Aerodynamics of High-Performance Wing Sails
J . otto S c h e r e r ^
Some of tfie primary requirements for tiie design of wing sails are discussed. In particular, ttie requirements for maximizing thrust when sailing to windward and tacking downwind are presented. The results of water channel tests on six sail section shapes are also presented. These test results Include the data for the double-slotted flapped wing sail designed by David Hubbard for A. F. Dl Mauro's lYRU " C " class catamaran Patient Lady II.
I n t r o d u c t i o n
The propulsion system is probably the single most neglect-ed area of yacht design. The conventional triangular " s o f t " sails, while simple, practical, and t r a d i t i o n a l , are a long way f r o m being aerodynamically desirable. The aerodynamic d r i v i n g force of the sails is, of course, j u s t as large and j u s t as i m p o r t a n t as the hydrodynamic resistance of the h u l l . Y e t , designers w i l l go to great lengths to fair h u l l lines and tank test h u l l shapes, while simply drawing a triangle on the plans to define the sails.
There is no question i n m y m i n d t h a t the application of the wealth of available a i r f o i l technology w i l l yield enormous gains i n yacht performance when applied to sail design. Re-cent years have seen the application of some of this technolo-gy i n the f o r m of wing sails on the l Y R U " C " class catamar-ans. I n this paper, I w i l l review some of the aerodynamic re-quirements of yacht sails w h i c h have led to the development of the wing sails.
For purposes of discussion, we can divide sail require-ments into three points of sailing:
• U p w i n d and close reaching. • Reaching.
• D o w n w i n d and broad reaching.
Some of the requirements of u p w i n d and d o w n w i n d sailing w i l l be discussed here. Reaching w i l l be recognized as an i n termediate condition w i t h the sail design requirements f a l l -ing between those of u p w i n d and d o w n w i n d sail-ing.
There are m a n y criteria w h i c h can be used to judge the quality of a sail design. For our discussion of high-perform-ance wing sails, t h é p r i m a r y criterion w i l l be to maximize the available d r i v i n g force (thrust) for a given t o t a l sail area. Such a sail w i l l maximize the speed of a racing yacht w i t h a given measured sail area or m i n i m i z e the size of the r i g re-quired for a cruising yacht.
Definition sketch of force and velocity vectors in upwind sailing
U p w i n d a n d c l o s e r e a c h i n g
Aerodynamic requirements for sailing u p w i n d and close reaching are basically the same. These points of sailing are characterized by having the apparent w i n d at a small angle to the course of the boat. T h i s situation is shown on F i g . 1. The angle between the apparent w i n d and the course is de-noted b y (3 and m a y vary f r o m about 25 deg f o r a fast, close winded boat to about 35 deg when close reaching. We m i g h t consider 30 deg as t y p i c a l for this p o i n t of sailing.
I t can be seen f r o m F i g . 1 t h a t the resultant force R, is nearly at r i g h t angles to the course so t h a t there is only a small t h r u s t force, T, compared w i t h a rather large heeling force, H. The resultant, R is composed of an aerodynamic
^ Head, Ship Propulsion and Research Division, H y d r o n a u t i c s , Inc., L a u r e l , M a r y l a n d .
Presented at the Chesapeake Sailing Y a c h t S y m p o s i u m , Annapo-lis, M a r y l a n d , January 19, 1974.
Hit lorce, L, n o r m a l t o the apparent w i n d and a drag force,
D, i n the direction of the apparent w i n d . I t is convenient to
express these forces i n terms of coefficients, nondimensional-ized w i t h respect to the apparent w i n d velocity, V, and the sail area, S. Thus:
r e s u l t i n g c o e f f i c i e n t (1)
Cr = T/y,pV's, t h r u s t coefficient (2) CH = H/%pV% heeling c o e f f i c i e n t (3)
= L/y,p}r-S, l i f t c o e f f i c i e n t (4) c„ = D/Y>pV-S, drag coefficient (5)
The t h r u s t and heeling force are related to the sail l i f t and drag by the expressions
C.;. = C,, sin/3 - Co cos/? (6)
(7)
U p w i n d and close reaching, i t is clearly desirable t h a t the sail should develop the highest possible thrust up to w i n d speeds where s t a b i l i t y or increased h u l l drag due to heeling force become i m p o r t a n t . Thereafter, the highest possible thrust w i l l be obtained when the. ratio of thrust to heeling force (CT/CH) or t h r u s t to heeling moment (CTVS/CM) is maximized. Heeling m o m e n t is simply the product of heeling force and the height of the center of effort:
M Hh _
where
H = heehng force
h = height of center of effort b = height of sail
X = h/b
A = aspect ratio = b^/S S = sail area
Thus, for any given sail geometry, CM is proportional to CH. hispection of equations (6) and (7) (or F i g . 1) indicates that reducing drag w i l l b o t h increase the available t h r u s t and decrease the heeling force. The question then becomes: What type of sail geometry w i l l provide the m i n i m u m drag, and thus m a x i m u m thrust, for a given l i f t coefficient, and what is the importance of increasing the available l i f t coeffi-cient?
Drag comes f r o m two sources: viscous or f o r m drag caused by the skin f r i c t i o n and turbulence of the air flowing over the sail and its supporting structure, and induced drag w h i c h re-sults f r o m lost energy i n the wake of the sail due to its f i n i t e span. These two types of drag are referred to as parasite drag, CD(P) , and induced drag, Cnn), respectively:
(9) hiduced drag is a f u n c t i o n of the vertical d i s t r i b u t i o n of aerodynamic loading—not sail area. W i t h constant w i n d velocity f r o m top to b o t t o m , the load d i s t r i b u t i o n w i t h least i n -duced drag is i n the f o r m of a semi-ellipse as shown i n F i g .
2(a). For this case, the induced drag is expressed as
where A is the aspect r a t i o : A^tys Thus, equation (10) can be w r i t t e n :
Cfl,, = C t ^ S / 7 r 6 2
( 1 0 )
( U )
( 1 2 ) from w h i c h i t can be seen t h a t the induced drag is propor-tional to l i f t coefficient squared and inversely proporpropor-tional to the square of the l u f f length or span b.
A e r o d y n a m i c Load A e r o d y n a m i c Load
Fig. 2(a) Semi-elliptic load distribution
Sail A r e a / \ < D i s t r i b u t i o n
Fig. 2(b) Load distribution with triangular sail
T h e presence of the h u l l and water surface under the sail, plus the vertical velocity gradients above the water surface, tends to distort the o p t i m u m vertical d i s t r i b u t i o n of loading away f r o m the semi-elliptical shape. I n p r i n c i p l e , i f the sail could be sealed to the h u l l along its foot, loading could be carried r i g h t down to the foot and the induced drag would be just cut i n half. The sail could be said to have an effective aspect ratio AE of j u s t twice its geometric aspect r a t i o .
In reality this benefit is d i f f i c u l t to achieve for two reasons. First, i n practice i t is d i f f i c u l t to o b t a i n a really tight seal between the foot of the sail and the deck. Even a small gap of only a few percent of the sail height w i l l ehminate m u c h of the p o t e n t i a l reduction i n induced drag. Second, the reduced w i n d velocity over the surface of the water, plus the dis-turbed air f l o w i n g over the h u l l , w i l l t e n d to d i m i n i s h the benefit of sealing the foot of the sail to the deck. I n addition, i t is rarely possible to obtain the o p t i m u m vertical distribu-tion of loading for the existing condidistribu-tions of v e r t i c a l w i n d gradient and gap under the foot.
I t m i g h t be noted t h a t i t is a physical necessity t h a t the vertical d i s t r i b u t i o n of loading go to zero at the free ends of the sail, t h a t is, the head and the f o o t ' i f the f o o t is not per -fectly sealed to the deck. The load d i s t r i b u t i o n f o r a triangu-lar sail m i g h t appear as shown i n Fig. 2(b).
In any case, the sail w i l l produce the same induced drag as an equivalent wing operating i n u n i f o r m flow with, an o p t i -m u -m load d i s t r i b u t i o n . The aspect ratio of t h i s equivalent wing is called the "equivalent aspect r a t i o , " AE, and m a y be either slightly greater or smaller t h a n the geometric aspect ratio of the sail. Thus, equation (10) can be w r i t t e n more generally as:
C„^ = C.^TTAE ( 1 3 )
Induced drag is of p r i m a r y importance i n u p w i n d sailing and w i l l actually l i m i t the m a x i m u m obtainable t h r u s t for most conventional sail configurations w i t h effective aspect ratios between two and three. T o understand this, i t is i n
-• N o m e n c l a t u r e — A = aspect ratio = b^/S
AE = effective aspect r a t i o b = sail span ( l u f f length) c = sail chord
CD = drag coefficient, equation ( 5 )
CH = heeling force coefficient, equations ( 3 )
. and (7)
CL = l i f t coefficient, equation (4)
CM = heeling m o m e n t coefficient, equation
(8)
CR = r e s u l t a n t force coefficient, equation (1) . CT = t h r u s t coefficient, equations ( 2 ) a n d ( 6 ) D = sail drag H = heeling force h = height of center of e f f o r t L = sail l i f t M = heeling m o m e n t iï = resultant sail force S = sail area T = t h r u s t U = boat speed V = apparent w i n d speed W = true w i n d speed X = defined as h/b
P = angle between apparent w i n d . a n d course
Sh. = h u l l drag angle = a t a n (H/T) 8s = sail drag angle = a t a n (L/D) p = air mass density
J U L Y 1 9 7 4
LIFT COEFFICIENT, C|_ EFFECTIVE ASPECT R A T I O , AE
Fig. 3 Variation of ttirust coefficient with lift coefficient for various Fig. 4 Variation of thrust coefficient with effective aspect ratios effective aspect ratios , for various lift coefficients
structive to rewrite equation (6) i n terms of induced and par-asite drag:
Cr = CL sin/3 - (CI^/TTAE) COS/J - C^^ cos/3 (14)
T h i s equation is p l o t t e d i n F i g . 3 and 4 for the u p w i n d case of /3 = 3 0 deg and no parasite drag. I t can be seen i n F i g . 3 t h a t for any effective aspect ratio, a m a x i m u m t h r u s t coeffi-cient, C T , is achieved at some given l i f t coefficoeffi-cient, CL, and t h a t f u r t h e r increasing the l i f t coefficient actually reduces the available thrust. T h i s m a x i m u m t h r u s t coefficient can be expressed as:
Cr„,,, = \CL* sin/3 - C^^ cos/3 ( 1 5 ) where C i * is the l i f t coefficient at C r t m a x ) and is given by
C t * = ( 7 r A £ / 2 ) tan/3 ( 1 6 )
From equations (15) and (16) i t can be seen t h a t the m a x i -m u -m t h r u s t is proportional to the effective aspect ratio.
To get an appreciation for the relative importance of the parasite drag, we note t h a t the parasite drag coefficient
(Cu{p)) m i g h t be between the values of 0.01 for a very clean
rig and 0.05 for a r i g where l i t t l e attention has been p a i d to unnecessary windage. T h i s would i n t u r n reduce the avail-able t h r u s t coefficient, C r , by an amount f r o m 0.00866 to 0.0433 respectively. While this is not an insignificant amount, i t can be seen by comparing this value w i t h CT values at t y p i c a l effective aspect ratios i n Fig. 3 t h a t the
par-asite drag is of m u c h less importance t h a n the induced drag losses.
Figure 4 is a crosspiot of F i g . 3 w h i c h again shows the i m -portance of aspect ratio. I n viewing this figure i t should he kept i n m i n d t h a t the aspect ratio of conventional sloop-rigged boats usually lies between two and three, while even the t a l l narrow rigs of the " C " class catamarans typically have aspect ratios of about f o u r and never exceed values of 5.5 for the most extreme designs.
I n reality, a boat w i l l achieve its m a x i m u m speed at l i f t co-efficients somewhat less t h a n those which yield the maximum thi-ust coefficient. T h i s is because the heeling force also in-creases w i t h increasing l i f t coefficient which, i n t u r n , inin-creases the h u l l resistance. I n a d d i t i o n , the preceding equations apply only to a sail i n an u p r i g h t position, and heeling w i l l also de-grade the sail's perforrnance.
Nonetheless, i t appears t h a t the p r i m a r y requirement for improving u p w i n d sailing is to design a sail w i t h the mini-m u mini-m possible induced drag. T h i s is mini-more i mini-m p o r t a n t than ei-ther the reduction of parasite drag or a t t a i n m e n t of, high lift coefficients.
Before leaving the requirements for u p w i n d sail design, it is of interest to examine the requirements for m i n i m i z i n g the angle /3, t h a t is, m i n i m i z i n g the angle between the apparent w i n d and the course of the boat. Looking again at Fig. 1, can be seen t h a t the angle /3 is equal to the sum of the two angles 5s and 5h. The angle 5s is the arctangent of the sail lift"
drag ratio and the angle 8h is similarly the arctangent of the hulls side force-resistance r a t i o . Thus;
/? = ATAN ( L / D ) + ATAN { H / T ) = 5, + 5* (17)
This relationship is often r é f e r r e d to as the "course theo-rem." Stated i n words, i t says t h a t the angle between the ap-parent w i n d and the boat's course is equal to the sum of the drag angles for the sail (6s) a n d h u l l (5h). T h i s relationship is true for a l l points of sailing b u t holds its greatest significance for the case of u p w i n d sailing. I t points u p the necessity of achieving high l i f t - d r a g ratios for the sail as well as the h u l l i f a close-winded boat is to result.
Downvi^ind s a i l i n g
Boats which sail straight d o w n w i n d and depend on aerody-namic drag of the sails for t h r u s t are h m i t e d to about half the speed of the w i n d . T h i s is because, as the boat sails fast-er, the apparent w i n d over the sails is reduced. Since the d r i v i n g force is reduced at a rate proportional to the square of the apparent w i n d speed and the h u l l resistance typically increases at a rate between the square and cube of the speed through the water, i t becomes very d i f f i c u l t to obtain any significant gains sailing straight before the w i n d .
However, no theoretical H m i t to speed made good exists for boats w h i c h tack downwind, and indeed iceboats, w i t h their very low resistance, can easily exceed the speed of the w i n d when tacking d o w n w i n d . W h i l e the high-performance cata-marans have not yet achieved a speed made good downwind which exceeds the w i n d speed, they do perform best when tacking downwind. Under such conditions the boat typically sails at about 45 deg f r o m straight d o w n w i n d and the appar-ent w i n d is j u s t about abeam; t h a t is, the angle is about 90 deg. T h i s condition is the same as broad reaching and is the one of concern i n the design of wing sails.
Sailing downwind is conceptually m u c h simpler than the u p w i n d problem. Sail drag is of secondary importance as i t acts n o r m a l to the course of the boat while the sail l i f t force, acting i n the direction of required thrust, is of prime impor-tance. Since an unstalled sail can produce m o r é t h a n twice the l i f t coefficient of a stalled sail, the downwind problem is basically one of designing a sail t h a t w i l l produce the highest possible l i f t coefficient before s t a l l .
There are two considerations i n achieving a high overall l i f t coefficient for a sail. The f i r s t is to provide a sail section shape which is capable of producing high l i f t coefficients. The second is to provide a sail p l a n f o r m and vertical load distribution such t h a t this h i g h l i f t coefficient can be achieved over the entire span.
H i g h section l i f t coefficients w i t h low f o r m drag are achieved by the proper shape of the sail cross section. L i f t coefficients are l i m i t e d by the phenomenon of " s t a l l . " A f o i l stalls when the angle of attack becomes so h i g h t h a t the f l o w can no longer adhere to the low-pressure side and separates f r o m the f o i l , leaving a t u r b u l e n t wake and causing the l i f t produced by the low-pressure side to be destroyed. There are two types of stall: leading-edge stall and trailing-edge stall.
Leading-edge stall occurs when the flow cannot adhere to the leading edge because of severe pressure gradients at the leading edge. T h i s type of stall can be delayed b y selecting the proper amount of camber and a good leading-edge shape.
Sail camber has probably received more attention t h a n any other factor i n sail design and therefore w i l l not be discussed f u r t h e r here. However, a good leading edge is very i m -portant i n b o t h achieving h i g h l i f t coefficients and low f o r m drag. The conventional f i x e d mast provides a very poor lead-ing edge. The t u r b u l e n t wake shed f r o m the lee side of such a mast leads to b o t h h i g h f o r m drag and leading-edge stall at rather low l i f t coefficients. Even the t h i n leading edge of a
Thin Section
> Wing Mast Section
Fig. 5 Foil sections tested
j i b is poor f r o m the standpoint of early leading-edge stall and is very sensitive to small changes i n angle of attack as w o u l d occur when sailing i n a seaway.
R o t a t i n g , a i r f o i l - s h a p é d masts provide improvement. The large w i n g masts currently i n vogue on the l Y R U " C " class catamarans provide substantial improvement i n leading-edge shape and have rendered the conventional m a s t nearly obso-lete on these boats.
Trailing-edge stall is more d i f f i c u l t t o deal w i t h . T h i s type of s t a l l is caused by the i n a b i l i t y of the low-energy air i n the boundary layer t o move f r o m the low-pressure region near the m i d - c h o r d of the lee side to the higher pressure at the t r a i l i n g edge. T h i s f o r m of stall usually l i m i t s the m a x i m u m l i f t coefficients of well-designed airfoils to values of two or less.
To achieve higher l i f t coefficients, s o m é f o r m of boundary-layer control is required to remove the low-energy air f r o m the surface of the f o i l . The most common f o r m of boundarylayer control is the slotted f l a p used on nearly a l l large m o d -e m a i r c r a f t .
I n the spring of 1973, A . F. D i M a u r o sponsored a series of tests at Hydronautics, Incorporated to determine the feasi-b i l i t y of using a doufeasi-ble-slotted f l a p to achieve h i g h l i f t coeffi-cients on a new wing sail for his " C " class catamaran Patient
Lady IL T h i s very ingenious w i n g was designed by D a v i d
H u b b a r d . I t consists of three panels: a leading-edge panel of 45 p e r c é n t of the chord w h i c h serves as the mast, a 15-per-cent chord 15-per-central p a n è l , and a 4 0 - p e r c é n t trailing-edge panel. T h e after t w o panels are hinged on a four-bar linkage f r o m the leading panel so t h a t i t can be cambered to sail on either tack. T h i s section was tested i n the Hydronautics
2 . 6 Z LU Ö O O 10 20 30 A N G L E O F A n A C K, a (degrees) 40 Z O u - 0 . 4 l 0.2 0 . 4 0 . 6 0 . 8 O 0.2 0 . 4 DRAG COEFFICIENT, 0 . 6 0 . 8
Fig. 6 Variation of lift coefficient witti angle of attack and lift coefficient versus drag coefficient for ttiln section
high-speed water channel i n b o t h a high-camber and low-camber configuration. For comparison, high- and low-cam-bered models of a conventional w i n g mast and a t h i n section similar to a j i b were also tested. Sections of the six models are shown i n Fig. 5.
The models have a 6-in. cord and a 15-in. span, giving them an aspect ratio of only 2.5. The results of these tests are presented on Figs. 6 through 8. These results have been corrected for tunnel boundary effects and converted to an as-pect ratio of 4, the asas-pect ratio of the f u l l scale r i g .
Each figure presents l i f t coefficient, Ci, as a f u n c t i o n of angle of attack, a, and l i f t coefficient, CL, versus drag coeffi-cient, CD, for each f o i l type. The drag coefficient plots also contain a reference induced drag line for aspect ratio 4 as given by equation (13). I n principle, the parasite drag is the difference between this reference induced drag line and the measured drag data. However, i t w i l l be noted t h a t i n Figs. 6 and 7 the measured drag is actually less t h a n the theoretical induced drag. I t is beheved t h a t this is caused by the aspect ratio correction procedure so t h a t , i n reality, these data actu-ally represent an aspect ratio of slightly greater t h a n 4. However, t h i s does n o t detract f r o m the relative comparison of the f o i l types.
T h e unusual behavior of the h i g h l y cambered t h i n section (Fig. 6) is of interest. T h i s behavior is the result of separa-t i o n occurring on b o separa-t h separa-the pressure and sucsepara-tion side asepara-t separa-the same time—an indication of excessive camber for a section w i t h such a t h i n leading edge.
However, of greatest interest are the results of the H u b -bard slotted section w h i c h e x h i b i t e d a m a x i m u m l i f t coeffi-cient of 2.4. T h i s is a very high value compared w i t h 1.9 for the wing mast and 1.7 for the t h i n section. Even more en-couraging is the f a c t t h a t the parasite drag is n o t greater t h a n t h a t of the wing mast i n the low-camber configuration. T h i s means t h a t this section w i l l provide i m p r o v e d down-w i n d sailing down-w i t h no penalty to u p down-w i n d performance. As a re-sult, this section has been adopted for the new wing sail on
Patient Lady II.
I n order to achieve a high overall l i f t coefficient for the en-tire sail, the enen-tire sail should be u n i f o r m l y loaded. Referring to F i g . 2(b), i t can be seen t h a t f o r a triangular sail the top portion tends to' be overloaded while the foot can never be f u l l y loaded.
As a result, the top w i l l stall before the b o t t o m and thus prevent the achievement of a high average l i f t coefficient for
- 0 . 4 ! -10 0 10 20 30 A N G L E OF A T T A C K , a , ( d e g r e e s ) - 0 . 4 I J L 40 0.2 0 . 4 0 . 6 0 . 8 0 0.2 0 . 4 0 . 6 0 . 8 DRAG COEFFICIENT, C ^
Fig. 7 Variation of lift coefficient witfi angle of attack and lift coefficient versus drag coefficient for conventional wing mast secti(
the entire sail. Obviously, i t is desirable to distribute the sail area i n a more or less elhptical fashion so t h a t i t tends to match the load d i s t r i b u t i o n . T h i s w i l l not only provide a re-duction i n induced drag, b u t higher overall l i f t coefficients.
The roach w h i c h can be supported w i t h f u l l - l e n g t h battens does a great deal to improve sail area d i s t r i b u t i o n i n the upper portion of the sail. The wide chord o f a wing mast f u r -ther helps to provide a good d i s t r i b u t i o n of sail area. How-ever, the foot remains a problem unless i t is sealed against the deck or cut back to a rather small chord.
T h e control of sail t w i s t is also an i m p o r t a n t factor i n ob-taining high overall l i f t coefficients. The presence of a verti-cal gradient i n w i n d velocity over the-water surface results i n a t w i s t to the apparent w i n d approaching the sail. Sailing upwind this t w i s t is very small, while on a board reach or tacking downwind the t w i s t i n apparent w i n d m a y be 20 to 30 deg or more between the top and b o t t o m of the mast for a fast boat. The reason f o r this can be seen by comparing Figs
^(a) and 9(b).
W h e n sailing to w i n d w a r d , Figure d(a), the w i n d generated by the speed of the boat makes an angle of only 45 deg w i t h
the true w i n d . W h e n combined w i t h the true w i n d , only a small angular t w i s t i n the apparent w i n d occurs even for a f a i r l y large difference i n t r u e w i n d speed between the top and b o t t o m of the mast.
However, when broad reaching as i n F i g . 9(b), the w i n d generated by the boat's speed makes an angle of about 135 deg w i t h the true w i n d . The geometry works out to cause a very large twist i n apparent w i n d direction between the top and b o t t o m of the sail.
Therefore, to operate efficiently over a wide range of cours-es, the sail must be capable of operating w i t h b o t h small and large amounts of t w i s t while s t i l l m a i n t a i n i n g good cross-sec-tional shape along the entire span. I n the case of the double-slotted f l a p section on Patient Lady II, this has been accom-plished b y d i v i d i n g the flaps i n t o three sections so t h a t the b o t t o m f l a p s can be set at higher angles of attack t h a n the upper flaps, thereby effectively creating a t w i s t when sailing downwind.
S u m m a r y
The f u t u r e of sail development holds great promise i f we
JULY 1974
z LU O u O io 20 30 A N G L E O F ATTACK, a ( degrees) 40 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.6 DRAG COEFFICIENT, C^
Fig. 8 Variation of lift coefficient witti angle of attack and lift coefficient versus drag coefficient for Hubbard double-slotted flap section
CO)
APPARENT WIND ALOFT
APPARENT WIND NEAR WATER
ANGULAR TV/IST IN APPARENT WIND
TRUE WIND ALOFT
TRUE WIND NEAR WATER
WIND FROM BOAT SPEED
ANGULAR TWIST IN
APPARENT WIND APPARENT WIND ALOFT TRUE WIND ALOFT
TRUE WIND NEAR WATER APPARENT WIND
NEAR WATER
WIND FROM BOAT SPEED
Fig. 9(a) Velocity diagram showing twist in apparent wind when F i g . S(b) Velocity diagram showing twist In apparent wind when
going to windward broad reaching
can advance f r o m the old soft-cloth sails and f i x e d masts. The technology already exists for m a j o r improvements i n sail design and performance. The adoption of aerodynamically clean wing sails w i l l eventually improve boat performance as well as lead to smaller, more manageable rigs.
I t appears t h a t the m a j o r requirement to improved u p w i n d sailing is the reduction of induced drag, while for d o w n w i n d sailing the most i m p o r t a n t problem is to achieve high h f t coefficients. Substantial room for improvement s t i l l exists i n both cases.
2 7 6
A c k n o w l e d g m e n t
The author wishes to express his sincere appreciation to Messrs. A . F. D i M a u r o , owner, and D a v i d H u b b a r d , design-er of Patient Lady II for pdesign-ermission to p u b l i s h the expdesign-eri- experi-m e n t a l data f r o experi-m their sail tests. T h i s is an especially wel-come a d d i t i o n to the available yacht sail data. T h e h willing-ness to make these data available for use b y potential com-petitors stands i n marked contrast to the general secrecy f o u n d among the designers and owners of highly competitive development boats.
