., and the proper amount of compression. The area of the diagram is the measure of the horse power for any given cycle. The diagrams (Pig. 118) are taken from an engine Otto Gas Engine using pure gas. The curve A is taken with the minimum amount of air requisite to give the best result. B and G show successively larger proportions of air. 100 THE TESTING OF C4AS AND OIL ENGINES ]\[(ttlldt\'< Ri'iiistfflnil I liilirdfor, iilJlih' hij I', (tdflivr. The diagram gives one cycle only, wliicli is not Fui. 119. Fid. 120. enono'h to "-ive a correct record of the work of a gas en gine, as successive explosions differ from o ne lot ENGINE TESTS AND BOILER EFFICIENCIES another. Mathot has devised the following way of getting over this diflB.culty : — ■ To the ordinary indicator (Figs. 119 and 120) is added a second paper drum T carried on B, which is clamped to the base of the ordinary drum by the hand- tightened nut 0. This drum T is actuated by clock- work, the speed of which is controlled by a special regulator. At each complete revolution of T the paper must be renewed. In order to obtain a diagram showing successive explosions or the ordinary closed diagram, the drum T or the ordinary drum may be brought into position under the pencil. In the case of the continuous registering indicator, the paper, which is in one long strip rolled up within a drum is drawn ofE into a second drum by the action of clockwork. Conditions necessary for Testing. Analysis of Diagrams. With regard to the working of these indicators we cannot, in our opinion, do better than quote the words of the inventor. There are many considerations to be taken into account, and the method employed varies in respect to which particular phase of the cycle it is desired to study. I. — To find the AmcMmt of Compression. Use a medium spring, of which the full play corre- sponds approximately to the maximum amount of compression, in order to obtain a curve on as large a scale as possible. The usual practice in the testing room is to drive 102 THE TESTING OF GAS AND OIL ENGINES the engine, light, by means of an electric motor, at varying speeds. The compression of the mixture of gas and air in the cylinder decreases as the number of revolutions of the shaft increases, owing to the resistance set up in pipes and valves, which resistance increases in proportion to the speed. Fig. 121 shows portions of two tracings, taken in different tests. Tig. 121. A. Speed of engine, 950 revolutions ; compression, 71 lbs. per square inch. B. Speed of engine, 1,500 revolutions; compression, 63 lbs. per square inch. Hence there is a drop of pressure of 11 '5 per cent. II. — To measure the Resistances to Admission, and Exhaust (Figs. 122, 123). We will show first the effect of the tension of the admission valve spring and of the area of the valve ; and then the effects of the area of the exhaust valve and of the length and shape of the exhaust pipe. Use a very light spring, the extent of play of which can be regulated by a pin, so as to obtain, on a relatively large scale, the depressions and resistances 103 ENGINE TESTS AND BOILEE EFFICIENCIES whict are respectively indicated by the curve corre- sponding to them, whether below or above the atmospheric line. 180 lbs. Fig. 122. A. Fig. 122. Tension of the inlet valve, 2-09 lbs. ; resistance to intake, -f atmosphere. B. Fig. 122. Tension of the inlet valve, 4-18 lbs. ; resistance to intake, f atmosphere. Fig. 123. A. Fig. 123. Exhaust into a trap ; resistance to exhaust, f atmosphere. B. Fig. 123. Exhaust into open air ; the exhaust pipe and trap being removed, the resistance to ex- haust is nil. One may assume that the amount of depression shown by the tracing is partly due to the inertia of the spring and the registering apparatus, as the spring is slackened abruptly on the opening of the exhaust valve. 104 THE TESTING OF GAS AND OIL ENGINES III. — To Govipare the Mean Pressures of Explosions hy means of Ordinates in Juxtaposition (Pig. 124). Use a strong spring, and adjust the speed of the paper drum so as to obtain ordinates corresponding as nearly as possible to the explosions. J. Fig. 124. Pure alcohol, explosive force from 400 to 450 lbs. per square inch. B. Fig. 124. Carburetted alcohol (electrine), ex- plosive force from 450 to 480 lbs. per square inch. C. Fig. 124. Essence of petrol (stelline), explosive force of from 480 to 530 lbs. per square inch. IV. — Analysis of the Cycle by means of open Diagrams representing Four Impulses. The speed of the engine from which the diagrams in Fig. 125 were taken was 1,200 revolutions per 450 lb. 300 lb. 150 lb. 'A Fig. 125. 106 ENGINE TESTS AND BOILEE EFFICIENCIES minute ; carburetted alcoliol was used ; maximum pressure of explosions, 425 lbs. ; mean compression, 64 lbs. ; pressure at the end of expansion, 21 '5 lbs., etc. Use a strong spring and let the paper move quickly over the drum. The four phases of the cycle will appear clearly, traced one after the other from right to left; that is to say, in reverse order to the unwind- ing of the paper, tracing an open diagram exactly showing the pressures at different stages of the piston travel. The tracing of the phases of the cycle is as true a record as if obtained by means of an indicator registering a closed curve. So far as concerns the reading of the diagrams, it does not matter if the movement of the paper is not rigidly in step with that of the piston of the engine. Efforts have been made to obtain open diagrams by means of registering apparatus in which the movement of the paper is actuated by the engine itself, but neither such apparatus, nor ordinary indi- cators, are suitable when the speed of the engine exceeds 400 revolutions per minute. V. — Analysis of the Effects of Inertia in the Indicator. Choice of 8pr%g (Fig. 126). Knowing the speed with which the explosions follow one another in engines used for propelling motor cars, it is evident that the effect of inertia of the various parts of the indicator must be visible on the diagram. The amount of these irregularities depends upon 106 THE TESTING OF GAS AND OIL ENGINES the weight of the moving parts and the area covered by them. The moving parts are the plunger and its rod, the spring and the lower arms of the parallel- ogram. The effect of inertia has been reduced to a minimum by keeping the weight down. The plunger is grooved out, all needless metal being cut away. The plunger rod is hollow and the lever arms are short and light. A Fig. 126. silver point, working on prepared paper, takes the place of a lead pencil, and light springs with small play are used. The interior of the cylinder above the plunger must be well oiled each time the spring is changed, and this oil at each throw of the plunger is splashed over the walls of the cylinder. If from want of precaution — particularly that of selecting a suitable spring — effects of inertia are produced, they are easily detected on the diagram, and need not be confounded with the curves repre- senting the phenomena in the engine cylinder. The cylinder of the indicator is kept cool by water circulating in a jacket. As the explosion chamber in the case of motor car 107 ENGINE TESTS AND BOILER EFFICIENCIES engines is very small, care must be taken not to sensibly increase it, or the working conditions will be altered. With this object in view, the indicator cylinder is so arranged that the plunger is no higher than the cock which shuts it ofE from the cylinder ; that is to say, there is no length of pipe leading to it. Diagrams taken with certain optical apparatus, in which the gases fill a long pipe of small section, show very considerable distortions. 108 CHAPTER VII. Mbasuee of Indicated H.P. Measurement of Mean Pressure — Trapezium Method. IF tlie line of the diagram undulates, a direct line must be traced, passing througli the middle of the undulations. This line is more true than the line of equal surface. If several curves have been traced, one over the other, a mean of them must be traced by hand. Fig. 127. This done, divide the diagram into ten equal sections by means of an apparatus (Fig- 127) con- 109 ENGINE TESTS AND BOILER EFFICIENCIES sisting of parallel equidistant rules, rising from a perpendicular base line, fixed by a set square ; then trace the mean height of each trapezium. The mean ordinate y^ is the arithmetical mean height of these ten sections. G-raham's screw (Fig. 128) gives y„, directly. It is constructed as follows : — a screw / tapped into the screw-nut e, carries at one end a disc whose circumference is equal to ten threads of the screw. Let e remain held in the hand without revolving, and trace over the ordinates of the diagram with the pointer d, the disc revolving as it rolls over the paper ; then it is clear that the distance a b will represent the mean ordinate j/^. Pig. 128. Again, the sum of the ordinates may be measured with a pair of compasses or a slip of paper. Having divided the diagram, measure the ordinates with a scale equal to ten times the scale e of the spring ; then add the various lengths together, and the sum is the mean pressure. In symbols. 102y lOe Another Method. In the case of very irregular curves, each trapezium 110 MEASURE OF INDICATED H.P. must be divided in 2, 3 or 4 equal vertical sections, and the mean heights taken, in order to arrive at the value of the area of the first trapezium. In Fig. 129 Fig. 129. the first trapezium is divided into two quarters and one half, the second and sixth are divided into one- third and two-thirds — then proceed as follows : — No. l,i(26 + 36) = 15-5 tenths of an inch i(31) = 15-5 „ 2,1(24) = 8-0 1(16) = 107 JJ 3, = 16-0 „ 4, = 11-0 J, 5, = 7-0 ,j 6,1(3) = 2-0 Sum of positive ordinates = 84-7 111 ENGINE TESTS AND BOILER EFFICIENCIES No. 6, i (1) = 0-3 , 7, = 3 , 8, = 6 , 9, = 7 , 10, = 6 Sum of negative ordinates = — 22"3. Therefore total sum = 62 "4. And therefore mean height = 6-24 tenths of an inch. The resultant positive difference (62'4) between the totals of the positive and negative ordinates must be divided by 10 (the number of divisions) in order to ascertain the mean ordinate of the diagram. Simpson's Method. Divide up the diagram (Fig. 130) into an even num- TiG. 130. ber n of equal spaces (the size of these being deter- mined by the degree of irregularity of the curves and the degree of exactitude required), Measure the ordinates y, yi, y^, . . . . y^. 112 MEASUEE OF INDICATED H.P. The mean ordinate is — ?/™ = L [y + ?/n + 2 (2/2 + 2/4 + • • • + yn-2) + 4 (^1 + 7/3 + . . . + ?/„_i)] Certain of the ordinates may, as in the case of y^ be zero, but this does not affect the formula. BemarJcs. Whatever the method employed, the result is more exact, although it takes longer to obtain, if the mean ordinate 1/^ of the upper curve and that ?/"m of the lower curve down to the line of absolute vacuum, be Fig. 131. taken separately, and the mean pressure found by the formula y^ = y'^ — y'\,. If y'^ and y"^ have been measured from the atmos- pheric line, 7/,„ = y'^ — y\ for non-condensing engines and y^ = y'^ + y\ for condensing en- gines. The first method — namely, taking the vacuum line as axis — is the more general, and there is less chance of error in confusing the positive and negative work when the diagram forms a loop. In the diagram Fig. 131 113 I ENGINE TESTS AND BOILER EFFICIENCIES the vertical shading sliows the area representing the positive work, and the obli(|ue sliading that represent- ing the negative work, the vacuum line being taken as axis. Amslers Phmimeter (Figs. 132, 133). This planimeter was in- vented in 1855 by Professor Amsler of Schaffhausen. As its name indicates, it measures the areas of sur- faces in one plane. By a slio'ht modification it can be used to measure the mean ])eight of a diagram. If the scale of the spring be differ- ent for extension and com- pression, we must measure separately the mean ordinate of that part of the diagram above the atmospheric line and the mean ordinate of the part below it. The paper upon which the diaofram is traced is placed on a smooth fiat sur- face. The distance apart of the points and (Fig. 132) are adjusted by moving the cursor along the bar until is nearly equal to 114 Fig. 132. MEASURE OF INDICATED H.P. the breadth of the diagram. The cursor is then clamped, and the final adjustment of the distance be- ween and is made by means of the tangent screw Fi«. 183. M. The zero of the wheel G is placed opposite its index / (Fig. 133), and the zero of the rolling wheel Fig. 134. D is placed accurately opposite the zero of the ver- nier E. The instrument is then placed on the plane in the 115 ENGINE TESTS AND BOILER EFFICIENCIES position shown in Fig. 134, and the needle point E of the movable arm is lightly pressed on the paper and is kept in its position by a weight placed on it. The pointer F is taken gently round the curve of the dia- gram in the same direction as the pencil of the indica- tor went. During this operation the rim of the rolling wheel D must constantly bear on the paper and must not move backwards or forwards over its edges. The point E therefore has to be carefully chosen. The pointer having made a complete circuit of the diagram, we read the numbers on the wheel Q, the rolling wheel D and the vernier E (Fig. 133). Suppose, for example, that the index J is between the 1 and 2 marked on wheel G, that the zero of the vernier points between 47 and 48 on the wheel D, and that the vernier reading is 3. Then the reading of the instrument is 147'3 and the mean ordinate is HF = 7-365. This may be in inches or centimetres depending on how the instrument is graduated. The number 20 is arranged by the maker's graduation of the instrument. Since the pointer F follows the trace made by the pencil of the indicator, no error results if the diagram is looped, as the reading of the instrument is propor- tional to the difference between the areas of the two portions of the diagram, and hence no correction has to be applied to the readmg in this case. Theory of the Planimeter. Consider the rolling wheel P in Fig. 185. Let its axis a c make an angle « with the line a b and make it traverse the line always keeping its axis parallel to its 116 MEASURE OF INDICATED H.P. original direction. When it arrives at b the wheel will have turned through exactly the same angle as if it had travelled first along a c and then along c b. From a to c its rotation would be zero, and from c to b there would be pure rotation ' with no slipping ; c b may therefore be taken as a measure of the rotation. Also c b = a b sin a. Suppose now that when the rolling wheel comes to b its axis is turned round until it makes an angle /3 Fig. 135. with a b. Now let it move back to a, the direction of its axis remaining fixed. The rotation in the opposite direction will be b d = a b sin /3. Therefore the effective rotation is a b (sin ^ — sin a). In Fig. 136 A and B are the two arms of the plani- meter, c the fixed point and d the tracing point. Let a d make with the line a b vi the angle /3. Draw an arc d f and let the angle f a m equal a, then keeping a f parallel to itself, move it into the position b g. Draw now the arc g e and finally move b g back to its initial position a d. 117 ENGINE TESTS AND BOILER EFFICIENCIES We have ab = de=fg and the area d e f g is equal to h' a b, -wliere h is the distance between the two parallel lines d e and / g. Now h = a d (sin ^ - sin a), therefore the area d e f g = ad x ah (sin /3 - sin a). If now we make the pointer follow the boundary d e g f d we see that during its passage from eto g the Tig. 136. rotation of the wheel is equal and opposite to its rotation when moving from / to d. From d to e the rotation of the wheel is prmDortional to a & sin /8, and from ^ to / it is proportional to a b sin a ; hence the total rotation is proportional to a 5 (sin ^ — sin a) and it is therefore proportional to the area d e f g. Suppose now that we have to measure the ariea ah m n (Fig. 137). "We can divide it up into a. series of strips whose boundaries are circular arcs traced by 118 MEASURE OF INDICATED H.P. the pointer of the arm B. By what we have just shown if we make the pointer move round a b c d a, the rolling wheel will register an amount proportional to the area of this element. In the same way we shall get the area of the second element by moving the pointer over ad ef g h a and so on. But we have seen that the path bee can be replaced by & e; hence, in conclusion, if we make the pointer travel Tig. 137. round the contour of the figure abemnha the reading of the rolling wheel will always be exactly proportional to the area of the figure. Planimeters can be marked so that they give read- ings in various scales. If the area is too large for the instrument we sub- divide it into several portions, find the area of these portions separately, and then their sum gives us the required area. 119 ENGINE TESTS AND BOILER EFFICIENCIES In special planimeters for indicator diagrams the arm B is made proportional to the breadth of the diagram, so that we can obtain the mean height directly. Mean Pressure. Whatever the method employed to determine the mean height of the diagram {y^), if & be the scale of the diagram, that is the deflection of the spring for 1 pound pressure per square inch of piston face, the mean pressure in lbs. will be given by e P = Uevolution Counter (Fig. 138). For slow speed machines we can count the number of revolutions per minute directly by means of a — 1/1 — IP JC © < o ^ o Fig. ^38. seconds watch. In general, however, the use of a revolution counter is more convenient. If counting a few hundred turns is sufficiently accurate for the test, then we can use a simple counter which is pressed by hand against the end of the axis 12U MEASURE OF INDICATED H.P. of the rotating shaft, and we count the minutes by means of a watch. The counter of A. Sainte (Fig. 138) is very convenient for this purpose. The triangular point is pressed firmly against the end of the axis of the shaft whose revolutions have to be counted. An endless screw causes the wheel which registers the tens to rotate, and a little pinion fixed on the axis of this wheel makes the wheel which counts the hundreds turn round. For a new reading we turn the zeros on each wheel opposite their indexes. To do this it is suflBcient to press the bridge supporting the first wheel with a finger, which puts the pinion out of gear and so both wheels can easily be set. When the pressure is removed it is brought back into gear by means of a little spring. For prolonged tests we use counters permanently fixed to the shaft. Galculation of the Indicated Power. Let p = the mean pressure of the steam in pounds per square inch on the piston face. ^ = the area of the piston face in square inches. D = the diameter of the piston face in inches. A''=the number of revolutions per minute of the fly wheel. L = the stroke of the piston in feet. 7 = the mean velocity of the piston in feet per minute. = 2NL. The indicated horse power will be given by the formula — 121 ENGINE TESTS AND BOILER EFFICIENCIES TTTP = ^PLAN ■ ■ ■ 33000 ^ U3OOO/ 9 TiA where F=|±^ = 0-0000606 LA and is constant for a given engine. We must be careful to take for A the mean of the areas of the two sides of the piston, deducting the space occupied by the piston rod. Example. Let Z> = 14 inches ; J. = 164 square inches. L = 4-5 feet; i\r=200. |j = 30-5 lbs. (found from the diagram). Then LH.P. = M^^ 33000 2 X 30-5 X 4-5 X 154 x 200 33000 = 266 Example of Compound Machine (Figs. 110, 111). Replacing p by -^ the formula becomes From the dimensions of the cylinders given in Chapter Y. we find — Front. Back. J. = useful area r H. P. cylinder 95 98 in square \ inches [ L.P. cylinder 277 280 122 MEASURE OF INDICATED H.P e = the scale of H.P. cylinder the springs used -r p pressure cylinder I vacuum 1 1 38-8 38-2 1 1 15-9 157 1 1 LA 33000e 16-3 16-1 H.P. cylinder 1-74 1-81 ("pressure 2-12 2-15 L. P. cylinder \ f, , „ o.ia •' (.vacuum 2"17 2uy Multiplying the last numbers by y^a -N where y^ is the mean ordinate found from the diagrams drawn in Figs. 110 and 111, and N is the number of revolu- tions given by the counters, we obtain the following numbers for the indicated horse power H.' The brake horse power H being determined also by one of the methods we shall describe shortly, we TT can find the efficiency i? = -=^ of the engine. JjL On no load H' = 6 and 17 = 0. ^. . , fl' = 561 frictional losses 1 r^ nm First trial ^ ,„ h o \ »? = 0-857 H=48 ) 8 J = 85-7% c T. . ijH'=69i frictional losses ) becond trial L > v = H=60j 9 ) ^, . , . . B^'=80] frictional losses \ Third trial ^^ gg I -^^ | »? = 86-3% For large machines in good working order we can assume that 1 lies between 80 and 90 per cent. For locomotives we assume that the useful power at the rim of the wheel equals 80 per cent, of the I.H.P. A knowledge of the approximate value of v enables us 123 ENGINE TESTS AND BOILER EFFICIENCIES to find roughly the brake horse power in those cases where a brake test is impossible. If the power expended on the piston be calculated (fli) instead of being deduced from the diagram {R') TT FT the ratio -^ is always less than — - and this ratio varies with the power of the engines as follows : Value of V for engines with ordinary expansion. Power 4-8 8-15 15-25 25-40 40-60 60-80 80-120 -1 5) 0-45 0-70 0-75 0-78 0.80 0-82 a- condensing 0-40 0-52 0-58 0-64 0-70 0-75 inon-condensing 0-45 0-52 0-60 0-65 0-70 0-75 0-80 Calculation of the Diameter of the Piston. The values of >] given at the end of the preceding paragraph enable us to calculate the diameter of the piston of an engine working under given conditions. We can determine p from the theoretical diagram. We have, if H be the brake and H' be the indicated horse power, H = >, E' 2pL X 07854I»^iV D- * pvri where v is the mean velocity of the piston in feet per minute. 124 33000 — n / 21000 a Il45 A / ^ ^ PLNr, ^ pLNri = 205 A / ^-^ MEASURE OF INDICATED H.P. Example. Suppose that we have to design a condensing engine which will satisfy the following conditions : ^=100 horse power. J9 = 30"l lbs. per square inch. ■z; = 360 feet per minute. »7 = 0"80 from the table given above. Hence D = 205 ^ 100 30-1 X 360x0-80 = 22 inches. Work done against Friction. This work is the difference H'-H between the brake horse power and the indicated horse power. The application of a brake to commercial engines is not always possible, and hence it is useful to be able to calculate it approximately. This can be done by the following method. Take the indicator diagram on no load, and calculate the work required to be given to the fly-wheel. When taking the diagram the engine must be disconnected from the external shafting. If there is still some gearing which the engine drives, the work done on it must be roughly calculated. The work done against friction measured in this manner must be a minimum value, for we have neglected the friction of the packing rings round the piston. Diagrams on no Load (Kg. 139). Although the diagram gives us the work done by the steam on the piston at no load, yet it is necessary 125 ENGINE TESTS AND BOILEK EFFICIENCIES to make sure that there is no leakage of steam round the piston. In order to do this we move the crank pin into its dead points before we admit the steam into the cylinder. Then, opening the cocks on both sides of the piston, we can make sure that there is no leakage of steam in the cylinder or in the pipes connected with it. In condensing engines we can find out if there is leakage by putting on the exhaust pipe a metallic rod, Fig. 139. the other end of which is held between the teeth. On stopping up our ears we can hear when there is no leakage, the steam going in jerks into the con- denser ; in other cases the noise is more prolonged , and the difference can easily be distinguished after a little practice. It is necessary also to keep the machine running at its normal velocity, and as far as possible to arrange so that the frictional pressures on the moving parts are the same as when th* engine is loaded, in order that the work calculated from the diagram may include all frictional losses. This condition cannot always be arranged in engines which have no variable expansion gear. 126 MEASURE OP INDICATED H.P. Inertia of the Flij-ivheel. When the machine is running at its normal speed of N revolutions per minute the steam cock is closed and the time {t) in seconds taken by the fly-wheel to come to rest is observed by means of a stop-watch. The angular velocity (w) of the fly-wheel initially equals — — - — and can be found. 60 The energy E in foot-pounds stored up in it is given by the formula: £/ = — o) 2 g where if is the mass of the fly-wheel in pounds, K its radius of gyration, and g is the acceleration produced by gravity, and it equals 32'2 in London. The aver- age power exerted by the frictional forces in stopping the fly-wheel will then be E '550 t In the above calculation we have neglected the inertia of the pulleys, gearing, etc. This could be taken into account by adding on to M K^ in the above formula, M^ K^+M.^ Ki + . . . where M^, M^ and E^, -S'j . . . are the masses and the radii of gyration of the other rotating bodies. The kinetic energy of rotating shafts is always very small, and can generally be neglected. The moment of inertia of the rim of a fly-wheel whose mass is M, and inner and outer radii R and r respectively, is : 127 ENGINE TESTS AND BOILER EFFICIENCIES The moment of inertia of the spokes of length I is r *3 where M' is their mass. Example. Suppose that the fly-wheel is making 60 revolutions per minute, and that it stops in 660 seconds when the steam is cut off. Let M =20,000 lbs. ; E = 10 feet ; r = 8 feet. ilf' = 6,000 lbs. ; Z = 8feet. We shall have / 2 ^ 60 Y \ 60 / 60 ' ''-'' .-. ^ = li^f^x 39-48 foot-pounds. = 1,084,000 foot-pounds. .•. Mean frictional horse power 1, 084,000 550 X 660 = 2-986. 128 CHAPTER VIII. Brake Horse Power. § 1. oedina-ry brakes. THE brake illustrated ia Fig. 140 was coastructed in 1821 by Prony. The power generated by the motor is expended in overcoming the friction of a collar placBd round a pulley, and the amount of the work done can be calculated from the force required to keep this collar in its place. Pig. 140. This brake can be applied to any motor whatever which produces a motion of rotation. The collar or chain of wooden blocks can be put directly on any convenient turning part of the shaft when we are measuring small horse powers. The 129 K ENGINE TESTS AND BOILER EFFICIENCIES brake is usually applied to the pulley of the motor. It is, however, convenient to have a special pulley which will fit any size of shaft. The large lever is placed preferably underneath so as to increase the stability, and a counterweight is added to it so that the centre of gravity of the whole may come directly underneath the axis. The oscilla- tions of the lever are limited to an inch or so by means of stops. If we place at the extremity of the lever (Fig. 140) an arc of a circle whose centre is in the axis of the pulley, the weight P will always act at the same distance L from the axis and the method will be more exact. The simple brake shown in Fig. 145 can be made anywhere. The two blocks of wood applied to the pulley are kept in position by two bolts which are joined above and below by iron bands. In Fig. 141 the brake band consists of wooden blocks, and it can be tightened by means of screws. The weight P is hung froii a hook fixed on one of the blocks. The friction is in this case distributed over a very large surface. For small horse powers the wooden blocks can be replaced by a copper band, which should be worked without the application of oil. 130 Fig. 141. BRAKE HORSE POWER Vertical Shaft (Fig. 142). The horizontal lever has a rope attached to its ex- tremity which passes over a vertical pulley and carries the pan for the weights. Sometimes, however, as in Fig. 142, the rope is attached to an oscillating triangle, which carries on one side the scale pan and on the Fig. 142. other a piston passing into a dash-pot P to prevent oscillations, and an index which moves along a scale E. V ' ^ _^T ■ ■ mm ' ■dl d"^ g — 1 ! m—.==p ^ '— — iir?s Fig. 143. The pulley can be covered underneath so that it forms a reservoir in which water can be kept circu- lating for cooling purposes. 131 ENGINE TESTS AND BOILER EFFICIENCIES In Fig. 143 another arrangement is shown. The pulley is provided with ribs in its interior, which are slightly inclined to the horizontal. "When water is poured from above the centrifugal force makes it flow outwards, and it is kept pressed against the rim of the wheel, where it descends step by step, keeping the surface cool. When the velocity is high the ribs can be horizontal, as the centrifugal force is sufficient to keep the water pressed against the rim. Procedure during a Test. The brake being mounted and the weight P being in position, we start the machine. The brake is gradually tightened by means of the nut a, which is on the side of least tension (Fig. 140). "We then increase or diminish the weight P until the brake is in equi- librium when the motor is running with its normal speed. "When the brake is working we can cool the surfaces on which the frictional forces are acting by means of a trickle of water containing about ten per cent, of dis- solved soft soap. To get a good solution soft water must be used. We employ also grease, lard, etc., or better, the more fluid oils, but they ought not to be used twice without being refiltered. The lubricant must not be altered during the trial, otherwise there is a risk of the friction becoming abnormal during the change, the brake seizing and the equilibrium being destroyed. The speed of the motor and the friction both vary during a trial. We restore a balance at the normal speed by screwing or unscrewing the nut a (Fig. 140) 132 BRAKE HORSE POWER and by altering the weight P. We can obviously also obtain the work done at various speeds, and so deter- mine at what speed certain motors — like turbines, for example — do their maximum work. If it is not necessary that the motor run at a fixed speed, and we obtain a balance by simply screwing and unscrewing the nut without altering the weight P, then the revolution counter will register the total number of turns made by the pulley during the test. In order to obtain a constant load it is necessary to maintain the temperature of the brake constant. We can effect this by regulating the flow of the soapy water. If this means is not sufficient, we can inject cold water into the interior of the pulley. This will in general reduce the flow of the lubricant. Volume of Water Beqvdred. The temperature caused by the frictional forces will be higher the greater the pressure per square inch of the rubbing surfaces. Each wooden block, there- fore, ought to press on as large a surface of the pulley as possible. A new brake always heats up more than an old one, because the surfaces of the blocks are not in such close contact with the pulley. The real surface of contact is less, and therefore the pressure per square inch is greater. The mechanical equivalent of heat being 778, a horse power will develop in an hour -^^x 3600 = 2545 B. T. U. //o 133 ENGINE TESTS AND BOILER EFFICIENCIES Suppose that t°F. is the initial temperature of the water and T is the temperature of the brake. Then if Q be the mass of water in lbs. required per horse power per hour — ^ _ 2545 ^~ T^t Example. Let ^ = 45° F. and T=95° F. then T-t= hO. Therefore Q is 51 lbs. or 5*1 gallons of water per horse power per hour. The least possible quantity of water required will be that corresponding to the total heat of evaporation of water at 212° F., i.e. 966 + 180 = 1146. Tj n 2545 Hence Q --^^^^^^ = 2'2 lbs. nearly. In practice it is necessary to use twice or three times the quantity of water calculated from the above formula, as all the water does not attain to the tem- perature of the brake. Calculation of the Brake Horse Potver. The weight P, including the weight of the scale pan, acts as if it were suspended by a weightless cord hung round a cylinder of radius L (Fig. 140). The balance being established and the speed uniform, the brake H. P. is given by the formula T w ^- H- ^- = 550 where T = the torque = P L foot-pounds, ft) = the angular velocity. 134 BRAKE HORSE POWER _ 2_7r N where N = the number of revolutions per minute. Therefore the 'IttPLN B. H. P. = 33000 and H = 0-0001904 PLN . . (1) if if stand for til e B. H. P. Mence also r = — f~\r (2) Knowing the speed of the engine (A'), the length of the lever of the brake (L) and the probable brake H. P. this formula will enable us to find P. If when the pulley is at rest the centre of gravity of the beam is not directly under the axis of the pulley (Fig. 140), a correction must be applied to the for- mula. Suppose, for example, that the weight of the beam Q' acts at a distance I from the vertical line through the axis of the pulley, then the weight Q, which, added to P, would produce the same torque, is given by — Q = Q'j^ It is also easy to [find Q directly. If the beam be supported by a round or angular bar placed under- neath it at the point where the vertical line through the axis of the pulley meets the surface of the beam, and if the end of it be supported by the pan of a spring balance, then the reading on the balance will give Q. This weight Q, which takes into account the weight of the beam itself, has to be added or subtracted from 135 ENGINE TESTS AND BOILER EFFICIENCIES P, according as the rotation of tlie pulley tends to raise or lower the beam. The formula (1) now becomes H = 0'0001904 {P + Q) LN (3) Calculation of the Dimensions of the Brake. Pulley. — The dimensions of this vary with the heat- ing, and this varies with the amount of the lubricant and with the quantity of water injected into the inte- rior of the pulley. It also varies according as the brake embraces the whole circumference of the pulley or a part of it only. Let D = the diameter of the pulley in feet. I = the breadth of the brake in feet. H = the horse power measured. K = the number of foot-pounds per second absorbed by the friction per square foot of surface. If the brake completely embraces the pulley, and if it is kept cool by the injection of water into the interior of the pulley, then we can use for large horse powers the following approximate formulae : — Dl= ^ovDl = ^ To find the number of foot-pounds per second ab- sorbed by a square foot of surface, we have — z X TT j> f = 550 ir. H Putting D I = -TK we find that K = 9000 approximately. "We shall see later that the Thiabaud brake (Figs. 148, 136 BRAKE HORSE POWER 149) absorbs nearly 15,000 foot-pounds of work per second per square foot of brake surface. When only a limited amount of water can be applied it is better to use the formulae — D Z = 3^ or D / = ^ The first equation gives K = 5400 foot-pounds. When the brake envelops the whole surface of the pulley and is cooled only by the lubricant it is necessary to make the pulley larger. In this case D I = zrjr OT D I = -Q Finally, if the brake envelopes only a portion of the surface of the pulley, it is necessary to still further increase its dimensions. For a given horse power the dimensions of the pulley are independent of the speed of the motor, as the frictional work per second on its circumference is the same at all speeds. Bolts. — In order to find the dimensions of the bolts we will consider the equilibrium of the upper block (Fig. 145). Screwing up the nuts increases the small elementary normal pressures p^ in pounds weight on the pulley rim, and these produce frictional forces /p„. 137 ENGINE TESTS AND BOILER EFFICIENCIES be tlie sum of the f rictional forces on the block. Since the brake is in equilibrium, we have by taking mo- ments for the two blocks — ^Fr = F L Also equating the work per second 2Fv = 550 JT, where ■?; is the velocity of the rim of the pulley in feet per second. Hence F = 275- V = 275-, ^ Nr 60 TT = 2600 ^7-^ nearly . . (4) Also taking/ = 0'2 we find that 2,,, = 13000 A^ .(o) We still have to determine the vertical resultant li. Considering one of the elementary normal pressures j9„ acting on an element ' a ' of the arc amb (Fig. 144), p^ is the vertical component, and ' c ' is the projection of ' a ' upon the chord c b. From the two right-angled triangles thus formed we get a G Therefore p« = - Pn f Hence ij = S — « a ^ 138 BRAKE HORSE POWER „ chord G h ' arc c Suppose the arc subtends an angle of 90 degrees at the centre of the pulley, then TT the chord a m h = t-D = 0-7854 D chord c b = diagonal of square = 07071 D 2 p^^ is therefore given by the formula 0-7071 // 11700 .(6) Fig. 145. Now writing the conditions for equilibrium, Q + Q' = B And taking moments I Q - I Q = F r 139 ENGINE TESTS AND BOILER EFFICIENCIES ••• Q- Q' = F~^ Hence Q = ^ {li + F~) (7) and Q! = ^{B - f'j) . . ■ ■ (8) Substituting the values of B and F from (4) and (6) in (7) and (8) and simplifying, we get approximately — Example. — Suppose that the ratio of if to iV is 2, that the radius of the pulley is 2 feet, and that / equals 2 feet 6 inches, we shall have Q 1250 X 2 (I . 2^) = 7,200 nearly. Supposing then that the working load on the tight bolt is to be 10,000 lbs. per square inch, we see that a bolt whose diameter at the bottom of the threads is one inch will be ample. The two bolts are, of course, taken of the same size. Beam. The weight P required in the given test which can be calculated a priori, en sillies us to calculate the sec- tion a X b oi the beam at the bolt Q. The bending moment = P (L~l) aW = B 6 B, the stiffness, being 120,000 pounds per square foot. 140 BRAKE HORSE POWER Example. Suppose that L = 10 feet, / = 2 feet, E = 100, and N = 60 Then from (2) „ 5250 H , . , , -T = — f~l\r~ = 1000 pounds weight nearly. If the breadth (a) of the beam is 8 inches, then its thickness b can be found by means of the above f ^ f^^ 72 6 x 10008 lormulae as follows : — fJ = loooOO x ^ 3 5' .-. b = 0-775 of a foot. ^ nine inches nearly. Detachable Brahe. This brake was constructed for the rapid testing of machines at the Dusseldorf Exhibition. The tightening of the brake can be done by means of an endless screw which acts on the slacker of the two bolts. This bolt is connected to the flexible band by means of a sys- tem of jointed levers which allows the brake to be rapidly put into or taken out of action. The extrem- ity of the long lever acts on the platform of a weighing machine situated in the horizontal plane passing through the axis. The reading of the weighing machine gives the total pressure, including the weight Q, due to the beam not being balanced initially. It is therefore necessary to find Q first of all, and then subtract it from the reading of the machine P, so as to find the P-Q of formula (3). The slacker of the two bolts works on 141 ENGINE TESTS AND BOILER EFFICIENCIES elastic washers, which ensures smooth runniBg during the trial. When the oscillations produced are too large, the apparatus can be completed by an hydraulic dash pot 142 BRAKE HORSE POWER consisting of a piston placed in water. So long as the movements of the piston are gentle the water has time to pass from one face of the piston to the other ; for jerky motions, however, the water offers a great re- sistance to the motion of the piston. A drawback to the use of this brake is the in- equality of the heating of the frictional surfaces. The upper block has a smaller surface in contact with the wheel than the lower band, and hence the pressure per square inch and the heating are greater than for the band. Societe Gentrale Brake. The faces of this pulley (Pig. 147) are enclosed by iron plates. Fig. 147. 143 ENGINE TESTS AND BOILER EFFICIENCIES The water coming from a high level reservoir flows by means of a central tube near the rim into the in- terior of the pulley, which it cools, and then flows out as shown in the figure. The brake is tightened by means of a nut operated by a wheel, and it works on the bolt on which there is the greater pull. It is necessary to put this brake on the extremity of the shaft of the motor, and this is not always possible. The Thiabaud Brake (Figs. 148, 149). In this brake, which is employed by the Italian Government, the water circulates in the pulley itself. The pulley, which is hollow, is divided into two parts, and is centred on the shaft (Fig. 148) by means of two V-shaped pieces of metal, which clutch the shaft and can be tightened by four nuts. The en- veloping brake is formed of two semicircles of iron fitted with wooden blocks. The lever consists of an iron rod, which can be fixed on the side which is the more convenient. The pull P is measured by a Roman steelyard, the end of which is fastened to the ground by a rod or cord q. The pulley has an interior channel a b, which is in communication during half a revolution with one of its junctions b, the other junction a being closed. One side communicates at c with an exterior opening d drilled in the pulley; the other side communicates with c' by means of the opening d'. The openings are covered by a collar e made in two pieces, which are fixed firmly to the brake by the gudgeon /, and it carries two tubes, o and s. If then cold water flows 144 BRAKE HORSE POWER through the tube o, it will alvfays penetrate by the opening d and the orifice r, notwithstanding the rota- C5^ 1 — r -«23^§^ Figs. 148, 149. tion of the pulley, and will come out by the opening rf' and the orifice c/ after having been carried round once. A thermometer enables us to read the temperature of the water coming out of the pulley. The friction 145 L ENGINE TESTS AND BOILER EFFICIENCIES of the collar e e is added to that of the brake, but the pull P takes this into account. The following results have been obtained with this brake : Diameter of pulley A in inches 12 15 18 22 Brake Horse Power 15 20 25 50 With the largest pulley — taking its breadth to be one-sixth its diameter — we find that the foot-pounds of work per second dissipated by a square foot of the surface of the brake are about 1 5,000. Carpenter^ s Hydraulic Brake (Figs. 150-152). The novel brake represented in Fig. 150 was in- vented by Professor Carpenter (see Engineering, January, 1894). The band of the brake which envelops the pulley is made up (1) of a simple flexible steel band a on which the f rictional forces act ; (2) of 146 BRAKE HORSE POWER a thin beaten copper tube h in which water is injected by a force pump ; and (3) of an exterior band of steel c made in two parts, which are fastened to the bars forming the lever of the brake. The brake is con- "W Fig. 151. Fig. 152. strained to oscillate within narrow limits. The high pressure water supply is led to the copper tube by means of flexible tubes, and it can be regulated by means of stopcocks. Since the diameter of the copper tube cannot vary, as it is pressed by the ex- terior steel sleeve, it follows that the effect of the hydraulic pressure is to press the interior face of the tube against the inner band, and so it increases the friction, and consequently the power absorbed. At the same time the circulating water carries away the 147 ENGINE TESTS AND BOILER EFFICIENCIES heat produced by the friction. It is in order to avoid the wearing away of the inner tube by friction that the flexible steel band a is interposed between it and the face of the j)ulley ; being prevented from turning, it has to support all the frictional we^r. The lever of the brake can act upon the little arm of a steelyard (Fig. 152) and the cursor can be moved by means of a screw. § 2. AUTOMATIC BRAKES. In these brakes once the adjustment is made the balance is maintained by means of the movements of th.e brake itself. Br alee tvith Spring Balance (Fig. 153). We add a spring balance (Fig. 153) in opposition to the spring in the ordinary arrangement. The Fi(!. 1B3. tension of the spring U adjusts itself corresponding with the equilibrium of the brake, and any excess is 148 BRAKE HORSE POWER measured by the spring balance q which is fixed to the ground. When the apparatus is in equihbrium the brake horse power can be calculated by adding to P the component due to q, Q being the weight re- quired to be added to P owing to the moment of the weight of the brake itself about the axis of the pulley. We have H= 0-0001904 {P + Q + qh LN If the friction increase owing to want of lubricant the brake is dragged in the direction of the arrow, but then the tension q increases and the point a is lowered, thus loosening the brake. Conversely if the friction diminish the brake is tightened. Oreuzot's Arrangement (Fig. 154). The clamping wooden blocks M (Fig. 154) each embrace a quarter of the circumference of the pulley. They are bolted to two iron bars which are connected at the back by two rods joined by a tension screw v which can regulate the distance apart of the blocks. In front the lower beam is connected to 6 in a similar manner, whilst the upper block supports the lever B at 0. This lever B is fastened to a spring at its other extremity q and carries a pan for weights p. Suppose, for example, that the point q is fixed, we see that the point o rises, the point h rises still further, and the brake tightens. On the other hand, if o falls, then h falls still further, and the brake is loosened. The bar of the lower block which forms the large lever of the brake is attached to a scale pan P by means of a cord passing over a pulley. Pure water 149 ENGINE TESTS AND BOILER EFFICIENCIES IS applied to the inside of the brake pulley and soapy water is applied outside. The spring q exerts a vertical force represented by q, and hence the tightening force on the brake equals a where p is the weight on the pan p. We see, if the rotation of the brake is in the sense ab^8" a=72" i=88" ^^^ •" Pig. 1B4. indicated by the arrowhead, that when P is too small the brake is turned round, B lowers, and thus q in- creases, and the brake being loosened, equilibrium is restored. If on the other hand P is too great, it tends to raise the brake and B; q then diminishes, and the brake tightens. In the trial runs of a Corliss Engine of 100 to 150 horse power, reported on by M. F. Delafond in 150 BEAKB HORSE POWER the Annales des Mines for 1884 the weight _p was varied from 176 to 726 lbs., whilst the tension of the spring varied from 22 to 220 lbs. The spring is measured and the tension q is indicated by a pointer which moves along a scale. In Fig. 154 is a tachometer which gives at each instant the speed of the pulley. "When we run a trial we first of all raise B ; this lets the machine start ; then we lower B and put weights on the pans P and p until the brake is in equilibrium at the required speed. Galculation of the Work. We first of all gauge the brake by putting weights on P until there is equilibrium. These weights have to be subtracted from the value of P observed during the trial in order to get the real value of P to substitute in the formula. Taking moments about the axis of the pulley we get Fr = PL + ql - pi' and for the work, 2xrAr 60 = 550 E ■: E = 0-0001904 {PL +ql-pl') N Amos or Appold Brake (Figs. 156-157). This brake is used by the Royal Agricultural Society. The two halves of the brake are joined in one place by a tension screw B (Fig. 155), which adjusts the brake load at the start, and in another place G by two bolts unequally distant from the rim (Fig. 158), and are joined by levers which have slots D through which 151 ENGINE TESTS AND BOILER EFFICIENCIES passes a fixed axle. The bolt connecting the weight E to the brake band must meet it at the same point as the horizontal line through the axis of the pulley. This position is indicated by an arrow head which corresponds to the fixed index /. Fig. 155 Fig. 166 ?^^^^^^55;??5S^?5?:^:^ Fig. 157. If there is too much frrction the brake is dragged round in the direction of the arrowhead (Fig. 155), but the bolts G being raised up, slacken the brake and so restore equilibrium. Conversely if the friction be insufl&cient the bolts G are lowered and thus tighten the brake. 152 BRAKE HORSE POWER We can see what happens in another way by considering how the line joining the axes of the bolts G turns round the fixed axle at D. When G rises this line is less inclined to the tangent to the circumference of the pulley, and hence the brake is loosened, and when G falls this line approaches the normal and thus tightens the brake. B (Fig. 157) is a water dash pot similar to those pre- viously described. When the brake is used to measure very small loads the oblique position of the tightening lever C D isa. drawback, as it produces certain frictionalforces which cannot be calculated. It is better in this case, therefore, to place the lever vertically (Pig. 158). The water cooling arrangement in the interior of the pulley is indicated in Figs. 155 and 157. The water enters by a tube 8, and after getting heated it leaves by the bent tube T. The small error due to the friction of D can be neglected in comparative tests of engines of about the same size. The friction due to this cause is about the one hundred and fiftieth part of the total friction. Fig. 158. 1B3 ENGINE TESTS AND BOILER EFFICIENCIES The Balk BraJce (Fig. 159). The pulley, provided with its brake, is mounted on a wagon which allows it to be rapidly moved from one engine to another. The automatic tightening move- ment can be easily understood from the figure. The Tig. 159 point a being fixed, if b is lowered by excessive friction the brake is automatically loosened and conversely. We find the resultant of the forces at b by equili- brating them with aweignt Q (Fig. 159). If then q be the distance of the weight Q from the vertical line through the centre of the pulley, and L be the distance of the line of action of P from the centre, then the Torque = PL — Q q. 154 BRAKE HORSE POWER The Braider Brake (Fig. 160). The pulley is surrounded by an iron band, which is kept in position by guides (Fig. 160). This band is able to support twice the weight P I p Tiir Fig. 160. required to obtain a balance. The tightening screw I is only used when setting up the brake. The lower guide G is connected by a hnk to two fixed cords F and F' ; D is a tightening screw and A is another one with a handle A G. These screws, A and D, press upon a band of iron fixed on the top guide G, which also carries an oil cup. The tightness 165 ENGINE TESTS AND BOILER EFFICIENCIES of these screws are first regulated by hand. We then put the handle C through a hole in a plate of metal held fixed by the cords L and L'. The screw A must also lie on the vertical through the axis, and conse- quently the handle must be parallel to the axis of the pulley. When this has been done the cup is filled with oil, and we turn the pulley by hand to make sure that the brake is working properly, and we then start the engine. So long as P is not hooked on to K, the cord F is stretched ; when we hang P on, the brake takes the position shown in the figure, and the cord F' is stretched. We now tighten the screw D until the friction causes equilibrium with the weight P, and the screw A is vertical when the indices H and H' are opposite one another. The weight P, which has been roughly calculated previously, is modified until we get a balance at the required speed. When this is the case the balance is maintained automatically. If the friction is insufiicient the brake tends to take the position shown in the figure, but the screw A now tightens, and equilibrium is established. On the other hand, if the brake be dragged round the handle G passes to the right of A, and the tension is relieved, diminishing the friction and restoring the balance. The screw A oscillates from the right to the left of the vertical line through the axis of the pulley. In consequence of the difficulties which arise in attaching the cords L and L' and the errors that result from their tensions, this arrangement is only suitable for small motors. 1B6 BRAKE HORSE POWER AnofliPV Arrniifjemenf. For engines of from 15 to 20 horse power M. Braner employs the arrangement shown in Fig. 161. The upper band of the brake carries an oil cup 0, and has at its extremity a bent lever E and a sleeve which carries the weight P. The lower band is Fig. 161. attached to the sleeve D, which forms the nut for the screw G. The brake can be tightened by means of the screw G which is fixed to the lever E, of which one part is attached to the band A by means of the spring B, and the other to a fixed point by means of the slack cord M. The safety ropes F and F' allow the brake a play of about four inches. 157 ENGINE TESTS AND BOILER EFFICIENCIES "We can tell when tlie brake is in its mean position by means of the index finger L. The weight P is calculated roughly before we begin the test. The brake is free when the screw G is slack, and when the weight P is not hooked on. In this case the cord M mmM Fig. 162. and the rope F are slightly stretched, and the machine runs freely. When P i* hooked on the rope F' is stretched. "We adjust the steam admission until it runs at its normal speed, at the same time turning the screw until the friction is sufficient to support P. In this case the rope F' is slaqk. Suppose now that owing to an increase in the value 168 BRAKE HORSE POWER of the friction the brake is dragged round with the pulley, the cord M becomes tight and slackens the brake. If, on the other hand, the weight P pulls it back, the cord M becomes slack and the spring 2^ tightens the brake. When equilibrium is established the tension of the cord M must be so small that it introduces no appreci- able error in the calculation. In this, as in all other brakes, it is necessary to provide some cooling arrangement to prevent the temperature rising above 176° F. (80° C), and to put the brake on as large a pulley as possible. Upon grooved pulleys or flywheels we may replace the flat band of iron by iron wires, one in each groove, the diameter of the wires being proportional to the stress they will have to withstand. In this case it is necessary to have as many tightening levers as wires, and hence the arrangement is complicated. Owing to this complication it is sometimes better to use a flat band with grooved pulleys. Another Arrangement. For machines greater than 20 horse power the preceding arrangement can be modified as follows : — The upper band is connected to the extremity of the lever A. C (Fig. 162), the lower band is jointed to the lever at B and the weight P is attached to A . Above the sleeve K is an oil cup, a cord fastened to G is connected to a weight M and the spring R is attached to the extremity C of the lever by means of a pulley block E. The string E G must point to the centre of the pulley when its tension is negligible and the end 159 ENGINE TESTS AND BOILER EFFICIENCIES of the string is held in the hand, and thus we can easily alter the tightness of the brake. The pulley G is not essential, but it enables us to make the adjust- ment more conveniently. The automatic adjustment of the brake is effected as formerly by the simultaneous actions of the cord M and the spring B. Resume. We see that in all these automatic brakes there is an error introduced by the tension of the cord, whether it is attached to a weight ilf or to a fixed point. Although this error is small, it cannot be neglected in accurate testing, and hence, when great accuracy is required, we use a simple brake. In comparative tests the error introduced by neglecting the tension of the cord is of little importance. Beer or Fetu-Deliege Brake (Fig. 163). The brake band is fixed at a and b to two iron bars bent to pass over the shaft. C C are two iron guide plates so adjusted that their weight balances the brake band about the centre of the shaft. The rod c is a continuation of the brake band, and it is connected to two rollers whose common axis is controlled by the rod d, which is attached to a fixed point lower down. Thefe rollers move over the curved edges of the plates C C, which are sectors eccentric to the shaft so arranged that when the weight rises the brake is loosened, and when it falls it is tightened. An iron box round the lower part of the brake 160 BEAKB HORSE POWER holds the cooling water, and a shield over the brake prevents splashing. Ii3r/ -gr TU tgr Fig. 163. "^ Gadiat Brake (Fig. 1G4). This brake, Avhich is to a certain extent automatic, has been designed by M. Cadiat, engineer to Mour- raille & Cie, of Toulon. The brake band is adjusted by means of a tension screw on the circumference of a grooved pulley ; some of the blocks fit into the grooves, and keep the brake in its place. A cord a h passes over a pulley and carries a scale pan, to which is attached a series 161 M ENGINE TESTS AND BOILER EFFICIENCIES of bars (Fig. 164) in such a manner that when the pan rises more of them are raised from the ground, thus increasing the tension, and when it falls back some of them are placed on the ground again, and thus reheve Fig. 164. the tension. The observer must note the number of bars suspended when making a test ; a and b are two stops which limit the play of the brake band and the lower part of the brake is immersed in soapy water which cools the circumference. Other Automatic Arrav/iements. The arrangement shown in Fig. 165 is a very simple one. One end of the brake band is attached 162 BEAKE HORSE POWER to the weight P, and the other end to a spring balance q and an additional weight p. The condition of equi- librium is Fr=Fr-{f + q) r. Hence the power can be obtained by writing P- {P "*" ^) foi" P ^n formula (1). When the friction increases the weight P tends to Fig. 165. Fia. 166. rise, its moment /-* r, however, remains constant; but since q diminishep, and therefore F increases, the load is increased, and equilibrium is re-established. Con- versely when P falls q is increased, and the load diminishes. This arrangement is variously attributed to Navier or to Easton and Anderson. The arrangement in Pig. 1 66 is a slight modifica- tion of that in Fig. 165. The two extremities of the brake band cross and are situated in the same vertical, and the tension q tends to maintain equilibrium. In 163 ENGINE TESTS AND BOILEE EFFICIENCIES these two arrangements the brake band can be a leather belt, or it can be simply a band of copper with graphite for a lubricant. Fig. 167. In Fig. 167 the tangential pull is measured by a weight P placed at the extremity of a lever or steel- yard. Imray Brake (Fig. 168). In this arrangement, which is suitable for the measurement of small powers, the arc enveloped by the brake diminishes as the friction increases, and conversely. The brake-band carrying the weight P is connected to a balanced sector A, and carries at its other extremity a weight q. If the friction increases the weight P rises, but as the arc of the pulley embraced by the band diminishes the friction is diminished, and hence equilibrium is soon established. If P fall, the load is increased, and a balance is soon obtained. 164 BRAKE HORSE POWER 31. Deprez Brake (Fig. 1 69). The two levers e c and e 5 of the friction blocks are jointed at e and e upon a disc B, and are connected to Fig. 168. a lever b o, making an angle « with the horizontal. The point corresponds to the centre of the pulley A which is keyed upon the shaft of the motor. At this point is hung a weight q, which is proportional to the tightness with which we wish the blocks to press on the pulley. It is evident that the weight Q will produce the maximum force on the blocks when the lever b o is horizontal, and will produce no effect at all on them when it is vertical. The tightness is therefore proportional to cos «. The disc B with the counterweight G is free on the shaft, and carries the weight P, which is to measure the work done. Suppose now (Fig. 169) that the moment of the 165 ENGINE TESTS AND BOILER EEEICIENCIES] frictional forces upon the pulley A are in equilibrium with the moment P L. If this friction diminish, the weight P is lowered, and at the same time the angle a diminishes, and hence Q exerts a greater tightening Pig. 169. force on the friction blocks, which increases the friction, and thus supports the weight P. Eecipro- cally when the friction increases P is raised; but the brake being slackened, equilibrium soon ensues. The normal pressures li upon the pulley A given by — . . (lower). are B Q cos a - Q cos a ao be a b ob ed (upper). li =(J cos a X X _ , a e d These ratios must give equal values of li From the practical point of view, the position of the weight Q must produce troublesome side friction, which will prevent smooth running. We do not believe that this brake has yet been constructed, and it looks rather impracticable. 166 BKAKE HORSE POWER Garpentier Bralce (Fig. 1 70). This arrangement requires two pulleys, one {A) keyed on the shaft, and the other one {B) idle. A cord fised to the idle pulley B, either by a cheek or otherwise, winds itself on that pulley and supports the weight P. On the other side the cord is wound round the fixed pulley, and supports a weighty). Suppose that the system is in equilibrium, and that the weights P and p do not move ; the pulley i? is then fixed, and the pulley A turns, rubbing against the cord . For the same weight p, the friction and consequently the tangential effort that the pulley A exerts on the cord u is greater the larger the number of turns, just as in the case of a capstan. If now the friction increases from any cause the pulley B and the weight P will be dragged round in the direction of the motion, and at the same time some of the cord on A will be unwound, thus relieving the friction, and hence equilibrium will soon ensue. If on the other hand the friction diminish, more cord will be wound on A, thus increasing it. 167 Fig. 170. ENGINE TESTS AND BOILER EFFICIENCIES For a given power it is necessary to adjust the two weights P and p, and to roll a certain amount of cord round A; but once equihbrium is established it is maintained automatically. It is at once seen that the above arrangement is more complicated than some of the others we have described, and that it is only suitable for small motors. A still more complicated brake has been con- structed on this principle (Fig. 171). It consists of three pulleys A, .1' and /?. j5 is placed between the Fig. 171. Others, and is idle, the other two being keyed to the shaft. The cord is replaced by leather straps, and the weight P is carried at the extremity of a level- on the same side as p, but so as to equilibrate it. As this apparatus requires a fourth pulley to be put in connection with the motir, it is more comparable to a dynamometer than to a brake, but it is only suitable for small powers. This construction seems to us to have little to recommend it, for, besides its complication, it has in practice the drawback of the difficulty of adjusting 168 BRAKE HORSE POWER the weights p and P, wliilst the hmits of automatic adjustment are very small. The arrangement (Fig. 1 66) is, in our opinion, much superior to those which precede it, firstly because it can be adapted to the pulley of the motor itself, and secondly because it is only necessary to adjust the weight P in order to obtain equilibrium. Brake and Indicator. Testing the brake horse power of machines in the workshop presents, as a rule, no great difficulty. It is often even more simply found than the indicated horse power, as the whole test can be made by the foreman fitter, and the final result ascertained more quickly than from the indicator diagram. In the actual brake test, however, of machines in daily use, difficulties arise. Besides the trouble and expense of setting up the brake we need to disconnect the engine from the shafting which ifc drives, and the test has to be sufficiently long to enable us to elimi- nate the errors due to the inertia of the rotating or reciprocating masses. An efficiency test should last for at least one day. Sometimes the brake can only be placed on a transmission shaft. In this case we must calculate the frictional work done between the brake and the machine, and add this on to the work done by the brake. We see that for a machine in daily use it will often be difficult to apply a suitable brake. Sometimes the simultaneous use of a brake and an indicator is desirable. It is sufficient to apply the brake only for the short time required to find out the 169 ENGINE TESTS AND BOILER EFFICIENCIES ratio of the brake to the indicated horse power, and then we can tell what happens subsequently from the diagrams. When the motor to be tested is coupled to other motors, and the load is variable, then, if it is impossi- ble to disconnect, we must arrange that its load is approximately constant by regulating the admission of the steam and taking off its governor. In this case the other machines have to supply more or less power depending on the load. The diagrams of the indicator will give the I.H.P. of the engine being tested. 170 CHAPTER IX. The Dynamo used as a Brake. Magnetic Brake. THE dynamo can sometimes be conveniently used as a brake. It is driven by the machine the brake power of which we want to measure, and the electric power it generates is expended in heating suitable resistances. If we measure the total electromotive force E of the dynamo by a suitable voltmeter and the current I by an ammeter, then the total electric power LI J generated is E I watts or —— , horse power. If the 740 commercial efficiency of the dynamo at this load is >?, then the mechanical power given to it by the machine is 746 n , and this is the brake horse power wanted. D[/itamovu'ter. The dynamo being a reversible machine can con- versely transform electrical power into mechanical power, and can be used to drive workshop machines or tools ; used in this manner it is called a motor. Multiplying the electrical power given to the motor by ri we at once deduce the power given out by the motor. We see, then, that the dynamo is also a transmis- sion dynamometer. 171 ENGINE TESTS AND BOILER EFFICIENCIES Use as a Brake. We couple a dynamo of sufficient power to the engine whose brake horse power has to be determined. The most suitable dynamo is one which is shunt wound, giving a practically constant pressure at con- stant speed. We arrange upon the engine shaft a suitable pulley, so that the dynamo runs at its proper speed when the engine speed is normal. The connections are shown in Fiof. 172. vmmM C ^^ A is a shunt dynamo. B is the field adjusting rheostat. C resistances to absorb the load. I) voltmeter key. ^^ E voltmeter. I ammeter. Fig. 172. The shunt current of the dynamo can be regulated by the hand switch at B, so as to obtain the proper voltage. We start the machine on open circuit, and when it attains its voltage we close the external circuit and regulate the load until the desired horse power is obtained. 172 THE DYNAMO USED AS A BRAKE Galcmlation of the Work. The reading of the ammeter gives us the current I, and the voltmeter gives us the voltage E. Let >] be the efficiency of the dynamo at the load E I watts, 7'= the brake horse power which has to be measured, then >/ r= electric power, = — — horse power. 746 ^ E I Therefore T= ^-l^ horse power. 746 v ^ Direct Measurement of i. We have first of all to determine the efficiency of the dynamo at various loads. These efficiencies can generally be had from the maker of the machine, but it is always preferable to find them ourselves. They can be obtained by calculation or by several experi- mental methods, all of which lead to the same result. A particularly convenient method is the one first employed by Mr. James Swinbiirne. The dynamo is a reversible machine, and so its efficiency as a motor is practically the same as its efficiency as a dynamo. Efficiency as a Dynamo. If we send a current T through the armature of a motor and PI be the potential difference at its ter- E I minals, then the power given to it is „ — ^. If now ^ ° 746 we apply a friction brake to a pulley on its shaft, and, 173 ENGINE TESTS AND BOILER EFFICIENCIES if T be the measured brake power absorbed by the frictional forces — rn EI 746 T ^ 746' ^ Jj] I Efficiency Curve (Fig. 173) E I If we measure kilowatts 1000 horizontally and efficiencies (»?) vertically, we obtain the efficiency curve (Fig. 173), and this curve remains practically always constant. 0.$ 0.2 0.1 o.O 05" 0.* 0.2 o^ A * k . h F e 7 Fig. 173. So long as the load does not pass certain values the efficiency of machines of certain sizes is much the same. The following table of approximate numbers will be found useful : — - « Horse Power 1 2 3 , 5 10 50 0-90 100 Efficiency 0-70 ' 0-78 0-81 0-82 0-83 0-92 Above 100 horse power the efficiencies attain values of 95 or even 97 per cent. 174 CHAPTER IX. A. Steam Turbines. Hypothetical Equivalent Indicated Horse Power. FOR steam turbines there is nothing analogous to the ordinary indicated horse power diagrams which "we get for reciprocating engines. The indi- vidual pressures on the many thousands of small blades cannot be ascertained, although the resulting power delivered by the engine to its shaft may be known and the amount of external work performed by it. For instance, when the turbine drives a dynamo, the electrical horse power generated in the latter can be accurately measured by instruments of precision. The efficiency of a dynamo can also be found by any of the various standard electrical methods, and hence the brake horse power of the turbine is known. The accuracy of this determina- tion is probably greater than in the case of the indicated horse power of an ordinary steam engine. It is customary to assume that in an ordinary steam reciprocating engine of good design the brake horse power is 86 per cent, of the indicated horse power (see Chapter VII.). This agrees closely with the mean of the results of many published tests of ordi- nary steam engines. For the sake of comparison we assume that in turbines the ratio of the brake to the indicated horse powers is also 0"86. Hence, knowing the brake horse power, we find the indicated. The 176 ENGINE TESTS AND BOILER EFFICIENCIES horse power found in this manner is called the liijpo- thetical equivalent indicated horse poiver. Marine Steam Turbines. A similar method is followed in mai'ine steam turbines. The resistance of the ship is calculated, and hence the " propulsive horse power " required to drive it at a given speed can be found. For vessels with ordi- nary reciprocating engines it is generally found that the propulsive horse power is about 55 per cent, of the indicated horse power. In some torpedo boats the ratio of the propulsive to the indicated horse powers may be as high as 0"6 and the lowest value is about 0*4. For cross-channel boats, liners, cruisers and destroyers we may take 0-55 as the ratio. The determination of the propulsive horse power has been made possible by the work of the late^Mr. William Fronde. He determined the resistance to passage through the water of a model of a ship in his testing tank, and then from his experimental results- calculated what the resistance of the ship would be. Knowing then the propulsive horse power and its ratio to the indicated horse power, we find the hypo- thetical equivalent indicated horse power of a marine steam turbine. It will be seen that the testing of a steam turbine is much simpler than the testing of an ordinary steam engine. It is also much less liable to get out of order. The only effect of bad priming on the part of the boiler is to make it turn a very little slower, whilst with a steam engine there is a great risk of the cover of the cylinder being blown off. 176 w CHAPTER X. Peopbbties op Steam. Equivalence of Worh and Beat. HEN heat bi/ its action does mechanical wurl; the quantity of heat that disappears is always exactly proportional to the worh done, and, conversely. We conclude from the above that heat and energy are measured in the same imits and are mutually convertible. The mechanical equivalent of heat is the amount of work required to raise the temperature of one pound of water one degree Fahrenheit. It is nearly 778 foot-pounds. Con- versely we could speak of the thermal equivalent of work. One foot-pound is equal to the rri-th part of a British Thermal Unit; i.e. the amount of heat required to raise the temperature of one pound of water one degree Fahrenheit (B.T.U.). The law of the equivalence of heat and work is independent of the nature and the constitution of the body ; like the law of universal gravitation it has been deduced from observation and experiment. Saturated Vapour. (See the tables in the Appendix.) Consider a pound of water contained in a cylinder whose sides are non-conductors of heat and the bottom part allowing heat to come through from a furnace. 177 N ENGINE TESTS AND BOILER EFFICIENCIES At a pressure of one atmosphere the water will boil at 212° F. If, however, we suppose that a weightless piston exerts upon the water a pressure p greater than the atmospheric pressure, then the water will heat above 212° F. So long as the pressure jj remain constant the temperature t does not change, however hot the furnace may be. The greater heat only makes it boil more rapidly. The vapour formed in the presence of water is called saturated vapour; that is, its pressure and density are the greatest possible corresponding to the temperature t of the boiling water. Reciprocally the pressure p of a saturated vapour depends only on the temperatiu'e t, and not on the volume which it occupies. Regnault has constructed very elaborate tables of pressures and temperatures which embody the results of his experimental re- searches. The tables we give in the Appendix have been calculated by Zeuner for every tenth of an atmosphere from Regnault's tables. The density d of water vapour is equal to 0'G22 of that of air at the same temperature and pressure. The weight of one cubic foot in pounds and the volume in cubic feet of one Dound are given in the Appendix at the temperature of 39° F., which is the temperature at which water has its maximum density. The mass of a cubic foot of water is 62-4 pounds nearly. The density d of water vapour or the mass in pounds of one cubic foot is equal to 0-622 times that of air at the same temperature and pressure. The mass of one cubic foot is d. pounds and the 178 PROPERTIES OF STEAM volume of one pound is — cubic feet. These quanti- ties are tabulated in the Appendix. At the temperature of 39° F. the volume of one pound of water is 0"016 of a cubic foot nearly, and the volume of one pound of water vapour at that temperature is 20 cubic feet. Hence the ratio of the volume of water vapour to the volume of water that produces it at 39° F. is -?^ ,i.e. 1250. At 212° F. ^ 0-016 this ratio is about 1650. Total Heat of Vaporization, U. This includes both the heat required to raise one pound of water from 32° F. to f F., and the latent heat of steam at t° F. Regnault gives the following formula : — f7= 1082 + 0-305 /. This quantity of heat increases with t. It is also the heat that leaves one pound of vapour in cooling down from t° F. to 32° F. Latent Heat, L. The heat given to a pound of water in order to turn it into vapour without altering its temperature is called the latent heat of steam. If L be the latent heat at f F,, then — L = 1114 - 0-695 t. We see that the latent heat L diminishes as the pressure and consequently the temperature rises. Superheated Steam. After the complete vaporization of a pound of water, if we continue the heating the steam becomes super- 179 ENGINE TESTS AND BOILER EFFICIENCIES heated. The greater the sixperheating the more nearly does the vapour when it expands obey Boyle's law. The specific heat of water vapour being 0'475 (or more simply 48) the heat required to superheat a pound of water from t'°F. to TF. is 0-475 (t-f), and the total heat contained in one pound of the vapour is 1082 + 0-305i' + 0-475 (M'). This is also the total heat that would be given up by a pound of superheated steam in cooling from t to 32° F. Saturated Steam. Compression. If we have saturated steam confined in a cylinder by means of a piston, and if we compress the piston, the heat due to the compression will more than com- pensate for the diminished volume, and hence the steam will become superheated. All vapours do not behave in this manner. Alcohol vapour, for example, is condensed by compression. Saturated Steam. Adiahntie Expansion. When the piston is allowed to expand, no heat being supposed to enter or leave the cylinder during the expansion, then theuacreased volume fails to com- pensate for the diminished pressure, and so some of the steam condenses and furnishes to the remaining steam the heat required to keep it in the form of vapour during the expansion. Towards the end of the stroke some of the condensed steam may be re-evaporated again. 180 PROPBETIBS OF STEAM Expansion- of a given Qnantifij of Vapour. If daring the expansion we supply the vapour with the heat required to maintain it in the gaseous form, the mass of the vapour will remain constant. In this case if p be the pressure in pounds per square inch and V be the volume in cubic feet, the approximate law of the expansion will be p w''°^ = constant. Boyle's or Mariotte's Law. If more heat be given to the vapour during the expansion than that required to keep it gaseous, it becomes superheated and it obeys Boyle's law very approximately, which may be given as follows : — The volume of a mass of gas varies inversehj as the pressure. Let V =the initial volume of the steam. o F=the final volume or the volume of the cylinder. P = the initial j)ressure. P' = the final pressure. We have ^ = ^ or P F„ = P'F= constant. o If we plot out a curve having volumes for abscissae and pressures for ordinates we get a hyperbola. Calculation of the Mean Pressure pj,^. We can calculate the mean pressure p,,^ of a theoretical diagram (Fig. 174) when we know the ratio of the expansion =, A knowledge of p^, is sometimes 181 ENGINE TESTS AND BOILEE EFFICIENCIES useful when we are designing an installation or when we are calculating the indicated horse power of an engine to which an indicator cannot be applied. The Fig. 174. total work of the steam during a stroke of the piston is j9„ V, and it is equal to the sum of the following : — (1) The work during admission P V^. (2) The work during expansion. Assuming Y Boyle's law, this equals P V^ loge -r^ c (3) The negative work done during the return stroke P'V. Summing up these three works and dividing by V, we get p„ = P^(yi0ge^)-P'. The following table gives the hyperbolic logarithms . V of the expansion ratio =^: — 182 PEOPERTIBS OF STEAM Hyperbulio Logaritlmn?, V log. hyp. V Idg. liyp. V log. llj'p. V Vo log. liyp. 1-4 0-3365 3-7 1-3083 6-0 1-7918 8-3 2-1163 J 1'5 0-4055 3-8 1-3350 6-1 1-8083 8-4 2-1282 1-6 0-4700 3-9 1-3610 6-2 1-8245 8-5 2-1401 1-7 0-5306 4-0 1-3863 6-3 1-8405 8-6 2-1518 1-8 0-5878 4-1 1-4110 6-4 1-8563 8-7 2-1633 1-9 0-6419 4-2 1-4351 6-5 1-8718 8-8 2-1748 2-0 0-6931 4-3 1-4586 6-6 1-8871 8-9 2-1861 2-1 0-7419 4-4 1-4816 6-7 1-9021 9-0 2-1972 2-2 0-7885 4-5 1-5041 6-8 1-9169 9-1 2-2083 2-3 0-8329 4-6 1-5261 6-9 1-9315 9-2 2-2192 2-4 0-8755 4-7 1-5476 7-0 1-9459 9-3 2-2300 2-5 0-9163 4-8 1-5686 7-1 1-9600 9-4 2-2407 2-6 0-9555 4-9 1-5892 7-2 1-9741 9-5 2-2513 2-7 0-9933 5-0 1-6094 7-3 1-9879 9-6 2-2618 2-8 1-0296 5-1 1-6292 7-4 2-0015 9-7 2-2721 2-9 1-0647 5-2 1-6487 7-5 2-0149 9-8 2-2824 3-0 1-0986 5-3 1-6677 7-6 2-0281 9-9 2-2925 31 1-1314 5-4 1-6864 7-7 2-0412 10 2-3026 3-2 1-1632 5-5 1-7047 7-8 2-0541 11 2-3979 3-3 1-1939 5-6 1-7228 7-9 2-0669 12 2-4849 3-4 i 1-2238 5-7 1-7405 8-0 2-0794 13 2-5649 3-5 1 1-2528 5-8 1-7579 8-1 20919 14 2-6391 3-6 1-2809 5-9 1-7750 8-2 2-1041 15 2-7081 The pressure P in the cylinder is always less than the pressure in the boiler. It is sometimes obtained directly by a manometer placed on the valve chest. The back pressure, or the pressure during exhaust, is 15'6 to 17 pounds per square inch in non-condensing engines and 2 '2 to 3 pounds in condensing engines. In the preceding calculation of the mean theoretical pressure ^„j we have not taken into account the volume of the steam in the clearance space. This modifies the pressure during the expansion, as the volume that expands is in reality F„ + V. If there is compression during the return stroke (cushioning), we have again to take the clearance space into account. ENGINE TESTS AND BOILER EEEICIENCIES Suppose that F„ = m V and V' = m' V, then we can show that »„ = P im+ (m + m') lege — , — ,\~P" or Where K = m + (m + m') loefp ,. ^ ' ° m+m We have calculated the values of K for a clearance m' equal to y\> and the results are given in the follow- ing table : — m tV 0-39 1 h 0-44 7 i i i i 0'55 0-62 1 :i 0-72 0-85 0-90 7 10 /o K 0-47 0-BO 0-950-98 The pressure calculated by this formula goes on the assumption that there is no lap or lead, and also it does not take account of re-evaporation. Theoretical Weight of Vapour per Horse Power Hour. The weight of vapour per horse power hour may be calculated from the mechanical theory of heat. We will not reproduce here the calculation which will be found in treatises on Thermodynamics, as it has no direct practical application. It is sufficient to indicate the results so that they may be compared with the weights of vapour calculated from the diagram. Absolute Pressure in Atmospheres. 1-B m 4 B 6 8 10 Pounds per Horse Power Hour Condensing. 15-4 12-7 11-8 11-3 10-9 10-3 9-9 Pounds per Horse Power Hour Non-Conden sing. 72-7 33-1 2B'4 22-9 20-7 18-1 16-B 184 PROPERTIES OF STEAM Weight of Drij Steam per Horde Power [lour. Warrington's Diagram. We have seen that the indicated work is given by the formula — H P = ^PLAN ■ ■ 33000 or 33000 H.P. .= lU x p x 2 L.A.N. when the area of the piston is expressed in square feet. When H.P. is 1 and^ is 1 the work per hour is 33000 X 60 = 144 x {2 L A N x 60) Hence if we call the volume swept out by the piston in one hour V, we have r= 2 L.A.N. x60 Therefore V = 13750 cubic feet. If the pressure j) be expressed in atmospheres, then since one atmosphere is 14'69 lbs. per square inch y, _ 13750 14-69 = 935-4 cubic feet. Hence at a pressure of one pound per square inch the volume of the fluid used per horse power hour is 13,750 cubic feet, and when the pressure is one atmos- phere it is 935-4 cubic feet. This volume will vary inversely as the pressure, so that we have V = — y — when p'„ is in pounds. P m jr 935-4 , • - + o or K = when w^ is m atmos. Pm If Fg be the volume of unit mass of the steam at the 186 ENGINE TESTS AND BOILER EFFICIENCIES fiaal pressure (p^) got from the indicator diagram, then the mass M of the steam will be given by 935-4 ilf = -4 P« f: The value of Fg for various values of p^ is tabulated in the Appendix. To find the expenditure of dry- steam, it is only necessary to divide p^. into the value 935-4 of -, which can be obtained from the last column Fe of the table. The final pressure of the steam in the cylinder (p^) is obtained from the indicator diagram. Gorrectiojis. The clearance spaces increase the steam consump- tion, but compression tends to diminish it. 1 SI. X o Vacuum Line ; Fig. 175. To take account of this action draw through the point K which determines the final pressure p^ (Fig. 175) the line h m parallel to o x. This 186 PROPERTIES OF STEAM line will cut in m the curve of compression pro- longed if necessary. The corrected mass of the vapour -Mj is given by kn In the curve A (Fig. 175) it will be seen that the final value of the back pressure during the com- pression is p^. The effect of the clearance space is therefore annulled. In this case we have hm _ -. kn In B and in ^ is less than unity, and in D and E kn •' it is greater. This ratio is a maximum in D, where the compression is zero. Example. In the diagram (Fig. 107) we have — j?e = 11 "4 and^OT = 17 lbs. per square inch. = 1*2 atmospheres. From the tables in the Appendix we find that V, = 33-7 and -^-5-^ = 277 27"7 The mass of the vapour will therefore be -— lbs. i.e. 23-1 lbs. T— found from the diagram = ~- kn 96 = 0-94 The corrected mass will therefore be 23"1 x 0'94 = 21-7 This mass, however, is not quite exact, as the steam is always more or less wet. 187 ENGINE TESTS AND BOILER EFFICIENCIES For accurate tests we can measure tke mass of tlie wet steam consumed by the method of direct measure- ment which we shall soon discuss. ApiMcation to Machines with Tioo Cylinders. The preceding method applies also to engines with two cylinders, Woolf or compound. The pressure j?^ at the end of the expansion is given by the diagram of the low pressure cylinder. It is necessary, however, to calculate the mean pressure p^^ common to the two cylinders. Suppose that we have determined the mean pressure p'„i in the high pressure cylinder, whose volume is V, and p"^ the mean pressure in the low pressure cylinder, whose volume is V. Then we may write Pm — P m 'Tt + Pm The correction can be made by finding the point m on the curve of compression of the low pressure cylinder. Example. To calculate the consumption of steam from the diagrams in Figures 110 and 111. The diagram Ogives Vi&p',^ = 31 '9 lbs. per square inch. The diagram B gives tis jp"„^ = 21-3 lbs. per square inch ; these being the mean of the pressures on the two sides of the cylinder. The ratio of the volumes =^ = -— — V 2-84 Hence the mean pressure will be i^™ - 1^ + 21-3 = 11-2 + 21-3 = 32-0 = 2-3 atmos. 188 PROPERTIES OF STEAM On prolonging the curve B we find that p^ = 14-2. 935-4 The tables give ns V, = 28 1 and ~^^ = 34-8 Hence ^ = -^f? = 15-2 lbs. 88 Correcting for compression, 15 '2 x -- =.- 15 lbs. Making an allowance of ten per cent, for the increased consumption due to the wetness of the steam, we find that the consumption is 16'5 lbs. per h.p.. hour. By actual measurement the consumption was found to be 16 '6 lbs. Direct Measurement. The consumption can be got directly by measuring the amount of water injected into the boiler. For small engines, especially when the boiler furnishes steam for other purposes, we can measure the consumption of wet steam by passing the exhaust steam into a surface condenser. The mass of water collected is the mass of wet steam consumed by the engine. JVet Steam. Primiiu/. In what precedes we have supposed that the steam is dry saturated vapour; but in practice this assump- tion is not permissible, as the steam coming from the boiler contains (except when superheated) a certain proportion of water. This result is due either to priming, or to a bad arrangement of the steam pipe of the boiler. Primmg. When the ebullition of the water in the boiler is very violent the steam carries over with it to the 189 ENGINE TESTS AND BOILER EFFICIENCIES cylinder a certain amount of water, and priming is said to take place. If the orifice of the steam pipe be too near the surface of the water in the boiler the priming will be increased. This wet vapour causes a loss of heat, because it is only the latent heat of the vapour that does work. In addition, the water getting over may cause the piston to rupture the end of the cylinder. "We can find out approximately the relative humidity of the steam by the appearance of a small jet of steam supplied by means of a cock in the dome of the boiler. We must not take this jet by means of a pipe to any great distance from the dome, as in passing along this pipe some of it would be condensed. So long as the jet of steam issuing from the cock is transparent or slightly grey, the vapour is dry ; if the vapour presents a whitish appearance it contains two to three per cent, of water ; but it is still considered dry steam. If the issuing vapour looks misty, then it is called wet steam, and the proportion of water is determined as follows : — Measurement of the Water Garried Over. Various methods of doing this have been proposed. We shall confine ourselves to describing two of them, namely : (1) the calorirtfttric or condensing method, and (2) the method of dissolving sea salt. First Method. We fix upon the steam pipe, close to the dome of the boiler, a cylindrical tube with a stopcock which has a flexible tube fastened to its nozzle. We heat 190 PROPERTIES OF STEAM the tube by allowing a certain amount of vapour to pass through it. Then we plunge the flexible tube into a suitable receptacle which is protected from loss of heat, and contains a mass M of water and a ther- mometer. This receptacle, or calorimeter, as it is generally called, can be gauged and calibrated, or, more simply, it may be placed on the scale pan of a balance. We allow the steam to condense in the water, but shut off the cock before the water attains 212 deg. F. Let If = the initial mass of the water in the calori- meter. / = the temperature of the water. a = the proportion of dry steam. h = the proportion of water. m = a + h, the increase of the mass of water. /' = the temperature of the steam in the boiler. f" = the temperature of the water in the calori- meter at the conclusion of the experi- ment. jij = the latent heat of steam at t' deg. F. Then since the number of units of heat gained by the water will equal the number lost by the wet steam, we have : a {L + t'-t") + h {t'-t")^M {f - t') and a + h = in. From these two equations the percentage quantity of water in the steam can easily be found. Second MetJiocl. In the second method we saturate the water in the boiler to a known degree by means of salt (n 191 ENGINE TESTS AND BOILER EFFICIENCIES ounces per gallon of water, for example). Now dry steam carries over no salt to the cylinder, and so all the salt that comes over has been taken by the prim- ing water. An analysis of the water got from the drain cocks of the cylinder will show us the amount of priming that is taking place. Condensation of Vapour. When vapour is in contact with cold water some of it will condense, and the quantity of heat lost by the vapour in condensing will be nearly all given to the water. A negligible amount will be given to the sides of the containing vessel and taken for re-evaporation. Let M= the mass of vapour which has to be con- densed, ilf = the mass of water required for this pur- pose. ^ = the temperature of this water (50° to 70° F.). ^' = the temperature of the mixture after con- densation. J; = the latent heat of steam at the exhaust pressure. Then after the condensation we shall have : M{L-f') = M' (t'-t). Hence M'^'i^l For example, when ^e exhaust pressure is two atmos. iv = 941. Suppose that i = 60° F., /' = 100° F., then ^,^941-100 ^^2-^ ^^ 40 Hence we require twenty-one pounds of water for every pound of steam condensed. 192 CHAPTBE XI § 1. Yaporization. FUELS. Calorific Power. ^PHB remark that fuels store up for us the heat of the sun, the source of all vegetation, has been attributed to Gr. Stephenson. Every body that is capable of combining with the oxygen in the air is said to be combustible. The combination is called the combustion, and during the process the heat and light are restored. The combustible materials of commerce contain (1) a certain quantity of oxygen and hydrogen combined in the proportion of 8 to 1, which forms water and does not furnish heat ; and (2) inert substances which do not give heat, such as nitrogen, the mineral matters which form the ash, pyrites or disulphide of iron which we can neglect on account of the feeble calorific power of sulphur ; and (3) carbon and free hydrogen which are the elements whose combustion produces the heat. The quality of a fuel is judged from its calorific power, its density, its cohesion, its appearance in the fire, and from the nature of the ash. The ash of bituminous fuels is apt to form a clinker which obstructs and burns the grate, whilst the ash 193 o ENGINE TESTS AND BOILER EFFICIENCIES of earthy fuels falls without obstructing the free passage of air. The calorific power P of a fuel is the number of British thermal units which a pound of it gives up on burnjng. According to Dulong it is equal to the sum of the calorific values of its elements, carbon and free hydrogen. Favre and Silbermann found that the calorific value of carbon G was equal to 14,546, and that of hydrogen was 62,028. In the analysis of fuels we take the oxygen and nitrogen together, as the latter is always of little importance. Since the constitution of water is eight parts of oxygen to one of hydrogen H, we see that the proportion of free hydrogen will be -I The formula of Dulong for pure combustion is P = X 14545 + ( ff- ^\62028 This law is not very exact for very dense bodies which have a large proportion of hydrogen, but their calorific powers have been found directly by experi- ment. Let a = the fractional quantity of water in the fuel, and 6 = the fractional quantity of ash produced. The true calorific value P' of the fuel will then be found from P' = P{l-a-b). "We have made the assumption (1) that the water vapour formed during the combustion is condensed to 32 deg., the total heat of vaporization being re- 194 VAPORIZATION stored ; and (2) that the ashes formed by the combus- tion are also cooled down to 32 deg. In the heating of locomotive boilers these assump- tions are not allowable. The steam which passes up the chimney takes with it 1,147 B.T.U. per pound, together with the heat 0'5 (i — 212) where t is the temperature of the gases in the chimney. If h be the average mass of the hydrogen contained in one pound of fuel, its combustion gives a mass of water 9 h, and the total quantity of water vaporized will he a + 'd h. It is further necessary to deduct from P' the heat which remains in the ashes and clinker, but these losses, together with that due to the temperature t of the gases in the chimney, are included in the losses due to the inefficiency of the furnace. The efficiency is obtained by finding the number of absolute units of heat generated by the combustion of the fuel. Hence we use the formula — P' = P {1-a-h) - 1114(a + 9/i). Commercial fuels may be divided into five classes — (1) Wood, charcoal. (2) Peat, turf. (3) Lignites, brown coal. (4) Coal, coke. (5) Anthracite. Wood. We class woods commercially into heart-woods and sap-woods. Woods for heating purposes are divided into new wood, drift wood, and wood with the bark removed. 19B ENGINE TESTS AND BOILER EFFICIENCIES Brisson gives the following values for the specific gravities of woods : — Heart-oak . . 1-17 Lime . . . 0-60 Beech, Ash 0-85 Willow . . 0'58 Alder, Apple . 0-80 Fir (male) . 0-66 Maple, Cherry 075 „ (female) 0-49 Elm, Walnut . 0-67 Poplar . . 0-38 Pear . . . . 0-66 Cork . . . 0-24 Wood always contains a certain proportion of water. It is only employed after being partially dried in the air, or dried in ovens at a temperature of about 300° F. The felling of trees is done during the winter. They then contain from forty to forty-five per cent, of water ; after six months they contain twenty- six per cent., after a year twenty per cent., and after eighteen months, seventeen per cent. However long they are exposed they always contain about fifteen per cent, of water. Woods which have been com- pletely dried in hot air ovens will, if left in the open air, gradually absorb moisture until they contain from fourteen to sixteen per cent, of water. Woods which have been dried at a temperature of about 280° P., contain approximately 0*5 of carbon, O'Ol of free hydrogen, 0'46 of oxygen and hydrogen in the ratio necessary to form water, O'Ol of nitro- gen, and 0'02 of ashes. By Dulong's law, • P = 0- 5 X 14500 + 0-01 X 62000 = 7870 B.T.IJ. approximately. Applying the required corrections, P' = 7870 -1114 (0-46 + 0-09). = 7257B.T.U. 196 VAPORIZATION Suppose the wood contains thirty per cent, of water, P' = 7257xO-7-1114xO-3. = 6746B.T.U. The table (A) gives the results of the experiments of M. Chevandier on the calorific power per cubic yard of various kinds of woods dried at 280° F. The calorific power of one pound of fuel varies be- tween 7600 and 8000, and is approximately equal to the number 7870 found above. A. — Experimental L esults by M. Chevandier. Nature of "Wood. Weight in lbs. per cubic 3'ard. Carbon. Free Hydro- gen. Calorific Power. Per cubic yard. Rel. /'Oak 607 315 4-37 4,900,000 1 ^r. Beech 607 312 4-42 4,850,000 0-994 Hornbeam ... 604 300 3-8 4,650,000 0'95 'u White Oak... 600 298 4-15 4,620,000 0-945 +3 Birch 565 . 288 6-1 4,580,000 0-939 Alder 490 250 4-95 3,970,000 0-812 o* Fir 465 237 4-37 3,720,000 0-762 ,Pine 430 235 2-98 3,450,000 0-706 r Beech 501 250 3-55 3,900,000 0-795 m "D 0) jz] Fir 480 245 4-52 3,860,000 0-79 ir Pine 470 240 4-37 3,800,000 0779 Hornbeam ... B97 242 308 3,740,000 0764 nM ^Birch 450 228 4-85 3,650,000 0-747 The above weights are calculated on the supposi- tion of sixty per cent, of solid wood to the cubic yard. A cord of wood has a volume of four and three-quarter cubic yards very nearly. Heart- woods burn at the surface, producing a large quantity of carbon, whilst sap-woods split in the fire and burn violently to the centre, giving out flames until they are all consumed. The more finely divided the wood is, the more rapid 197 ENGINE TESTS AND BOILEK EFFICIENCIES the combustion and the higher the efficiency, because the air is better utiUzed; but splitting up the wood is expensive. Wood Carbon. This is obtained by carbonizing the wood in stacks, and the return varies with the temperature as follows: — From 300° to 500°, return = 37 to 40 %. From 540° to 650°, return = 32 to 36 %. (red charcoal). From 670° to 780°, return- 18 to 31 %. (black charcoal). From 780° to 2,400°, return = l7 to 18 %. (charcoal is hard and black). The return, which is found by weighing, varies for black charcoal from eighteen to twenty per cent. The weight of a cubic foot varies according to the wood it is made from : — For oak and beech . . 16 to 17 lbs. For birch . . . . 15 to 16 lbs. For pine . . . . 14 to 15 lbs. According to Ebelmen the mean composition of dry carbon is as follows : — Carbon 0-875. Hydrogen 0-03. Oxygen and Nitrogen . . , 0'075. Ash ..... . 0-02. The free hydrogen is nearly 0'02, and hence — P = 0-875 X ] 4500 + 0-02 x 62000. = 13930 B.T.IT. Hence, making allowance for the ash, we get for the pure carbon 14200. 198 VAPORIZATION For a carbon containing 6 per cent, of water and 4 per cent, of ash we have : P' = 14200 X 0-9.- 1 1 14 (0-OG + 9 x 0-04). = 12780-1114x0-42. = 12300. The relative values of carbons are as their weights per cubic foot. Tan Baric. Saivclust. These combustibles are burned in special furnaces. Theoretically they have the same calorific value as the fuels from which they are derived. Tan bark, after it is pressed, contains about 48 per cent, of water, 8 to 12 per cent, of ash, and weighs about 52 lbs. per cubic foot. Its true calorific value deduced from that of dry wood containing 2 per cent, of ash will be — P = 7257 (1 - 0-48 - 0-1) - 1114 x 0-48. -2500 B.'l'.U. nearly. Allowing an efficiency of 40 per cent, we shall have — — i.e. 0'88 lbs. of steam per pound of combustible consumed. Actual trials have given 0-82 pound of steam for every pound of tan bark, and '90 pound of steam for every pound of sawdust consumed. These combustibles burn much better when they are mixed with oil. It is difficult to utilize them properly, as part of the burning material is carried into the smoke-box. Peat and Turf. Turf (mossy, fibrous, or brittle) results from the 199 ENGINE TESTS AND BOILER EFFICIENCIES decomposition of vegetable matter. This is easily- seen in the upper layers, but a little way down in the denser and darker lower layers the remains of the vegetation can no longer be noticed. Turf dried by being placed in the air contains about 20 to 30 per cent, of water, depending on the locality, and from 10 to 25 per cent, of ash. The weight of a cubic foot varies from 40 to 48 pounds. The combustible is light and spongy, obstructing the free passage of the air. It burns badly, and its smoke has a pungent and dis- agreeable odour. After grinding and washing it is made into briquettes. Turf improves by being dried at 212° F. ; above this temperature it decomposes. It has, however, to be used immediately after being heated, as it re-absorbs moisture very rapidly. According to Reguault and Marsilly, dry turf con- tains on an average 0'57 of carbon, 0'06 of hydrogen, and 0'37 of oxygen and nitrogen. The free hydrogen is therefore 0-06 - ^= 0-0137. 8 The calorific power will be given by P = 0-57 X 14500 + 0-0137 x 62000. = 8114. And the true calorific power will be P' = 8114—llf4 (9x0-06). = 7512. If the turf contain 8 per cent, of ash, and 25 per cent, of water, F=7512x0-67-1114x0-25. = 4755. 200 VAPORIZATION Carbon from Turf. This is obtained by carbonizing layers of turf in tubs or ovens made of stone ware or of sheet iron. The return is from 40 to 45 per cent, of a carbon containing from 15 to 20 per cent, of ash. The gases that come from the combustion of the car- bon retain the characteristic odour of burning turf. The carbon from Bssones has 18 per cent, of ash, and a calorific power equal to 0'82 x 14500 = 11890. Lignites. These combustibles mark the transition stage be- tween peat and coal. They are sometimes brown with a woody texture, and have an earthy appearance, sometimes black with a woody texture, and sometimes homogeneous with a resinous fracture. These last are similar to coal. Regnault distinguishes between the imperfect lignites or the fossil woods and the perfect lignites or woods passing into bitumen. They are characterized by the proportion of oxygen, hydrogen, and carbon (or coke) which they contain. The calorific power P of the pure combustible has been determined directly by Scheurer-Kestner and Meunier. Nature. Coke % H H P P. Imperfect lignite. 75 5 to 6 4 11,620 9,000 Perfect lignite. 65 to 70 4 4 6 12,780 9,900 Bituminous. 35 to 40 1 to 2 14,040 10,800 With 0-08 of water and 0*10 of ash for the three 201 ENGINE TESTS AND BOILER EFFICIENCIES varieties, we obtain the true calorific values P'. Also for perfect lignite we have — P' = 12780 X 0-82 - 1114 (0-08 + 9 X 0-04). = 10480-490. = 10000 B.T.U. nearly. COALS. There are a great number of varieties. Regnault and G-runer divided them into five classes : 1 . Non-caking coal (long flame). 2. Gas coal. 3. Coking coal. 4. Coking coal (short flame). 5. Anthracite (short flame). Non-caking Coal. Scotch coal and Sandkohle (Germany) are of this kind. They give 60 per cent, of a coke which is pulverulent or only slightly adherent, and they burn with a long flame which lasts only a short time. These coals are put straight on the bars, but they give less heat than the others we mention below. The mass of a cubic foot averages 44 pounds. They are rarely used in France ; the French coals which resemble them most closely are those of Saint filoi, those of the upper strata at Blanzy, and those of Montceau. 6as CoaT. Cherry Coal. These coals form a cake on the fire without choking it. They are the best coals for steam-raising purposes and for making gas. The flenu of Mons and the Oannel coal of Lancashire are the best qualities. They are more abundant in France than the pre- 202 VAPORIZATION ceding, and form the upper beds of the Pas-de-Calais, of the Loire, of Comnaentry and Blanzy. CoHng Coal. BaclclwMe (Germany). This coal is of a lustroiis black colour ; it is not very hard, and splits in layers. In the fire it cakes and gives a light vapoury smoke. It is not suitable for metallurgical operations. A good coke is made from this coal. On the grate it obstructs the free circula- tion of the air and burns the fire bars, but it gives out a great deal of heat. This coal is plentiful in France, in the basins of Saint-Etienne, of the Nord, and of the Pas-de-Calais. A cubic foot weighs be- tween 44 and 50 pounds. Cuking Goals (short flame). These coals block the fire less than the preceding, and give a harder coke. They are very suitable for metallurgy. In Belgium they are called hard (dures) because they last (durent) a long time in the fire. They are pulverulent. In France they are found at Creusot, Saint- fitienne, Brassac, Huy, le G-ard and le Nord. M. Delautel has made at Brest comparative tests of various kinds of this coal. Taking the calorific power of Cardiff coal as unity, he has found — Coal d'Anzin . . 1-05 to 1-01. Roche-la-Moliere 0-95 to 0-94. Ordinary la Loire . . 0-90. Newcastle . . . 0-84. Blanzy (Montceau). . 078. Long flame (Montceau) . 0"74. 203 ENGINE TESTS AND BOILER EFFICIENCIES Anthracite (short flame). Anthracite is of a dull, black colour, is difficult to ignite, and burns slowly without smoke. When rapidly heated it is apt to break into pieces. The coke got from it is pulverulent. It is rarely used in France, and is not burned on fire bars. A cubic foot of it weighs 53 lbs. The calorific power of various kinds of coal has been measured directly. The following table B gives the mean value of (1) the elementary composition, and (2) the return in coke of the five types of coal which we suppose pure. It also gives (3) the calorific power P', and (4) the quantity of water taken in at 32° F., which would be converted into steam. B. — Mean Results of Five Types of Goal. Nature of Percentage Elemy- Comp. Katio. H Mean Cal. Power of Pare Coal. Water initially at32° Vaporized at 223-6° per pound of coal. Coke. % C H Nature. Non- Caking Coal (long flame). 75 to 80 5-5 to 4-5 19-5 to 15 4 3 14,400 to 15,300 6-7 to 7-5 50 to 60 Pulverulent or only slightly coherent. Gas Coal. 80 to 85 5-8 to 5 14-2 to 10 3 2 15,300 to 15,660 7-6 to 8-3 60 to 68 Caked and porous. Coking Coal. 84 to 89 5 to 5-5 11 to 5-0 > 15,840 to 16,740 8-4 to 9-2 68 to 74 74 to 82 Caked, but with crevices. Coking Coal (short flame). 88 to 91 5-5 to 4-5 6-5 to 5-5 1 16,740 to 17,280 9-2 to 10 Caked and compact. Anthracite (short flame). 90 to 93 4-5 to 4 5-5 to 3 1 15,840 ■ to 17,100 9 to 9-5 82 to 90 Brittle or pulverulent. 204 VAPOEIZATION For a bituminous coal containing 0-02 of water and O'lO of ash, the proportion of hydrogen will be 0"88 X 0-05 = 0-044 and P' = 15570 X 0-88 - 1114 (0-02 + 9 x 0-044) = 13700-1114x0-616 = 13000 nearly. This is how we have calculated P' in Table D. We make a direct analysis of coal as follows — after drying we find the proportion of water hygro- metrically absorbed, we distil the coal in a closed vessel and find the quantity of coke produced. Then burning what is left over after the distillation we find the ash. The drying is done at a temperature of 230°, about a quarter of an ounce of coal being put in a beaker or between two watch glasses. The burning is done by placing about one-eighth of an ounce of coal well pulverized in a porcelain cap- sule in a small furnace suitably warmed to a white heat so as to prevent the formation of coke, which retards the process. We experiment on several cap- sules at once and take the mean of our results. The burning lasts a quarter of an hour for the coke and two hours for the coal. The experiments of Scheurer-Kestner and Brix (Table C) agree with the preceding table. Taking 1152 thermal units for a pound of steam at 233-6° F., we have deduced the efficiency K of each type of pure coal. It will be seen that we can adopt 6 as the mean efficiency of coal. Coal which contains carburetted hydrogen is liable to spontaneous combustion when it is piled in large 205 ENGINE TESTS AND BOILER EFFICIENCIES heaps, especially if damp or if it contain pyrites. It is necessary in this case to keep it well ventilated. If it contains too great a percentage of pyrites it may be necessary to keep it under water. Gas coal alters rapidly in the air ; the loss of the gas may amount to as much as 30 per cent, per month when left exposed. In practice the proportion of ash is from 6 to 10 percent, with medium-sized lumps, and attains from 10 to 20 per cent, with mixed coal of all sizes, depending on the skill of the stokers and the nature of the coal. C. — Results of Vaporization (Brlch Furnaces). Nature of Coal. 1. Long Flame Coal. Mine Gerhardt (Saarbriiok) Mine Leopold (Silfesie sup.) Louisenthal (Saarbriiok) Montoeau (Saone-et-Loire) 2. Gas Coal. Priedriohsthal (Saarbriiok) , Altenwald . . . . , 3. Coking Coal. Ronchamp .... Le President (Saarbriiok) Proportion ia 100 of Coal. Water. 510 410 3-57 4-97 1 2-54 w Ash. 6-84 51 12-28 10-28 12-7 13-5 16-19 2-28 Water vaporized at 233-6° F. per. lb. of coal. Com- mercial. Pure. P4 6-85 6-1 6-06 6-2 6-31 6-95 7-62 811 7-78 6-72 7-29 7-41 7-73 8-27 9-16 8-47 Efficiency. 6 II S Briquettes. The good qualities are moulded under pressure and, at a high temperature, into blocks; the poor qualities are 206 VAPORIZATION made into blocks with pitch. Their calorific power is calculated from that of the coal of which they are made. We suppose the coal to be pure and correct for moisture and ash. Golce (Table B). Coke is made from coal by subjecting it to a high temperature in a suitable oven so as to get rid of its volatile constituents. The amount of ash it yields varies from 4 to 15 per cent., or even more, as we go from the large lumps to the pulverized coke ; and it depends, of course, on the coal from which it was made. It contains from 2 to 10 per cent, of water. Small coal which has been well washed gives purer and more highly priced coke than that produced with- out washing the coal. The cubic foot weighs from 24 to 30 lbs. Gas coke weighs 18 lbs. per cubic foot. The calorific power of coke has not been determined directly ; we can deduce it from that of carbon by the formula — P = 14500 (l-a-b). According to M. de Marsilly dry coke contains on an average 0'04 of hydrogen and 0"06 of ash. For a coke containing 0"02 of water and 0"10 of ash the pro- portion of hydrogen is reduced to 0'035, from which P' = 14500 X 0-88 - 10:2 (0-02 + 9 x 0-035) = 12760-1092 X -335, = 12400 nearly. Anthracite. Anthracite is more lustrous than coal ; it does not 207 ENGINE TESTS AND BOILER EFFICIENCIES soil the fingers, and only burns well at a high temper- ature and when spread in a thick layer. French anthracites are not abundant ; they crumble in the fire and contain on an average 2 per cent, of water and 4 per cent, of ash. The calorific power of the pure combustible varies from 14,760 to 15,840 B.T.U. The cubic foot weighs about 30 pounds. In Table D we have tabulated the number of pounds of steam produced by different combustibles at a pres- D. — Calorific Powers. 1 i Calorific Power. Volume of gas V. in cubic feet. Volume at 572° F. Weight of water in pounds vaporizedin practice at 6 atmos. P. Pi. Wood dried at 284° P. 2 7,290 160 336 3-75 Wood (ordinary) . 30 2 4,768 133 279 2-5 Tan bark .' . . 48 12 2,537 114 239 0-9 Peat 25 8 9,133 5,051 140 294 2-8 Lignite (perfect) . 8 10 12,770 10,000 176 370 512 Coals. Non-caking . 4 8 14,850 12,860 222 465 6-5 Gas coal .... 2 10 15,570 13,320 ■ 6-83 Coking coal . . ,, 16,290 13,860 -256 536 7-1 " Coking coal (short J flame) .... ,, jj 17,000 14,510 7-34 Half Anthracite (h= 4) ,, ,, 16,460 13,860 268 568 7-2 Anthracite . . . 2 4 17,530 15,960 282 590 7-3 Wood Charcoal . 6 4 12,860 12,860 256 536 6-5 Coke (good quality) 2 5 1 12,440 273 573 6-4 sure of six atmospheres, calculated on the assumption of a 60 per cent, efficiency (except in the case of tan bark). The numbers are given in the last column, and the heat required per pound of steam at this pressure is 1,170 B.T.U. 208 COMBUSTION For long flame coal (non-caking) we have 13320x0-6 nooM. = D'8d lbs. 1170 The weights of water vaporized are those we would get in everyday work with a tubular boiler. § 2. Combustion". The Volume of Air required for Combustion. Ordinary atmospheric air coutains 79 per cent, of nitrogen and 21 per cent, of oxygen. Oxygen weighs 1'43 oz. per cubic foot, and air weighs 1"29 oz. per cubic foot at the standard temperature (32° F.) and pressure (29'9 inches of mercury). It follows that one ounce of oxygen is contained in --— -— , i.e. 3'33 cubic feet of air at the standard 0-21 X 1-43 temperature and pressure. For carbonic acid gas containing 72'73 per cent, of oxygen and 27*27 per cent, of carbon, the amount of oxygen necessary to 72'73 burn one ounce of carbon is , i.e. 2"667 ounces. Hence 3-33 x 2-667, i.e. 8-8 cubic feet of air per ounce of carbon, are required. Since water is composed of 88-9 per cent, of oxygen and 11-1 per cent, of hydrogen, the amount of oxygen necessary to burn one ounce of hydrogen is ^^py' i.e. eight parts of oxygen to one part of hydrogen. Hence we require 8 x 3-33, i.e. 26-64 cubic feet of air per ounce of hydrogen. When we know the quantity of carbon G and of free 209 p ENGINE TESTS AND BOILEE EFFICIENCIES hydrogen contained in one ounce of the combustible matter, then we can find the volume of air necessary for its combustion by means of the formula — F = Cx 8-88 + 26-64 (H-^). In this formula V is in cubic feet, C, H and are in ounces. Example. Suppose that we have one pound of wood containing 30 per cent, of water, and that its constituents are Carbon . . . 0-35. Hydrogen . . . 0-042. Oxygen and Niti-ogen 0-294. Water . . . 0-3. Ash .... 0-014. The free hydrogen is 0-042- -'^ = 0-005. The volume of air required to burn a pound of wood will be — 0-35 X 8-88 X 16 + 0-005 x 26-64 x 16 = 51-84. For dry coal containing 12 per cent, of ash and water and 88 per cent, of pure combustible material, we get from Table B the average values of the con- stituents to be as follows : — Carbon . . 0-775 x 0-88 = 0-682\ Hydrogen . . 0-05 x 0-88 = 0-044 Oxygen . . 0-175 x 0-88 = 0-1.54 1 Water and Ash =0-12 The free hydrogen will be — 0-044-^ = 0-025, 210 = 1-000 COMBUSTION and the volume of air necessary for tlie combustion of the one pound of coal will be — 0-682 X 8-88 X 16 + 0-025 x 26-64 x 16 = 108 cubic feet. In practice two or three times this amount is allowed, as the combustion is never perfect and the door of the furnace is frequently opened. According to the experiments of Scheurer-Kestner and Meunier the maximum efficiency of combustion occurs when the air is about 33 per cent, in excess of the calculated quantity required. After the combustion the volume of the gas is the same as that of the air, as carbonic acid gas has the same volume as the oxygen which formed it, but it is increased by the volume of the vapour formed by the hygrometric water in the fuel and by the combustion of the hydrogen. The volume of this vapour is about 9-6 cubic feet for each pound of peat or wood in the dry state and 12-8 cubic feet when they are moist. For coal it is about 6-4 cubic feet per pound. Table D gives as the required volume of gas V double the theoretical value plus the volume of the vapour. For example, we have for dry coal — 7 = 2x108 + 6-4 = 222-4. The volumes of air got from Table D apply to furnaces with a free draught. It is generally accepted that in the case of forced draught, whether by steam blast or fan, the volume of air necessary per pound of fuel is six or seven tenths of V. 211 ENGINE TESTS AND BOILER EFFICIENCIES The final volume Vt of tlie gases in tlie chimney is given by — 7, = F[1 + 0-002(^-32)] where V is their volume at 32° F. and i is the temperature in the chimney. For Example — ^ = 302; Ft = l-54 F. t = 402; Ft = l-74 F. Combustion in the Furnaces. We have seen that carbon and hydrogen are the only elements whose combustion produces heat. The carbon is fixed (coke and wood charcoal) or is con- tained in volatile hydrocarbons. Coke and wood charcoal can be called the solid fuels, as they only burn on the surface which is made luminous. The fuels which contain hydrocarbons are decomposed by the heat, and combustible gases are disengaged which burn but are only luminous at the surface of contact with air. On subdividing the fuel and consequently the flames, we increase the surface of contact with air, and the combustion is more rapid and more complete. The heat produced by burning a substance is dissipated (1) by the current of air which takes place round the body and (2) by radiation. According to Peclet the ratio of the radiating power to the total calorific power is about 25 per cent, for fuels which burn with a flame and about 50 per cent, for carbons. The following table gives the weight of oxygen and the volume of air which contains that weight necessary 212 COMBUSTION to burn one pound of hydrogen or one pound of carbon, the latter of which is transformed into car- bon monoxide G or carbon dioxide C Og and the number of thermal units produced by thecombustion : — Combustible. Theoretical Requireraents. B.T.a. Pounds Oxygen per pound Fuel. Cubic feet of Air Hydrogen gas 8 2-666 1-333 427 142 71 62,032 14,500 4,400 Carbon perfectly burned (CO2) . Carbon imperfectly burned (C 0) Difference 10,100 Combustion of Carbon C. At the commencement of the combustion one pound of carbon C unites with 2'666 lbs. of oxygen and forms 3'666 pounds of C 0^, at the same time giving out 14,500 B.T.U. The volume of the C 0^ is the same as that of the air which formed it, but its density is greater. The combustion is then complete. If, how- ever, there is not sufl&cient air, the 3'666 lbs. of C O2 absorb one pound of carbon and form 4"666 lbs. of G 0. The heat disengaged by the two pounds of carbon transformed into C is 2x4400 = 8800. The loss of heat resulting from the absorption of the second pound of carbon is therefore 14500-8800 = 6700. If now we supply to the 4'666 lbs. of CO the oxygen required to complete the combustion — namely 213 ENGINE TESTS AND BOILER EFFICIENCIES 2"666 lbs., it will burn with a blue flame, and we shall have 7-333 lbs. of CO,. The heat set free will be 2 x 10100 = 20200, which, added to the heat produced by the CO, namely 8,800, gives 29,000 units of heat. This is exactly equal to the heat set free by the complete" combustion of two pounds of carbon (2 x 14500). Couibusfion of Hydrocarbons. These gases, mixed with a sufficient quantity of air, burn with ablue flame producing carbon dioxide COa and water in the same way as gas for lighting purposes. If, however, they are raised to a red temperature before their mixture with the air required for combus- tion they are decomposed. The hydrogen burns first, and a part of the carbon is set free. This carbon burns in its turn if there is sufficient oxygen, and if the temperature of the mixture is sufficiently high. On the other hand, when the combustion is in- complete, and the carbon remains suspended in the gas, then smoke will be formed, which, on cooling, deposits soot. Once formed, smoke cannot be burned. In order to avoid its production it is necessary to mix with the combustible gas a sufficient quantity of air at a sufficiently high temperature, so that the combustion may be complete. This very simple rule, however, cannot be entirely realized in practice, at least with ordinary furnaces. In a gas-producing plant we can consume nearly all the smoke, but this kind of plant is not suitable for continuous work over lengthened periods. 214 COMBUSTION Management of the Fire. We shall only discuss in this place the combustion of coal. We know that the gas resulting from the combustion of the air flowing in must be at a very high temperature in order to obtain the most perfect com- bustion. The turning back of the flames upon the fire bridge produces this heating of the gases, and the combustion is better than when the gas rises verti- cally from the fife-grate. The combustion is completed in the space behind the furnace called the combustion chamber. It is necessary to prevent the flames play- ing on the tubes of the boiler before the combustion is complete, as otherwise the gases are cooled, and large quantities of smoke and soot are produced. The combustible gases being carried up the chimney often take fire on coming in contact with the open air. Attempts have been made to increase the heating of the gas and to suppress smoke by injecting steam or air either at the sides of the furnace, or at the fire- bridge, or the door, etc., either continuously or inter- mittently. We shall not describe all the systems for consuming smoke. None of them up to the present have been completely successful. An excess of air supply is preferable to an insufficient supply, for the loss of heat due to heated air passing up the shaft is less in the former case than it is in the latter, owing to the imperfect combustion. Smoke consumption needs a large supply of air ; it is there- fore not the most economical. The combustion can- not be perfect, and hence there is always some smoke formed. 215 ENGINE TESTS AND BOILEK EFFICIENCIES A clever stoker can produce the same results as the best mechanical devices invented. Instructions on this subject are given by the Seine Hygienic Council, and we abstract from them the follow- ing : — " The origin of smoke is in the volatile products given off abundantly from most fuels, such as the various kinds of coal, peat, wood, etc., when subjected suddenly to a high temperature. The most important of these products is carburetted hydrogen, which is itself extremely combustible. In order to burn it, however, we must see (1) that it is supplied with sufficient air, and (2) that the temperature of the mixture is sufficiently high. If these two conditions are not complied with in the furnace or in the flues connected with it, then the carburetted hydrogen undergoes a decomposition, from which there results a large quantity of soot or of carbonin minute particles, which is carried along by the gases passing up the chimney. When we throw on a fire-grate covered with glowing coke a quantity of coal sufficient to cover it to a depth of eight or ten inches, then the particles of coal which are in contact with the coke decompose rapidly ; the temperature of the furnace thus suddenly falls and at the same time the passage of air through the grate is obstructed. Neither of the two conditions necessary for the coifbustion of the carburetted hydrogen is reahzed, and hence torrents of black smoke issue from the chimney. Under these circum* stances the introduction of air by the furnace door, or by any opening above the layer of coal, will have little effect, because the temperature is insufficient to make 216 COMBUSTION the gaseous products burn. The smoke gradually decreases in intensity as the coal gets converted into coke by losing its volatile constituents ; the pieces cake together, leaving spaces between them by which the air again gets into the furnace, and so the combus- tion increases. If we rake the mixture of coal and coke before the distillation of the volatile constituents is complete, we bring portions of coal not yet carbonized into contact with fragments of. glowing coke, and so the distillation becomes more rapid, and the chimney begins to smoke again. " Furnaces which have a grate area sufficiently large to allow the coal to be spread out on it in a thin layer, preferably even not covering it, give little smoke, especially if the coal be put on in small quantities at a time, and if the stoker is careful to put the new coal at the front part of the grate, so that the gaseous products of the distillation arrive at the flues only after they have passed over the coke in the back part of the furnace, where sufficient spaces are left for the entry of the air. The production of smoke is increased when the grate area is too small for the quantity of coal which has to be burned on it in a given time, and when the stokers manage it badly, putting large quantities on at long intervals. Other things being equal, the smoke will be more abundant the more bituminous the coal, and the more it cakes. The dry coals from some parts of the North of France, and from the neighbourhood of Charleroi in Belgium, give very little smoke in ordinary furnaces when burned with ordinary care. Coke produces no smoke ; the gases yyhich flow from the top of the chimneys of furnaces 217 ENGINE TESTS AND BOILER EFFICIENCIES supplied with this material are colourless, carrying with them only a little extremely fine dust." Coal containing little carburetted hydrogen — as for example, Cardiff coal — gives very little smoke, and has the great advantage of not being liable to sponta- neous combustion even when accumulated in great quantities. When we throw a small piece of coal about the size of a finger on the furnace, it opens out gently as it burns, the middle remaining unchanged until the combustion begins to act there. It is not necessary, therefore, to rake the furnace fire often, since the un- burnt portions of coal can drop between the fire bars into the ash pit. The thickness of the layer of coal on the grate must always be uniform, and be proportional to the draught, but it should not be less than 4 or greater than 6 inches. The stoker should regulate by the flame, which is white when the combustion is good. A red flame is a sign of incomplete combustion due to the layer of fuel being put on too thickly. We feed the fire by putting on the fuel where the layer appears too thin. Large pieces of coal must be broken by the pick in the direction of the cleavage, so as to avoid the formation of dust. The dust can be thrown in a thin uniform layer on the fire when it is in full blaze. We must take care tSbt to put too thick a layer at one point, nor to put it where the fire is not very active. With very large grates we obtain the best combus- tion by stoking each half of the grate at alternate intervals. 218 STEAM TEIALS § 3. — Steam Trials. The commercial efficiency of the engine and boiler depends not only on how the steam is utilised in the engine, but also on the steaming power of the boiler. If we measure the weight of the water injected into the boiler and the weight of fuel burnt, at the same time that we measure the indicated or brake horse power, we shall obtain complete data to determine the actual efficiency. We also obtain the steaming power of the boiler ; that is, the weight of steam produced per pound of fuel. The quantity of steam produced per pound of fuel depends on the quality of the fuel, the design of the apparatus, the way it is treated, and especially on the smartness of the stoker. It has to be remembered also that the results of steam trials are only comparable when they have been made in the same furnace for different fuels or in different furnaces for the same fuel, and in the two cases by the same stoker. When the nature of the fuel that is to be used in the test is specified the contractor determines the percentage efficiency that he can guarantee, knowing the calorific power of the fuel, and he designs his furnace so that the combustion may be as perfect as possible. When the nature of the fuel is not specified he will naturally employ that which will produce the greatest heat for a given weight. From the point of view of commercial production it is obvious that the best fuel is that which produces the greatest quantity of steam for a given price. Suppose, for example, that we have to test two kinds 219 ENGINE TESTS AND BOILEE EFFICIENCIES of coal in the same furnace and under the same conditions. Suppose that a thousand pounds of one fuel costs the user ten shiUings, and turns 6,500 lbs. of water into steam. We obtain — — = 650 lbs. of steam for one 10 shilling. Suppose also that a thousand pounds of the other fuel cost eight shillings and produce 5,000 lbs. of steam ; then we get — ~ — = 625 lbs. of steam for one shilling. Hence the dearer coal is the more economical. If the steam produced works an engine of 100 horse power, taking 25 lbs. of steam per horse power hour and working ten hours a day for 300 days in the year, then the cost of the fuel per annum will be — "With coal at ten shillings per 1,000 lbs., 300x10x100x25 „.^« -,Q 650 = ^'^^ ^^'- With coal at eight shillings per 1,000 lbs., 300 X 10 X 100 X 25 nrt^n 625 ^ = ^^°^- The annual gain will therefore be about £23. Also we shall need less storage space. It will be seen at once that these calculations have a direct bearing on practice. * Trials of this kind have been made by P. Ducos upon English coal. The pressure of steam in the boiler was about five atmospheres absolute, or about 69 lbs. effective pressure, and the feed water wag brought back at 90° F. 220 STEAM TRIALS Coal. Price in Sbillings. Steam per lb. of Coal. Per Ton. Per 2,200 lbs. of Steam. Compared with Cardiff. Cardiff. Liverpool . Newcastle . Coke with 6 per\ cent, of water/ 30 26 29 28 3-833 4-876 5-261 5-259 1 1-27 1-37 1-37 7-816 5-332 6-507 5-324 Cardiff, although the dearest coal, is the most economical. The Management of Stecvm Trials. Readings should not be taken until the fire has got well alight, so that the losses due to heating the brick- work, etc., may be the same as in ordinary working. The trials should be over as long an interval of time as possible. They can be made without upsetting the ordinary work of the factory. At the commence- ment of each test we must thoroughly clean out the grate and the flues, then when the furnace is burning in its normal working condition we must calculate roughly the quantity of coal in the grate, and make allowance for this at the end of the test. In general we take the total consumption of fuel to be that burned during the test, together with the coal left on the grate at the end of the test, less the quantity of coal on the grate at the beginning of the tests, and the unburnt coal that has dropped through the fire bars. A preliminary test on the fuel is made to determine how much ash and water it contains, from which we can deduce the ratio of the pure coal in a given mass of combustible. The measurement of the water can be made directly 221 ENGINE TESTS AND BOILER EFFICIENCIES in any of the following ways — (1) from the number of strokes and the dimensions of the feed pump, (2) by a meter, (3) by automatic feeders, (4) by graduated tanks. This last method is the one employed in very accurate tests. In Fig. 176 the arrangements for measuring the water are shown. Fig. 176. The tube of the feed pump is immersed in a closed reservoir a. This reservoir is surmounted by a smaller one h, such as a cask with the top staved in. A stopcock placed at the bottom of this cask permits water to flow into the reservoir a. The cask h is first of all weighed empty. It is then weighed full of water up to the index c. The difference between these two weights will give us accu- rately the weight of water in the cask, and this can be replenished as often as necessary. We measure the quantity of water used during the number of hours the trial lasts. We measure also the weight of 222 STEAM TRIALS the fuel burnt, and hence we find the number of pounds of water evaporated per pound of fuel. As we can also find the mean indicated horse power during the run from the indicator diagrams, we can deduce the weight of steam consumed per horse power hour or the weight of fuel consumed per horse power hour. Condensed Water taken over. "We must arrange at the extremity of the steam pipe, just before it comes to the cylinder, a blow-off cock for the condensed water in the pipe. The weight of that water has to be deducted from the weight of the water injected into the boiler during the test. As we always mean by steam consumption the weight of the dry steam consumed, it is necessary to deduct further the weight of the water taken over bodily into the cylinder (the priming water) from the weight of water injected into the boiler. We have given two methods of measuring the priming water in Chapter X. Water frovi the Cylinder Cocks. The water obtained from the drainage cocks of the cylinder or the cylinder jacket must not be deducted from the observed consumption. Certain manufacturers give guarantees of consump- tion of steam, the consumption being the quantity of water injected into the boiler less the weight of the condensed water in the cylinder jacket. Others take this into account by taking ten per cent, off the ob- served weight. But the user should not allow these restrictive clauses to be put in the specification. 223 ENGINE TESTS AND BOILER EFFICIENCIES The efficiency can either be given in pounds of steam produced per pound of coal (gross) or per pound of pure coal, the ashes and the contained water being deducted from the gross weight. Correction. We arrange so that at the end of the test the water in the boiler may have the same level and be under the same pressure as at the beginning of the test. If this is not the case a correction has to be made. "We must first of all read the exact levels of the water in the boiler at the beginning and the end of the test. The readings on the tube are not correct, because the water in it is colder than the water in the boiler ; it is therefore denser and at a lower level. If we open the cock of the tube for an instant the water in the tube will be renewed and will now have the same temperature as the water in the boiler. Its height is then read before the water has time to cool down. The difference of the heights h^ (Fig. 177) increases with the difference of the temperatures and becomes important when the \^ter gauge is too far from the boiler. Suppose that the water in the gauge is at 1 04° F., then its coefficient of expansion is 0'000259. Let the heights li and ¥ (Fig. 177) be expressed in feet, then — 224 STEAM TKIALS h=}i-h' = h' [1+0-000259 {t-104)]-h' = 0-0002o9 (i-104) /^'. If h^ be expressed in Indies, then /i, = 0-00311 (i-104) // Absolute Atmo- spheric Pressure. 1 212 2 4 6 8 10 356-5 Temperature t. 248 291-2 318-2 339-5 h, in inches. 0?Ah' 0-45 h' 0-57 h' 0-66 W 0-73 h' 0-79 h' Density of the n-QPic; Water. ' ^ ^°° 0'947 0-937 0-930 0-927 0-923 When records have been taken of the exact readings of the water and pressure gauges before and after the trial, then Regnault's tables give us the corresponding temperatures. To make the required correction we must calculate the number of British thermal units contained in the boiler before and after the trial. We calculate the volume V that the water would have at 32° F. by the formula — F= Ii 1+0-000259 {i-32) The densities given in the table above are found by this formula. We then calculate the number of B.T.U. contained (1) in the corrected weight of the water ; and (2) in the metal of the boiler, taking the mean specific heat of iron for temperatures between 0° and 200° to be 0-115 (Dulong and Petit). We can neglect the different quantities of heat contained in the vapour itself and the effects of ex- pansion. 225 Q ENGINE TESTS AND BOILER EFFICIENCIES Knowing the number of units gained or lost by the boiler we can find the number of pounds of steam vaporized, which is the equivalent of this, and so correct our calculation. Example. Suppose that an "Elephant " boiler is 3'94 feet in diameter and 49 '2 feet long. Suppose also that at the end of the test the level of the water has fallen 3'94 inches, and that the pressure has fallen from 6 to 4 atmospheres. If the feed water is at 59° F., then we shall have — Apparent Volume. i Pressure. ' Temp. /. t—bd. Before the Trial.! 3_938 gallons. 6 318 2B9 After the Trial. ' S,.542 gallons. 4 1 291 232 Correcting the volumes to 32° F. Before the trial 3938 x 0-93 = 3,663 gallons at 32°. After the trial 3542x0-937 = 3,318 „ Hence the difference = 345 gallons. Before the trial 36630 x 259 - 9,486,000 B.T.U. After the trial 33180 x 232 = 7,698,000 „ Hence the difference = 1,788,000 „ The weight of the boiler was 33,000 lbs. It has therefore lost 33000 X 0-115 X (318-291) B.T.U. i.e. 92,460 units. The total loss of hoat is therefore 1,880,000. This represents -^-^ISS^, i-e. 250 lbs. of 7200 - coal at least. 226 In Water. In Coal. 1,584 gallons. 845 „ 2,750 lbs. 260 „ 1,929 gallons. 3,000 lbs. STEAM TRIALS If we have expended during the trial correction Hence the real expenditure is . Therefore the real evaporative power of a pound of the fuel is i.e. 6-4 lbs. of water. ouUU If the level of the water were higher instead of being lower after the test, then the corrections would have to be subtracted from the readings got during the trial. When a test is made during the everyday running of the boiler, we get too high an evaporative efficiency for the fuel when priming takes place When the test can be made during an interval in the regular work, we can avoid priming by proceeding as follows : — We let the engine run on light load, but at its normal speed, which is kept as constant as possible, so that the steam flows over slowly but regularly. The surplus steam is lost through the safety valves. We measure the coal and the water as in the preceding test. We have neglected the fuel burnt during the heat- ing up of the boiler. This error is of small impor- tance during a lengthy test, but we have to take it into account when comparing different kinds of boilers. A boiler which has a great volume of water, like an " Elephant " boiler for example, will take on the first day a large amount of fuel in order to raise steam, but on subsequent days it will take very little, owing 227 ENGINE TESTS AND BOILER EFFICIENCIES to the large amount of heat stored up in its mass. A boiler which holds little water will, on the contrary, require practically the same amount of fuel each day. The comparison, therefore, will not be accurate unless we take into account the total quantity of fuel burnt per day for several days. We have already mentioned that the water injected into a boiler can be measured by a water meter. The readings of this meter will give us important infor- mation about the working of the boiler, just as the integrating indicator informs us of the working of the engine. For example, if we compare the readings of the meter with those of the recording indicator, and with the quantity of coal burnt, we can see the rate at which the boiler can produce steam, and whether there is priming or not. We can also find out whether incrustations are taking place or not, by comparing the readings with those obtained some weeks previously. These records are also a test of the competence of the stoker. Testing the Combustion. When the combustion is perfect the only gases in the flues are carbon dioxide CO^, which has the same volume as that of the oxygen which formed it, and nitro- gen. But in practice there is always a certain quan- tity of carbon monoxide GO, whose volume is double that of the oxygen which formed it, and in addition there is the oxygen in the unburnt air. The Orsat apparatus, which is only a modification of that of Regnault and Schloesing, elaborated by M. Salleron, the manufacturer, allows us to estimate rapidly the 228 STEAM TRIALS three gases, 0, GO, and GO.,, contained in the products of corabustion. A knowledge of these enables us by subtraction to find the nitrogen, and consequently to know what is the volume of air corresponding to a cubic foot of the gaseous mixture. The apparatus is composed of (1) an aspirator G and a burette M, which serves to measure the volume, of the gas at the beginning of the experiment, and after its absorption by each reagent ; (2) a series of three absorption vessels A, B and G, in which the Fig. 178 absorption of each gas is effected by a suitable re- agent ; and (3) a small bellows S, which can free the tube from stale gases by putting the apparatus in connexion with the flue. is a flask containing dilute hydrochloric acid and hence having no power to absorb carbonic acid gas. This flask is in communication, by means of 229 ENGINE TESTS AND BOILER EFFICIENCIES a rubber tube L, witli the lower part oi a graduated vessel M called a burette, whicli is itself jacketed witb a glass vessel full of water, so that the measurements are all made at the same temperature. The upper extremity of the burette is connected to a horizontal glass tube TT', which has a stopcock at E, and is joined to three vertical tubes by cocks i, j and Zc. These tubes are connected by rubber tubing to the upper extremities of glass vessels A, B and C, called absorption vessels, whilst the lower extremities are immersed in the liquids contained in the flasks D, E and F. All the joints are made air tight by wrapping wire round the rubber tubing, and the openings d, e and / of the flasks are closed with rubber stoppers. The apparatus is connected with the space containing the gas to be analysed by means of the rubber tubing V which is fixed to the horizontal glass tube. Finally a bellows S fixed to the side of the box and com- municating with the glass tube by the cock r enables us to extract the air frgm V. For our tests we want to know the relative propor- tions of the carbon dioxide, of the carbon monoxide, and of the oxygen in the products of combustion. The reagents used are (1) a solution of sodium hydroxide which absorbs carbon dioxide ; (2) a solution of potas- sium pyrogallate which absorbs oxygen ; and (3) an ammoniacal solution oi^uprous chloride which absorbs carbon monoxide. The absorption vessels A and B contain a large number of glass tubes which are wetted by the solutions and so increase the extent of surface in contact with the gas and thus hasten the absorption. 230 STBiM TRIALS contains a roll of copper gauze whicb, dissolving in the dilute hydrochloric acid, gives rise to cuprous chloride, and thus the cuprous chloride, which is decomposed by the carbon monoxide, is re-formed by the surplus ammonium chloride present, and so the action is continuous. The potassium pyrogallate and the ammoniacal cuprous chloride absorb oxygen, and hence we must not allow these liquids to come in contact with the air which fills the flasks E and F. With this object in view the liquids are covered with a layer of petroleum about half an inch thick, for it is absolutely necessary in these operations to prevent any action in the receiv- ing jars. Suppose now that we have to perform an analysis of the gases in a flue. Opening the cock B so that the apparatus is in connexion with the atmosphere, we raise the flask G. The acidulated water fills the burette, driving out the air. We then close the cocks B, iandj, open the cock h, and take out the stopper/. Lowering the flask G, the absorption vessel G is filled with the solution in F owing to the suction produced. We adjust the level of the liquid to the graduated mark on the tube just over the absorption vessel, then we close the cock k. We next open the cock B,, and raising G, we again fill the burette ; then closing B, opening j and taking out the stopper e, we suck the liquid in the flask E into the absorption vessel B. Repeating these operations for the third time we fill the absorption vessel A. with the liquid in D. We now open the cock B, then raising the flask G, we fill the burette with liquid up to the first graduation 231 ENGINE TESTS AND BOILER EFFICIENCIES on the upper part of the tube. We then close the cock B and make communication with the flue by the tube N (Fig. 1 78). We open the cock r and work the bellows sucking the flue gases into the tube 7, which is also freed of air or gases formed in the preceding operations. After several seconds, when we are certain that the tube V is filled with the gases, which have to be analysed, we close the cock r and open B, so that the tubes T and F are in communication, and are shut off from the bellows. The water pours into the flask whilst the burette fills with the gases, and when they have come to the same level we shut the cock B to separate the apparatus from the flue and the bellows, and we make certain that the volume of the gas we are going to experiment on occupies 100 divisions of the burette. We open the cock i and raise the flask O ; the water forces the gas into the absorption vessel A, which contains sodium hydroxide. The bundle of glass tubes multiplying the extent of the surfaces in contact, the carbon dioxide is absorbed ; we then lower the flask Q, the gas returns into the burette, and the sodium hydroxide again fills the absorption vessel A. We adjust its level by the mark on the tube and close the cock i. We now place the flask Q so that the water in it is at the same level as in the burette, so that the gas is at the atmospheric pressure and read the volume the gas occupies. The difference between the readings before and after the operation gives us the volume of the carbon dioxide absorbed by the soda. We open next the cock j and go through the same operations for the absorption vessrel B, which contains 232 STEAM TEIALS potassium pyrogallate. We thus find the volume of oxygen in the gases. Finally we proceed in the same manner with the absorption vessel G, which contains an ammoniacal solution of cuprous chloride, and this gives the volume of the carbon monoxide. What remains after these three operations is the nitrogen, which cannot be dissolved by any of the preceding reagents. In order that the absorptions may be complete it is necessary to wash several times the gases in each absorption vessel. We do not pass from one vessel to another until consecutive readings are identical. The sodium hydroxide used has a specific gravityof 36 deg. Baume (1'332). The more concentrated the sodium hydroxide is, the more rapid is the absorption of the carbon dioxide. It is necessary then to change the liquid in the flask D when the reaction is too feeble ; that is, when nearly all the alkali has been transformed into carbonate. The potassium solution has the same concentration as the sodium. It is advisable to add the pyrogallic acid at the time of the experiment, the quantity being proportional to the oxygen that has to be absorbed. The ammoniacal cuprous chloride is obtained by the solution of the cuprous chloride in a liquid formed of a mixture of two thirds of a saturated solution of chlorhydrate of ammonia, and of one-third of ordinary ammonia (22 deg. Baume or 1'18). The cuprous chloride also absorbs oxygen. Hence, in order that the last operation give us the exact quantity of carbon monoxide it is necessary that no oxygen be left unabsorbed by the second operation. 233 ENGINE TESTS AND BOILER EFFICIENCIES The making of the cuprous chloride being slow, it is sometimes an advantage to replace this by hypoclilorous acid (HCIO) which has also the property of absorbing carbon monoxif^e. The ordinary commercial crys- tallised salt is partially altered by exposure to the air. Some of it is put into the flask F and dissolved in hydrochloric acid, and to reduce it to the condi- tion of a protochloride some copper turnings are added to it. The liquid, which is at first brown, soon loses its colour. We keep it under a layer of petroleum as we have mentioned above. Suppose that we have initially 100 cubic inches of gas, and let X = the volume of the nitrogen. 7/ = the volume of the oxygen and the carbon dioxide. z = the volume of the carbon monoxide. We shall have X + y + z = 100 -, 'x 79 and = -_ _ z 21 1 7/ + — 1 2 / Eliminating y between these two equations we find 100 X = 7900 - 79 — 2 Hence having found z by analysis, we can deter- mine ;('. % 234 APPENDIX Weight of Fud burnt per Hour. Boilers with, brickwork flues have a mean efficiency rj = OQ of the calorific power of coal, and for tan-bark and sawdust >; = 0-4; With the same apparatus furnished with reheaters a mean efficiency of );=0-6 was obtained (Table C). ■ For fire tube or water-tube boilers — ri =. 0-74 to 0-75; A boiler having both a brickwork furnace and tubes has a mean efficiency j? = 70. These ratios have been found taking the calorific power of the pure combustible and using the formula P' = P{1~ a-h). For fuels which absorb moisture readily, like tan bark or saw- dust, we must calculate P' as in table D. Example. — Suppose that we have to raise per hour 2,200 lbs. of steam ata pressure of six atmospheres (73-5 lbs. gauge pressure) in a fire-tube boiler, the feed water being at 60° F. with coking coal (short flame), P'= 14,510 (Table D). The weight of fuel required per hour will be 2200 (1180-60) Q = 0-75 X 14510 226 lbs. Chimneys and Flues. Their dimensions are deduced from empirical formulae. According to d'Arcet the section S at the summit of a chimney whose height is 33 feet must be one-third of the surface of the grate and correspond to a weight of 66 lbs. of coal burnt per hour per square foot of section. This rule is in agreement with the more general formula of 236 APPENDIX Montgolfier. Let S be the section in square feet, Q the weight of coal burnt per hour in pounds, and H the height of the chimney, then -S = 0-088 -j=^ and ,Sv/5' = 0-088 Q . • • • («) f^ 30 40 50 60 80 100 150 200 VH 5-48 i 6-32 7-07 7-75 8-91 10 12-2 14-1 Other authors suggest the following rules — /S' = J of the surface of the grate (coal). 8 = 1 oi the surface of the grate (wood). Peclet in his Traite de la Chaleur has proved — 1. That the, draught of a chimney is proportional to ^/H. 2. That there is no advantage gained by letting the products of combustion enter the chimney at a temperature greater than 482° F. It is better to utilize the heat in the boiler and not let the gases escape until they have been cooled to 350 or 400° F. 3. That the real velocity V of the gases in the chimney is less than one-fifth of the theoretical velocity. For grates burning 21 lbs. of coal per square foot of surface per hour and for < = 572° F., Peclet found that H and V were connected as follows : H in feet. V in feet per second 32-8 65-6 98-4 60 80 9-2 The cubic feet of gas which passed up the chimney per hour in the three cases per square foot of cross section were 6 x 3,600, i.e. 21,600, 28,800 and 33,120 respectively. Supposing that 290 cubic feet of air were required for every pound of coal con- sumed, we can burn per square foot in the three cases 74, 96-5 and 107 lbs. per hour respectively. The ratio of these weights is approximately the same as the ratios of the square roots of the heights ( \/H). In practice it is generally assumed that _^ 236 S = Jc- APPENDIX If the chimney be at some distance from the boiler, k is generally taken as equal to three-fourths of the value given above (0-088). The table below, giving the heights of the chimneys at the Paris Exhibition of 1878, justifies taking Ic as 0088. If we wish to express (S as a function of the horse power N, and if we use m lbs. of coal per horse power hour, the formula can be written — S = K m N K' N If we admit as good practice wi = 5 lbs. we shall have .fir' = 0-75x 0088x5 = 0-33 toX' = 0-088x5 = 0-44i Taking the first number we find that the admissible horse- power for a given chimney can be found by the formula The following table has been calculated from this formula : — Admissible Power for Given Chimneys. Section Heiglit of Chimney in eeet. H. Feet. in Square Feet. 60 70 80 90 100 150 1 0-785 Horse Power. N. 18-3 19-6 21 22-4 23-5 28-7 2 3-14 73 78-7 84-2 89-5 94-2 115 3 7-07 165 178 190 201 212 260 4 12-6 294 315 337 358 378 462 5 19-6 455 491 527 557 589 720 6 28-3 660 712 760 808 850 1040 7 38-5 890 962 1014 1094 1178 1407 8 50-3 1172 1264 1350 1436 1508 1846 1 The Babcook & Wilcox Co., in their book on " Steam," use K'=0-3, but they increase the diameter of the chimney in order to take account of the friction of the issuing gases. It is, however, not justifiable, as we have shown in this work, to compare this co-efficient with those obtained by Tredgold, d'Arcet, and Pcclet, because the modern consumption of coal per actual horse power hour is not comparable to that with which those authors worked. 237 APPENDIX For fuels other than coal which require V cubic feet of air per pound for combustion, coal requiring V cubic feet, we can suppo.se that the new section S' will be given by the formula For peat and wood 7^ is 128 and for coal V is 256. Hence 16 2 The draught being directly proportional both "to S and to •/H, a little consideration will show that it is more economical to increase the section than to increase the height. In deter- mining the section it is necessary to take into account possible future extensions of the plant, but it is a mistake to have it too great, as this would cause down draughts. In towns in France the height is generally fixed at 984 feet (30 metres). It must be sufficiently high to prevent the vertical component velocity of the wind having any influence on the velocity of the issuing gases. The horizontal component of the velocity has no appreciable effect on the draught. Other things being the same, draughts are more troublesome with low chimneys than with high ones. The height must also increase with Q, the quantity of coal burnt per hour, in order that the issuing smoke may be sufficiently diluted with air as not to be a nuisance to the neighbourhood and not spread smuts over those products of the factory which are kept out of doors. According to an ancient rule which experts still use, a factory chimney must be at least ten feet higher than tiie roof of any house within a radius of 164 feet (50 metres). In order to verify the above formulae we have constructed a table of the heights of the chimneys, etc., at the Paris Exhibition of 1878. The height H is ^ken from the fire-grate. The ratios — indicate the weight of coal' burnt per hour per S square foot of the section at the top of the chimney, on the iiypothesis that one pound of coal is burnt per square foot of grate surface. 238 APPENDIX Chimneys at the Paris Exhibition of 1878. Boilers at the 187)3 Exhibition. H., above the grate D, diameter at top 8, section in feet . g, surface of grate S ratio Coal burnt per square foot 5=0088 — £ gives D'= 10 10-2 3-76 ^ w 95 98 .S-9 2-95 10-5 5-9 106 41 7 20-4 3-28 ^ : CO cb 3 4 5 fi 7 108 108 114 120 122 2-95 3-28 31 2-95 2-85 5-9 7-3 6-5 5-9 5-6 33-4 105 74 39 37 5-6 14 11 6-5 6-5 20-4 102 10-2 20-4 20-4 2-62 3-28 304 31 3-45 o 137 4-6 14-7 93 6-5 20-4 41 The mean value of-^- for Nos. 1, 4 and 5 is 12. We conclude S that those grates burn only half the quantity of coal per square foot of grate surface that the others do. It will be seen that the formula Q ^ = 0-088 -^ gives values of the diameter D' which are very nearly equal to Z), with the exception of the sheet iron chimney (2), where we have had to use the formula ^ = 0044^^ At the Sugar Kefinery of Bourdon (Puy-de-D6me) the two principal chimneys are 214 feet high, measured from the level of the grate, and their diameter at the top is 7'4 feet. One of them receives (1) the smoke of six furnaces heating Elephant boilers (Gail) which have 5,200 square feet of heating surface, and (2) the smoke from the furnaces of five tubular boilers (Call) which have 6,700 square feet of heating surface. Hence there are altogether 11,900 square feet of heating surface. Now the mean value of the coal burnt per hour is 4,180 lbs. and hence 035 of a pound of coal is burnt per hour per square foot of heating surface. The formula 239 APPENDIX S = 0-088 -^- gives a diameter of 5-7. The real diameter 74 feet, which is known to be too great, corresponds to the formula ^ = 0-147 -^ Chimneys with Forced Draught. The section in this case is about one-eighth that of the grate surface when the horse power is between two and four, and about one-fifth that of the grate for horse powers between sixteen and twenty. The height varies from 8 to 12 feet for locomotive boilers to 30 feet for boilers which may be described as half- stationary. These heights are, of course, subject to local regula- tions. Construction. The round form is always to be preferred. A little pit just underneath the flues receives the deposit of soot. We employ curved bricks and cement in building the chimney. They are constructed also in stone with Portland cement. For tall chinmeys we place the bricks in layers which have the same diameter for lengths of every three or four feet. It is best to have no cornice, but it is necessary to surround the top with curved metal plates bolted together. The exterior batter should be at least about 3 in 100. Every stage should be 20 to 30 feet in height and every step back about 3' 5 inches, the breadth of a brick. With curved bricks these step backs are multiplied, and they may be only about an inch. The interior diameter diminishes from the bottom to the top of the chimney. In order to diminish the total weight of the construction upon a bad foundation a sheet-iron cylinder is constructed which has a layer of bricks as thin as possible inside. We place lightning conductors on tall chimneys. The space protected by their influence is a cone whose vertical height is the conductor and the radius of its base equals 1'75 times its height. Temporary chimneys are often made in sheet iron and painted or, better, galvanized. We make their ends slightly conical to 240 APPENDIX keep out the rain. They are kept in position by galvanized iron wire-ropes. Stability of Chimneys. If we consider a chimney as an elastic solid firmly fixed in its base, we have from the theory of the strength of materials (a) Where R = the maximum force per square foot of base, to = the area of base = tt (r^ — r'^). P = the weight of the chimney above base. IJ. = S pxy (see Fig. 179) = F y. = the moment of the external forces. S — the area of the exterior surface ah A B. f = the pressure of the wind per square foot. / = the moment of inertia of the section. _7r (/-r'^) for a round chimney. = the distance of the fibres furthest from the neutral axis 0. y. C L ^b ^ -ar if 1 1 1 1 / 1 1 k 1 1 SpK.P ^ '' I ■^-■".r 1/ \ % 1 1 ' \ r B-^'-^ \ ii i h xVo V/ J, H-^:ii .A -4 Tig. 179. 241 APPENDIX 'Tha volume of the chimney shown in Fig. 179 is approximately equal to the mean of the area of its ends multiplied by its per- pendicular height. The density of the brickwork is about 106 lbs. per cubic foot. The pressure exerted by a gale is estimated at 60 lbs. per square foot on a plane surface placed perpendicularly to the direction of the wind in an exposed position. In valleys and when the chimneys are partly protected by other buildings the pressure rarely exceeds 40 lbs. per square foot. It can also be proved thai it is only half this amount per square foot of cylindrical surface. Hence p = 30 lbs. or 20 lbs. Dividing the trapezium ah A B (Fig. 179) into two triangles by joining 4 and 6, we get the following equation to find y, the height of the centre of pressure. „ T-Ji h , h 2h Su = D~ X - + d ~ X — . ^ 2 3 2 »- 3 h^ ' =- (D+2d). 6 Multiplying by p we get the moment fi — lu. = Sy ^ 30 = 5h- {D + 2d) fi = Sy X 2»= ^^h' {D + 2d). Substituting these values of ft in (a) above we get the approx- imate formulae — R P „- rh' {D + 2d). .,, ~ ±6-5 A-~r-,~ . . . (b, ft) r' — r'* P rh'{D + 2d). For iron chimneys r differs very little from r', and taking p = 20 lbs. per square inch we have P ^ h'jD + 2d ). CO !■! r^(r-r') R=~ ^m " z.^::'- ■ ■ ■ (c) When iron chimneys are steadied by guy ropes, the part of the 242 APPENDIX chimney below the point of attachment is only subjected to a P pressure — . CO The force F = S p (Fig. 177) produces a compression increasing P from to B which is added on to the compression - . p From to A, F produces an extension which opposes — and is a maximum at ^. At A there is compression or extension according as R is positive or negative. Ajjplioation of Formula to a Chimney 95 feet high. P the weight of the chimney at the foot of the 95 feet is 240,000 lbs. r = 4-92 feet ; r' = 3 feet ; (^ = 4-4 feet ; p CO = 47 '3 square feet and — = 5090 ft) Substituting these values in (&') we have 4-92 X (95) ' (9-84 + 2 x 4-4) R= 5090 ±4-5 = 5090 ±4.5 (4-92)' - 3* 45000 X 18-64 505 = 5090 ± 7540. hence R per square inch = 35-3 ± 51-1. Hence for compression R = 86'4 lbs. per square inch and for extension R= 15'8 lbs. per square inch. Hard bricks well baked, sometimes called " Burgundy " bricks, with hydraulic mortars or the cements which are preferably employed crush under a load of 1,800 to 2,000 lbs. per square inch, and break on extension under a load of 200 to 250 lbs. per square inch. In practice the compression must not, exceed 15C 243 APPENDIX to 180 lbs. per square inch, and the extension should not be greater than one-fifth of that for which rupture occurs, i.e. it should not exceed 40 or 50 lbs. per square inch . The section of a flue should be at least equal to that of the chimney. It increases on approaching the furnace because the volume of the gases is greater and because there are usually more abundant deposits of soot. The section for the passage of the gases over the fire bridge is about 60 per cent, of the area of the grate. The first flue under the boiler is generally sufficiently high to aUfl w the smoke and ash carried over to drop into a lower channel. The section of the flues which follow is about 75 per cent, of that of the first or 50 per cent, of the area of the grate. Furnaces with Ordinary Grates. Grates are generally raised about two feet from the ground, and are either horizontal or preferably incUned downwards from the front to the back at the rate of 1 J to 2 inches per foot of grate. The bars are fixed loosely on bearers and are generally made of cast iron; Their length varies from IJ feet to 2^ feet, and they are made thinner towards the lower edge so as to give access to the draught and facilitate the falling of ashes and the cooling of the bar. The space between the bars varies from J to f of an inch, and the empty space is about a third or a fourth of the total surface of the grate. The thickness of the ends of the bars keeps the dimensions of these spaces fixed, and as a further precaution in the case of long bars a boss is made at their centres to prevent them closing up. Bars must be free to expand in every direction, and to f aciUtate this an extremity is often cut on the slant. ' Thin bars alter less and subdivide the air better under the fuel. For a given space between the bars (J to | of an inch) they also give more air space for a given area of grate. The drier the fuel and the more it is divided or the more it divides in the fiie like anthracite and dry coal, the more it is necessary to reduce the size of the spaces between the bars. For large coal these spaces must be wide enough to allow the rake to go through and the bars must be stronger. Grates are 244 APPENDIX sometimes made of special laminated iron bars. In this case two or three of the bars are riveted together. The surface of the grate can be calculated by counting that it must burn 8 to 12 lbs. of coal per square foot per hour when the combustion is slow, and 14 to 20 lbs. of coal per square foot per hour for rapid combustion. The latter system is preferable, especially for high powers, as it allows us to use smaller grates, which are easier to manage. In furnaces which use forced draught, whether steam blast or fan, we can burn from 40 to 80 lbs. of coal per square foot per h^ur. In order that a grate may be easy to manage it must not be longer than 5 or 6 feet and broader than about 3 if the combustion be rapid or 5 if it be slow. The wall at the end or fire-bridge rises from 8 inches to 1 foot 4 inches in height above the level of the bars according to the thickness of the layer of fuel. Single doors are generally 8 inches high and from 8 to 12 inches broad ; double doors are from 10 to 12 inches high by from 16 to 24 in breadth. They are mounted on an inner door of sheet-iron and are separated from the grate by a cast-iron base from eight to sixteen inches broad. The following table indicates the most suitable thickness of the layer on the grate for various fuels, the weight burned per square foot and the shortest distance between the grate and the boiler. > Nature of Fuel. Knely divided coal Nuts . Dry Coal Coke . Wood Tan Bark Feat. Turf Sawdust Tiiiclrness of layer (inches). 2 to 31 4 to 6 6 to 8 8 to 12 ]2tolG Pounds burned per square foot. 0-9 to 1-3 1-3 to 2-2 2-2 to 2-85 4-4 to 6-6 6-6 to 7-7 2-2 Minimum dial .from boiler to grate (inches). 12 to 16 ns to 19-5 ditto 21-5 to 23-75 23-75 to 29-5 ditto 19-5 to 21-5 The distance of the boiler from the grate is a little farther when the surfaces are very large. When we wish to get more power from a given boiler it is generally more economical to buy a higher grade coal than to , 245 APPEHDIX increase the thickness of the layer on the grate, which would make it burn badly and give us a low efficiency. Grates for sawdust and tan-bark must be large in order to diminish the velocity of the draught, which has a tendency to take the burning particles along with it. Hence we must have large flues and they must be frequently cleaned. Ash Pit. The ash pit must ofier to the air a free passage at least equal in section to that of the chimney. The use of a water tank underneath the furnace has certain advantages. First, the unburnt pieces of coal can be used over again ; then, secondly, the air drawn under the grate is not heated by the burning ashes, the maximum amount »f oxygen is furnished for the combustion and the bars are less heated, and finally the stoker can see the state of the fire by watching its reflection on the water. The ash pit must be provided with gates which, when the register is closed, suppress all draught and keep the fire alight from evening to morning. Boiler. The thickness of the plates has practically no influence on the transmission of heat from the furnace gases to the water. The heat transmitted is proportional to the difference of temperature between the two sides of the plates. In boilers where the heating is on the exterior surface, the heating from below is much more efiicacious than the heating from above. First, because of the convection ciirrents, the hotter water continually rising and the colder water flowing underneath. Hence the difference of temperature between the gas and the water is greater and the bubbles of vapour which are formed rise rapidly, whilst the vapour which accumulates in the upper part as in water-tube boilers circulate slowly and gives up its heat, thus rendering the transmission of heat throughout the mass of the boiler more gentle, as the specific heat of steam is only 0'5. Secondly, because the upper part of a boiler is covered quickly with ashes which prevent the contact with the warm furnace gases. Also it is convenient to make the arches of the furnace rest on the upper side of the boiler. In the lower surface of the boiler the transmission of the heat 24G APPENDIX can be modified by incrustations of lime. It appears iiiore active with a tbin deposit after the boiler has been in use some time than with new iron plates. The transmission of heat is accelerated by a well designed circulation of the water in the boiler. The feed water must be injected into the lowest and coldest part of the boiler. According to theory we ought to utilize the heat as near to the fire as possible, or where the temperature is a maximum, and not allow the products of combustion to escape until they were cooled down as far as practicable. No advantage, however, results from cooling them below 400° F. The direct heating surface must be as near to the grate as the nature of the fuel permits (see the table given above). In flues the ratio of the heating surface to that of the brick work must be as great as possible, so that the loss of heat by the brickwork may be a minimum. These losses are small when the furnace is embanked in the ground. Evaporation per Square Foot. The greater the heating surface for a given quantity of coal burnt, or the less coal burnt for a given heating surface, the higher is the efficiency. But this rule, which is as old as the invention of boilers and has suggested reheaters, has in practice a limit below which the advantage is nothing since the heat absorbed by the furnace is practically constant. The maximum efficiency appears to correspond to a con- sumption of 035 to 0-4 lb. of coal per square foot of heating sur- face per hour. If we burn upon the grate per hour 18 lbs. of good coal per square foot of surface, the heating surface wUl be about fifty times that of the grate. If we burn 04 lb. of good coal per square foot of heating surface, then the water raised in temperature from 60° F. to 310° F. (6 atmospheres) and evaporated will be 14500 ^ , . ^ 0-4 K = 5 pounds per square loot. Adopting the efficiencies mentioned before, tubular boiliis will evaporate 247 APPENDIX 5x0-5 = 2-5 pounds per square foot. Tubular boilers with reheaters will evaporate 5 xO-6 = 3 pounds per square foot. " Mixed boilers " will evaporate 5x0-7 = 3-5 pounds per square foot. Fire-tube boilers will evaporate 5 xO-75= 3-75 pounds per square foot. These numbers are the ones generally used, and their ratios are 12, 15, 18 and 20. If we increase the evaporation too much there will be priming;. Proportions of Various Types. The proportions or ratios between the heating surface and C the grate area — for various types of boiler are given in the S table below. Also the ratio between the total heating surface and rp C the volume of water — and the ratio of — ; i.e. the ratio of the s orrate area to the section of the tubes. o The boilers are of five types — 1. Galloway boilers. 2. Half-tubular. 3. Fixed furnace and tubes. 4. Locomotive. 5. Water- tube, heated from the outside. Volume of Water (0). Healing Surface per Cubic Foot of Water. In non-tubular boilers the volume of the water may be six or ten times as much as that evaporated per hour. Suppose thai we have an evaporation of 0065 of a cubic foot of water per sqm re foot of heating surface per hour. The heating surface per cubic foot of water will be With the ratio 6 ; .... = = 2-56 6 X 0-065 0-39 With the ratio 10 ; .... = — — = 1-54 10 X 0065 0-65 For the half-tubular and the fire-tube boilers this ratio rises 248 APPENDIX from 30 to 4-5. Finally, for water-tube boilers (tubes outside) this heating surface per cubic foot of water rises to 9 and 21. The small volumes of water reduce the space occupied by the boiler and allow powerful generators to be used in central districts. Volume of Vapour (V). This volume is generally from two to two and a half times that evaporated per hour, but as before there is no fixed rule. It is one-fifth the volume of the water in Elephant boilers, although it is often equal to the volume of the water in boilers which produce steam rapidly. Heating SuT-face. VolTimed. S3 u « Tubes. S , S o ^ t M N ' '' e3 (D ii (S ij Cf-I ^OJ oj ,D tM «H CfHUH u EH S •1 13 E3 to II i 1 o at 1 M g g r^ ■3 1' -.3 CQ .2 •5 S rt "S ^ 1 1 ^ MS' T C S s. 0. T. "5" 0. V. U n. n 8. u Villette . . 21 1086 450 1535 53 740 141 2-14 102-1 10-7 Eschger . 13 495 496 40 268 98 1-83 46-4 10-7 — Galloway 36-5 1150 1160 33 812 230 1-43 172 6-7 — Chevalier O. et. D. . . 29 860 645 1495 30 635 159 2-44 176 6 — Ditto . . . 28 772 322 1094 29 708 254 1-58 172 4-5 "■ — ^^ Meunier 27-4 1130 1130 41 338 162 3-36 79 14 1-3 7-7 ^ a- Fontaine 22-5 1180 258 1438 62 460 120 3-05 73 16 1-38 6 " =3 Lebrun 36 1870 64-5 1935 52 530 98 3-66 65 29 2-65 6 ■gajste. Cle. U 720 720 52 223 77 3-06 48-5 15 0-83 5-6 ■^§\ Faroot . 30-5 1720 171 1891 66 495 240 3-8 126 13-6 1-62 6-8 . rSulzer . 14 450 268 708 33 194 84 3-66 17-7 26 0-96 5-4 o >\ SiSraphin 22-8 1150 226 1375 50 296 120 4-56 28-7 40 1-3 6-5 o'-gi Fives ^ S [ Lille . 23-6 1240 — 1240 52 148 148 8-25 98 12 1-34 6-5 .§ JBarbe g Petry . u -! Mao Nicol 45 1525 1525 34 353 152 4-26 130 12 — — 19-4 646 — 645 33 106 95 6-1 30.2 22 — — ■2 de Naeyer 37-5 1700 — 1700 46 177 106 9-75 — — — — ^ Belleville 41 1245 — 1245 30-6 53 — 23'5 — -1-|- 249 APPENDIX Healing Surface per Square Foot of the Surface of ttie Water. This ratio varies from 5 to 8 and has a mean value of 6-5. The higher this ratio the more violent is the ebullition and the greater is the priming. Safety Valves. The diameter of safety valves in inches is determined by the following formula — i=^y 1-42 p +8-5 (a) where p = the effective pressure in pounds per square inch and 0= the total heating surface in square feet. The breadth of the seat of the valve does not exceed 24 mils. for small boilers and 80 mils, for large boilers. The diameters of the safety valves in the following table are calculated by means of formula (a) above : — Heatiti^ Surfaet iu scjt.are fpet. Diameters of Safety Valves in Inches. Gauge Pressure in lbs. per square inch. C. ill 50 60 70 80 90 100 110 120 20 0-77 0-70 0-64 0-60 0-57 0-54 0-51 0-49 0-47 40 1-08 0-99 0-91 0-85 0-80 0-76 0-72 0-69 0-66 60 1-33 1-21 112 104 0-98 0-93 0-89 0-85 0-81 80 1-53 1-39 1-29 1-20 113 1-07 102 0-98 0-94 100 1-72 1-56 1-44 1-34 1-27 1-20 1-15 109 105 120 1-88 1-71 1-58 1-47 1-39 1-32 1-25 1-20 115 140 203 1-85 1-71 1-59 1-50 1-42 1-36 1-30 1-25 160 216 1-98 1-82 1-70 1-60 1-52 1-44 1-38 1-32 180 2-30 2-09 1-93 1-80 1-70 1-61 1-54 1-47 1-41 200 2-42 2-21 2-04 1-90 1-79 1-70 1-62 1-55 1-49 250 2-71 2-46 2-28 213 200 1-95 1-81 1-73 1-66 300 2-97 2-70 2-50 2-33 2-19 2-08 1-98 1-89 1-82 400 3-44 3-12 2m 2-68 2-54 2-40 2-30 2-18 210 500 3-83 3-48 3-22 301 2-83 2-69 2-56 2-45 235 600 4-20 3-82 3-53 3-29 310 2-94 2-81 2-68 2-58 700 4-54 413 3-81 3-56 3-35 3-18 303 2-89 2-78 800 4-84 4-42 4-08 3-80 3-58 3-40 3-24 310 2-98 900 5-16 4-68 4-32 4-02 3-81 3-60 3-45 3-27 315 1000 ' 5-41 4-93 4-55 4-25 4-00 3-80 3-62 3-46 3-32 1250 606 5-51 509 4-76 4-48 4-25 405 3-88 3-72, 1500 6-63 603 5-58 5-21 4-91 4-66 4-43 4-24 4-07 2000 7-67 6-97 6-44 601 5-66 5-37 512 4-89 4-70 260 APPENDIX COMPARATIVE TABLE OP PRESSURES. Atmospheres Effective lbs. per Effective lbs. Atmospheres Absolute. sq. la. per sq. in. Absolute. 1 0-000 10 1-68 1-5 7-35 20 2-36 2 14-69 30 3-04 2-5 22-04 40 3-72 3 29-38 50 4-40 3-5 36-73 1 60 5-08 4 4407 70 5-77 4-5 51-42 80 6-45 5 58-76 90 7-13 5-5 6611 100 7-81 6 73-45 110 8-49 6-5 80-80 120 9-17 7 8814 130 9-85 7-5 95-49 140 10-53 8 102-83 150 11-21 8-5 110-18 160 11-89 9 117-52 170 12-57 9-5 124-87 180 13-25 10 132-21 190 13-93 10-5 139-56 200 14-61 EFIECTIVE PRESSURE AND TEMPERATURE. E ffective Pressure lbs. per sq. inch. T. Temperature. 212° F. Effective Pressure lbs. per sq. incb. T. Temperature. 75 322- r P. 5 227-6 „ 80 326-0 „ 10 240-3 „ 85 329-6 „ 15 250-9 „ 90 332-8 „ 20 260-2 „ 95 336-6 „ 25 268-3 „ 100 339-8 „ 30 275-7 „ 110 ' 346-0 „ 35 282-4 „ 120 351-8 „ 40 287-5 „ 130 357-2 „ 45 294-3 „ 140 362-4 „ 50 299-6 „ 150 367-1 „ 55 304-7 „ 160 371-9 „ 60 309-4 ., 170 376-2 „ 65 313-9 „ 180 380-4 ,. 70 318-1 „ 190 384-5 „ 200 388-4 „ 251 APPENDIX PROPERTIES OP SATURATED STEAM. Absolute Pressure. Tempera- Total Heat Weight of V. Volume 935-4. Atmos- pheres. lbs. per 5q. incli. ture in degrees F. in lbs. from 32° F. 1 cubic ft. in lbs. of 1 lb. in cubic ft. T. •1 1-469 115-16 1117-06 •004279 233-7 4^002 •2 2-938 140-81 1124-89 ■008256 121-2 7^723 •3 4-407 157-10 1128-04 •01157 86-46 1081 •4 5-876 169-25 1131-77 •01618 61-79 1514 •5 7-345 179-10 1134-75 -01949 51-31 18-23 •6 8-814 .187-30 1139-07 -02335 42-83 21-84 •7 10-283 194-50 1140-52 •02709 36-92 25-34 •8 11-752 201 1143-23 •03058 32-71 28-63 •9 13-221 206-10 1144-99 •03418 29-26 31-97 10 14-690 212 1146-60 •03773 26-51 35-30 •1 16-159 216-8 1148-27 •04123 24-25 38-57 •2 17-628 221-3 1149-44 -04477 22-34 41^88 ■3 19-097 225-5 1150-72 •04826 20-72 45-14 •4 20-566 229-4 1151-91 •05175 19-32 48-41 •5 22-035 233 -r 1153-04 •05524 17-94 52-14 ■6 23-504 235-8 1154-12 -05872 17-03 54-93 •7 24-973 239-9 1155-13 -06215 16-09 58-11 •8 26-442 243 1 1155-99 •06560 15-25 62-76 ■9 27-911 246 1157-02 ■06896 14-50 64-52 2-0 29-380 249-1 1157-90 •07243 13-80 67-75 •1 30-849 251-8 1158-77 •07577 13-20 70-87 •2 32-318 254-5 1159-58 •07921 12-63 74-09 ■3 33-787 257 1160-37 -08256 12-12 77-23 •4 35-256 259-7 1161-13 -08594 11-63 79-89 •5 36-725 262 1161-86 -08930 11-20 83-52 •6 38-194 264-4 1162-58 -09268 10-79 86-70 •7 39-663 266-7 1163-27 -09603 10-41 89-82 •8 41-132 268-8 1164-33 -09936 10-07 92-94 •9 42-601 271 1164-58 -1041 9-605 97-38 3 44-070 273 1165-21 -1060 9-434 99-15 •1 45-539 275 1165-81 -1092 9-152 102 2 •2 47-008 276-8 1166-43 -1126 8-882 1053 •3 48-477 278-9 1167-01 -1159 8-630 108-4 •4 49-946 280-7 1167-59 -1192 8-389 111-5 ■5 51-415 282-5 1168-14 -1223 8-181 114-4 •6 52-884 284-3 1168-69 -1258 7-949 117-7 •7 54-353 286-2 1 1169-23 -1291 7-747 120-8 •8 55-822 287-9 1169-75 -1323 7-558 123-8 ■9 57-291 289-6 1170-25 -1356 7-372 126-9 40 58-760 291-2 1170-75 -1389 7-199 129-9 ■1 60-229 292-8 1171-24 •1421 7-037 1329 ■2 61-698 294-3 1171-73 •14.54 6-877 136-0 ■3 63-167 295-9 1172-19 -1487 6-716 139-1 •4 64-636 297-5 1172-66 -1519 6-585 142-1 •5 66-105 298-9 117311 •1552 6-446 145-1 252 APPENDIX PROPERTIES OP SATURATED STEAM.— continued. Absolute Pressure. Tempera- ture in iegrees F. Total Heat in 1 lb. from 32° P. Weight of 1 cub. ft. in lbs. V. Volume of 1 lb. in cubic ft. 935-4 Atmos- pheres. lbs. per sq. inch. V. ■6 67-574 300-4 1173-56 -1583 6-316 148 1 ■7 69043 301-8 1173-99 -1616 6-187 151-2 ■8 70-513 303-7 1174-43 -1647 6-074 154-1 ■9 71-981 304-7 1174-86 ■1681 5-951 157-1 5-0 73-450 305-9 1175-27 ■1712 5-839 160-2 •1 74-919 307-4 1175-69 -1745 5-732 163-2 •2 76-388 308-7 1176-08 -1776 5-630 166-2 ■3 77-857 309-9 1176-48 ■1808 5-530 169-1 ■4 79-326 311-1 1176-84 -1847 5-414 172-8 •5 80-795 312-5 1177-27 -1873 5-340 175-2 ■6 82-264 313-9 1177-63 -1904 5-2.52 178-1 •7 83-733 314-9 1178-01 -1936 5-165 1811 ■8 85-202 316-2 1178-39 -1968 5-081 184-1 •9 86-671 317-5 1178-75 -2000 4-999 187-1 6 88-140 318-6 1179-11 -2032 4-921 190-1 •1 89-609 319-6 -1179-47 -2064 4-846 193-1 •2 91-078 320-9 1179-81 -2095 4-773 196-0 •3 92-547 322 1180-17 -2127 4-700 199-0 •4 94-016 323-3 1180-51 -2159 4-631 201-9 8-5 95-485 324-1 1180-83 -2191 4-565 204-8 •6 96-954 325-2 1180-97 ■99,9'>, 4-501 207-8 •7 98-423 328-3 1181-50 ■2254 4-437 210-8 ■8 99-892 329-5 1181-83 -2286 4-375 213-8 •9 101-361 330-5 1182-15 -2316 4-317 216-7 7-00 102-830 331-5 1182-47 -2347 4-260 220-1 ■25 106-503 332-1 1183-26 -2427 4-121 227-0 ■50 110-176 334-7 1184-02 -2505 3-992 234-3 ■75 113-849 337-1 1184-76 -2584 3-870 241-7 8-00 117-522 339-5 1185-48 -2662 3-758 249 ■25 121 195 341-7 1186-18 -2740 3-650 256 ^4 ■50 124-868 343-9 1186-86 -2817 3 550 263 5 ■75 128-541 347-9 1186-93 -2895 3-453 270-8 9 00 132-214 348-3 1188-19 -2973 3-363 278-1 •25 135-887 350-4 1188-85 -3050 3-278 285-3 ■50 139-560 352-4 1189-47 -3126 3-199 292-4 •75 143-233 354-5 119009 -3205 3-120 299-7 10 00 146-906 356-5 1190-70 -3282 3 047 307-0 •25 150-579 358-3 1191-27 -3359 2-977 314-2 ■5C 154-252 360-3 1191-85 -3436 2-911 321-4 ■75 157-925 362-1 1192-23 -3513 2-841 329-3 1100 161-598 364-1 1192-98 •3589 2-786 3357 263 APPENDIX DIAMETERS AND AREAS PROM 1 TO 1000. No. 0. 0-a. . n-4. 0-6. 0-8. 1 0-7854 1-131 1-539 2-011 2-545 2 3-1416 3-801 4-524 5-309 6-1575 3 7-0686 8-042 9-079 10-179 11-341 i 12-566 13-854 15-205 16-619 18-096 5 19-635 21-237 22-902 24-630 26-421 6 28-274 30-191 32-170 34-212 36-317 7 38-48'5 40-715 43-008 45-365 47-784 8 50-265 52-810 55-418 58-088 60-821 9 63-917 66-476 69-398 72-382 75-430 10 78-540 81-713 84-949 88-247 91-609 11 95-033 98-520 102-070 .105-683 109-359 12 113-098 116-899 120-763 124-690 126-680 13 132-733 136-848 141-026 145-267 149-572 14 153-938 158-368 162-861 167-115 172-034 15 176-715 181-459 186-265 191-13 196-07 16 201-06 206-12 211-24 216-42 221-67 17 226-98 232-35 237-79 243-28 248-85 18 254-47 260-16 265-90 271-72 277-59 19 283-53 289-53 295-59 301-72 307-91 20 314-16 320-47 326-85 333-29 339-79 21 346-36 352-99 359-68 366-44 373-25 22 380-13 387-08 394-08 401-15 408-28 23 415-48 422-73 430-05 437-44 444-88 24 452-39 459-96 467-59 475-29 483-05 25 490-87 498-76 .506-71 514-72 522-79 26 530-93 539-13 547-39 555-72 564-10 27 572-56 581-07 589-65 598-28 606-99 28 615-75 624-58 633-47 642-42 651-44 29 660-52 669-66 678-87 ' 688-13 697-46 30 706-86 716-31 725-83 735-42 745-06 31 754-77 764-54 774-37 784-27 794-23 32 804-25 814-33 824-48 834-69 844-96 33 855-30 865-70 876-16 886-68 897-27 34 907-92 918-63 929-41 940-25 951-15 35 962-11 973-14 984-23 995-38 1,006-60 36 1,017-87 1,029-21 1,040-60 1,052-09 1,063-62 37 1,075-21 1,086-87 1,098-58 1,110-4 1,122-2 38 1,134-1 1,146-1 1,158-1 1,170-2 1,182-4 39 1,194-6 1,206-9 1,219-2 1,231-6 1,244-1 40 1,256-6 1,269-2 « 1,281-9 1,294-6 1,307-4 41 1,320-3 1,333-2 1,346-1 1,359-2 1,372-3 42 1,385-4 1,398-7 1,412-0 1,425-3 1,438-7 43 1,452-2 1,465-7 1,479-3 1,493-0 ^ 1,506-7 44 1,520-5 1,534-4 1,548-3 1,562-3 1,576-3 45 1,590-4 1,604-6 1,618-8 1,633-1 1,647-5 46 1,661-9 1,676-4 1,690-9 1,705-5 1,720-2 47 1,734-9 1,749-7 1,764-6 1,779-5 1,794-5 48 1,809-6 1,824-7 1,839-8 1,855-1 1,870-4 49 1,885-7 1,901-2 1,916-7 1,932-2 1,947-8 50 1,963-5 1,979-2 1,995-0 2,0109 2,026-8 254 APPENDIX [DIAMETERS AND AREAS FROM 1 TO 1000 {continued). No. 0. 0-2. 4. 0-6. 0-a. 51 2,042-8 2,058-9 2,075-0 2,091-2 2,107-4 52 2,123-7 2,140-1 2,156-5 2,173-0 2,189-6 53 2,206-2 2,222-9 2,239-6 2.256-4 2,273-3 54 2,290-2 2,307-2 2,324-3 2,341-4 2,358-6 55 2,375-8 2,393-1 2,410-5 2,427-9 2;445-4 56 2,463-0 2,480-6 2,498-3 2,516-1 2,533-9 57 2,551-8 2,569-7 2,587-7 2,605-8 2,623-9 58 2,642-1 2,660-3 2,678-6 2,697-0 2,715-5 59 2,734-0 2,752-5 2,771-2 2,789-9 2,808-6 60 2,827-4 2,846-3 2,865-3 2,884-3 2,903-3 61 2,922-5 2.941-7 2,960-9 2,980-2 2,999-6 62 3,019-1 3,038-6 3,058-2 3,077-8 3,097-5 63 3,117-2 3,1371 3,157-0 3,176-9 3,196-9 64 3,217-0 3,237-1 3,257-3 3,277-6 3,297-9 65 3,318-3 3,338-8 3,359-3 3,379-9 3,400-5 66 3,421-2 3,442-0 3,462-8 3,483-7 3,504-6 67 3,525-7 3,516-7 3,567-9 3,589-1 3,610-3 68 3,631-7 3,653-1 3,674-5 3,696-1 3,717-6 69 3,739-3 3,761-0 3,782-8 3,804-6 3,826-5 70 3,848-5 3,870-5 3,892-6 3,914-7 3,936-9 71 3,959-2 3,981-5 4,003-9 4,026-4 4,048-9 72 4,071-5 4.094-2 4,116-9 4,139-6 4,162-5 73 4,185-4 4,208-4 4,231-4 4,254-5 4,277-6 74 4,300-8 4,324-1 ' 4,347-5 4,370-9 4,394-3 75 4,417-9 4,441-5 4,465-1 4,488-8 4,512-6 76 4,536-5 4,560-4 4,584-3 4,608-4 4,632-5 77 4,656-6 4,680-8 4,705-1 4,729-5 4,753-9 78 4,778-4 4,802-9 4,827-5 4,852-2 4,876-9 79 4,901-7 4,926-5 4,951-3 4,976-4 5,001-4 80 5,026-5 5,051-7 5,076-8 5,102-2 ,5,127-6 81 5,153-0 5,178-5 5,204-0 5,229-6 5,255-3 82 5,281-0 5,306-8 5,332-7 5,358-6 5,384-6 83 5,410-6 5,436-7 5,462-9 5,489-1 5,515-4 84 5,541-8 5,568-2 5,594-7 5,621-2 5,647-8 85 5,674-5 5,701-2 5,728-0 .5,754-9 5,781-8 86 5,808-8 5,835-9 5,863-0 5,890-1 5,917-4 87 5,944-7 5,972-0 5,999-5 6,027-0 6,054-5 88 6,082-1 6,109-8 6,137-5 6,165-3 6,193-2 89 6,221-1 6,249-1 6,277-2 6,305-3 6,333-5 90 6,361-7 6,390-0 6,418-4 6,446-8 6,475-3 91 6,503-9 6,532-5 6,561-2 6,589-9 6,618-7 92 6,647-6 6,676-5 6,705-5 6,734-6 6,763-7 93 6,792-9 6,822-2 6,851-5 6,880-8 6,910-3 94 6,939-8 6,969-3 6,999-0 7,028-7 7,058-4 95 7,088-2 7,118-1 7,148-0 7,178-0 7,208-1 96 7,238-2 7,268-4 7,298-7 7,329-0 7,359-4 97 8,389-8 7,420-3 7,450-9 7,481-5 7,512-2 98 7,543-0 7,573-8 7,604-7 7,635-6 7,666-6 99 7,769-7 7.728-8 7,760-0 7,791-3 7,822-6 The End. Butler & Tanner, The Selwood Printing Works, Fiome, and London,