CORNELL 
 
 UNIVERSITY 
 
 LIBRARY 
 
 FROM 
 
 renn '-'r Der,noU 
 
Cornell University Library 
 V331 .S62 
 Elements SJtJSSVJliiMSiBi 
 
 olin 
 
 3 1924 030 752 343 
 
B Cornell University 
 B Library 
 
 The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924030752343 
 
COl'YRIGHT 1904 
 
 iV NORMAN L. SKENE 
 
 BOSTON, MASS. 
 
 All Rig-hti Reserved 
 
 O 
 
 PRESS OF 
 
 THOMSON & COMPANY 
 
 9 Murray Street 
 
 New York, U. S. A. 
 
ELEMENTS 
 
 OF 
 
 YACHT DESIGN 
 
 BY 
 
 NORMAN L SKENE, S. B. 
 
 NKU YORK, U. S. A. : 
 
 THE RUDDER PUBLISHING COMPANY 
 1904 
 
PREFACE 
 
 THIS book is intended to be a concise and practical presentation of 
 the processes involved in designing a modern yacht. There is at 
 present an almost utter lack of material of this character which is 
 in accord with modern American practice, and 'it is thought that the 
 book may find a useful place among works on yacht architecture. It is in- 
 tended to be thoroughly practical in character, all mathematics and 
 theoretical presentations having been eliminated as far as possible, so that 
 the operations may be readily grasped by men without technical education. 
 
 A special feature of the book is the series of curves on plates VI, VII, 
 VIII and IX, for determining the proportions of sailing yachts of various 
 sizes. These have been prepared by the writer from data on a large num- 
 ber of yachts, and should prove of great assistance in roughing out a de- 
 sign. The methods presented for determining stability have been selected 
 with reference to their applicability to small work, and are not ordinarih- 
 to be found in works on naval architecture. 
 
 The various operations involved in designing a sailing yacht are il- 
 lustrated in the text by work on the thirty-foot water line sloop whose 
 plans are given on plates I, II, III and IV This is intended to be a 
 conventional ratl'jer than an ideal design, and was chosen on account of its 
 suitability for purposes of illustration. The complete data on this design 
 is given in the appendix. 
 
 The author is indebted to Prof. C. IT. Peabody, of the Massachusetts 
 In.stitute of Technology, for criticism and suggestion. 
 
 N. L. S. 
 
CONTENTS 
 
 CHAPTER I. 
 
 PAGE 
 
 General Discussion i 
 
 CHAPTER n. 
 Methods of Calculation 5 
 
 CHAPTER HI. 
 Displacement 18 
 
 CHAPTER I\' 
 The Lateral Plane 24 
 
 CHAPTER V. 
 Design 28 
 
 CHAPTER \'I. 
 Stability 33 
 
 CHAPTER \'TT. 
 Ballast 48 
 
 CHAPTER Vni. 
 The Sail Plan 54 
 
 CHAPTER IX. 
 Construction 59 
 
 APPENDIX. 
 Tables 71 
 
LIST OF PLATES 
 
 L Lines of Thirty-Footek. 
 
 n. Construction Plan of Thirty-Footer. 
 
 IIL Cabin " " 
 
 IV. Sail " " 
 
 \'. Stability Figures. 
 
 VL Curves of Ratios ok Beam to Length. 
 VII. " " Draught. 
 
 VIII. " " Freeboard .\nd Sail Area. 
 
 IX. " ■' DlSPL.\CEMENT. 
 
ELEMENTS OF YACHT DESIGN 
 
 CHAPTER I. 
 
 ni-lXKRAL DI^CL'SSION. 
 
 THERE are four general characteristics sought after in yacht design — 
 seaworthiness, large cabin accommodations, beautv and high speed. 
 These properties are in a measure antagonistic, and it is impossible 
 to combine them all in one design, in fact seldom do we we see a suc- 
 cessful combination of more than two of them. The best the designer can 
 expect to do is to embody in his design the qualities especially desired, 
 treating the other features in such a manner as to render their deficiencies 
 as inconspicuous as possible. 
 
 In yacht designing one is less hampered than in any other branch of 
 naval architecture, and the designer has many opportunities to depart from 
 precedent and study the results of new ideas in design and construction. 
 This is most fortunate, and to it may be attributed the great advance 
 which has been made in the art in recent years. 
 
 The most marked development of form which has occurred is in the 
 shape of the bow. This is the natural outcome of racing rules, which used 
 water-line length as a basis of com.parison. It was found that sail-carry- 
 ing power could be increased independently of water-line length by in- 
 crease of over-all length, especially in the bow. This increasing of the 
 stabilitv is the principal function of overhangs, and results from an in- 
 crease in area of load water line plane and a general shifting to leeward 
 of the center of buoyancy when heeled. There is scarcely any limit to 
 the increase in stability which may be secured b}- lengthening and broaden- 
 ing the overhangs. This idea has been carried to such an extent as to 
 render imperative the adoption of rules more stringent than those based 
 simply on sail area and water-line length in order that boats of wholesome 
 typ2 may continue in the racing. Such rules are necessarily somewhat 
 complex, and it is not until recently that am- have been devised which were 
 at all promising. The complete success of these rules has yet to be proved 
 by extended use. As a temporary refuge against the machine racing boat 
 a great deal of racing has been done in one-design and closely restricted 
 classes. While these afford good racing they must be regarded in the 
 light of a makeshift rather than a solution of the rating-rule problem. 
 
2 ELEMENTS OF YACHT DESIGN 
 
 They do not permit of much latitude of design, and for that reason are 
 not of great benefit to the science of yacht architecture. 
 
 The problem of designing a sailing yacht with speed as a foremost 
 consideration is a most complex one. External conditions to which a 
 yacht is subjected, such as force and direction of wind, condition of sea, 
 etc., are constanth' changing so that the attainment of a given speed ma}- 
 not be sought but rather such a form as shall be easily driven at all speeds 
 within appropriate limits. Nor is this the only consideration, for ease of 
 form must be to some extent sacrificed for sail-carrying power. A har- 
 monious adjustment between power and resistance should be sought. The 
 problem of steam yacht design is much more simple, as there the hull 
 may be so designed as to be most easil}- driven at the desired speed, for, 
 contrary to early theories, the hull most easily driven at one speed is not 
 most easily driven at all speeds. Then, again, the power-driven yacht 
 travels ordinarily on an even keel and the form of the yacht need be but 
 little afifected by considerations of stability. 
 
 The resistance which a vessel encounters in passing through the water 
 is made up of three kinds — frictional resistance, wave-making resistance, 
 and eddy-making resistance. 
 
 Frictional resistance is the resistance due to the friction of the water on 
 the surface of the vessel and depends upon the area of the surface, the 
 nature of the surface, the length and shape of the surface. We are large- 
 ly indebted to the late Mr. Froude for our knowledge of this form of re- 
 sistance. Skin friction, as it is called, forms a large portion of the total 
 resistance at low speeds, and is of course decreased by cutting down the 
 area of wetted surface. It does not pa}-, however, to economize unduly 
 on area of lateral plane for the sake of cutting down the area of wetted 
 surface. It is obviously of great importance to have the immersed sur- 
 face as smooth as possible. 
 
 Wave-making is a phenomenon, a full discussion of which would be 
 out of place here. It is the chief source of resistance at high speeds and 
 varies nearly as the displacement for similar forms. It is obvious that de- 
 creasing the displacement is the most effective way of cutting down re- 
 sistance, other things being equal. 
 
 Eddy-making occurs at the stern post, if it is too wide, or at other places 
 where the stream lines terminate abruptly, and is of slight importance in 
 the ordinary yacht. The aft edge of centerboard, rudder, shaft struts, etc., 
 should be well fined away to avoid the formation of eddies. The forward 
 edge may simply be well rounded to avoid eddies at that point. 
 
 Let us now consider some types of racing boats produced under very 
 
ELEMENTS UF YACHT DESIGN 3 
 
 lax restrictions. First, let us take the type developed where the length on 
 the water line is the only restriction. The type found to be the fastest 
 under these conditions is the extreme scow with enormous overhangs and 
 carrying a very large amount of sail. The power to carry this lig is 
 gained by great beam and over-all length. The weight of the crew con- 
 tributes somewhat to the sail-carr}-ing power, there being no ballast what- 
 ever. The overhangs are ver}- broad and flat and project over the water 
 at a very small angle with the surface. This permits the boat to gain 
 length rapidly when heeled and greatly diminishes the retarding com- 
 ponent of the impact of waves when going to windward. The waves 
 strike the low overhang with great violence, but the blow is largely in an 
 upward direction and does not tend to retard the boat as much as where 
 the overhang presents a greater angle with the water plane. The wider 
 and flatter the overhangs the less must be their angle of incidence with 
 the water plane. To preserve the continuity of the very gradual lines of ap- 
 proach the entire underbody must be shoaled as much as possible. This 
 compels a very small displacement and a reduction of weight wherever pos- 
 sible. The construction of this type of boat is the lightest possible and must 
 be designed with great care to withstand the enormous stressestoiwhichsuch 
 a boat is subjected. An elaborate system of trussing furnishes the gener- 
 al strength, the hull proper being mere basket work. 
 
 Another type is that produced where the amount of sail to be carried 
 is the only limitation. Here the problem is to produce the fastest possi- 
 ble hull for the given sail area and the stabilit)- is made merely sufficient 
 to properly carry the sail under racing conditions. This is found to be 
 a narrow, shoal, centerboard boat of extremely long and easy fore and aft 
 lines, small displacement and consequent light construction. The stability 
 is entirely that of form and of the weight of crew, there being no ballast 
 whatever. The fastest type under the old rule 
 
 L. W. L. -f- y S. A. 
 R. L. = 
 
 is probably a cross between the two just described. From the foregoing 
 we may conclude that for considerations of speed alone the stability should 
 be entirely that of form rather than of ballast. 
 
 The factors for speed which have been touched upon are unfortunate- 
 ly detrimental to safety and seaworthiness and for this reason are se- 
 verely taxed by most rating rules. These commonly compel a certain dis- 
 placement or weight of ballast and limit the amount of sail, the over-all 
 
4 ELEMENTS OF YACHT DESIGN 
 
 length or the freeboard, and in other ways strive to produce a boat which 
 shall be seaworthy as well as fast. 
 
 The form of the cruising boat has been influenced to an undesirable ex- 
 tent b)- the racing boat, and the prevailing tj'pe of small cruiser to-day is 
 afflicted with long overhangs, shoal body, and pared away lateral plane. 
 This is to be deplored, as such boats fall far short of the vaLe they should 
 possess as cruisers, considering the amount of money, labor and material 
 put into them. There is no doubt that properly treated overhangs are of 
 value in a seaway, but they must be short, high and fairly sharp in section. 
 Water-line length has no bearing on the usefulness of a cruising boat. 
 The modern boat of rational proportions has proved itself superior in 
 every way to the plumb-stemmed and clipper-bowed craft of a few years 
 ago, and the value of a moderate amount of overhang as a factor for sea- 
 worthiness is firmly established. The extensive adoption of generous 
 overhangs on fishing schooners is evidence of this. Plenty of deadrise is 
 desirable in a cruising boat, as it makes a boat easier in a seaway and af- 
 fords more headroom in the cabin by permitting the floor to be placed 
 lower down. The matter of lateral plane is discussed in a separate 
 chapter. 
 
CHAPTER II. 
 
 METHODS OF CALCULATION. 
 
 A LARGE proportion of the calculations of the naval architect revert to 
 the determination of the area and position of center of gravity of 
 a figure bounded by a curve. Two methods are in common use for 
 these determinations, numerical and instrumenatal. The instruments 
 used for the latter method are the planimeter and integrator. Theplanimeter 
 measures areas alone. It is an inexpensive instrument, and is practically 
 indispensable to the yacht designer. The integrator is a more expensive 
 instrument, and while it is not indispensable for small work it is a practical 
 necessity for large work where the saving of labor resulting from its use 
 is very considerable. The integrator commonly measures areas and their 
 moments about a . given axis. Some integrators have in addition an at- 
 tachment for measuring the moment of inertia of the area. Some of the 
 uses of the planimeter and integrator will be explained later. 
 
 The principal methods of obtaining areas numerically are by the use 
 of Simpson's first or one-third rule, and by the trapezoidal rule. Refer- 
 ring to fig. I, let the area of the figure ABCD be required. AD is a straight 
 
 a 
 
 •<5 
 
 
 ■0 
 
 p--.^ 
 
 a 
 
 O 
 
 %) 
 
 FIG. I. 
 
 line, BC a smooth curve, and a, b, c, d, e, are ordinates drawn perpendic- 
 ular to AD at a distance s apart. The area of the figure is then by Simp- 
 son's rule : 
 
 Area=/3S (a4-4b-f2c4-4d+e) 
 
 This rule may be used with any odd number of ordinates. To apply the 
 trapezoidal rule, simply add together all the ordinates, subtract half the 
 
O ELEMENTS OF YACHT DESIGN 
 
 two end ordinates and multiply the sum by the common interval. Refer- 
 ring to figure 1 the area by the trapezoidal rule is : 
 
 Area=s ( i^a+b+c+d+i^e) 
 If the bounding curve started at A and ended at D, making the end or- 
 dinates zero, the area would be : 
 
 Area=s (b-|-c-{-d) 
 This rule may be used with any number of ordinates. 
 
 The trapezoidal rule deals with the figure as though it were bounded 
 by a broken line — that is, in fig. 2 the area ABFG by the trapezoidal rule 
 is equal to the sum of the trapezoids ABCJ, JCDI, IDEH, and HEFG. 
 
 Fir.. 2, 
 
 The area between BC, CD, DE, and EF and the curve is entirely neglected. 
 This error is unimportant if the ordinates are sufficiently nu- 
 merous, or if the curve is very flat. Where there is a re- 
 verse in the curvature the loss on the convex portion 
 of the curve is offset partially or entirely by the gain on the concave por- 
 tion. Simpson's rule assumes the portion of the curve BCD (fig. 2) to 
 be an arc of a parabola tangent to mn (drawn parallel to BD) at C and 
 the area BCD is added to, or subtracted from the area of the trapezoid 
 ABDI, according as the curve is convex or concave. 
 
 For the purpose of comparing the two rules let us apply them to the 
 segment of the circle shown in fig. 3. This curve being entirely convex 
 
ELEMENTS Ol'- YACHT DESIGN 
 
 7 
 
 and steep at the ends shows the trapezoidal rule at its worst. The height 
 of the arc is four inches and the length of the chord twelve inches, making 
 the interval i.2 inches with eleven stations. The calculation is as follows : 
 
 STATION 
 
 ORDINATE 
 
 SIMPSON S 
 MULTIPLIERS 
 
 FUNCTIONS 
 OF AREAS 
 
 I 
 
 
 
 I 
 
 
 
 2 
 
 1. 90 
 
 4 
 
 7.6a 
 
 3 
 
 2.92 
 
 2 
 
 5.84 
 
 4 
 
 3-54 
 
 4 
 
 14.16 
 
 5 
 
 3.89 
 
 2 
 
 ■77S 
 
 6 
 
 4.00 
 
 + 
 
 16.00 
 
 7 
 
 3-89 
 
 2 
 
 778 
 
 8 
 
 3-54 
 
 4 
 
 14.16 
 
 9 
 
 2.92 
 
 2 
 
 5-84 
 
 10 
 
 1.90 
 
 i 
 
 7.60 
 
 II 
 
 
 
 I 
 
 
 
 Sum 
 
 28.50 
 
 86.76 
 
 Area by trapezoidal rule=28. 50X1.2=34.20 square inches. 
 Area by Simpson's rule=86.76X"/3 =34-7o square inches. 
 
 Knowing the radius of the arc the correct area of the segment is readily 
 found by direct computation to be 34.63 sq. in. The errors then amount 
 to 1.2 per cent, for the trapezoidal rule and 0.2 per cent, for Simpson's. 
 The latter is in excess of the correct amoLint while the former is below. 
 
 In order to compare these rules still further the area and center of 
 gravity of the curve shown in fig. 4 have been worked out by both rules. 
 
 FIG. 4. 
 
 This is the curve of areas of a yacht having a prismatic coefficient of 
 .51. The common interval is 4 inches. To obtain the correct area the 
 trapezoidal rule with a very large number of ordinates was used giving 
 121.82 square inches. This area is of Course still approximate but the error 
 
ELEMENTS OF YACHT DESIGN 
 
 is almost infinitesimal and may be disregarded, 
 follows : 
 
 TRAPFZOTDAL 
 
 The calculation is as 
 
 SIMPSON'S 
 
 STA. 
 
 OR!'. 
 
 ARII. 
 
 MOM 
 
 
 
 
 
 s 
 
 
 
 I 
 
 48 
 
 4 
 
 1.92 
 
 9 
 
 I.71 
 
 3 
 
 S.I3 
 
 3 
 
 3.36 
 
 2 
 
 6.72 
 
 4 
 
 4.8s 
 5.83 
 
 I 
 
 
 4.8s 
 
 S 
 
 18.62 
 
 6 
 
 5.87 
 
 I 
 
 5.87 
 
 7 
 
 479 
 
 2 
 
 9-58 
 
 S 
 
 2,68 
 
 3 
 
 8.04 
 
 9 
 
 83 
 
 4 
 
 3-32 
 
 10 
 
 
 
 S 
 
 
 
 
 30.40 
 
 26.81 
 
 
 
 
 18.62 
 
 ORD. 
 
 O 
 
 .48 
 I.71 
 3-36 
 4.8s 
 
 SIMPS. 
 
 MULT-. 
 
 I 
 
 4 
 2 
 
 4 
 
 FUNCS. 
 AREAS 
 
 
 
 1.92 
 
 342 
 1344 
 
 970 
 
 FUNCS. 
 MOM. 
 O 
 
 7.68 
 
 10.26 
 
 26.88 
 
 9.70 
 
 5 
 
 S.80 
 
 4 
 
 23.32 
 
 
 
 54- 52 
 
 6 
 
 5.87 
 
 2 
 
 11.74 
 
 I 
 
 11.74 
 
 7 
 
 479 
 
 4 
 
 19.16 
 
 ' 
 
 38.32 
 
 8 
 
 2.68 
 
 ' 
 
 S.36 
 
 3 
 
 16.08 
 
 9 
 
 ■83 
 
 4 
 
 3.,?2 
 
 4 
 
 13.28 
 
 10 
 
 
 
 I 
 
 
 
 5 
 
 
 
 
 91-38 
 
 79,42 
 
 
 
 
 
 
 54-52 
 
 K.I9 
 
 24.90 
 
 .\rea by trapezoidal rule^30.40,><4^i2i.6o square inches. 
 .\rea bv Simpson's rule=9i.38xV3— 121.84 square inches. 
 
 3.IQ 
 
 Center of g-ravity by trapezoidal rule= 
 of sta. 5. 
 
 30.40 
 
 24.90 
 
 X4=i.o8 inches to the left 
 
 Center of gravity by Simpson's rule= — — -X4=i-09 inches to the left 
 of sta. 5. ^''"^ 
 
 The percentage errors are then, for the trapezoidal rule, .24 per cent. ; 
 for Simpson's rule, .04 per cent. The diflference in the positions of thecen- 
 ter of gravity of the figure given by the two rules amounts to but .00025 of 
 the base. 
 
 The process by which the center of gravity is found is briefly as fol- 
 lows : a station is selected near the middle of the length of base, in this 
 case station 5, and each ordinate for the trapezoidal rule or function of 
 areas for Simpson's rule is multiplied by the number of intervals between 
 it and the station selected. These functions of moments are added separ- 
 ately on each side of the station about which moments are taken, the cen- 
 ter of gravity being on the side of the larger sum. The difference of these 
 sums divided by the sum of the ordinates for the trapezoidal rule or by 
 
ELEMENTS OF YACHT DESIGN 9 
 
 the sum of functions of areas for Simpson's rule multiplied by the distance 
 between stations gives the distance from the center of gravity to the sta- 
 tion about which moments were taken. 
 
 The comparisons just made of the working of the trapezoidal and 
 Simpson's rule show the latter to be the more accurate. The trapezoidal 
 rule, however, is quite accurate enough if a sufficient number of stations 
 are taken (nine or more are recommended) and will be used for all cal- 
 culations in the ensuing pages. It is superior to Simpson's rule in that 
 
 FIG. 5. 
 
 it may be used with any number of stations and involves much less numer- 
 ical work in its application. These considerations more than atone for 
 its being slightly less accurate. Some special calculations will now be 
 presented. 
 
 The area of a triangle is equal to one-half the product of its base by 
 its altitude, thus the area of the triangle ABC (fig. 5) is equal to Yi (AC 
 X Bm). The center of gravity of the triangle is at p, the point of inter- 
 section of Ac and Cn, n and o being the middle points of AB and BC re- 
 spectively. 
 
lO 
 
 EI.EMKNTS OF YACHT DESIGN 
 
 The area of a quadrilateral having no two sides parallel is found by 
 dividing the figure into two triangles and finding the area of each separ- 
 ately. Thus the area of AP.CD (fig. 6) is equal to Vi (ACXBm) +>4 (AC 
 
 FIG. 6. 
 
 X Dn). The center of gravity is on a line connecting the centers of the 
 component triangles. In fig. 7, m and n are the centers of the triangles 
 .\BD and BCD, while o and p are the centers of the triangles ABC and 
 ACD. Draw lines mn and op. Their point of intersection, x, is then tin- 
 
 FIG. 7. 
 
ICI.KMENTS OF YACHT DESIGN 
 
 II 
 
 center of the figure ABCD. A somewhat quicker method of finding the 
 center of such a figure is shown in figure 8. Draw the diagonals Ac and 
 Bd. Lay off Cn=Am. Draw Bn. Bisect Bn and Bd, o and p being the 
 
 FIG. 8. 
 
 middle points. Draw Do and np. Their point of intersection, x, is the 
 center of gravity of the figure. 
 
 It is often necessary to find the common center of two areas or weights. 
 In fig. 9 let W and w represent two weights having their centers of grav- 
 
 C 
 
 
 vy 
 
 FIG. g. 
 
 ity at a and b. Their common center lies at c on the line ab. Taking mo- 
 ments about a, the distance ac is equal to 
 
 wXab 
 
 W+w 
 
 There are various methods employed for finding the approximate area 
 of wetted surface of hull. These in general consist in applying Simpson's 
 or the trapezoidal rule to the half girths below the water line taken at 
 each station. The difficulty lies in determining the correct interval, as 
 
12 
 
 liLEMENTS OF YACHT DESIGN 
 
 the distance between stations on the surface of the skin is greater than at 
 the centeriine and is constantly varying. Taylor's mean secant method 
 IS probably the most accurate method for determining wetted surfaces. 
 In applying Taylor's method each station is divided into a number of equal 
 spaces below the water line as in fig. lo, where the lines MN and OP di- 
 
 FIG. TO. 
 
 vide the stations into thirds. At a point 1'. on station 3, the line AC is 
 drawn normal to the station and stopping at A on 2 and C on 4. Now let 
 us pass a plane through AC perpendicular to the plane of the paper. Fig. 
 II shows this plane revolved into the plane of the paper. A'C is the pro- 
 jection of AC. If now we take a piece of paper and mark off on one 
 edge of it the distance AA'. which is twice the distance between sta- 
 tions, and then divide this distance decimally, we have a scale for meas- 
 uring normals. If with this scale we measure AC fig. 10 (:=A'C fig. 
 11) we have at once the tangent of the angle A' AC. Now in a table of 
 natural functions find the secant corresponding to this tangent. The se- 
 cant gives the distance AC in terms of AA'. Next find the distance AC 
 in the same manner at the other ooints on the station and find their mean. 
 
ELEMENTS OF YACHT DESIGN 
 
 13 
 
 Multiply the half girth by this mean secant. Treat the half girth at each sta- 
 tion in the same manner and sum up by the trapezoidal rule, using for s the 
 actual distance between stations. The result is a very close approximation 
 to one-half the wetted surface. Table I, of the appendix, gives tangents 
 advancing by hundredths and the corresponding secants. The following 
 
 calculation is for the wetted 
 method. 
 
 thirty-footer by Taylor's 
 
 STATION J 
 
 At L. W. L 1.038 
 
 " M N 1.033 
 
 ■ OP 1.031 
 
 '■ Keel 1. 031 
 
 .SECANTS 
 
 fi 7 
 
 1.036 1.026 1. 016 
 
 1.028 1. 016 t.007 
 
 1. 024 1. 016 i.ooS 
 
 1.036 1.013 1.005 
 
 1.003 
 1. 001 
 1. 001 
 
 I.OOI 
 
 9 
 1. 000 
 1. 000 
 
 I.OOI 
 1.000 
 
 10 
 
 1.006 
 1.007 
 
 I.OII 
 1.002 
 
 II 
 
 I.0I8 
 
 1.024 
 1.006 
 
 1.002 
 
 12 
 1.026 
 1.031 
 1.028 
 I.013 
 
 Sum, 
 
 .4.133 4.124 4.071 4.036 4.006 4.001 4.026 4.050 4.098 
 
 Yz end ord 1.035 
 
 Difference 3098 
 
 Divide by 3 1.033 
 
 Half Girths I.S4 
 
 Corrected Half Girths.. 1.59 
 
 1.036 
 3.0S8 
 
 1. 020 
 2.78 
 
 2.86 
 
 1.020 
 
 3-051 
 
 I.OI7 
 
 4-2'', 
 
 4-30 
 
 I.OII 
 
 3-025 
 1.008 
 S-63 
 S-68 
 
 1.002 
 3.004 
 
 I.OOI 
 
 6.05 
 6.06 
 
 1. 000 
 3.001 
 1. 000 
 6.26 
 6.26 
 
 1.004 
 
 3.022 
 
 1.007 
 
 6.42 
 
 6.46 
 
 I.OIO 
 
 3.040 
 I.0I3 
 6.26 
 6.35 
 
 1.020 
 3-078 
 1.026 
 
 4-35 
 4.46 
 
 The corrected half girths are the products of the two preceding lines. 
 
 The sum of the corrected half girths is Z14.02. The wetted surface of the 
 
 hull is then 
 
 44.02X % X2X3=352-2 sq. ft. 
 
 The factor 'A corrects for scale, the half girths having been measured in 
 
14 ELEMKiNTS OF ^'ACHT DESIGN 
 
 inches on the drawing. The factor 2 allows for both sides and 3 is the dis- 
 tance between stitions. To the immersed area of hull we must add that 
 of rudder and centerboard. These are respectively 24.8 and 25.6, mak- 
 ing the total area of wetted surface 402.6 sq. ft. 
 
 The application of Taylor s method is somewhat laborious and for 
 small work the bilge diagonal method will do well enough. This method 
 consists in taking the half girths as before and applying the trapezoidal 
 rule using a corrected interval. This interval is obtained by multiplying 
 the distance between stations by the length of a bilge diagonal between 
 the stations at the forward and after points of immersion and then divid- 
 ing by the length of the load water line. 
 
 To obtain the moment of inertia of a water line about its longitudinal 
 axis measure the half-breadths at each station, cube them, apply the trape- 
 zoidal rule to the cubes of ordinates and multiply the result by two-thirds. 
 If the ordinates are measured in inches, as is generally most convenient, 
 and the drawing is to other than the one-inch scale, the sum of the cubes 
 must be multiplied by the cube of the inverted scale. The cubes of ordi- 
 nates should be taken from a table of cubes of numbers. The calculation 
 for the moment of inertia of the L. W. L. of the thirty-footer about a lon- 
 gitudinal axis is as follows : 
 
 ST A. 
 
 ORD. 
 
 CUBES 
 
 INCHES. 
 
 OF ORD. 
 
 4 
 
 I.-13 
 
 2.92 
 
 5 
 
 2.52 
 
 16.00 
 
 6 
 
 3-31 
 
 36.26 
 
 7 
 
 3-91 
 
 S9-78 
 
 8 
 
 4.29 
 
 78.9s 
 
 9 
 
 4-37 
 
 8345 
 
 10 
 
 4.19 
 
 73-56 
 
 II 
 
 3-74 
 
 52.31 
 
 12 
 
 2.88 
 
 23.89 
 
 427.12 
 
 I— 427.12x^3 X3Xi%y=202s. 
 
 The factor 3 is the distance between stations and {%y corrects for 
 scale, the ordinates having been measured in inches. 
 
 To find the moment of inertia of a water line about a transverse axis 
 through its center of gravity we must first find the area of the water line 
 and the position of its center of gravity. We may then find the moment 
 of inertia of the water line about the midship section and make a cor- 
 
ELEMENTS OF YACHT DESIGN I5 
 
 rection to obtain the same about the center of gravity of the water line. 
 Referring to the following computation on the thirty-footer we have in 
 the second column the half-breadths of the load water line plane measured 
 in actual inches on the drawing. 
 
 STA. 
 
 ORD. 
 
 ARM, 
 
 TUNC. FOR 
 C. G. OF L. W. L. 
 
 ARM. 
 
 FUNC. FOR I 
 
 4 
 
 ^•43 
 
 ■5 
 
 7-15 
 
 
 3 
 
 35-75 
 
 5 
 
 2.52 
 
 4 
 
 ro.08 
 
 
 4 
 
 40.32 
 
 6 
 
 a-.^i 
 
 3 
 
 9.93 
 
 
 3 
 
 29-79 
 
 7 
 
 3-91 
 
 2 
 
 7.82 
 
 
 2 
 
 15.64 
 
 8 
 
 4.29 
 
 I 
 
 4.29 
 
 
 I 
 
 4.29 
 
 9 
 
 4-37 
 
 
 
 3927 
 
 
 
 
 
 
 10 
 
 4.19 
 
 1 
 
 4.19 
 
 
 I 
 
 4.19 
 
 II 
 
 3-74 
 
 2 
 
 7.48 
 
 
 2 
 
 14.96 
 
 12 
 
 2.88 
 
 3 
 
 8.64 
 
 
 3 
 
 25.92 
 
 30.64 20.31 170.86 
 
 The third column gives the number of spaces each ordinate is from 
 the midsection. The product of the second and third columns gives the 
 functions for center of gravity of water line. The area of the water line is 
 30.64X2Xy3X3=245.i sq. ft. The factor 2 allows for both sides, % 
 corrects for scale and 3 is the distance between stations. The center of 
 gravity is 
 
 39.27—20.31 ^ g^:; f^ ^^^-^ ^f g^^_ 
 
 30.64 ^'^ ^ 
 
 Multiplying the functions for center of gravity again by the lever arms, we 
 get the functions for moment of inertia. These are all added together 
 and for the moment of inertia about station 9 we get 170.86X2XV3 X3 
 X 3^ = 12302. 
 
 The factor 2 allows for both sides, ^ corrects for scale, 3 is the in- 
 terval and s" corrects for the lever arms, being in each case the number of 
 intervals instead of the actual distance in feet between each ordinate and 
 the midsection. Now to find the moment of inertia about the center of 
 gravity of the water line we must subtract the area of the water line 
 times the square of the distance between its center of gravity and the mid- 
 section. This correction is 245.1X1.86^—848. The moment of inertia 
 about the center of gravity is then 12302 — 848=11454. 
 
 The calculation of the weight of the yacht is of great importance where 
 there are definite limitations as to ballast and water-line length. The 
 weight of each member should be calculated or estimated separately, the 
 
l6 ELEMENTS OF VACHT DESIGN 
 
 process for structural members being to find the volume and multiply 
 by the density. Table II gives average values for the densities of various 
 materials entering into the structure of the yacht. The volume of the 
 planking is found by multiplying its area in square feet by its thickness in 
 feet. The area is found in the same manner as the v^^etted surface, the 
 half girths being taken from planksheer to rabbet line. The volume of 
 the frames is found by multiplying the area of surface next the plank- 
 ing by the mean moulded depth. The area of outer surface depends on 
 the siding and spacing, thus if the frames were sided two inches and spaced 
 fourteen inches the area would be ^/i2X%=y7 that of the planking. The 
 volume of the deck is found by multiplying its area, which 
 is readily found, by its thickness. The volume of the beams 
 is found in the same manner as that of the frames. The volume of the 
 deadwood is found by applying the trapezoidal rule to the areas of trans- 
 verse sections taken at regular intervals. The volumes of long members 
 like stringers, clamps, spars, etc., are equal to the length multiplied by 
 the mean sectional area. Table III gives the weights of spruce spars of 
 various diameters. The most convenient methods of obtaining the weights 
 of other portions of hull, rig and equipment will be apparent. Tables IV 
 and \' give weights of sails and fastenings. Care must be taken that noth- 
 ing is omitted from the schedule of weights. There are some things such 
 as paint, cabin fittings, personal effects, etc., which elude calculation and 
 whose weight must be estimated. A fair allowance for outside paint is 
 nine pounds per hundred square feet of surface over plain wood, nineteen 
 pounds for canvas. The calculation of weights for the thirty-footer is 
 given on page 50. 
 
 The accuracy of weight calculations on wooden boats is vitiated by 
 the variation in densities of woods but with care, fairly close results may 
 be obtained. This difficulty does not exist with the metal construction as 
 the densities of plates and shapes are very accurately known and of course 
 do not vary appreciably. 
 
 The plating of metal yachts is not of uniform thickness but is made 
 heavier in localities which are especially stressed. For this reason the skin 
 can not be dealt with as a whole but the weight of each plate or group of 
 plates of the same weight must be figured separately. The dimensions of 
 the plates should be taken from the shell expansion. The length how- 
 ever, is not shown correctly in the expansion and a correction should be 
 made by multiplying by the secant of the angle which a diagonal through 
 the given plates makes with the centerline. The weight of plates is expressed 
 in pounds per square foot, and a forty-pound steel plate is considered to be 
 
ELEMENTS OF YACHT DESIGN 17 
 
 an inch thick, making five pounds to the eighth of an inch. A bronze 
 plate an inch thick weighs 43 pounds per square foot. 
 
 The length of frames and reverse frames should be measured on the 
 bod}' plan, making allowance for clips and doubling.s. The sum of the 
 lengths of frames of the same size is to be multiplied by the weight per 
 foot to get their weight. Weights of keels, keelsons, stringers and other 
 longitudinal members may be found from their length, allowing for cur- 
 vature, multiplied by their weight per foot. The weight of floors, deck 
 stringer-plates, bracket and tie-plates may be calculated from their area 
 and weight per square foot, allowing for lightening holes if any are cut. 
 In finding the weight of deck beams their length should be measured along 
 the upper crowned side and allowance should be made for the part turned 
 down to form the bracket, if this construction is used. The weights of 
 vertical laps, butt straps, liners under outer strakes and rivets may be 
 computed, but the calculation would be very laborious, and it is customary 
 to allow for these items by arbitrary percentages taken from practice. A 
 fair allowance for these items is — butts, liners and rivets in plating, 10 per 
 cent. ; rivets in frames and reverse frames, 5 per cent. ; rivets in floors and 
 brackets 3 per cent. 
 
 Small yachts should be weighed after completion whenever possible 
 as a check on the calculations. Naval vessels are often weighed during con- 
 struction, that is, the weight of all the material worked into the ship is 
 carefully recorded as well as the weight of all refuse taken out. This pro- 
 cedure might be employed to advantage in important yacht work. 
 
 Calculations for longitudinal strength and of stresses set up when 
 among waves are sometimes made. As these calculations are very com- 
 plex and are made only on very large or very lightly built steamers, it is 
 thought unnecessary to give space to them here and the reader is referred 
 to works on general naval architecture for these calculations. 
 
 In conclusion it may be said that the designer should avoid long hand 
 figuring for computation, using logarithms or calculating machine ex- 
 clusively, as otherwise, any extended calculation is so laborious as to ren- 
 der the work unprofitable. The ordinary slide rule is quite good enough 
 for a large portion of the calculations on small yachts. Logarithms leave 
 the work in a much more convenient form for reference than ordinary 
 figuring and are especially valuable for finding powers and roots of num- 
 bers. In addition they are more expeditious and more accurate than or- 
 dinary figuring. 
 
CHAPTER III. 
 
 DISPLACEMENT. 
 
 ANY object floating in water displaces its own weight, that is, if 
 the object were placed in a vessel full of water, an amount would 
 run over equal to the weight of the object. Displacement of yachts is 
 commonly expressed in pounds up to 35 or 40 feet water line and in 
 tons of 2,240 pounds above that size. The displacement is determined from 
 the lines of the yacht as will be explained later. There are approximately 
 35 cubic feet of salt water and 36 of fresh water in one ton. In one cubic 
 foot there are 64 pounds of salt water and 62.4 pounds of fresh water. 
 
 The center of buoyancy is the center of figure of the submerged 
 portion of the vessel. The upward force of the buoyancy of the water 
 may be considered to act at this point and the weight of the vessel to act 
 at the center of gravity. The centers of buoyancy and gravity must be 
 in the same vertical line or the vessel will alter its trim so as to bring them 
 so. 
 
 In a yacht it is important to know the longitudinal position of the cen- 
 ter of buoyancy when the yacht is erect, in order to be able to distribute 
 the weights so that the yacht will trim properly. The vertical position of 
 the center of buoyancy is not so important, athough a knowledge of its 
 position is useful, as will be shown later. Its transverse position is, of 
 course, in the central vertical plane. 
 
 If we plot the areas of the various transverse sections on a base line 
 as in fig. 4, we have what is known as the curve of areas. The area of 
 this curve gives us the displacement of the yacht, and the center of gravity 
 projected on the base line gives us the longitudinal position of the center 
 of buoyancy. The process of determining displacement and longitudinal 
 position of the center of buoyancy is best explained by a concrete example, 
 the calculation for the 30- footer being as follows : the quantities opposite 
 the station numbers are the planimeter readings of each half section in 
 square inches. The distance between stations is 3 feet. 
 
ELEMENTS OF YACHT DESIGN 19 
 
 
 1/2 A SQ. IN. 
 
 ARM . 
 
 MOM. 
 
 4 
 
 •45 
 
 5 
 
 2.2s 
 
 5 
 
 i.6s 
 
 4 
 
 6.60 
 
 6 
 
 348 
 
 3 
 
 10.44 
 
 7 
 
 541 
 
 2 
 
 10.82 
 
 8 
 
 6.62 
 
 6.71 
 
 I 
 
 
 6.62 
 
 9 
 
 36.73 
 
 10 
 
 5.80 
 
 I 
 
 .5-80 
 
 II 
 
 379 
 
 2 
 
 7.58 
 
 12 
 
 i-SS 
 
 3 
 
 4.6s 
 
 3546 18.03 
 
 Displacement=35.46X2X'V9 X3X64=24207 lbs. 
 
 C B= 3^-^3~~'^^°3 X3— 1.58' for'd sta. 9=16.42' aft of sta. 3. 
 
 The factor 2 is for both sides of the yacht, '% corrects for scale, 3 
 is the distance between stations required in the application of the trape- 
 zoidal rule, and 64 is the weight of one cubic foot of salt water. 
 
 The vertical position of the center of buoyancy inay be found by tak- 
 ing the areas of water lines spaced at equal intervals from the load line 
 down and summing up their moments in the same manner as for the longi- 
 tudinal position. The vertical position is more readily found by the in- 
 tegrator if one be available, using the load line as an axis. The use of 
 the integrator is described in chapter VI. 
 
 The determination of the proper displacement of a yacht is the most 
 important step in laying out a design. The displacement must equal the 
 sum of the weights of the various members of the yacht and its contents 
 or the yacht will not float as designed. The logical procedure then is 
 to ascertain the component weights and make the displacement equal to 
 their sum. For a design where the limitations as to the water-line length 
 and amount of ballast are very stringent, the best procedure is to lay out 
 a preliminar}' design which shall have the proper displacement and gen- 
 eral dimensions as nearly as it is possible to estimate them and to then 
 make calculations for weight on this design as outlined in chapter II. The 
 displacement for the final design will then be made equal to the sum of 
 these weights. For cruising boats it does well enough to estimate the 
 proper displacement from data on .successful boats of similar type and after 
 calculating the weight, to assign an amount of ballast to supply the de- 
 ficiency of weight. If the proper displacement is known fairly close and 
 
20 ELEMENTS OF YACHT DESIGN 
 
 a portion or all of the ballast is to be carried inside, the 'calculation for 
 weight may be dispensed with as the amount of weight is easih' adjusted 
 to secure the desired flotation. The curve of displacement on plate IX 
 will serve as a guide in estimating displacement for sailing yachts. 
 
 The best position for the center of buoyancy is something of which 
 ver}- little is known. An examination of the data for a large number of 
 representative existing yachts shows its position to lie generally between 
 50 to 56 per cent, of the load water-line length from its forward end. 
 From 52 to 54 per cent, is a suitable position for cruising boats. 
 
 The fineness of a design is commonly represented by three coefficients. 
 These are the midsection coefficient or ratio of midsection to the cir- 
 cumscribed rectangle, the block coefficient or ratio of the volume of the 
 displacement to the volume of the circumscribed parallelopipedon and the 
 prismatic coefficient or ratio of the volume of the displacement to the 
 volume of a solid whose length is equal to the length of the water line and 
 having a constant sectional area equal to that of the mid section. It is 
 also the ratio of the area of the curve of the transverse areas to the area of 
 the circumscribed rectangle. The last coefficient is the most important for 
 our purposes. The area of midship section of the thirty-footer is 
 
 6.80 X-^X'% =-'4.2 sq. ft., 
 
 and the prismatic coefficient is equal to 
 
 24207 
 
 30X24.2X64 
 
 =.522. 
 
 For steam yachts and launches, the prismatic coefficient generally 
 lies between .54 and .60. For centerboard boats having little external 
 keel it varies from .53 to .61. -For boats of the semi-keel type from .Soto 
 .54 For the modern keel boat it varies from .46 to .50. Having decided 
 on a suitable prismatic coefficient for a design the area of the midsection 
 is readily calculated for a given displacement as follows 
 
 . _ D cu. ft. 
 ' ~LWLXPC 
 
 The form of the curve of areas is a matter of considerable significance, 
 as it shows the manner in which the displacement is distributed longi- 
 tudinally. A design may be perfectly fair and sweet yet have an undesir- 
 able distribution of the displacement as revealed by the area curve. The 
 
ELEMENTS OF YACHT DESIGN 21 
 
 form of the curve has undoubtedly great influence on the wave-making 
 resistance and should of course be that of least resistance for a given 
 displacement and speed. According to the wave-form theory as pro- 
 posed by Colin Archer in 1877, the curve should take the form of a 
 wave line. A discussion of resistance and the wave-form theory would 
 not accord with the purpose of this book, and the application of the theory 
 to j-acht design will simply be given. The wave form theory requires the 
 curve of areas to be a curve of versed sines for the forebody or .6 of L. W. 
 L. and a trochoid for the afterbody. The length of forebody in well- 
 formed )^achts is generally between 54 and 58 per cent, of the water-Hne 
 length, that is. the midsection or point of greatest sectional area is in the 
 neighborhood of 56 per cent, of the water-line length from the forward 
 end. 
 
 FIG. 12. 
 
 Before proceeding further it will be well to give the construction for 
 the curve of versed sines and the trochoid. Suppose in fig. 12 it is de- 
 sired to construct a curve of versed sines of length AC. Let AB be the 
 diameter of generating circle. Divide the semi-circumference into a num- 
 ber of equal divisions. Divide the base line, AC into the same number 
 of equal divisions. Draw liner, parallel to AC through a, b, c, and perpen- 
 diculars through a', b', c'. The points of intersection a", b", c", lie on 
 the curve. Fig. 13 shows the constrviction for the trochoid. The semi- 
 circumference and base line are spaced off as before. Draw the chords Aa, 
 Ab and Ac. Draw a' a", b'b", c' c", parallel and equal to the chords Aa, 
 Ab and Ac. The points a" b" c" lie on the curve. The area of the 
 versed sine curve is always equal to one-half product of base 
 line by diameter of generating circle, that is, its coefficient is .5. The tro- 
 
22 
 
 EI.IIMENTS OF YACHT DESIGN 
 
 choid has a varying coefficient dependent on the ratio of diameter of gen- 
 erating circle to base line, the coefficient increasing with the ratio. The 
 height of the trochoid ma}- be increased to pass through any desired point, 
 having first drawn it with the proper diameter of generating circle to 
 give the desired coefficient, by multiplying each ordinate by the height 
 at the point through which the curve is to pass divided by the ordinate 
 of the original curve at the same point. 
 
 There is undoubtedly an advantage in having; the area curve conform 
 to the wave-form theory. Its importance, however, should not be over- 
 estimated, as this in itself will not produce a speedy design, and, on the 
 contrary, many successful yachts have a curve differing widely from that 
 
 B 
 
 prescribed by the wave-form theory. The area curves of steam yachts and 
 centerboard boats having little external keel may be made to take an ex- 
 act wave form, decreasing, however, the length of forebody from .60, the 
 water line length to .56 or .57 to accord with modern practice. In boats 
 having a pronounced external keel it is desirable to treat boat and keel 
 separately, making the areas of the boat proper take the wave form. Table 
 \T gives a series of factors for constructing wave- form curA-es having 
 various prismatic coefficients. 
 
 To construct an area curve using these factors divide the base line be- 
 tween the forward and after points of immersion into ten equal parts. 
 Erect ordinates at these points, and having selected a suitable prismatic 
 coefficient, multiply the area of mid.ship section by the factors of the curve 
 having that coefficient and plot these quantities on the ordinates. .\ curve 
 through these points will have the wave form and its prismatic coefficient 
 and position of center of buoyancy will be as indicated in table \^T. Curves 
 
ELEMENTS OF YA(.HT DESICN 23 
 
 having other prismatic coefficients may readily be constructed b> using 
 various other ratios of diameter of generating circle to base. An excellent 
 method of design is to start with the curve of areas and make the areas 
 of transverse sections conform to the curve. In this way all irregularities 
 in the curve are avoided and the displacement and position of center of 
 buoyancy are sure to work out as intended after the design has been 
 faiired up. This method of designing from the area curve is explained 
 more fully in chapter V. 
 
CHAPTER W. 
 
 THE LATERAL PLANK. 
 
 THE term lateral plane is applied to the vertical, longitudinal projec- 
 tion of the under-water body of the vessel. The center of lateral 
 resistance is the point at which the lateral pressure of the water on 
 a boat sailing close-hauled may be considered to be concentrated. It 
 is practically impossible of determination and is considerably farther for- 
 ward than the center of figure of the lateral plane. The reasons for this 
 are that as the boat moves forward it is constanth' entering solid water, 
 increasing the pressure at the bow and decreasing it toward the stern where 
 the water is more or less disturbed. The wave which is piled up under tli(> 
 lee bow tends also to increase the pressure in the region of the bow. More- 
 over, the contour of the lateral plane when the yacht is heeled is quite dif- 
 ferent from that in the erect position. The position of the center of buoy- 
 ancy is also considered to affect the position of the center of lateral re- 
 sistance. 
 
 Since we cannot determine the true center of lateral resistance we must 
 assume a center for reference in placing the center of our sailplan. Thecen- 
 ter of lateral plane is generally used for this purpose, although some design- 
 ers use a center lying on a line between the centers of buoyancy and of the fin 
 6r centerboard, disregarding entirely the hull in shoal-bodied boats. This 
 point probably bears a more constant relation to the true center of lateral 
 resistance than the center of lateral plane. In either case the proper dis- 
 tance fore and aft from the reference point to the center of the sail plan 
 must be determined experimentally from existing boats of the given type. 
 
 It is found that to secure satisfactory results the fore and aft position 
 of the center of lateral plane must lie within certain definite limits. Its 
 position is commonly located with reference to the forward point of im- 
 mersion, its distance from that point being expressed in terms of the wa- 
 ter line length. In most yachts this distance is between 54 and 58 per 
 cent, of the water line. In the majority of cases 56 or 57 per cent, will 
 give the best results. In cases where the center of the sail plan is neces- 
 sarily very far aft, as in the old-fashioned catboats, the center of lateral 
 plane may be placed as far back as 60 or 61 per cent. Very small center- 
 
ELEMENTS UI" YACHT DESIGN 25 
 
 board craft often have their centers very far forward with apparently good 
 results. In centerboard boats it is well to have the center of the board 
 somewhat ahead of the general center so that when the board is raised 
 the general center may move aft, making the boat steer better off the 
 wind. 
 
 The necessary amount of lateral plane is something for which no very 
 definite rules can be stated, as it varies greatly with the type of boat ; thus a 
 centerboard boat requires relatively less lateral plane than a keel boat, as 
 the centerboard being a plane surface is more effective in resisting lateral 
 pressure than the somewhat rounded surface of the keel. The type of rig 
 and amount of sail carried also have a bearing on this question. A con- 
 venient comparative method of approximating the area of lateral plane 
 is by the ratio of lateral plane to area of midsection. This ratio worked out 
 for a large number of representative yachts is found to vary from 4.0 
 to 6.0. The higher ratios are found in the clipper-bow type with a long 
 keel, entirely convex in contour. For keel boats of ordinary type the ratio 
 should lie between 4.25 and 5.50. Centerboard boats may in general have 
 a slightly smaller ratio than keel boats of similar type. For illustration, 
 the thirty-footer has an area of midsection of 24.2 sq. ft. Taking a ratio 
 of 4.65 the area of the lateral plane should be approximately 24.2X4.65^ 
 1 12.5 sq. ft. 
 
 Bilge boards are much more effective in resisting lateral pressure than 
 a centerboard as they are nearly vertical when the boat is heeled down 
 beating to windward and present a surface normal to the direction of 
 pressure. On this account the area of each bilge board may be made 
 much less than the necessarj' area of a centerboard for the same boat 
 (about .7 as great). The decreased wetted surface and capsizing tendency 
 of bilge boards commend their use on shoal racing boats. 
 
 Designers differ as to whether the rudder should be considered a part 
 of the lateral plane or not, but the best practice is to disregard it and the 
 figures given above for area and center of lateral plane are for the plane 
 exclusive of rudder. In a properly balanced yacht there is but little pres- 
 sure on the rudder when sailing by the wind, and for this reason the rud- 
 der can hardly be considered a factor in resisting lateral pressure. An 
 exception may be made in some types such as catboats, where it is im- 
 practicable to secure a proper balance by placing the rig far enough for- 
 ward. The angle of weather helm and consequent loss of speed in such 
 boats is reduced by increasing the area of the rudder so that the rudder 
 may be considered lateral plane when comparing boats of this type. The 
 area of rudder required varies widely with different types. Its size may 
 
26 KLEilENTS OF YACHT DESIGN 
 
 be advantageously stated in terms of the area of lateral plane exclusive of 
 rudder or ratio of rudder to lateral plane. Table VII gives suitable val- 
 ues of this ratio for various sizes and types of )achts. Selecting a ratio of 
 .II for the thirty-footer we get for area of rudder II2.5X-II = I2.4 
 sq. ft. 
 
 The shape of the lateral plane has great influence on the performance 
 of the yacht. The modern tendency is toward a concentration of the plane 
 fore and aft. This has its advantages for racing boats as such a plane is 
 more efficient and consequently may have less area and less wetted sur- 
 face than one whose area is more widely distributed fore and aft. Quick 
 turning is another advantage pertaining to this type. The fact that those 
 features of design tending to produce speed are detrimental to seaworthi- 
 ness when carried to a high degree holds true in the case of the lateral 
 plane and for this reason the fore and aft concentration of lateral plane 
 should be avoided on cruising boats. Boats with this type of plane have 
 a tendency to fall off and steer badly in a heavy sea, they must be finely 
 balanced and carefully steered at all times, their balance is greatly af- 
 fected by reefing and varies with different strengths of wind. If a boat is 
 to lie hove to well the lateral plane must be well spread out in a fore and 
 aft direction. 
 
 The forward portion of the lateral plane is most effective for lateral 
 resistance, and for this reason the leading edge should be made as long 
 as possible. To carry out this idea the keel bottom should have consider- 
 able drag or slope, as then the leading edge extends from the bow aft to 
 the rudder and is constantly entering solid water all along its length. 
 
 The exact form of the calculation for area and center of lateral plane 
 depends on the character of the design. If the plane is regular in con- 
 tour, the trapezoidal or Simpson's rule may be used. If such a plane has 
 a centerboard the areas and centers of hull and board should be found 
 separately and the combined center found b\' taking moments about a 
 convenient point. In the case of a very irregular contour the plane should 
 be divided into a number of portions in such a way that the area and center 
 of each may be readily figured. Moments of each are then taken about a 
 convenient point, the sum of the moments divided by the sum of the areas 
 giving the distance from the point to the total center. The cardboard 
 method of determining the center of lateral plane is susceptible of sufficient 
 accuracy if used with care, and is much more expeditious than calcu- 
 lation. The calculation of area and center of lateral plane of the thirty- 
 footer is as follows : the first column gives measurements on each station 
 in inches from the water line to the keel bottom. 
 
ELEMENTS OF YACHT DESIGN 2^ 
 
 STA. 
 
 OED. 
 
 ARM. 
 
 MOM. 
 
 4 
 
 .60 
 
 S 
 
 3-00 
 
 S 
 
 1.27 
 
 .1 
 
 S.08 
 
 6 
 
 2.40 
 
 3 
 
 7.20 
 
 7 
 
 3-35 
 
 2 
 
 6.70 
 
 8 
 
 3-50 
 3.60 
 
 I 
 
 
 
 35-0 
 
 9 
 
 25.48 
 
 10 
 
 Z-1i 
 
 I 
 
 3-73 
 
 II 
 
 3.8s 
 
 2 
 
 7.70 
 
 12 
 
 2.36 
 
 3 
 
 7.08 
 
 24.66 18.51 
 
 Area=24.66X Vs X3=98.64 sq. ft. 
 
 Distance center is forward of station 0= ' /^ X3^=-8s ft. or 17. is ft. 
 ^ , -' 24.66'^'' -^ ' ^ 
 
 aft of 3. 
 
 This area neglects a small triangle at the forefoot between stations 6 
 
 and 7, also one at the after end of keel between stations 11 and 12. It is 
 
 too great by the amount of the triangle whose hypothenuse is a straight 
 
 line from the water line on 14 to the stern post on 12. These errors are 
 
 due to the fact that the trapezoidal rule assumes the figure to be straight 
 
 between ordinates. To make these corrections let us take moments about 
 
 station 3. 
 
 98.64X17-15=1692 
 
 1st triangle .86X10.50= 9 
 
 2nd " 1.67 X25.35= 42 
 
 mi. 17 1743 
 
 3rd " 1.32 X28.64= j8 
 
 99.85 XI 7-07= 1 705 
 
 The center of lateral plane exclusive of centerboard is 17.07 ft. abaft 
 sta. 3 or 56.9 per cent. The board has an- area of 12.80 sq. ft. and its cen- 
 ter is 16.70 ft. back. Taking moments of hull and board 
 
 99.85X17-07=1705 
 12.80X16.70= 214 
 112.6 Xi7-04=i9i9 
 
 The total C- L. P. is then 17.04 ft. abaft sta. 3 or 56.8 per cent. 
 
CHAPTER V. 
 
 DESIGN. 
 
 BEFORE starting a design it is well to fix upon the principal dimensions 
 which include length over all, at the water line, beam at water line, ex- 
 treme draught, area of lateral plane, displacement and area of midship 
 section. Having settled upon the type and water-line length, the other pro- 
 portions are generally arrived at by some sort of comparison with existing 
 boats. As an aid in making such comparisons the curves on plates \'I, VII, 
 VIII and IX have been prepared. Thesecurves are based on data taken from 
 a large number of successful existing yachts and may be considered thor- 
 oughly representative of current American practice. Plate VI gives ratios 
 of beam at water line to length on water line for cruising boats, and plate 
 VII gives extreme draughts. For this work yachts have been divided 
 into three classes, viz., keel boats with all outside ballast, semi-keel boats 
 with a small centerboard and all or nearly all the ballast outside, and cen- 
 terboard boats having all or nearly all the ballast inside. It will be noted 
 that the differences between the types so marked in the smaller sizes dis- 
 appear almost altogether in the larger boats. The small sizes vary greatly 
 as to beam and draught and the first part of the curves simply represents 
 a fair average value for these quantities. In general, a boat having greater 
 beam than is shown by plate VI, will have less draught than is indicated 
 on plate \TI for the same water line length and vice versa. The larger 
 sizes of yachts conform m.ore closely to the curves. Plate VIII gives 
 curves of sail area and least freeboard to top of rail. It was found im- 
 practicable to make any distinction for type in drawing these curves. 
 Plate IX gives average values for displacement, being expressed in pounds 
 up to forty feet water line and in tons of 2,240 pounds above that size. 
 
 These curves will be found of great value in blocking out the propor- 
 tions of a new design. By their use comparison is made of the proportions 
 of a large number of existing yachts of the given size instead of with only 
 one or two as is generally the case. It is understood that these curves ap- 
 ply only to cruising boats. It should not be inferred that the dimensions 
 of a well-proportioned boat must lie on or very near the curves, as many 
 excellent designs show quite a divergence from them, especially in the 
 
ELEMENTS OF YACHT DESIGN 
 
 29 
 
 smaller sizes. On the other hand, if the proportions indicated by the 
 curves for the given water line length are adhered to, a design may be 
 produced which will be of excellent proportions in the light of present 
 practice. 
 
 In order to illustrate the process of laying out a design, the procedure 
 followed in the case of the thirty-footer will be given. Having settled 
 upon a thirty-foot water line, semi-keel cruiser of normal proportions, the 
 principal dimensions were taken from the curves as follows : the ratio of 
 beam at water line to water-line length as indicated on plate \'I is .385. 
 The beam. then should be 30X.385=ii.S5 ft. or about 11 feet 7 inches. 
 'Plate Vn gives slightly over five feet draught at 30 feet water line. Plate 
 VIII gives for the least freeboard 2.43 feet or about 2 ft. 5 in. The dis- 
 placement curve shows about 24,000 pounds at 30 feet water line. 24,200 
 pounds was taken as a safe fig-ure. The next step is to determine the 
 proper area of midsection to give this displacement. A suitable prismatic 
 coefficient for this type of boat is .50 to .52. Using .52 the area of mid- 
 section should be 
 
 24200 
 
 64 
 
 30X-52 
 
 24.2 sq. ft. 
 
 The half area in square inches on the drawing will be 24.2X/^X'/i6= 
 6.81 sq. in. The area of lateral plane should be about 24.2X4-65=112.5 
 sq. ft. as explained on page 25. 
 
 We now have sufficient data to enable us to block out the design. It 
 will be assumed that the reader has some knowledge of lines and is fa- 
 miliar with meaning of the terms elevation, half-breadth plan, body plan, 
 etc. The first step is to draw the profile using the least freeboard, draught, 
 area and center of lateral plane already fixed upon. It is a good plan to 
 draw a preliminary profile at half the scale of the lines and enlarge the 
 final profile from that. The object in doing this is to reduce the drawing 
 to such a size that the eye can take in the entire drawing at a glance and 
 study the way in which each 'portion harmonizes with the whole. A very 
 good way is to draw the sail plan first. In this way the effect of the rig 
 on the general appearance of the boat may be studied and the sheer line, 
 profile of bow and stern, etc., drawn so as to harmonize in the best man- 
 ner. On the preliminary profile the freeboard at bow and stern and 
 the length and contour of the overhangs are determined. The contour of 
 lateral plane may also be drawn in on this plan, being altered and redrawn 
 
30 
 
 ELEMENTS OF YACHT DESIGN 
 
 until area and center come as intended. The final profile may then be en- 
 larged from the preliminary sketch. 
 
 The midship section should be drawn in next at the proper distance 
 from the forwarl point of immersion. This distance was made 56 per 
 cent, of the water-line length= 16.81 ft. for the thirty-footer. The section 
 is drawn with the water-line beam, draught and area already assigned and 
 with the height of rail and draught given by the profile at that point. The 
 shape of the section is of great importance, as it influences the form of 
 the entire boat. The most suitable shape of midship section is found by 
 experience. It must possess the elements of speed, stability and sea- 
 worthiness combined in the proportions best adapted to the type of boat 
 in hand. In general, the shoal flat section contains the elements of speed 
 in higher degree than a narrower and more V-shaped section. This is 
 within certain limitations and has numerous exceptions. 
 
 Having drawn in the midsection, we may next direct our attention 
 to the half-breadth plan. The m.idsection gives us a point amidships through 
 which to draw the sheer or deck line. The best shape for this line is also 
 
 FIG. 14. 
 
ELEMENTS OF YACHT DESIGN 3 1 
 
 a matter of judgment based on experience. It is a good plan generally 
 to have the widest point on deck a little abaft the widest point at the load 
 line giving what is known as the raking midship section. A preliminary 
 load water line may be drawn next and the half-breadths at deck and load 
 line transferred to the body plan. We now have three points on each sta- 
 tion on the body plan through which to draw the transverse sections, the 
 top of planksheer, load water line and keel bottom. The usual procedure 
 from this point is to draw in the stations by eye, fair them up, draw a dis- 
 placement curve and see if the displacement comes out near enough. A 
 much better method is tQ draw an arbitrary displacement curve to start 
 with and make the area of each station conform to that indicated by the 
 curve for that station. This course was pursued in designing the thirty- 
 footer. It is somewhat difificult to preserve the area of the section during 
 the process of fairing up, but it may be done with care and practice. Where 
 the yacht has an appendage, as is usually the case, we must deal with the 
 areas of sections above the centerline. By centerline is meant a line pass- 
 ing through the points P on each section (fig. 14), where the prolongation 
 of the flat of the bottom intersects the central plane. The areas above 'cen- 
 terline are the areas above the dotted line, all below that line being con- 
 sidered the appendage. 
 
 The thirty-footer's half area of midsection in square inches on the 
 drawing is 5.89. A boat of her type should have a prismatic coefficient for 
 the portion above centerline of about .52. In constructing the curve of 
 areas above centerline, the factors in column 2, table VI were used. This 
 gives for areas of half sections above centerline in square inches : 
 
 STA. 
 
 y-2 MID SEC. 
 
 SQ. IN. 
 
 FACTORS 
 
 y2 A SQ. IN. 
 
 4 
 
 5-89 
 
 
 .080 
 
 ■47 
 
 5 
 
 
 
 
 .285 
 
 1.68 
 
 6 
 
 
 
 
 " -560 
 
 330 
 
 7 
 
 
 
 
 .808 
 
 4-77 
 
 S 
 
 
 
 
 .972 
 
 5-73 
 
 9 
 
 
 
 
 .983 
 
 5-79 
 
 10 
 
 
 
 
 .823 
 
 ^.85 
 
 II 
 
 
 
 
 ■SO7 
 
 2.98 
 
 12 
 
 
 
 
 .167 
 
 .98 
 
 The stations were drawn and altered until the area of each was as indicated 
 above and these areas were adhered to in fairing up. The curve of areas 
 above centerline is drawn in on plate I with the curve of areas below center- 
 line superposed. This shows very markedly the decided bump amidships 
 in the curve caused by the appendage. 
 
32 ELEMENTS OF YACHT DESIGN 
 
 Having drawn in and faired the upper body the appendage may be 
 drawn in and its displacement computed. A sHght variation in the dis- 
 placement of the appendage is easily efifected in order to bring the total 
 displacement to the desired figure. 
 
 .\ brief outline of the process of fairing lines may be of value at this 
 point. The design is faired by taking sections through the boat in varous 
 planes, longitudinally on water lines, buttocks and diagonals and trans- 
 versely on the stations. After the transverse sections have been drawn in 
 as nearly fair as possible b}' eye, the diagonals, buttocks, etc., are developed 
 and the sections are altered until all these developments are; perfectly fair 
 curves. The operation of fairing should be commenced with those longi- 
 tudinal sections whose planes are most nearl}- perpendicular to the con- 
 tour of the- transverse sections. These are generally the diagonals. Hav- 
 ing faired the boat by the diagonals, the water lines or buttocks are de- 
 veloped next. It is important to take a sufficient number of these, as a 
 boat may be apparently perfectly fair b}- the diagonals and yet exhibit pe- 
 culiar places in the ends when the water lines come to be drawn in and 
 vice versa. The intersections of water lines and buttocks in the elevation 
 must correspond with those in the plan. The procedure is varied some- 
 v.'hat according to the type of boat ; thus in a shoal, flat craft some of the 
 buttocks would be developed first. The designer, as he gains experience, 
 varies the procedure and adopts methods which he has found of especial 
 value to him. 
 
 The practice of making a model from the lines is to be recommended, as 
 sometimes slight imperfections in the design are made apparent b\' the 
 model, where it would be difficult or impossible to detect them in the lines. 
 The practice of making the model first and the lines from the model is 
 now practically obsolete. 
 
 After the completion of the design the computations for weight, stabil- 
 ity, etc., should be made in order to ascertain whether or not the design 
 will fulfill requirements in a satisfactory manner. These computations 
 are dealt with elsewhere. The final operation is to take offsets from the 
 design from which to lay the boat down full size in the mould loft. 
 
CHAPTER VI. 
 
 STABILITY. 
 
 THE Statical stability of a vessel is the moment of the couple formed 
 by the weight and buoyancy. In fig. 15 W L is the water line in the 
 erect position, W L', the water line, when heeled to the angle B under the 
 action of the wind or some other force, B, the position of the center of 
 
 FIG. 15. 
 
 buoyancy in the erect position, B' the position of the center of buoyancy 
 when heeled to the water line W L'; G is the position of the center of 
 gravity and a is the distance between lines passing through G and B' per- 
 pendicular to W L'. The intersection at M of the perpendicular through 
 B' with the centerline is known as the metacenter : G M is called the meta- 
 centric height. As long as G is below M the stability is positive, that is, 
 the vessel will tend to return to the erect position when inclined. With G 
 at M the stability is said to be neutral and with G above M the stability 
 
34 ELEMENTS OF YACHT DESIGN 
 
 is negative and the vessel will take an inclination until it reaches a posi- 
 tion where G is below i\I. 
 
 The transverse statical stability of a yacht is equal to the displacement 
 multiplied by a, the righting arm. The process of determining the sta- 
 bility at any angle of heel consists then in finding the distance apart of 
 the centers of gravity and of buoyancy in a direction parallel to the water 
 line at that angle. It is evident that the stability is dependent upon two 
 factors, that of weight and construction as affecting the position of G 
 and that of the form of hull as affecting the position of B'. 
 
 The center of gravity, G, lies of course on the centerline of the yacht 
 in the erect position. Its vertical position on that line may be found by 
 direct calculation, by approximation and by experiment on the completed 
 yacht. The calculation for vertical position of the center of gravity is 
 similar to that for longitudinal position as performed in chapter VII. The 
 weights of the component members of the structure and equipment are 
 found together with their vertical distances from a reference line, usually 
 the base line or load water line. The moments of the weights are summed 
 up and divided by the total weight, giving the distance of the center of 
 gravity from the reference line. This is a very laborious process, too 
 much so for ordinary small yacht work, and it is simpler and generally 
 sufficient to arrive at the position of the center of gravity by an approx- 
 imation. A simple method of approximating its position is to divide the 
 weight of the )'acht into several portions, as, for instance, the weight of the 
 rig taken at the center of effort, the hull proper taken at the center of its 
 profile, the deadwood taken at its center of profile, and the lead keel taken 
 at its center, which may be computed or estimated closely. Adding the 
 moments of these weights about the water line and dividing by the total 
 weight, we have a very close approximation to the correct position of the 
 center of gravity. The application of this approximation to the thirty- 
 footer is as follows : 
 
 ABOVE L. W. L. 
 
 ITEM WT. ARM. MOM. 
 
 Rig 1200 21 25200 
 
 Hull 8980 .8 7180 
 
 Equipment 1800 o o 
 
 Crew . 600 3 180 
 
 12580 34180 
 
 BELOW L. W. L. 
 
 ITEM WT. ARM. MOM. 
 
 Deadwood 1820 3.0 5460 
 
 Lead 9800 4. i 40200 
 
 II 620 45660 
 
ELEMENTS OF YACHT DESIGN 
 
 35 
 
 C. G. below L. W. L.= 
 
 45660—34180^ 
 12580+ 1 1620 
 
 .474 ft. 
 
 After the yacht is built and afloat the center of gravity may be ac- 
 curately located by an inclining experiment. Inclining experiments should 
 be performed whenever possible, as the knowledge of the position of the 
 center of gravity obtained in this way is of great assistance in approximat- 
 ing the position for a new design of the same type. Let us consider, first, 
 the case where an inclination is produced by raising a quantity of ballast 
 or other weight from the hold to the deck and then moving it outboard. 
 
 In fig. 16 w is the weight which has been raised from the hold where it 
 occupied the position w" With the weight at w, the center of gravity is 
 at some point G. Now if the weight is moved outboard a distance s, to 
 the position w' the center of gravity moves from G to G', causing an angle 
 of inclination 6, which is indicated by a plumb bob attached to a deck beam 
 at a. It is a good plan to have the plumb bob hang in a bucket of water 
 as shown so as to steady it. The distance it swings b c is noted on a stick 
 across the top of the bucket. 
 
36 ELEMENTS OF YACHT DESIGN 
 
 Now the distance GG', which the center of gravity has nioved is equal to 
 
 wX s 
 Disp. 
 
 AI is the position of the metacenter and is found by computation from 
 the lines as explained later, then 
 
 GM=GG'Cot^=^^X^^ 
 Disp. b c 
 
 a b and b c are readily measured, so that we may solve for G M giving 
 us at once the height of the center of gravit}' with the weight on deck at 
 w. If d is the distance w has been raised, the center of gravity with w 
 at w" will be lowered b}' the amount 
 
 wXd 
 Disp. 
 
 Where there is no weight aboard which may be used for inclining the 
 yacht it is necessary to employ some weight which is not a portion of the 
 yacht's equipment. Let IM be the position of the metacenter calculated for 
 the immersion with his extra weight aboard. Then as before 
 
 G.M=GG'Cot^=;^><-^^X^'^ 
 D+w b c 
 
 which gives G as the position of the center of gravity with weight on board. 
 Now with the removal of the weight, the center of gravity will be lowered 
 by the amount 
 
 wXh 
 Disp. 
 
 where h is the height of w above G. 
 
 The experiment should be conducted on a still day in a location where 
 there is no sea or current. All bilge water should be pumped out and no 
 one besides the observer should be aboard when the readings are taken. 
 After taking a reading the weight should be shifted to the other side an 
 
ELEMENTS OF YACHT DESIGN 37 
 
 equal distance from the center line and a second reading taken. Two dif- 
 ferent inclinations should be used, taking a double reading for each. The 
 angles should be from one to three degrees. 
 
 For small angles (up to about lo degrees) the height of ]\I remains 
 practically constant. The righting arm is equal to G A'l sin6 and the 
 stability equals DXG M sin6i. 
 
 We have then simply to determine the metacentric height in order to find 
 the stability ; this is known as the metacentric method of determining sta- 
 bility and is applicable only to very small angles of inclination. 
 
 The height of the metacenter above the center of buoyancy is equal to 
 the moment of inertia of the water-line plane divided by the volume of the 
 volume of the displacement or 
 
 B M=i. 
 
 As the demonstration of this is somewhat complicated it is deemed inadvis- 
 able to give space to it here, and the reader is referred to works on theoret- 
 ical naval architecture for this demonstration. We have seen in Chapter 
 II, page 14, how to determine the moment of inertia of a water line about 
 its longitudinal axis. For the thirty-footer, the transverse moment of 
 inertia of the load water line works out at 2025. The height of the trans- 
 verse metacenter above the center of buoyancy is 
 
 B M=i =-?^=5.36 ft. 
 V 378.2 ■' -^ 
 
 378.2 is the displacement in cubic feet. Now GM=BM — EG so that we 
 have to locate B and G in order to determine GM. The methods of determin- 
 ing the heights of the centers of buoyancy and of gravity have already been 
 dealt with. In the 30-footer, the center of buoyancy is very nearly one foot 
 below the center of gravity and the righting arm at 10 degrees is then, by 
 the metacentric method, about 4.36X-i74=-76 ft. 
 
 The metacentric height for longitudinal inclinations is analagous to 
 that for transverse inclinations and is found in the same way with the dif- 
 ference that the moment of inertia of the water line is taken about a trans- 
 verse axis through its center of gravity. As worked out on page 15, the 
 longitudinal I for the thirty-footer, is equal to 11454 and B M is then 
 equal to 
 
 It is evident that for small inclinations the metacentric height is a 
 
38 ELEMENTS OF YACHT DESIGN 
 
 measure of the stability. This leads to a consideration of suitable values 
 of G M for various classes of yachts. In racing yachts, where the sail area 
 is unlimited, the metacentric height is made as great as possible either by 
 placing the center of gravit}- very low or by greatly increasing the moment 
 of inertia of the water line. A large metacentric height represents great 
 stiffness and tendency to return quickly to the upright from small in- 
 clinations. This causes violence of motion when among waves and is to 
 be avoided in power-driven craft where the steadying effect of sail is ab- 
 sent. It is a popular error that great stiffness is essential to a comfortable 
 power craft. On the contrary, boats having ver}- small metacentric heights 
 are often the most steady at sea. This holds in a way in the case of sailing 
 yachts, and for this reason cruising yachts have in general smaller meta- 
 centric heights than racing boats. The value of GM for steam yachts of about 
 100 feet water line should be about 1.5 feet, for steamers of 200 feet water 
 line it lies in the neighborhood of 2 feet. 
 
 As stated, the amount of metacentric height is an indication of the sta- 
 bility for very small angles only, and for this reason cannot be used for 
 determining sail-carrying power and is no indication of the range of sta- 
 bility. It is especially useful in investigating the condition of steamers 
 in various states, such as without coal in the bunkers, with coal and stores 
 aboard, and in the launching condition. In order to have a complete 
 knowledge of the stability of a yacht, we must determine the lengths of 
 righting arm at various and wide angles of heel. If we plot these values 
 as ordinates, using angles of heel as abscissae, we have a curve of right- 
 ing arms. This curve for the thirty-footer is shown in fig. i, plate V. 
 From this curve the length of righting arm for any given angle of 
 heel is readily interpolated. The actual stability or righting moment is, of 
 course, obtained by multiplying this righting arm by the displacement. The 
 points to be noted in a stability curve are the angle at which the stability 
 is a maximum, the amount of stability at that angle and the range of 
 stability. The curve of the thirty-footer shows a range of 127 degrees, 
 or greater than could possibly occur from effects of wind pressure alone. 
 Many heavily-ballasted keel racing boats have a range of stability of 180 
 degrees, the stability at no time being negative. On the other hand lightly- 
 ballasted centerboard boats, while having large metacentric height and 
 great stability at small angles, have a limited range, reaching their limit 
 sometimes at as low as 50 or 60 degrees. 
 
 The amount of stabilit)- at small angles, as obtained from the meta- 
 centric height, is dependent solely upon the position of the center of grav- 
 ity and the form of the underbody. At large angles, however, the amount 
 
ELEMENTS OF YACHT DESIGN 39 
 
 of freeboard and general form of the upperbod}- plays a very important 
 part. An increase of beam increases the height of the first part of the 
 curve of righting arms, while an increase of freeboard increases the length 
 of the curve. 
 
 There are numerous methods of determining stability at large angles 
 of heel, most of which are too cumbersome and laborious in their appli- 
 cation to be of value for yacht work. The three methods, a discussion of 
 which follows, have been selected with especial reference to their applica- 
 bility to small yacht work. These methods are : 
 
 1. Blom's Method. This a purely mechanical method, and consists 
 in pricking off on very thin card from a tracing of the body plan, the shape 
 of the underwater portions of evenly-spaced transverse sections at a given 
 angle of inclination and up to a water line cutting off the required displace- 
 ment. These are pasted lightly together in their correct relative positions 
 and their common center of gravity determined. This is done by sus- 
 pending the sections from two or more points at the edge of the card and 
 noting where plumb lines from the points of suspension intersect. This 
 point is the center of buoyancy at that angle and the distance between the 
 centers of buoyancy and of gravity in a direction parallel to the water line 
 is easily measured. If this process is pursued for other angles at inter- 
 vals of about ID degrees, we may then draw a curve of righting arms. 
 
 2. Heeled Longitudinal Sections. 
 
 This method is by direct computation, and as an example of its appli- 
 cation, the righting arm for the thirty-footer at 20 degrees heel, has 
 been worked out. The work is recorded in the table on page 40. 
 
 In fig. 2, plate V, the water lines, W L' and W" L" are drawn so 
 as to cut off the same displacement as W L and represent an angle of heel 
 of 20 degrees. Longitudinal sections perpendicular to W L' and W" L" 
 are drawn at a, b, c, etc. The sections are spaced a foot apart, and section g 
 passes through thecenter of gravity G, found by the approximation, already 
 given. Referring to the table, the measurements recorded in the columns 
 headed a, b, c, etc., are the distances in feet from the inclined water line 
 to the intersection of the longitudinal and transverse sections. By draw- 
 ing two inclined water lines W L' and W" L", we avoid the necessity of 
 drawing a double body plan like fig. 3. Mea.surements for the forebody 
 are taken from W L' as far as section h and from W" L" for sections i 
 and j. Measurements for the afterbody are taken from W" L" as far as 
 section i with the exception of station 12 on section h, where the distances 
 from the first to the second intersection by h is measured. Sections i and 
 j are measured from W L'. After the measurements are all taken, the 
 
40 
 
 ELEMENTS OF YACHT DESIGN 
 
 ^ OliOM CSOOtN.O'Ot^ro 
 
 =:oq fTi fn -rt \o C^ *-< n ^ Nvo 
 -\o rN.O\od r^ioi-I fb^'od oi 
 
 r;\0»n-t<r)(s mOmcic^ 
 
 01 
 
 ^ 
 
 o 
 
 00 
 
 ^s 
 
 s^ 
 
 
 ^ 
 
 ■-¥,"0 
 
 &c 
 
 rt — (J *0 oj 
 
 00 
 
 to 
 
 g'g' 
 
 oi \d 
 
 >=« 
 
 ONOi-t-i-oi-xrs.ot'vool -N 
 '-' 1-^ oi (>i (>i oi >-" " K 
 
 "8 8 
 
 
 M W l-H .-, 
 
 O 10 o 
 (N CO •-. 
 
 
 
 01 fN. 
 
 00 01 
 
 
 10 
 10 
 
 f^i 
 
 00 -r 01 vjD 
 
 
 1-3 oi 
 
 IS 
 
 01 
 
 ^' 
 
 -; ■ in uS 
 
 
 
 8 
 
 =2=^ 
 
 ^ 
 
 
 
 i-O 
 
 
 g S'S.g^ 
 
 « 
 
 h- c>i 
 
 oi 
 
 oi 
 
 r-i 
 
 
 < 
 
 
 1^ 
 
 
 10 
 
 k 
 
 01 vo 10 00 -t 
 
 w PO fO >- 
 
 C 
 
 ^ Pi 
 
 01 
 
 oi 
 
 01 
 
 ^' <-I ' 10 \o 
 
 l-xi-HtxOOQrrjOli-'r^ Pi 
 
 O -1-")-0l\OO PO'-' fO 
 
 '^i 01 01 01 w ►-I ' -f- 01 
 
ELEMENTS OF YACHT DESIGN 
 
 41 
 
 columns are added and their sums multiplied by the spacing of the sta- 
 tions, in this case three feet, give the areas of the sections a b c, etc., in 
 square feet by the trapezoidal rule. The areas are then transferred to 
 the column at the right headed areas, and added together. The sum of 
 the areas multiplied by the spacing of the sections ( i foot) , gives for the 
 heeled displacement 374.85X1X64=24000 lbs. 
 
 The area of each section is multiplied by its distance in feet from g, 
 the section passing through the center of gravity G, and the moments on 
 each side of g are then added separately. The difference of the sums of 
 moments divided by the sum of the areas of sections gives 1.41 feet for 
 the length of the righting arm at 20 degrees. 
 
 3. The Mechanical Integrator. Theuseof the integrator reduces greatly 
 the amount of labor in making stability calculations, and for this reason 
 is now used practically to the exclusion of numerical methods, by naval 
 architects, who have much stability work to do. Fig. 17 is a diagram of 
 a common form of the instrument. The integrator runs on a steel track 
 T. P is the tracing point. The disc at A records area readings, and 
 disc M records moment readings. Some forms of the instrument have 
 still another disc for finding moment of inertia of plane figures. 
 
 FIG. 17. 
 
42 
 
 ELEMENTS OF YACHT DESIGN 
 
 In using the integrator, the track is first set parallel to and at the cor- 
 rect distance from the axis of the figure b}- means of the gauges G and G'. 
 In figure 17 the instrument is placed for finding the righting arm of a 
 yacht at 30 degrees inclination. The line a a' is the axis about which mo- 
 ments are taken. This line passes through the center of gravity G, and 
 makes an angle of 30 degrees with the centerline. .\lthough it is con- 
 venient to have the axis pass through the center of gravity, it is not es- 
 sential, for a correction in length of righting arm is readily made as shown 
 
 FIG. 18. 
 
 in fig. 18. Suppose the righting arm about an axis A C is found to be 
 C B. Nov,' if the center of gravity is at G, the true righting arm will be 
 
 G Br=C B+G C 
 
 =C B+G A sine 
 
 that is, if the center of gravity is below the intersection of the axis with 
 the centerline, we must add to the arm as found the distance from G to in- 
 tersection with the axis times the sine of the angle. If G is above the in- 
 tersection, G A sin^ is to be subtracted. 
 
 If we set the discs of the integrator at o, and then sweep the tracing 
 point around a transverse section, we may take readings of the discs 
 
ELEMENTS OF YACHT DESIGN 43 
 
 which, when multiphed by the constants of the instrument, give us the 
 area and moment of the section. The moment divided by the area gives 
 the distance from the axis to the center of the section. If this is done for all 
 the sections of the boat and the areas and moments of the sections summed 
 up, we may get the displacement and righting arm. The application of this 
 method requires a double body plan such as is shown in fig. 3, plate V. In 
 that figure the afterbody is drawn in dotted to avoid confusion. 
 
 The area and moment readings may be taken and recorded separately, 
 but an easier and quicker way is to sweep the tracing point around each 
 of the sections in succession, without stopping to take readings until all 
 have been traced. Care must be taken not to omit any sections. The final 
 readings give the sum of the areas and moments of the sections. These 
 readings have simply to be corrected for the constant of the instrument 
 and for scale before finding displacement and arm. 
 
 The sums of the moment and area readings for the thirty-footer at 20 
 degrees inclination were respectively 19.00 and 34.99. The constants of 
 the instrument were 4 for moments and 2 for areas. The righting arm is 
 equal to 
 
 i9.ooX4X% _^ ^, .. 
 34.99X2X'%"" '^^ 
 
 "727 corrects the moment reading for scale, being the cube of the inverted 
 scale %. The area reading is corrected by multiplying by "! 9, the square 
 of the inverted scale. 
 
 If the moment disc goes backward, the final reading has to be sub- 
 tracted from one and the center of the figure is on the side of the axis 
 away from the track, otherwise it is on the same side as the track. 
 
 The displacement in the inclined position is of course the same as when 
 erect. An inclined water line is drawn which it is estimated will cut oi? 
 the right displacement and the displacement to this line determined. The 
 displacement will be in error by the amount of a slice whose thickness is 
 equal to amount of the excess or deficiency in displacement to the heeled 
 water line divided by the area of the water line, which is found by measur- 
 ing the widths of the water line on each station and applying the trape- 
 zoidal rule. With this correction, a new water line is drawn parallel to 
 the trial line, which will cut ofif nearly the right displacement and the sta- 
 bility for the portion below this line worked out. 
 
 It is sufficient in general to determine the stability for a constant dis- 
 placement as the changes in flotation due to consumption of stores, etc., are 
 very slight, especially in sailing yachts. In large, ocean-going steam 
 
44 
 
 ELEMENTS OF YACHT DESIGN 
 
 yachts, however, considerable changes in displacement may occur on a voy- 
 age due to consumption of stores and coal, and it is advisable to work out 
 in such cases the stability at various displacements as well as at various 
 angles of inclination. 
 
 If we find the righting arm for several displacements at the same angle 
 of inclination, we may draw what is known as a cross curve of stability, 
 having displacements for abscissas and righting arms for ordinates. This 
 is the converse of the ordinary curve of stability which has angles of in- 
 clination for abscissas, the displacement remaining constant. A set of 
 cross curves is shown in fig. 19. If we wish to draw an ordinary curve 
 for any given displacement, say 158 tons, we draw an ordinate at that 
 point, and with the values of righting arm for the various angles at this 
 ordinate we draw an ordinary curve, using angles for abscissae. The 
 cross curves shown in fig. 19 were drawn with an assumed constant po- 
 sition of center of gravity. The center of gravity alters its position, of 
 
 TONS Disp. 
 
 FIG. 19. 
 
 course, with a change in loading and displacement and a correction should 
 be made for this as shown on page 42. 
 
 The m.ethods of determining stability which have been discussed, as- 
 sume the yacht to be at rest and in still water. These conditions are of 
 course absent when a yacht is under sail and the actual stability will in 
 general, be greater than the calculated, due to the support afforded by 
 waves at bow and stern. This difiference is very great in the case of racing 
 boats with long and low overhangs. For this reason stability work on 
 modern yachts must be considered comparative rather than quantitative, 
 that is, data obtained on sail-carrying power for a given type of boat should 
 be used only for work on boats of that type. For instance, we may wish 
 
ELEMENTS OF YACHT DESIGN 45 
 
 to knov/ a suitable value for wind pressure for a particular type, in figuring 
 sail area as shown on page 55. Having found the stability for a yacht 
 of the given type having a suitable sail area, assuming the yacht at rest, 
 we may equate the righting and heeling moments as follows : Disp.XanTi= 
 AXhXpXcos^. A is the sail area, h is the vertical distance between 
 the centers of efTort and lateral resistance, and p the pressure of the wind 
 on one square foot of sail. All the quantities in this equation are known 
 except p which is readily found by solving the equation. In this way val- 
 ues of p may be found for different types, which used in conjunction with 
 the stability determined in the ordinary manner, enable us to apportion the 
 sail area in accordance with the stability. The stability of steam yachts 
 when under way, is very nearly as calculated. 
 
 A phenomenon of importance in connection with stability is the fluct- 
 uation in apparent or virtual weight of the yacht when among waves of 
 sufficient size to lift her bodily. As the yacht is lifted on a wave it acquires 
 a certain amount of momentum which tends to decrease the dispacement 
 and virtual weight when the wave commences to subside. The virtual 
 weight is a minimum when on a crest, and it is increased correspondingly 
 in the trough. The direct effect of this on the stability is obvious when we 
 remember that stability is the product of weight and righting arm. This 
 variation of stability when among waves, the force of the wind remaining 
 constant, is the chief cause for a yacht's inability to carry the same amount 
 of canvas in rough water as in smooth. 
 
 So far we have considered only statical stability. We have next to con- 
 sider d3'namical stability. This is the amount of work expended in heeling 
 the yacht to a given angle. This work is done in raising the center of grav- 
 ity, depressing the center of buoyancy, wave-making, eddy-making, and 
 in overcoming frictional resistance. The last three items increase with ra- 
 pidity of motion and are of slight importance for slow inclinations. The 
 curve of dynamical stability is the integral of the curve of statical stability ; 
 that is, the dynamical stability at a certain angle is equal to the area of the 
 curve of righting moments up to that point. Thus we see that the area 
 as weh as the shape of the curve of righting moments is of importance. 
 
 The period of oscillation is the time consumed in swinging from an in- 
 clined position to the opposite position under the influence of the stability. 
 It is expressed theoretically by the following formula : 
 
 / R2 
 T=.554F GM 
 
46 ELEMENTS OF YACHT DESIGN 
 
 R is the radius of gyration and GM the metacentric height. It will 
 be seen that T varies as the radius of gyration and inversely as the square 
 root of the metacentric height. 
 
 The period of oscillation has a very important bearing on the question 
 of speed, as it depends both on the form and the amount and distribution 
 of the weight, as will be seen from the formula. It appears to be of ad- 
 vantage to make the radius of gyration as large as practicable for trans- 
 verse inclination, and as small as possible for longitudinal inclinations. 
 This is accomplished b\- spreading the weights transversely and concen- 
 trating them amidships longitU|dinalh-, thus increasing- the radius of 
 g>Tation and the value of T. This is the reason for "winging out" the bal- 
 last in shoal, centerboard boats. The radius of gyration is increased with- 
 out affecting the metacentric height. Transverse distribution of ballast is 
 not possible in boats having outside ballast. 
 
 As we have seen, the total stability is made up of the stability due to 
 form and that due to weight. Now for any given ratio of ballast to dis- 
 placement, there is probably a certain combination of stability of form and 
 weight more effective for speed under ordinary conditions than any other. 
 This is one of the fundamental principles of _\'acht design and is, moreover, 
 one of the least understood. The proportion of stability due to weight to 
 the total varies in the same direction as the ratio of ballast to displace- 
 ment. There is absolutely no data as to what this proportion should 
 be for varying ratios of ballast to displacement. Scientific experi- 
 mentation along this line would be very difficult, if not impossible, 
 but the results would be of immence value to a skillful designer. 
 A faulty distribution of stability between form and weight is responsible 
 for the failure of many racing yachts, the error being generally in giving 
 too large a proportion of stability to weight, that is, in placing the ballast 
 too low- 
 
 A knowledge of the longitudinal and transverse metacentric heights 
 is of value in determining the change of trim or inclination consequent up- 
 on moving a weight from one portion of the yacht to another. The mo- 
 ment to change trim one inch is equal to 
 
 , — foot pounds or foot tons. 
 
 12XL 
 
 D is the amount of the displacement in pounds or tons, GM the meta- 
 centric height or distance from the center of gravit}- to the longitudinal 
 metacenter, and L is the water-line length in feet. The change of trim 
 
ELEMENTS OF YACHT DESIGN 47 
 
 is taken as the sum of the amounts by which the boat sinks at the 
 stern and rises at the bow, or vice versa. The longitudinal GM for the 
 thirty-footer is 29.29 ft. The moment to change trim is then 
 
 24200X29.29 ^ ,^ , 
 
 —^ — - ^ — ^^=1969 ft. poimds. 
 12X30 
 
 Suppose we wish to determine the change in trim due to moving a 
 lOO-lb. anchor from the bows to the lazarette, a distance of about 29.5 feet. 
 The moment of the weight of the anchor is then 100X29.5^2950 ft. lbs., 
 and the change of trim is 
 
 2950 . „ 
 
 —y—=ix mcnes. 
 1969 
 
 The longitudinal metacentric height is approximately the same as the 
 water-line length, so that for rough calculations the moment to change 
 trim one inch may be taken as one-twelfth the displacement. 
 The moment to produce one degree heel is equal to .01745 XDXGM, 
 where GM is the transverse metacentric height and D the displacement. 
 
 For the thirty-footer this moment is .01745X24200X4-36=1841 ft. 
 lbs. 
 
 A boat weighing 150 lbs. would be about 8 feet outboard if carried 
 on davits and would produce a heeling moment of 150X8=1200 lbs. The 
 angle of heel produced would be 
 
 1200 
 18^1=- ^5 
 
CHAPTER VII. 
 
 BALLAST. 
 
 THE function of ballast is to increase the stability due to weight, This 
 is done by increasing the displacement and by increasing the meta- 
 centric height GM through a lowering of G. The proper ballast- 
 ing of a yacht is of vital importance. With cruising boats, considerations 
 of safety and ability demand a liberal amount of ballast. Where speed 
 alone is the only consideration, however, it is desirable to reduce the 
 amount of ballast to a minimum, the sail-carrying power being furnished 
 by increased stability of form and by the weight of crew. The nice adjust- 
 ment of stability of form and of weight, according to type as discussed in 
 the chapter on stability is of great importance in all cases. 
 
 Lead is more commonly used for ballast than any other material on 
 account of its high density. Its use permits of great concentration and 
 lowering of weight and consequent increa.se in weight stability. Excess 
 in this direction, however, is a common error. Lead has the further ad- 
 vantage over iron of being uninjured by the action of water. Iron, on the 
 other hand, is much cheaper than lead and may be incorporated in the 
 arrangement for longitudinal strength. Certain types of boats, notably 
 centerboard boats, requiring a considerable amount of inside ballast, per- 
 form better with stone or iron ballast than with lead. An explanation of 
 this is that the stone and iron being of smaller density than lead, are of 
 greater bulk for equal weights, thus raising the center of gravity and dis- 
 tributing the weight so as to afford a better combination of stability of 
 form and of weight, and a more suitable value for transverse time of os- 
 cillation than would result if lead were used. Transverse distribution and 
 longitudinal concentration of ballast are to be sought in general. 
 
 A convenient method of comparison of the weight of ballast carried 
 in different types is b\' the ratio of ballast to displacement. This ratio for 
 keel cruising boats should lie between .40 and .55. For the semi-keel type the 
 ratio should lie between .30 and .45, being generally in the vicinity of .40. 
 Centerboard cruising boats with inside ballast should have a ratio of from 
 .25 to .40, the ratio lying most commonly between .30 and .35. It is im- 
 possible to state any values of this ratio for racing boats, as the amount of 
 
ELEMENTS OF YACHT DESIGN 49 
 
 ballast is dependent upon the rule under which the boat is built, and varies 
 from zero in the classes with little or no restrictions up to the values stated 
 for cruising boats in classes where the restrictions are more stringent. The 
 ratio ballast to displacement for the thirty-footer is .405. 
 
 In all cases it is well to provide for the carrying of a small portion at 
 least, of the balla.st inside the boat. Boats carrying all inside ballast are 
 found to require considerable experimentation as to position and distri- 
 bution of ballast before securing the best results. From this it seems al- 
 together likely than many racing boats with all outside ballast are not sail- 
 ing in their best form on account of the ballast not being in the most suit- 
 able position longitudinally or vertically, particularly the latter. It is dif- 
 ficult to experiment with the vertical position of the ballast but the longi- 
 tudinal position and resultant trim is readily varied if some inside ballast 
 be carried. 
 
 In designs where the entire amount of ballast is to be carried on the 
 keel, it is necessary to make very careful computations for weight and po- 
 sition of center of gravity if accurate results are to be expected. To do 
 this the weight and center of each item entering into the structure and 
 equipment of the yacht must be ascertained. The methods of computing 
 the weights of the various members have been given in chapter II. Care 
 must be taken that nothing be omitted from this calculation. Longitudinal 
 moments must be taken about a convenient axis, usually the midship 
 section so that the position of the center of gravity may be calcu- 
 lated. The distance from the center of gravity of each member to the 
 midship section, multiplied by its weight gives the moment. The moments 
 of weights forward of the midship section are summed up separately from 
 those aft and the difference between the sums of moments divided by the 
 sum of the weights, gives the distance of the center of gravity of the yacht 
 from the midship section. Now, in order that the boat may trim as de- 
 signed, the moments of boat and ballast taken about the center of buoy- 
 ancy must be exactly equal, their weights being on opposite sides of the 
 center of buoyancy. The amount of the ballast is made equal to the dis- 
 placement minus the sum of the other weights. To illustrate this process 
 the computation for weight and center of gravity of the thirty-footer is 
 given below. 
 
so 
 
 ELEiMIiNTS OF YACHT DESIGN 
 
 WEIGHTS FORWARD OF STATION 9- 
 
 
 ITEM 
 
 \\T. 
 
 ARM . 
 
 MOMENT 
 
 Keel 
 
 5^5 
 
 7-^ 
 
 3940 
 
 Planking 
 
 2182 
 
 I- 1 5 
 
 •^515 
 
 Frames 
 
 1 104 
 
 i-'S 
 
 1270 
 
 Deck 
 
 1 130 
 
 •03 
 
 34 
 
 Deck Beams 
 
 277 
 
 ■03 
 
 8 
 
 Shelves 
 
 114 
 
 2. 
 
 228 
 
 Clamps 
 
 133 
 
 2.3 
 
 306 
 
 Stringers 
 
 179 
 
 2 
 
 358 
 
 Floors 
 
 350 
 
 5- 
 
 1750 
 
 Plank Fastenings 
 
 95 
 
 I-I5 
 
 109 
 
 Deck Fastenings 
 
 62 
 
 ■03 
 
 
 
 Other Fastenings 
 
 190 
 
 .10 
 
 19 
 
 House Deck 
 
 135 
 
 I. 
 
 135 
 
 House Coaming 
 
 ^^3 
 
 1.8 
 
 402 
 
 House Beams 
 
 67 
 
 I. 
 
 67 
 
 Mast Step 
 
 52 
 
 9.5 
 
 4-93 
 
 Deck Straps 
 
 35 
 
 10.4 
 
 364 
 
 Rail 
 
 49 
 
 2.3 
 
 113 
 
 Knees 
 
 75 
 
 I. 
 
 75 
 
 Breasthook 
 
 iS 
 
 23- 
 
 413 
 
 Ceriterboard 
 
 170 
 
 1,8 
 
 306 
 
 Bitt 
 
 14 
 
 19.6 
 
 274 
 
 Paint 
 
 ISO 
 
 I. 
 
 ISO 
 
 Cabin Floor 
 
 136 
 
 2.4 
 
 327 
 
 Cabin Floor Beam^ 
 
 ; 18 
 
 2.4 
 
 43 
 
 Deck Fittings 
 
 50 
 
 2. 
 
 100 
 
 Mast 
 
 S17 
 
 9-5 
 
 4910 
 
 Bowsprit 
 
 46 
 
 24.6 
 
 1 130 
 
 Staysail 
 
 21 
 
 14-3 
 
 300 
 
 Jib 
 
 23 
 
 20. 
 
 460 
 
 Blocks 
 
 55 
 
 8. 
 
 440 
 
 Running Rigging 
 
 85 
 
 9- 
 
 76s 
 
 Standing " 
 
 90 
 
 ii-S 
 
 103s 
 
 Windlass 
 
 50 
 
 19-5 
 
 973 
 
 Anchors 
 
 160 
 
 19. 
 
 3040 
 
 Cables 
 
 200 
 
 18. 
 
 3600 
 
 Lockers 
 
 270 
 
 .04 
 
 11 
 
 Ice Box and Ice 
 
 275 
 
 9.2 
 
 2530 
 
 Washbowl 
 
 25 
 
 4- 
 
 100 
 
 Water Closet 
 
 90 
 
 7-7 
 
 693 
 
 Tanks and water 
 
 800 
 
 2.7 
 
 2160 
 
 Galley Fittings 
 
 80 
 
 6. 
 
 480 
 
 Pipe Berths 
 
 30 
 
 13-3 
 
 399 
 
 Bulkheads 
 
 232 
 
 1.6 
 
 371 
 
 Personal Effects 
 
 250 
 
 1-5 
 
 375 
 
 10832 
 
 37573 
 
ELEMENTS Ol" YACHT DESIGN 5^ 
 
 WEIiQHTS AFT OF STATION 9. 
 
 iTEjr 
 
 WT. 
 
 .VRM. 
 
 MOMENTS 
 
 Deadwood 
 
 1820 
 
 17 
 
 3095 
 
 Tail-Featlier 
 
 61 
 
 '4-5 
 
 885 
 
 Silk 
 
 168 
 
 2.4 
 
 403 
 
 Transom 
 
 41 
 
 19.8 
 
 812 
 
 Tie Rods 
 
 10 
 
 .2 
 
 8 
 
 Rudder Tube 
 
 TO 
 
 11.8 
 
 118 
 
 Cockpit Coaming 
 
 170 
 
 10.6 
 
 1800 
 
 Steering Gear 
 
 30 
 
 12.2 
 
 366 
 
 Mainsail 
 
 116 
 
 4- 
 
 464 
 
 Main Boom 
 
 171 
 
 8.3 
 
 1420 
 
 Gaff 
 
 66 
 
 I. 
 
 66 
 
 Carpet 
 
 35 
 
 1.2 
 
 42 
 
 Berths 
 
 225 
 
 2.1 
 
 472 
 
 Cushions 
 
 15 
 
 2. 
 
 30 
 
 People 
 
 600 
 
 10. 
 
 6000 
 
 3568 15981 
 
 Now dividing the difference of the moments by the sum of the weights 
 
 37573—15981 2I592_ 
 
 10832+3568 1450 
 
 :1.50 
 
 we have 1.50 feet for the distance, the center of gravity is forward of the 
 midsection. Now the center of buoyancy is 1.58 feet forward of the mid- 
 section so that the center of gravity comes .08 feet aft of the center of 
 buoyancy. The weight of the lead will be made equal to the displacement 
 minus the sum of the weights, 24207 — 14400^9807 or about 9800 lbs. 
 It would be desirable to carry a portion of the ballast inside for trimming, 
 but for purposes of illustration it has all been placed on the keel in this de- 
 sign. The moment of the ballast must of course equal the moment of all 
 the other weights, then 
 
 9800 X arm = 1 4400 X -08 
 
 14400X.08 , 
 
 arm=r3^!=?— ^.12 ft. 
 
 9800 
 
 The center of gravity of the lead must then be .12 feet forward of the cen- 
 ter of buoyancy or .20 feet forward of sta. 8^, in order that the boat may 
 trim properly. 
 
 The next step is to determine the top of the lead on the design so that 
 
52 ELEMENTS OF YACHT DESIGN 
 
 it will have the required weight and position. To do this a trial line is 
 drawn and the weight and center of the portion thus cut off is determined. 
 With this as a guide, another line is drawn which is estimated will correct 
 the errors in weight and center of the first trial line. If there is still 
 an error, another trial is made and so on until the correct line is found. 
 The volume of the lead is found in the same manner as the volume of the 
 hull in the calculation for displacement. Keel sections are drawn at fre- 
 quent intervals, 1.5 feet on plate I, and the areas of these sections are 
 taken with a planimeter. The volume and center are then obtained by 
 the application of the trapezoidal rule. Where there is a slot cut through 
 the keel for a centerboard, the volume of the portion cut out is determined 
 and its moment is subtracted from the total moment. The computation 
 for the thirty- footer is as follows : 
 
 STA. 
 
 PLAN. REAI'ING 
 
 ARM. 
 
 MOMENT 
 
 6 
 
 .01 
 
 S 
 
 ■05 
 
 6K2 
 
 ■17 
 
 4 
 
 .68 
 
 7 
 
 •.i5 
 
 3 
 
 1.05 
 
 rA 
 
 •V 
 
 2 
 
 .84 
 
 8 
 
 ■44 
 .40 
 
 I 
 
 
 ■44 
 
 8/2 
 
 3.06 
 
 9 
 
 •36 
 
 I 
 
 •36 
 
 9K2 
 
 ■32 
 
 2 
 
 .64 
 
 10 
 
 ■25 
 
 3 
 
 ■75 
 
 10^ 
 
 .19 
 
 4 
 
 .76 
 
 2.91 2.51 
 
 Total weight=2.9iX2X"'/9X 1.5X710=11020. 
 710 is the weight in pounds of one cubic foot of lead. 
 
 Center of gravity^ '^ ^ "'^ X i.5=.283 ft. for'd sta. X3/^. 
 
 Now the area of the portion cut out by the slot is 5.72 square inches on 
 the drawing or 5.72X'V9=to.i7 -sq. ft. 
 
 The thickness is two inches or .167 feet. The weight cut out is then 10.17 
 X.i67X7io=i202 pounds. Its center of profile is .95 feet forward of 
 station 8'/2. Now taking moments and subtracting 
 
 ii05oX-283=3n9 
 
 I202X.95= II42 
 98T8X -20 1977 
 
ELEMENTS OF YACHT DESIGN ' 53 
 
 We get .20 feet for the distance which the center of gravity of the lead 
 is forward of station 8j4. 
 
 The calculation for longitudinal position of the center of gravity is ab- 
 solutely necessary when all the ballast is to be carried on the keel, in 
 order that satisfactory results may be assured. The relative positions of 
 the center of buoyancy and of gravity vary so widely in different designs 
 that an estimation of the proper position for the center of the ballast is 
 apt to lead to disappointment. The many cases of faulty trim which are 
 constantly occurring may be attributed to carelessness in this matter. 
 
CHAPTER VIII. 
 
 THE SAIL PLAN. 
 
 THE simplest method of determining the amount of sail for a new design 
 is by direct comparison with some boat of known performance and 
 of approximately the same type. This is the usual method. As an aid 
 in estim.ating the sail area, the curve on plate VIII has been drawn, using 
 water-line length as a basis of comparison. The sail areas of a large num- 
 ber of successful yachts were used in constructing this curve, and it may 
 be considered thoroughly representative of modern practice for cruising 
 boats. It was found that no distinction could be made between keel and 
 centerboard boats, especially above twenty feet water line. Using this 
 curve for the thirty-footer we get 1280 square feet as a suitable area. 
 
 A method of comparison for sail area is by the ratios of sail area to 
 area of wetted surface, and sail area to area of midsection. The former 
 ratio is generally about 3 though it varies between 2 and 4. The ratio of 
 sail area to area of midsection is used a great deal by French naval archi- 
 tects, and is a very good method of comparison. This ratio should be be- 
 tween 45 and 55 for cruising boats. For the thirty-footer it is 53.2. The 
 ratio of sail area to displacement is also used. Theoretically, the sail area 
 should vary as the two-thirds power of the displacement. Let Sj and Dj 
 be the sail area and displacement of a certain boat, and S^ and D^, the sail 
 area and displacement of another boat of exactly the same form but of dif- 
 ferent dimensions ; then 
 
 2/l 2/-. « "D '^ 
 
 S,:S,= d/^ D/^orS., = ^l-^A- 
 
 The correct procedure, theoretically, is to apportion the sail area in 
 accordance with the stability making the heeling and righting moments 
 equal for a reasonable angle of heel, say, twenty degrees. The righting 
 moment is equal to the displacement times the righting arm for the given 
 angle, as explained in chapter W. while the heeling moment is equal to 
 
ELEMENTS OF YACHT DESIGN 
 
 55 
 
 the pressure on the sails, or pressure per unit area times the area, multiplied 
 by the vertical distance between the centers of effort and lateral resist- 
 ance. This distance decreases, of course, as the angle of the heel increases, 
 varying as the cosine of the angle. The pressure of the wind on sails 
 for a good whole-sail breeze is generally considered to be a little over one 
 pound per square foot of area, say i.i5povuids. Thisisnot theabsolutepres- 
 sure of the wind such as mechanical engineers use in designing structures 
 but a sort of constant, determined as on page 45. The assumptions made 
 here are that the sails are perfectly fiat surfaces lying in the central plane of 
 the boat, and that the wind blows in a direction perpendicular to the longi- 
 tudinal axis of the boat. These conditions are, of course, not realized, and 
 for this reason p must be considered a factor for wind pressure. 
 
 Equating the heeling and righting moments at 20 degrees for the 30- 
 footer, we have AXi.i5X24.6X-94=2420oXi4i. 24.6 is the distance 
 in feet between the centers of effort and lateral resistance ; .94 is the cosine 
 of 20 degrees; 24200 is the displacement in pounds and 1. 41 is the right- 
 
 FiG. 20. 
 
56 
 
 EI.F.MICNTS Ol' YACHT DICSIC.N 
 
 ing arm in feet at 20 degrees. Solving the equation we get for the area 
 1283 square feet. 
 
 The area of the sail plan is easily found by dividing it up into triangles 
 and finding the area of each by measuring its base and altitude and taking 
 half the product. Fig. 20 shows the manner in which these measurements 
 were taken on the thirty-footer. The mainsail was divided into the tri- 
 angles A B D and B C D, A b and a C being the respective altitudes. 
 
 The area of the mainsail is then V2BD ( Ah-\-3.C) . The altitudes of 
 forestaysail and jib are G c and J d and their areas are 
 
 Forestavsail^j4E FXGc 
 Jib ' =>S TI iXjd 
 
 By the center of effort of a sail plan is generally meant the center of 
 gravity of the areas of all the sails. The true center of pressure is con- 
 
 e 
 
ELEMENTS OF YACHT DESIGN 57 
 
 siderably ahead of the center of gravity of the sails, and its exact position 
 is impossible to determine. The position of the center of lateral resistance 
 is also impossible to calculate, and as the positions of these two important 
 'points are unknown, it is convenient and customary to use instead the 
 center of gravity of the sail plan and the center of lateral plane, the lead 
 being the distance the former is ahead of the latter. 
 
 In finding the center of effort, the center of each sail is found and the 
 center of the system is then found by taking moments. Fig. 21 gives the 
 construction for center of effort of the thirty-footer. In finding the cen- 
 ter of the mainsail, the second construction given in chapter II for center 
 of a quadrilateral, with no two sides parallel, was used. A b was laid off 
 equal to aC ; b B was drawn and bisected, its middle point being at d. Bd 
 was also bisected, its middle point being at c. The center of the sail is 
 at O, the point of intersection of b c and D d. The center of the jib was 
 found by bisecting H I and H J, g and h being the middle points respec- 
 tively and drawing I h and J G ; the center is at M, their point of intersec- 
 tion. The center of the forestaysail, X, was found in a similar 
 manner. The combined center is obtained by finding the center of two 
 sails and then combining with a third, and so on for any number of sails. 
 The areas of the sails for the thirty-footer are, mainsail 934 sq. ft., fore- 
 staysail 174 and jib 177. The center of staysail and jib is found at P by 
 taking moments about M 'thus : 
 
 MP=i74XMN^ ^^_ 
 174+177 
 
 Now taking^ the moment of the mainsail about P, we get the center of 
 all three sails at Q, its distance from P being 
 
 P 0=-^-^4?^-°=:6.8 ft. 
 ~ 1285 
 
 The vertical projection of Q on the water line at R gives a convenient 
 point for locating the fore and aft position of the center of effort. 
 
 The proper lead or distance between the centers of effort and lateral 
 plane varies widely with the type of boat. It is conveniently expressed as 
 a fraction of the water-line length. For racing machines of the scow type 
 it varies from o to .15, the balance of these boats depending largely on their 
 trim; for shoal, full-ended centerboarders, the lead lies between .05 and 
 .10; for full-ended keel racing boats the lead is generally a little less. For 
 cruising boats of normal form the lead is about .03. In the larger sizes 
 
58 ELEMENTS OF YACHT DESIGN 
 
 the lead is generally smaller and the center of effort is often placed over and 
 sometimes abaft the center of lateral plane. This is frequently done in 
 the case of catboats for structural reasons, being one of their defects, how- 
 ever. The only way of determining the proper lead is by direct compari- 
 son with some well-balanced boat. Even then it is very difficult to get it 
 right in the case of long, full-ended racing boats, and the designer gen- 
 erally resorts to the unscientific device of a movable mast. ^lany design- 
 ers neglect the topsails when figuring the center of effort, but it is the opin- 
 ion of the writer that they should ahva\ s be included in the calculation, as 
 serious defects in balance have resulted from neglecting them. 
 
 The area of sail decided upon has to be subdivided into a number of 
 sails in a manner consistant with ease to handling, appearance, and effici- 
 ency. The principal rigs in use to-day are the sloop, schooner and yawl. 
 
 The sloop rig is the most efficient, and the yawl the most easily handled. 
 The yawl rig for this reason is becoming more and more commonly used. 
 For the thirty-footer, the double headsail, polemast rig was chosen as be- 
 ing best adapted to this size and type of boat. It is more efficient than the 
 yawl rig and is aTjout as easily handled. 
 
 ^^'e are very much in the dark as to the most efficient shape of sails. By 
 shape is meant the proportions of the sail and not the amount of flow or 
 draught and general set of the sail. .V discussion of the latter would be 
 unprofitable here as it lies within the province of the sailmaker rather than 
 the designer. Every designer has his own theories as to what constitutes 
 an efficient form of sail. Xearly all agree that the forward portion of the sail 
 is the most eft'ective, and that for this reason excessively long booms should 
 be avoided. The relative lengths of head and hoist vary widely with the 
 practice of different designers, some preferring a long hoist with short 
 gaff, while others make head and hoist about equal. The sail should be 
 drawn as it is to be cut, bearing in mind that when the sail is set and fully 
 peaked up. the peak angle or angle between head of sail and axis of mast 
 is from one to three degrees less than that to which the sail is cut. For 
 a boat without a topsail, the peak angle of the mainsail should not be made 
 lessthan twenty-seven degrees. This is the peak angle to which the main- 
 sail of the thirty-footer is drawn. When topsails are used the peak angle 
 should be about 42 degrees for the mainsail, and 48 degrees for the fore- 
 sail in schooners. Low booms and low-cut jibs should be avoided as they 
 are in the way, and are not efficient when the boat is heeled well down. 
 High-pointed jibs are inefficient, as they do not draw well and tend to back- 
 wind the mainsail. There should be considerable space between jib and 
 mainsail so as to allow a free passage of wind to the mainsail. 
 
CHAPTER IX. 
 
 CONSTRUCTION. 
 
 AN intimate acquaintance with methods of construction is imperative 
 to the successful designer, as in many cases the form must be adapt- 
 ed to the method of construction to be employed in building the 
 yacht. This is particularly true of the region of the fin in sailing 
 yachts. Moreover, the designer must be thoroughly familiar with the 
 method of construction to be pursued in building, in order that he may 
 determine what the weights will be and provide sufficient displacement ac- 
 cordingly. 
 
 The hull of a yacht, particularly an extreme racing yacht, is subjected 
 to a very complicated system of stresses, among which are those produced 
 by the forces acting on the ma.st, by the leverage of keel or centerboard, 
 by the impact of waves against the hull, and by the tension of the rigging. 
 The designer must thoroughly understand the nature of these stresses in 
 order to be able to design an efficient structure to withstand them. By an 
 efficient structure is meant one where there is no useless weight, and where 
 each member is carefully proportioned to the work it has to do. As dis- 
 placement is the principal factor for resistance, the saving of weight is of 
 the highest importance where extreme speed is sovight. To save weight 
 systematically, each member entering into the structure of the yacht must 
 be carefully designed for the highest efficiency. This necessitates a thor- 
 ough knowledge of the physical properties of the various materials used 
 in the construction. 
 
 The outer skin is the principal member of the yacht's structure, as it 
 is the realization of the desired form, and is, in a sense, the boat itself. All 
 other members may be regarded as auxiliaries in assisting the skin to main- 
 tain its function. The principal member for longitudinal strength is the 
 keel, though the skin, deck, stringers, etc., contribute very materially. The 
 transverse strength is supplied mainly by the frames and deck beams. 
 These are assisted in their work by stringers, clamps, floors and knees. 
 
 There are various methods of determining suitable scantlings or sizes 
 of the various members of the yacht's structure. The most natural way is 
 to be guided by the scantlings of an existing yacht of about the desired 
 
6o 
 
 ELEMENTS OF YACHT DESIGN 
 
 size and type which has proved itself under service conditions to be strong 
 enough and structuralh' well proportioned. Racing boats often have their 
 scantlings specified by the rules of the particular class for which they are 
 built. It is theoretically possible to compute the necessary sizes for the 
 principal members, but this method is utterly impracticable for ordinary 
 work on account of the immense amount of mathematical labor involved 
 as well as the uncertainity of the exact nature of the stresses to which the 
 yacht is subjected. Something along this line may be done, however, in the 
 case of large yachts of extreme or unusual proportions. In the case of large 
 cruising yachts, the building rules of one of the classification societies furnish 
 the best guide for the determination of suitable scantlings. These building 
 
 FIG. 22. 
 
ELEMENTS OF YACHT DESIGN 6l 
 
 rules are based upon the results of practice as well as upon the deductions of 
 scientific research, and may be relied on to produce a substantial and dur- 
 able hull. It is becoming more common for yachts to be built in accord- 
 ance with the rules of one of the classification societies, as they may 
 rqadily be insured if so built, whereas, a yacht independently designed, al- 
 though possibly superior to one built under the rules, must be completely 
 surveyed before being accepted as a risk. 
 
 The classification societies whose rules are most used for yacht con- 
 struction in this country are Lloyd's Register of Shipping and the Amer- 
 ican Bureau of Shipping. Lloyd's Register publishes a set of rules es- 
 pecially for yacht construction in steel, composite and wood. These rules 
 are applicable to yachts of all sizes from about twenty feet water line up- 
 wards. The .scantlings required under these rules are somewhat in excess 
 of those usual to American practice, particularly in the smaller sizes. Un- 
 der Lloyd's rules the principal scantlings are assigned according to what 
 are known as transverse and longitudinal numbers, which are obtained as 
 shown in figures 22 and 23. 
 
 The transverse number is equal to J-^B+D-j-}2G+2N (fig. 22), and 
 regulates the sizes of frames and floors. The longitudinal number is equal 
 to the transverse number multiplied by the length obtained as shown in 
 fig- 23. 
 
 The longitudinal number regulates the dimensions of planking, keel, 
 stem, sternpost, rudder-stock, shelves and fastenings. The beams are pro- 
 portioned according to length. The number for equipment is equal to the 
 longitudinal number plus twice the product of the length and height of 
 any erections that may be fitted. 
 
 There are three general forms of yacht construction, the all-metal, the 
 all-wood and the composite. These will be dealt with briefly in order. The 
 all-metal construction is the most common for yachts of over eighty feet 
 water line. The advantages of this construction are great strength, dur- 
 ability and increased cabin accommodations. Steel is the usual material 
 used, although aluminum and bronze are sometimes employed, the former 
 on account of its light weight and the latter on account of its smooth sur- 
 face. It is doubtful whether the smoother surface of bronze compensates 
 for its greater weight as compared with steel. 
 
 The midship section of the 100-foot schooner yacht shown in fig. 24, 
 will serve to illustrate the principal features of construction in steel. The 
 sizes of members are expressed as follows : plates in pounds per square 
 foot of area or in twentieths of an inch thickness. A steel plate one inch 
 thick weighs about forty pounds per square foot or two pounds for each 
 

 o 
 
ELEMENTS OF YACHT DESIGN 
 
 63 
 
 twentieth of an inch thickness. Angle bars, I bars, etc., are rated accord- 
 ing to the dimensions of their legs, and their weight per lineal foot or 
 thickness in twentieths of an inch. 
 
 CONSTRUCTION SECTION 
 
 /OOFt-W.L. ■Sfe.cl Sch. 
 
 Seefe of faef 
 
 \ri<,niic</ Kcc/ plate cs Ib^ 
 
 FIG. 24. 
 
 The keel of the schooner shown in fig. 24 is a twenty-five pound plate 
 flanged at the sides and riveted to the garboard strake. The latter and the 
 sheer strake are heavier than the remainder of the plating, as they are sub- 
 jected to greater stresses. The system of plating shown is the ordinary 
 "clencher" or "in and out" style. Flush plating is often used above the 
 
64 ELEMENTS- OF YACHT DESIGN 
 
 water line on yachts for the sake of appearance, but it is heavier, more ex- 
 pensive, and not so strong as the "clencher" system. The frames are steel 
 angles 3"X23>2"X5-5 pounds spaced 22" Each pair of frames is' tied 
 together at the feet by floor plates. The keel plate is attached to the floor 
 plate by short angle clips. Deep frames, consisting of plate riveted to or- 
 dinary frames, are fitted at the ma.sts to take the strain of the rigging. 
 Angle irons, known as reverse frames, extend across the top of each floor 
 plate and are riveted to the backs of the frames. These tie the frames to- 
 gether very securely and stiffen the floor plate. The keelson shown con- 
 sists of a flat plate and two angles riveted together. The deck beams are 
 bulb angles and are supported in the middle by steel pillars. They are at- 
 tached to the frames bv bracket plates. The brackets are often welded on 
 the beam itself. 
 
 A deck stringer plate is worked all around the vessel between the beams 
 and the wood deck. This is connected with the sheer strake by an angle 
 bar as shown. Anothej" angle some ten inches inboard and parallel to 
 the deck line is riveted to the stringer plate, and the space between the two 
 angles forms a waterway to drain water to the scuppers. The bulwarks 
 are of 7j/4-pound plating, riveted to sheer strake and supported at frequent 
 intervals by stanchions. They should be capped by a broad teak rail. The 
 deck is of white pine plank laid parallel to the centerline and bolted to deck 
 beams. The bilge stringers consist of a pair of angles riveted back to 
 back. Steel plates are fitted at each mast beneath the wood deck, and 
 these are connected with the deck stringer plate by diagonal tie plates to 
 take the strain of masts and prevent the deck from wringing. 
 
 The balla.st is lead stowed inside the fin and covered with a layer of 
 cement. Limber holes are cut through the floor plates at the surface of the 
 cement to allow bilge water to drain to the lowest point. 
 
 The all-wood construction is almost universal in this country for yachts 
 of less than fifty feet water line. Plate II is the construction plan of the 
 thirty-footer and may be taken as typical of construction in wood. The 
 following paragraphs are descriptive of the various members and of the 
 customary materials with their relative values. 
 
 Planking — The woods commonly used for planking of yachts are yel- 
 low or hard pine, cedar, white pine, Spanish cedar and mahogany. Other 
 woods such as cypress and oak are occasionally used, but they are less suit- 
 able than those first mentioned. Yellow i)ine is a tough, durable wool and 
 is obtainable in very long lengths. It is quite a heavy wood and for that 
 reason its use is confined to cruising boats. Cedar is a light, easily-worked 
 wood and does not absorb water badly. It is obtainable in short lengths 
 
ELEMENTS OF YACHT DESIGN 65 
 
 only, which necessitates a large number of butts in a boat of any length. 
 White pine resembles cedar very much, but is less durable. It is used 
 largely for the inner skin of double-planked boats. Spanish cedar and ma- 
 hogany are quite extensively used for planking, especially on racing boats, 
 although they are considerably heavier than cedar. Their use is partly on 
 account of their handsome appearance when finished bright, but more es- 
 pecially because they stay in place and retain a smooth finish better than 
 other woods. Double planking is now quite extensively used on expen- 
 sively built boats. The advantages claimed for double planking are great- 
 er strength and less liability of leaking, less weight, and a smoother sur- 
 face. The last point is the only advantage at all marked, the others being 
 doubtful. The best method of double planking is to make the inner skin 
 nearly as thick as the outer, neither skin being calked. Watertightness is 
 secured by applying white lead very thickly between the skins. This acts 
 as a cement, binding the two skins together and squeezing out through 
 the seams renders them watertight. Calking is unnecessary and prevents 
 the surface being as smooth as it otherwise would be. In fastening double 
 planking the inner skin is first tacked in place, and then both skins are 
 through fastened to the frames. Between the frames the inner skin should 
 be fastened to the outer with brass screws. The principal types of fast- 
 enings used for planking are copper nails riveted on burrs, brass screws, 
 chisel-point galvanized-wire nails, and galvanized-cut nails. Their value 
 as fastenings stands about in the order given. 
 
 Frames — Oak is the usual material for frames, although American elm 
 and hackmatack are admirably adapted to the purpose. Frames are of 
 two kinds, steam-bent and sawed. Steam-bent frames are lighter for the 
 same strength and are used in yachts up to about thirty feet water line. 
 Where bent frames are used, the form of the boat is determined by moulds 
 made from the design enlarged to full size in the mould loft. These are erect- 
 ed in their proper places on the keel, being spaced from two to four feet 
 apart. After a sufficient number of ribbands have been fastened to the 
 moulds, the frames may be put in hot, fastening them against the ribbands 
 where they cool in shape. The bevel is obtained by putting a twist in the 
 frame. Some builders bend their frames around moulds to a little great- 
 er curvature than they will have in the boat, and after they have dried they 
 are cut to the proper bevel and put into the boat cold. This method en- 
 tails more labor than the first. In small craft with little deadrise the frames 
 may be made continuous from rail to rail. Where the frames are separate 
 on each side, as is generally the case, the strength at the centerline must be 
 
66 ELEMENTS OF YACHT DESIGN 
 
 preserved by connections known as floors. Frames larger than two inches 
 square cannot be bent readily. 
 
 Where frames are too large to bend, the sawed frame construction is 
 used. Each frame is usually double and is built up of several short 
 lengths from natural crooks sawed to shape. These short lengths "break 
 joints" on the two halves of the frame, thus preserving the strength. The 
 usual practice is to use all sawed frames in yachts over forty feet. In 
 yachts between twenty-five and forty feet water line a combination of 
 sawed and bent frames is commonly used, every other or every third frame 
 being sawed. This system of framing is used on the thirty-footer (see 
 plate II). With this method the boat is ribbanded up on the sawed frames, 
 the bent frames being put in in the usual way. 
 
 Keel — Keels are generally made from oak, though where a boat is to 
 remain in the water most of the time, maple is much better. Elm, beech and 
 birch also make good keels. Keels are of various styles, according to the 
 type of boat. Fig. 25 shows the construction of a small, shoal centerboard 
 boat. Here there is no keel proper, the longitudinal strength being furn- 
 ished by keelsons notched over the frames which are continuous from rail 
 to rail, fore and aft of the box. The port bedlog extends aft for a keelson, 
 while both bedlogs are through fastened to the forward keelson, which is 
 on the centerline. Fig. 26 shows a somewhat similar construction for a 
 small keel boat. Here all the frames are continuous and the keelsons ex- 
 tend inboard far enough to get a good fastening into the deadwood. The 
 strength amidships is furnished by the deadwood. The construction of a 
 larger keel boat is illustrated by fig. 23. All the frames box into the keel, 
 and transverse strength at the centerline is preserved by floors at frequent 
 intervals. The keel is deep enough to furnish the necessary longitudinal 
 strength without a keelson. Another style of keel is that of the thirty- 
 footer shown on plate II. * 
 
 Stringers etc. — Stringers, shelf and clamp are usually of yellow pine. 
 Oak is sometimes used and spruce where especial lightness is desired. 
 
 Deck — White pine is almost universally used for decks. Where it is 
 finished bright the seams are payed with some elastic seam composition 
 after being calked. Yachts with a house generally have the deck planks 
 sprung parallel with the planksheer. Where a yacht is flush-decked or 
 has a house running straight fore and aft, like the thirty-footer, the deck 
 planks usually run straight, as this makes a little more shipshape appear- 
 ance. Canvas-covered decks are used a great deal for small yachts, as a 
 tight deck is thus secured with a thinner planking than could be used other- 
 wise. The deck planks should be matched boards of most any light wood. 
 
^ 
 
 ttl 
 
 
 O 
 
ELEMENTS OF YACHT DESIGN 69 
 
 Deck Beams — Oak is commonly used for deck beams, though spruce 
 may be used where extreme lightness is a desideratum. Beams are sawed 
 to shape unless the crown is excessive, when they must be steamed and 
 bent. Extra heavy beams should be located at masts, at ends of house and 
 cockpit, and at skylights on other deck openings. These are termed main 
 beams. Other intermediate beams continuous across the boat are called 
 auxiliary beams, and the beams along each side of the house are known as 
 half beams. 
 
 Miscellaneous — Floors are of oak or galvanized wrought iron. Bronze 
 keel bolts should not land on iron floors, as galvanic action is liable to 
 occur. Keel bolts are generally of Tobin or other strong bronzes, which 
 have an elastic limit of about 30000 pounds. The lower end is commonly 
 enlarged by forging to hold the lead, but it is better practice to thread and 
 nut both ends, as forging reduces the strength of bronze. Lloyd's Reg- 
 ister gives very complete rules for the determination of sizes of keel bolts 
 based on width, depth and sectional area of the lead and on the spacing of 
 the bolts. Customary working loads for various diameters of bolt are 
 given roughly in the following table. 
 
 1770 
 
 Knees and stem are of natural crook oak or hackmatack. Tie rods 
 and deck straps as shown on plate II, are very effective. The tie rods at 
 mast communicate a portion of the thrust of the mast to the main beams 
 thus relieving the keel. The deck straps are let into the beams and are 
 well fastened to deck plank and beams. - They resist the wringing tendency 
 of the mast. 
 
 The foregoing covers very briefly the principal points of construction in 
 wood. Table VIII gives a representative schedule of scantlings for cruis- 
 ing boats of various water-line lengths. The weights of various woods are 
 given in table II. \ 
 
 The composite constntction is a combination of the all-wood and all- 
 metal construction and is used largelv on yachts of from fifty to ninety feet 
 water line. With this construction the frames, floors, reverse frames, keel- 
 son, stringers and deck beams are of steel, while the keel, planking and 
 deck are of wood. Sometimes a part of the frames and deck beams are 
 of wood also. Fig. 27 is the midship section of a seventy-five-foot 
 schooner and is typical of the composite construction. A flanged steel 
 
 DIAMETER 
 
 y^" 
 
 %" 
 
 ■K" 
 
 li" 
 
 r" 
 
 i%" 
 
 i?4" 
 
 lYs" 
 
 d per bolt, lbs. 
 
 200 
 
 300 
 
 440 
 
 600 
 
 790 
 
 990 
 
 1230 
 
 1480 
 
70 
 
 ELEMENTS OF YACHT DESIGN 
 
 plate is bolted on top of the wood keel and to this the frames are riveted. 
 Floor plates, clips and reverse frames complete the strength at the center- 
 line. 
 
 The wood keel is of maple nine inches thick. The lead is cast in one 
 piece and the bolts pass through the keel and set up on the inside of keel 
 plate. Other features are similar to the all-metal construction. 
 
 i.^i^e.f' W.Pine. 
 
 Locust ^fanchtons ' 
 
 ncirerse frames stop /lere 
 
 Angle 3'K3"t f.9Lk3 
 
 ffe versa fromc-t t '"£ 'x J J lit. 
 
 ^Flanged Kae/ P/aTe M Lhs . 
 ■.iviaph Keel mou/ded S ' 
 
 ij-' Bronze Boitt 
 
 covsr/iucr/o/v 9i:ct/on 
 7S' ■SchooriB'r 
 
 \Scafe of Feet 
 
 FIG. 27. 
 
APPENDIX 
 
 DATA ON THIRTY-FOOT W. I.. CRUISER. 
 
 Length O. A 4S' 9" 
 
 L.W.L 30' o" 
 
 Beam Extreme 12" o' 
 
 " L. W. L II' 7" 
 
 Draught Extreme S' 2^' 
 
 " to Centerline 2' 11" 
 
 Overhang For'd 7' o" 
 
 Aft 8' 9" 
 
 Freeboard For'd 3' 7" 
 
 Aft 2' 8" 
 
 Least 2' s" 
 
 Area of Midship Section 24.2 Sq. Ft 
 
 " " Lateral Plane (Board down) 112.6 " 
 
 " "L.W.L " 245.2" 
 
 " " Wetted Surface (Board down) 402.6 " 
 
 " " Sails total 1285 " 
 
 " " Rudder 12.4 " 
 
 Displacement Above Centerline 20800 Lbs. 
 
 Below " 3407 " 
 
 " Total .- 24207 " 
 
 C. B. from For'd End L. W. L 16.42' 54-8% L. W. L. 
 
 C. E. " ■ " " " 16.15' 53-8" " 
 
 C. G. L. " ■' " '■ 16.30' 54.4 " 
 
 C.L. P." " " " 17.04' 56.8" 
 
 Prismatic Coefficient (using total Midship Section) 522 
 
 L.W.L. " ...." 705 
 
 Lbs. per Inch Immersion at L. W. L 1307 
 
 Ratio Ballast to Displacement 405 
 
 " Sail Area to Area Midship Section 53.2 
 
 " Lateral Plane to Area Midship Section. 4.65 
 
 " Rudder to Lateral Plane no 
 
 Weight of Hull ', . . 10800 Lbs. 
 
 " "Rig 1200 " 
 
 " " Crew 600 " 
 
 " " Ballast 9800 " 
 
 " " Equipment 1800 " 
 
72 ELEMENTS OF YACHT DESIGN 
 
 TABLE I 
 NATURAL TANGENTS AND CORRESPONDING SECANTS. 
 
 TANGENT 
 
 SECANT 
 
 TANGENT 
 
 SECANT 
 
 TANGENT 
 
 SECANT 
 
 TANGENT 
 
 SECAN 
 
 .010 
 
 1. 000 
 
 .160 
 
 I.OI3 
 
 .310 
 
 1.047 
 
 .460 
 
 I.IOI 
 
 .020 
 
 1. 000 
 
 .170 
 
 I.OI4 
 
 .320 
 
 1.050 
 
 .470 
 
 1. 106 
 
 .030 
 
 1. 000 
 
 .180 
 
 I.O16 
 
 ■330 
 
 1-0S3 
 
 .480 
 
 1. 109 
 
 .040 
 
 I.OOI 
 
 .190 
 
 I.O18 
 
 ■340 
 
 1.056 
 
 .490 
 
 1. 114 
 
 .050 
 
 I.OOI 
 
 .200 
 
 1.020 
 
 ■350 
 
 1.060 
 
 .500 
 
 1. 118 
 
 .060 
 
 1.002 
 
 .210 
 
 1.022 
 
 .360 
 
 1.063 
 
 .510 
 
 1. 123 
 
 .070 
 
 1.002 
 
 .220 
 
 I 024 
 
 ■370 
 
 1.066 
 
 .520 
 
 1. 127 
 
 .080 
 
 1.003 
 
 .230 
 
 1.026 
 
 .380 
 
 1.070 
 
 ■530 
 
 1.132 
 
 .090 
 
 1.004 
 
 .2_10 
 
 1.028 
 
 •390 
 
 1.073 
 
 •540 
 
 M37 
 
 .100 
 
 1. 00s 
 
 .250 
 
 1. 03 1 
 
 .400 
 
 1.077 
 
 •550 
 
 1. 141 
 
 .110 
 
 1.006 
 
 .260 
 
 1033 
 
 .410 
 
 1.081 
 
 .560 
 
 1. 146 
 
 .120 
 
 1.007 
 
 .270 
 
 1.0.36 
 
 .420 
 
 1.085 
 
 •570 
 
 1.151 
 
 .130 
 
 1.008 
 
 .280 
 
 1.038 
 
 •430 
 
 T.089 
 
 .580 
 
 1.156 
 
 .140 
 
 I.OIO 
 
 .290 
 
 1. 04 1 
 
 .440 
 
 1.093 
 
 •590 
 
 1. 161 
 
 .ISO 
 
 I.OII 
 
 .300 
 
 1.044 
 
 •450 
 
 1.097 
 
 .600 
 
 1.166 
 
ELEMENTS OF YACHT DESIGN 73 
 
 TABLE II 
 WEIGHT OF A CUBIC FOOT OF SUBSTANCES. 
 
 AVERAGE 
 NAME OF SUBSTANCE WEIGHT POUNDS 
 
 Aluminum 162 
 
 Anthracite 54 
 
 Ash 40 
 
 Birch 40 
 
 Bronze 525 
 
 Butternut 35 
 
 Cedar, white or red dry 30, soaked 40 
 
 Spanish 35 
 
 Cement 55 
 
 Copper rolled 548 
 
 Elm 35 
 
 Gasoline 42 
 
 Hackmatack 35 
 
 Iron, cast 450 
 
 " wrought 4.80 
 
 Lead, cast 710 
 
 Mahogany 53 
 
 Maple 48 
 
 Oak dry 50, soaked 56 
 
 Pine, Oregon 35 
 
 " white 28 
 
 " yellow dry 40, soaked 45 
 
 Spruce 31 
 
 Steel Plates and Shapes 490 
 
 Teak SO 
 
 Water, fresh 62.4 
 
 " salt 64.0 
 
74 
 
 ELEMENTS OF YACHT DESIGN 
 
 TABLE III 
 
 WEIGHTS OF SPRUCE SPARS PER FOOT OF LENGTH 
 {For Oregon Pine Multiply by 1. 13) 
 
 DIAM. 
 
 WT. 
 
 DIAM. 
 
 WT. 
 
 DIAM. 
 
 WT. 
 
 DIAM. 
 
 WT. 
 
 DIAM. 
 
 WT. 
 
 3" 
 
 1.62 
 
 5^ 
 
 4.96 
 
 7/2 
 
 10.10 
 
 954 
 
 17.I 
 
 14 
 
 35-3 
 
 s'A 
 
 I. go 
 
 5/2 
 
 5-43 
 
 754 
 
 10.8 
 
 10 
 
 18.0 
 
 H'A 
 
 37.8 
 
 3/2 
 
 2.20 
 
 SJ4 
 
 S-9S 
 
 8 
 
 "■5 
 
 10^ 
 
 19.8 
 
 IS 
 
 40.S 
 
 3V4 
 
 2.53 
 
 6 
 
 6-S4 
 
 8H 
 
 12.2 
 
 II 
 
 21.8 
 
 is;/2 
 
 43-2 
 
 4 
 
 2.88 
 
 6J4 
 
 7.02 
 
 8^ 
 
 13.0 
 
 11^ 
 
 23.8 
 
 16 
 
 46.0 
 
 4% 
 
 3.25 
 
 6y2 
 
 7.60 
 
 8M 
 
 13.8 
 
 12 
 
 25-9 
 
 16/2 
 
 48.8 
 
 4% 
 
 3.65 
 
 654 
 
 8.20 
 
 9 
 
 14.6 
 
 12^ 
 
 28.1 
 
 17 
 
 S2.0 
 
 4^ 
 
 407 
 
 7 
 
 8.82 
 
 9>4 
 
 15-4 
 
 13 
 
 30.2 
 
 17^ 
 
 55-0 
 
 5 
 
 4-SO 
 
 7V4 
 
 9.46 
 
 9^ 
 
 16.2 
 
 u'A 
 
 32.7 
 
 18 
 
 58.3 
 
 TABLE IV. 
 
 WEIGHTS OF SAILS IN POUNDS PER mo SQ. FT. OF AREA. 
 Cloths 16" JVide Cloths 20" IVide 
 
 NO. 
 
 WT. 
 
 oz. 
 
 WT. 
 
 000 
 
 262 
 
 12 
 
 14. 1 
 
 00 
 
 24,9 
 
 10 
 
 12.6 
 
 
 
 23-7 
 
 8 
 
 II.O 
 
 I 
 
 22.5 
 
 
 
 2 
 
 21.2 
 
 Cloths 28y2" 
 
 Wide 
 
 3 
 
 20.0 
 
 7 
 
 6.9 
 
 4 
 
 18.8 
 
 6 
 
 6.0 
 
 5 
 
 17-5 
 
 5 
 
 5-0 
 
 6 
 
 16.2 
 
 4 
 
 4.0 
 
 7 
 
 150 
 
 
 
 8 
 
 13.8 
 
 
 
 9 
 
 12.6 
 
 
 
 ID 
 
 114 
 
 
 
ELEMENTS OF YACHT DESIGN 75 
 
 TABLE V 
 
 FASTENINGS 
 Number of Nails in one Pound 
 copper nails galv. boat nails galv. wire nails 
 
 H" 
 
 710 
 
 500 
 
 800 
 
 H" 
 
 600 
 
 450 
 
 700 
 
 i" 
 
 495 
 
 400 
 
 550 
 
 iH" 
 
 320 
 
 300 
 
 400 
 
 i^" 
 
 213 
 
 200 
 
 260 
 
 iH" 
 
 IS5 
 
 135 
 
 170 
 
 2" 
 
 113 
 
 PS 
 
 no 
 
 Wa 
 
 85 
 
 68 
 
 80 
 
 2}4" 
 
 65 
 
 SO 
 
 70 
 
 3" 
 
 44 
 
 33 
 
 57 
 
 3/3" 
 
 30 
 
 24 
 
 43 
 
 4" 
 
 20 
 
 20 
 
 30 
 
 
 
 TABLE VI 
 
 
 
 , 
 
 AREA 
 
 CURVE FACTORS 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 P.C. 
 
 •307 
 
 .519 
 
 ■530 
 
 •SS7 
 
 C. B 
 
 52.8% 
 
 53-4% 
 
 53-9% 
 
 35-3% 
 
 I 
 
 .080 
 
 .080 
 
 .080 
 
 .080 
 
 2 
 
 .285 
 
 .285 
 
 .285 
 
 .285 
 
 3 
 
 .560 
 
 .560 
 
 .560 
 
 .560 
 
 4 
 
 .808 
 
 .808 
 
 .808 
 
 .808 
 
 S 
 
 •972 
 
 .972 
 
 .972 
 
 .972 
 
 6 
 
 .978 
 
 .Q83 
 
 .9S3 
 
 .988 
 
 7 
 
 .800 
 
 .823 
 
 .850 
 
 .900 
 
 8 
 
 ■447 
 
 •507 
 
 •557 
 
 .677 
 
 9 
 
 .138 
 
 .167 
 
 .200 
 
 .296 
 
 Mid section 56% of L. W. L. abaft forward point of immersion. 
 
76 ELEMENTS OF YACHT DESIGN 
 
 TABLE VII 
 RATIOS OF RUDDER TO LATERAL PLANE 
 
 L. W. L. 
 
 20' 14 
 
 25 12 
 
 30 II 
 
 35 10 
 
 40 095 
 
 45 085 
 
 50 080 
 
 60 '. 070 
 
 70 060 
 
 80 056 
 
 90 052 
 
 100 050 
 
ELEMENTS OF YACHT DESIGN "]"] 
 
 
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 1=1 iz; 5 E 
 
 . _ . . CO VO t^ -^ 
 
 > p 
 
 w 
 
 CO 
 
 ^ to 
 
 ^ ^ 
 
M 
 (-1 
 
 C-i 
 
PLATE III. 
 
PLATE IV. 
 

 
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INDEX 
 
 PAGE 
 
 Analysis of righting couple 33 
 
 Areas of plain figures 9 
 
 Areas of sails 56 
 
 Ballast, amount of 48 
 
 Calculation of weights 16 
 
 Center of buoyancy, fore and aft 
 
 position ig 
 
 vertical position. 19 
 
 Center of eflfort 56 
 
 Center of gravity, plain figures 9 
 
 sails 57 
 
 of the yacht 34 
 
 Center of lateral plane 24 
 
 Change of trim due to shifted weight. 46 
 
 Co-efficient for wind pressure 55 
 
 Composite construction 69 
 
 Correction for change in position of 
 
 C. of G 42 
 
 Cross curves of stability 44 
 
 Curve of areas of transverse sections. . 18 
 
 Curve of righting arms 38 
 
 Determination of proportions 29 
 
 Displacement, calculation of 19 
 
 determination of amount. 19 
 
 Dynamical stability 45 
 
 Heel, angle of, due to shifted weight. .47 
 Inclining experiment for finding 
 
 C. of G 35 
 
 Lateral plane, area of 25 
 
 shape of 26 
 
 Lead of centre of effort 57 
 
 Lines, fairing up process 32 
 
 Metacentric height, definition 33 
 
 determination of.. 37 
 
 suitable values. . . .38 
 
 Midship section, area of 20 
 
 PAGE 
 Moment of inertia of water line, 
 
 long, axis 14 
 
 of water line, 
 
 trans, axis 15 
 
 Prismatic co-efficient 20 
 
 Resistance, nature oi 2 
 
 Rigs 58 
 
 Rudders, size of 26 
 
 Sail area, determination of 54 
 
 Sails, shape of 58 
 
 Scantling, determination of 60 
 
 Simpson's rule 5 
 
 Stability, Blom's method 39 
 
 division of 46 
 
 heeled longitudinal sections. 39 
 
 integrator method 41 
 
 metacentric method 37 
 
 Steel construction 61 
 
 Table of area curve factors 75 
 
 data on thirty-footer 71 
 
 ratios rudder to lateral plane . 76 
 scantlings for wooden con- 
 struction 77 
 
 sizes of keel bolts 69 
 
 weights of fastenings 75 
 
 weights of materials 73 
 
 weights of sails 74 
 
 weights of spars 74 
 
 Trapezoidal rule 6 
 
 Trochoid, construction of 22 
 
 Versed sines, construction of curve. ..21 
 
 Wave form theory 21 
 
 Wetted surface, area by bilge diago- 
 nal method 14 
 
 area by Taylor's 
 
 method 12 
 
 Wooden construction 64 
 
7i \/ D D E H 
 
 What -To 
 
 SERIES 
 
 The CaLbin Plan Book 
 
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 sail craft from twenty to one hundred feet over all 
 
 TKe Schooner Book 
 
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 TKe Racer Book 
 
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 TKe Cact Book 
 
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 cats. Reprinted from The Rudder 
 
 Express paid ^f^ ^ flfl Same size and 
 
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 Easy boat to build ; everything straight. Just the craft for a boy to begin with. Can be built very cheaply. Either 
 
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R.\idder Oiy Series 
 
 On Yachts and 
 Yacht Handling 
 
 By Thomas Fleming Day 
 
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 On Seamanship On Sails as an Auxiliary 
 
 On Boats in General On Reefing 
 
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 On Seagoing Boats On Rigging 
 
 On Stranding 
 
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THE (*^ 
 
 RUDDER 
 
 the Magazine for Yachtsmeti 
 
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