Systematic model series
in the design of the
sailing yacht hull
by Pierre DeSaix
Ship & Yacht Division Davidson Lalroratory
42
Introduction
The design o f the saiUng yacht h u l l is p r i n c i -p a l l y influenced by r a t i n g rules. For over a century the designer's e f f o r t in developing a new yacht h u l l has been directed towards creating a design w h i c h w i l l sail fast b u t also rate well under aparticular rule. U n f o r t u n a t e l y , those who write rules have l i t t l e or no k n o w -ledge of the exact effect on speed the parameters they choose to rate actuaUy have. A clever designer is one w h o w i l l find the proverbial loophole a n d can design a h u l l w h i c h rates l o w a n d sails fast as w e l l .
T h e t o w i n g tank f o r many years has proved an invaluable t o o l to those f o r t u n a t e designers having the use o f one a n d the background o f several " t a n k tested" designs. T h r o u g h the use o f model tests, a designer can evaluate the effect o f h u l l changes on sailing performance o n a proposed design w i t h i n the f r a m e w o r k o f a n existing rule. Figure 1 illustrates the effect o f rules o n the design o f two similarly sized c r a f t , each recently developed t h r o u g h the use o f a model testing t a n k . The slack bilges a n d n a r r o w ends o f t h e "One T o n n e r " are i n sharp contrast to the c r a f t designed f o r the Cruising C l u b o f A m e r i c a Rule, yet each h u l l is considered successful i n its class. I t is n o t obvious that the i n d i v i d u a l design features o f these two c r a f t contribute to h i g h speed through the water or l o w r a t i n g . The particular rule itself may l i m i t development. F o r instance, the 5.5-meter class f o r many years c o u l d n o t have a separate spade rudder.
The improvement i n performance i n the sailing yacht as a result o f i n d i v i d u a l development m o d e l tests has been p a i n f u l l y slow. D u e to cost a n d available time, a designer must dh-ect his e f f o r t towards producing the best design f o r his client. He cannot explore systematically the effect o f any one parameter o n yacht per-formance. I t took nearly 10 years f o r the keel p r o f i l e o f the 5.5-meter yacht to evolve (see figure 2). The performance o f the 12-meter class has improved since V I M was first de-veloped i n a t o w i n g tank i n 1937. T h e changes i n the m a j o r parameters affecting speed, sail area, waterline length a n d displacement are s h o w n i n T a b l e 1.
T o s i m p l i f y the task o f starting a new design, certain limits o f general f o r m characteristics have been set d o w n by design offices. H e n r y a n d M i l l e r ' t h o r o u g h l y define the f o r m charac-teristics f o r a wide variety o f c r a f t ranging f r o m small-day sailers to heavy cruisers. T h e i r paper represents the state-of-the-art o f yacht design. Rhodes^ states that both the Universal and I n t e r n a t i o n a l yacht racing measurement rules require the same m i n i m u m displacement f o r a given length, that is, ( 0 . 2 L W L + 0 . 5 f and admits using this as a yardstick i n assaying the relative displacement o f a proposed yacht. Rhodes f u r t h e r gives a g r a p h s h o w i n g o p t i m u m values o f prismatic coefficient against speed and length. U n f o r t u n a t e l y , neither Reference 1 or 2, n o r any other literature o n yacht design provides the designer w i t h the effect o n speed changing any o f t h e s e parameters. The designer must rely o n l i m i t e d m o d e l tests o r attempt t o i n t u i t i v e l y m o d i f y an already successful design. This paper is directed towards the serious
yacht designer and also perhaps to those i n -volved w i t h the creation o f rating rules. The author wishes to demonstrate the value o f systematic model series in evaluating the effect of certain f o r m parameters o n yacht perfor-mance regardless o f the "rules o f the day." The two series presented here by no means guarantee a " b r e a k t h r o u g h " i n yacht design. While these data w i l l no d o u b t be extremely useful to the designer, it is however only a small beginning. The results have answered some serious questions. I t is hoped the w o r k w i l l encourage others i n the same position as the author to contribute systematic data f o r the use o f the i n d i v i d u a l yacht designer. Model tests and results o f the sailing yacht General
The techniques o f testing yacht models have long been established. It is true that the meth-ods o f actual force measurements, turbulence stimulation, use o f sail coefficients vary with particular t o w i n g tanks. However, the basic principles are essentially those o f Davidson.^ Crago^ summarizes the methods o f yacht per-formance predictions f r o m model tests. Crewe^ illustrates the effect o f sail performance on w i n d w a r d behavior a n d discusses the methods of deriving w i n d w a r d performance f r o m tank tests essential f o r a proper evaluation o f the series results presented here. I t is not the purpose o f this paper to detail the methods o f testing and prediction o f performance; the references listed above should provide the reader w i t h a good background.
Briefly, the yacht test yields the f o l l o w i n g : 1. upright resistance
2. heeled resistance w i t h o u t sideforce 3. heeled resistance w i t h sideforce 4. Sideforce w i t h leeway
5. righting m o m e n t 6. yawing m o m e n t
Results are presented as curves o f upright and heeled resistance (at zero sideforce). The heeled resistance w i t h yaw and sideforce, and righting moment, are most conveniently presented i n terms o f actual sailing performance: speed-made-good to w i n d w a r d and/or speed t h r o u g h the water at various headings to the w i n d - a l l against true w i n d speed.
Beam-draft series
Tests o f systematically varied models have been
successful i n the past. The T a y l o r Series has even served as a guide f o r the choice o f pris-matic coefficient f o r the sailing yacht! I t was logical to embark on a systematic series f o r the sailing yacht.
Conceived i n 1947, the beam-draft series was based o n O l i n Stephen's N . Y . 3 2 as a parent f o r m . ( M o d e l A i n figure 3) T w o variations were made; M o d e l B is simply M o d e l A w i t h all half-breadths increased by a factor o f 4/3. For M o d e l C the heights o f the buttocks were increased by 4/3. This variation results i n a 4/3 increase i n displacement as w e l l .
The author added Models D and E which have geometrically similar sections as B and C but reduced to size to give the same displacement as the parent. U n f o r t u n a t e l y , the depth o f the keel varied i n p r o p o r t i o n to the d r a f t . I n the final analysis, i t w o u l d have been better to maintain the same keel profile while varying the beam-draft series. Extensive tests were run o n the parent. However, i t wasn't u n t i l Models D and E were added to the series that all testing was completed and finally reported f o r the first time i n this paper. Complete data are presented i n Reference 6.
Prismatic series
A l l previous model series o f displacement craft demonstrated the importance o f prismatic coefiicient on h u l l resistance. A review o f 64 fixed keel cruising yachts developed in the tanks at Davidson L a b o r a t o r y revealed that 59 models h a d a prismatic coefiicient i n the range 0.50-0.58; t h i r t y - f o u r models had a
figure I
Effect of rating rule on design of two similar craft figure 2
Keel profile variations, 5.5 meter class
prismatic coefficient i n the range 0.52-0.54: One model h a d a = 0.40 and one a pris-matic, Cp = 0.70. I t was decided to test aseries of three models o f equal displacement and the same lateral plane. The parent was a N . Y . 32 ( M o d e l A ) m o d i f i e d to give a ligher displace-ment a n d a smaller, more modern lateral plane. The parent ( M o d e l 1, figure 4) had a = 0.53, M o d e l 2 a Cp - 0.43, and M o d e l 3 a C^ = 0.61. The area curves o f the series appear on figure 5. The sections f o r the low and high prismatics were reduced or enlarged f r o m the parent t o give the required section area. The lines were then faired, keeping the lateral plane and dis-placement equal to the parent. This resulted i n models having extreme hollows i n the water-lines or extreme fullness. The models were modified at a later date by straightening the waterlines as m u c h as possible forcing more shape into the buttock lines, thereby keeping the curve o f areas the same.
Model test data
D a t a f o r the beam-draft series were obtained on the original Davidson Yacht Balance. The data were restricted to upright resistance and heeled testing over the narrow range o f speeds and offerees to predict w i n d w a r d performance. The results are presented as curves o f upright resistance a n d predicted speed-made-good to w i n d w a r d .
Tabic 1
Development of 12-meter class
Constel-Columbia lation Wcatherly American
Gleam Vim Grctel Eagle Intrepid Intrepid Early
I930's 1938 1958-1962 1964 1967 1970
Waterline Length, ft 45.0 45,5 46.3 47.0 47.5 48.6
Displacement, Ib 60,000 60,400 63,400 64,000 66,000 70,000
Sail Area, ft^ 1890 1880 1820 1800 1750 1725
Heeling Force for 30-de8 Heel Ang!e,lb 3100 3300 3600 3750 3832 4700
Speed-made-good, knots
Light Wind 5.0 5.0 5.0 4.9 5.0
5.0
Moderate Wind 6.3 6.4 6.5 6.6 6.7 6.8
MODEL V l / H * 1.01 ft^LOa.*!' J4T fl • 0 )0 I 0 /
/
W ^
^ - ^ ^ " " ^ UOOEL NODCL'C-i / H • I.CT • - — •3
yy
^ — - " " ' ^ H O D I L ' D " • / H • «_OT M O D E L Z O H I G t N A L MODEL Z A L T E R E D I \ L MODEL 5 A L T E R E D Cp =0 S l J LThe new yacht dynamometer n o w i n use at Davidson L a b o r a t o r y permits testing i n tlie heeled condition over a wider range o f speeds and yaw angles. D a t a f o r the prismatic series are presented as curves o f u p r i g h t resistance and heeled resistance at zero sideforce. Curves o f heeled resistance a n d sideforce squared, yawing moment, sideforce a n d yaw angle are also presented. D a t a over a wider range o f conditions permit prediction o f n o t o n l y w i n d w a r d performance but h u l l speed f o r all points o f sailing over a range o f true w i n d speeds.
Emphasis is placed o n resistance. The effects o f stability andsail area can readily be calculated; however, t o really improve a yacht's perfor-mance, one must be able to reduce resistance. The effects on resistance o f the f o r m parameters investigated here w i l l be discussed i n detail. A l l data were expanded to a full-size waterline length 3 2 . 0 - f t . R i g heights and vertical center of gravity were constant f o r a l l models. G i m -crack sail coefficients were used to predict w i n d w a r d performance. O f f w i n d performance was predicted using data available f r o m Spens.^ Particulars f o r models o f b o t h series are f o u n d i n T a b l e 2,
Results
B e a m - D r a f t Series
U p r i g h t resistance data showing the effect o f beam-draft ratio at constant displacement appears on figure 6. The wider h u l l has lower resistance above 6 knots. The n a r r o w beam is burdened w i t h h i g h resistance over the entire speed range. The effect o f displacement on upright resistance appears on figures 7 and 8. W h i l e having generally lower resistance, the wider model suffers a higher percentage i n -crease i n resistance due to added displacement. The effect o f beam-draft r a t i o o n the rate o f increase o f heeled resistance w i t h (sideforce)^ (figure 9) varies w i t h keel depth. The widest model ( D ) has a disproportionately higher rate o f added drag, however. A d d e d displacement appears to make a m i n o r difference i n the rate o f increase o f induced drag. There is some advantage to increased displacement at 2 0 ° and 30" heel. (Figure 10).
The w i n d w a r d performance (figure 11) favors M o d e l D , BIH = 2.07, w i t h a distinct advan-tage above 11 knots w i n d speed. The narrow h u l l (B/H = 1.17) is the poorest over the entire w i n d speed range. A d d e d displacement
figure 3 Beam-draft series figure 4 Prismatic series figure 5
Section area curves figure 6 Beam-draft series: beam-draft ratio figure 7 Beam-draft series: displacement figure 8 Beam-draft series: displacement figure 9 Beam-draft series: displacement figure 10 Beam-draft seri displacement
upright resistance, effect of
upright resistance, effect of
upright resistance, effect of
reststance increase, constant
Tabic 3
Percentage changes in best V,„„ at constant V / - for changes in sail area and stability Percentage change in best V , , , ,
V T
knots
Vrag knots
- 1 0 % S A +10%SA —10%Stab +10%Stab
A 7.5 3.87 , —3.36 + 2.07 —1.03 — .26 13.0 5.10 —1.37 + .59 —1.18 + 1.18 19.5 5.51 + .36 — .91 —2.36 + 1.64 B 7.5 4.18 — .96 + 1.43 — .72 + 1.68 13.0 5.11 — .78 + .59 — .98 + .98 19.5 5.60 — .36 .00 — .71 + .36 26.0 5.70 + .70 —1.05 —1.23 + .88 C 7.5 3.73 —2.95 +2.95 + .80 + 1.07 13.0 4.90 — .82 + .82 —1.43 + 1.22 19.5 5.34 — .37 + .37 —2.62 + .94 D 7.5 3.92 —2.04 + 1.79 —1.02 + .25 13.0 5.05 —. 99 + 1.39 — .20 + .20 19.5 5.66 — .35 — .35 —1.06 + .18 26.0 5.62 + 1.60 — 1.78 —2.85 + 1.60 E 7.5 3.68 —3.26 + 1.90 —1.63 .00 13.0 4.70 — .64 + .64 —2.13 + 1.06 19.5 5.04 + .40 — .20 —4.77 +4.37 Table 2 Particulars — fiill size
Model A B C D E 1 2 3
Length, L , ft 32.0 32.0 32.0 32.0 32.0 32.0 32.0 32.0 Displacement, J , Ib 25,450 33,930 33,930 25,450 25,450 21,650 21,650 21,650 Wetted surface, WS, ft^ 344 438 445 379 385 295 281 299 Vertical center of Gravity
V.C.G., f t below L 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20
Sail Area, SA, ft^ 865 1048 1048 865 865 780 780 780
C E H , ft 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.50 CEAO, f t 11.80 11.80 11.80 11.80 11.80 11.80 11.80 11.80 Beam-draft ratio, B, H 1.56 2.07 1.17 2.07 1.17 1.49 1.38 1.62 Displacement-length ratio.
347 462 462 347 347 297 297 297
Sail Area-volume ratio.
SA"2/(Vol)i'3 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 Prismatic coefficient, Cp .53 .53 .53 .53 .53 .53 .43 .61 Scale Ratios Length 10 Area 100 Volume 1000 Displacement 1027 Speed 3.16
14
16
improves tlie w i n d w a r d performance o f the narrow boat while i t has no effect o n p e r f o r m -ance o f the wider models o f the series, ( f i g u r e l 2) One o f the m a j o r effects o f b e a m - d r a f t and displacement changes is on the f o r m stability o f t h e series. The w i n d r e q u i r e d to heel 30° is 15 knots f o r M o d e l E ( n a r r o w and l i g h t ) while i t is over 28 knots f o r M o d e l C (wide a n d heavy). F o r the results presented, the r i g height and vertical center o f gravity were held con-stant. T h e sail area was p r o p o r t i o n e d t o the rate o f sail area t o volume, S A ' / ^ V o U / ^ = 4. This appears to be the value used by most designers submitting lines f o r testing at Davidson Laboratory. These are a d m i t t e d l y s i m p l i f y i n g assumptions. T h e n a r r o w , deep yacht w o u l d surely have a lower V . C . G . w h i l e increased displacement generally allows a higher ballast r a t i o a n d lower L . C . G . T h e stiffer vessel c o u l d theoretically c a r r y more sail. As a first a p p r o x i m a t i o n , the above as-sumptions appear reasonable.
Table 3 has been included to provide the effects on w i n d w a r d performance o f changes i n sail area a n d stability.
Results Prismatic Scries
Figures 13, 14, a n d 15 present the resistance at zero sideforce f o r 0, 10, 20, 30° heel. F o r prismatic coefficients 0.43 a n d 0.53, resistance generally increases w i t h heel angle. H i g h prismatic coefficient = 0.61 shows a definite reduction i n resistance w i t h heel angle i n the speed range 6 to 8 knots where most w i n d w a r d sailing is done.
Heeled data are presented f o r M o d e l 1 (Cp = 0.53). The resistance is seen to vary linearily w i t h sideforce squared (figure 16). T h e rate o f change o f resistance w i t h sideforce squared is a measure o f the effectiveness o f the h u l l a n d keel as a l i f t i n g surface. T h e higher the rate, the less effective the h u l l is as a l i f t i n g surface. The author is reluctant to use the t e r m "aspect r a t i o " since a l l yacht hulls are o f very l o w geometric aspect ratio.
The rate o f increase is seen i n figure 17 n o t t o vary m u c h w i t h speed u n t i l above 7 k n o t s , when the resistance increases at a m u c h more r a p i d rate. There is also some loss i n h u l l efiiciency w i t h heel angle.
Since the keels were the same f o r each m o d e l i n the prismatic series one w o u l d expect little difference in the rate o f resistance increase. There is some small advantage to h i g h pris-matic, Cp = 0.61. U n f o r t u n a t e l y , the speed range o f the beam-draft series was n o t as high as the prismatic, a n d a c o m p a r i s o n o f the resistance rate increases between series cannot be readily made. The slope o f the resistance figure 11
Beam-draft series: constant displacen figure 12
Beam-draft series: effect of displacen figure 13
Prismatic series: resistance at zero : figure 14
Prismatic series: resistance at zero ! figure IS
Prismatic scries: resistance at zero ; figure 16
Prismatic series: model I Cp = 0.53, scaled to full-size, resistance versus s
line f o r Cp ^ .53 (Prismatic Series) is less tfian that f o r Model A parent M o d e l (beam-draft series) however indicating some improvement in h u l l efficiency w i t h the newer keel profile. The sideforce coefficient-yaw angle relationship appears to be independent o f speed, the curves can be collapsed f o r heel angle as well (figure
18).
Y a w moment and sideforce coefficients (figure 19) show a less definite trend w i t h speed and heel angle. (Sideforce in this case o n l y is measured at right angle to the hull centerline.) Prismatic coefficient has a pronounced effect on the upright resistance o f the series. T h e high prismatic, Cp = 0.61, has the lowest resistance above a speed o f 7.4 knots. There appears to be no advantage to the lowest prismatic, Cp = 0.43 (figure 20).
A g a i n , as in the beam-draft series, the heeled data are best presented as actual sailing per-formance. Speed-made-good to w i n d w a r d f o r the series are presented on figure 2 1 . T h e per-formance o f M o d e l 1, Cp = 0.53, is appreci-ably better to w i n d w a r d over a wide range o f w i n d speeds. The l o w prismatic is better to w i n d w a r d below a w i n d speed o f 8 knots. I n high winds above 24 knots, high prismatic, Cp = 0.61 may be better.
The sailing performance o f the three models for all points o f sailing is given on figure 22. The reaching results using sail coefficients f r o m Spens" have been faired i n t o the w i n d w a r d results calculated using Giracrack to give a complete polar p l o t . L o w prismatic shows a small advantage i n light winds, o f f the w i n d while i n strong w i n d there is a distinct advan-tage to the high prismatic f o r m o f f the w i n d . Conclusions
The t w o series presented i n this paper are not intended by any means to provide all necessary i n f o r m a t i o n f o r a designer in creating a w i n n i n g boat to a given rule. The testing o f a systematic model series as reported here does illustrate a relatively r a p i d means o f obtaining the effect o f a given parameter on sailing performance. B o t h series should be extended to l i g h t dis-placement {A/(.0[Lf = 250). The keel p r o f i l e should have been the same f o r a l l models. The keel p r o f i l e could also have been reduced in area and a more eflficient keel section used f o r the beam-draft series.
I n spite o f certain limitations the beam-draft series provided valuable data o n the f o l l o w i n g :
1. effect o f displacement f o r two beam-draft ratios
2. effect o f beam-draft ratio on f o r m stability 3. effect o f beam-draft on upright resistance 4. effect o f beam-draft on w i n d w a r d
perfor-mance
I t appears advantageous to keep the w i d e r yacht light, and the narrow one heavy. The beam-draft ratio o f 2.07 a t a AI(.Q\Lf = figure 17
Prismatic series: resistance increase vcrsus speed figure 18
Prismatic series: model I Cp = 0.53, (est data scaled to full-size, side force versus yaw angle figure 19
Prismatic series: model I Cp = 0.53, test data scaled fo full-size, side force versus yaw moment figure 20
Prismatic series: upright resistance
= 3 4 7 seems to have the best a l l - a r o u n d per-formance. I f the lateral plane were the same f o r M o d e l D (B/W = 2.07) as the parent M o d e l A , the w i n d w a r d performance o f D w o u l d have been f u r t h e r enhanced.
The prismatic series illustrates the dramatic effect this parameter has on sailing perfor-mance. The magnitude o f the v a r i a t i o n was greater than any designer w o u l d attempt and perhaps now some intermediate values o f pris-matic should be added to the series.
The lowest prismatic gave generally the best performance in light air while the high pris-matic gave the best performance i n strong w i n d reaching and running. The " n o r m a l " prismatic had by far the best w i n d w a r d performance over the usual w i n d speeds encountered. The
advantage o f a high prismatic was cleariy shown o n the upright resistance o f the series. A m a j o r refairing o f the waterlines o f the t w o extremes o f the prismatic series d i d not materially alter the upright resistance or the w i n d -w a r d performance. This substantiates the major effect prismatic coefficient has o n per-formance.
Further remarks
The series presented in this paper deals w i t h a particular craft, a moderate to heavy displa-cement vessel w i t h the keel faired into the h u l l i n such a manner as to give n o sharp definition between keel and h u l l in contrast to the light displacement fin-keel yacht. The designer must also concern himself w i t h other types o f sailing
c r a f t . The fin-keel yacht and shoal draftcenter-boarder are t w o examples. The systematic m o d e l series approach is applicable here as w e l l . Barkla" presented the results o f a beam-draft series based o n a fin-keel 5.5 meter as a parent f o r m . For this series, the keel profile and sections were kept the same f o r all models. DeSaix'" demonstrated the fin-hull interaction f o r a 5.5-meter h u l l . I t is possible w i t h some l i m i t a t i o n s to predict the effects o f keel changes o n performance.
Evaluations o f keel p r o f i l e changes are avai-lable i n separate works by K . M a c L a v e r t y , ' ' and in less detail by DeSaix.'-.
T a n n e r " presents the results o f tank tests o f a 1/12-scale model o f a 50-ft waterline shallow d r a f t ketch w i t h three alternative keel
append-21
ages: a centerboard, leeboards and bilge keels. The effects o f the fore a n d a f t positions o f a fin keel are available i n References 14 and 15. The c o n t r o l o f the sailing yacht is of equal importance as the potential speed. M i l l w a r d ' ^ presents a design procedure f o r a spade rudder. The c o n t r o l p r o b l e m is briefly discussed in Reference 17.
I t is hoped the results o f t h e two series presented w i l l encoiu-age others towards the same type of experimentations. Rules change and new yachts must be developed to rate well against them. Identification o f the i m p o r t a n t f o r m parameters affecting performance and a true evaluation o f their eflï'ects o n speed can be achieved through the use o f systematic model test series a n d s h o u l d lead to a more r a p i d development o f successful sailing c r a f t than has been achieved t h r o u g h the development w o r k o n i n d i v i d u a l yachts.
The bibliography included w i t h this paper should provide the designer w i t h additional i n f o r m a t i o n o f a more or less systematic nature w i t h w h i c h to evaluate his proposed design.
Bibliography
1. Henry, R. G. and Miller, R. T., "Sailing Yacht Design - A n Appreciation of a Fine A r l " , Paper N o . 9 Presented at Annual Meeting, The Society of Naval Architects and Marine Engineers, Novem-ber 1963.
2. Rhodes, Philip L . , "Modern Yacht Design',
The Experts' Book of Boating, Prentice-Hall, Inc.,
Englewood Cliffs, N . J. 1958.
3. Davidson. K . . "Experimental Studies of the Sailing Yacht," S N A M E , 1937.
4. Crago, W. A . , "The Prediction of Yacht Per-formance From Tank Tests," Paper Read in Southampton at a Meeting of the Southern Joint Branch of The Royal Institution o f Naval Archi-tects and The Institute of Marine Engineers, March 1962.
5. Crewe, P. R., "Estimation o f Effect of Sail Performance on Yacht Close-Hauled Behaviour," Paper No. 3 Read al the Joint Meeting of the R I N A and the Institution of Engineers and Shipbuilders in Scotland in Glasgow, February 1964. 6. Yonkers, W. F., "Model Tests of Five Related Sailing Yacht Forms," Prepared for Stevens Institute of Technology, Department of Ocean Engineering, Special Problem OE-400, September 1970.
7. DeSaix, P., "Slatistical Evaluations of tlie Effect o f Form Variations on the Resistance o f Sailing Yachts," Stevens Institute ofTechnology, Davidson Laboratory Letter Report 906, January 1965.
8. Spens, P., "Methods of Predicting Sailing Per-formance Off the W i n d , " Davidson Laboratory, Unpublished.
9. Barkla, H . M . , "Tests of Four Related Yacht Forms," SIT, D L Technical Memorandum 132, October 1962.
10. DeSai.\, P., " F i n - H u l l Interaction of a Sailing Yacht M o d e l , " SIT, D L , Technical Memorandum 129, March 1962.
11. MacLaverly, K., "Tests of a 5.5 Metre Yacht Form Wilh Various Fin Sweepback Angles," Universiiy of Southampton, Report N o . 17, February 1966.
12. DeSaix, P., "Experiments with End Plate and Keel Profile Shape Variations on a 5.5 Meter Yacht," SIT. D L , Technical Note 589, May 1960. 13. Tanner, T., "Tank Tests of a 50-ft W . L . Ketch with a Number of Alternative Keel Appendages," Universiiy of Southampton, Tech. Note 506, Feb., 1970.
14. "Model Tests to Determine the Effect on Sailing Yacht Resistance of Varying the Fin Location Fore and A f l , " Universiiy of Southamp-ton Technical Note No. 505. October 1969. 15. DeSaix, P., "The Effect of Keel Position on the Upright Resistance o f Two Sailing Yachts," SIT D L , Technical Note N o . 686, March 1963. 16. Millward, A . , "The Design of Spade Rudders for Yachts, University of Southampton, Report 28, December 1969.
17. Spens, P. G., DeSaix, P. and Brown, P. W., "Some Further Experimental Studies of the Sailing Yacht," Transactions, The Society of Naval Architects and Marine Engineers, Vol. 75, 1967.
figure 21
Prismatic series: windward performance figure 22
Prismatic series: polar diagram of sailing per-formance
