Aerodynamics of High-Performance Wing Sails

Aerodynamics of High-Performance Wing Sails
J.
otto Scherer^
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.
Introduction
The propulsion system is probably the single most neglected 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
driving force of the sails is, of course, just as large and j u s t as
important 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 airfoil technology w i l l yield enormous
gains i n yacht performance when applied to sail design. Recent years have seen the application of some of this technology i n the f o r m of wing sails on the l Y R U " C " class catamarans. I n this paper, I w i l l review some of the aerodynamic requirements 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 requirements into three points of sailing:
• U p w i n d and close reaching.
• Reaching.
• Downwind and broad reaching.
Some of the requirements of upwind and downwind 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 downwind sailing.
There are many criteria which can be used to judge the
quality of a sail design. For our discussion of high-performance wing sails, t h é p r i m a r y criterion w i l l be to maximize
the available driving 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 minimize the size of the r i g required for a cruising yacht.
Definition sketch of force and velocity vectors in upwind
sailing
U p w i n d a n d close r e a c h i n g
Hit lorce, L, normal to the apparent wind and a drag force,
Aerodynamic requirements for sailing u p w i n d and close D, i n the direction of the apparent w i n d . I t is convenient to
reaching are basically the same. These points of sailing are express these forces i n terms of coefficients, nondimensionalcharacterized by having the apparent wind at a small angle ized w i t h respect to the apparent w i n d velocity, V, and the
to the course of the boat. This situation is shown on F i g . 1. sail area, S. Thus:
The angle between the apparent w i n d and the course is denoted by (3 and may vary f r o m about 25 deg for a fast, close
resulting coefficient
(1)
winded boat to about 35 deg when close reaching. We m i g h t
consider 30 deg as typical for this point of sailing.
Cr =
(2)
T/y,pV's,
t h r u s t coefficient
I t can be seen f r o m Fig. 1 that the resultant force R, is
(3)
heeling
coefficient
=
H/%pV%
CH
nearly at right angles to the course so t h a t there is only a
(4)
l i f t coefficient
=
L/y,p}r-S,
small thrust force, T, compared w i t h a rather large heeling
force, H. The resultant, R is composed of an aerodynamic
(5)
c„ =
D/Y>pV-S,
drag coefficient
^ Head, Ship Propulsion and Research Division, Hydronautics,
Inc., Laurel, M a r y l a n d .
Presented at the Chesapeake Sailing Y a c h t Symposium, Annapolis, M a r y l a n d , January 19, 1974.
270
The thrust and heeling force are related to the sail l i f t and
drag by the expressions
C.;. = C,, sin/3 - Co cos/?
MARINE
(6)
TECHNOLOGV
(7)
A e r o d y n a m i c Load
A e r o d y n a m i c Load
Upwind and close reaching, i t is clearly desirable that the
sail should develop the highest possible thrust up to wind
speeds where stability 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 thrust to heeling moment (CTVS/CM)
is
maximized. Heeling moment is simply the product of heeling
force and the height of the center of effort:
M
Hh
Sail A r e a
_
/
Fig. 2(a)
where
H = heehng force
h = height of center of effort
b = height of sail
X = h/b
A = aspect ratio =
S = sail area
b^/S
Thus, for any given sail geometry, CM is proportional to CH.
hispection of equations (6) and (7) (or Fig. 1) indicates
that reducing drag w i l l b o t h increase the available thrust
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 coefficient?
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 which results 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 distribution of
aerodynamic loading—not sail area. W i t h constant w i n d velocity f r o m top to bottom, the load distribution w i t h least i n duced drag is i n the f o r m of a semi-ellipse as shown in Fig.
2(a). For this case, the induced drag is expressed as
(10)
where A is the aspect ratio:
A^tys
(U)
Semi-elliptic load
distribution
Fig. 2(b)
\
< Distribution
Load distribution with
triangular sail
The 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 principle, i f the sail
could be sealed to the h u l l along its foot, loading could be
carried right 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 ratio.
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 obtain 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 much of
the potential reduction in induced drag. Second, the reduced
w i n d velocity over the surface of the water, plus the disturbed air flowing over the hull, w i l l tend to d i m i n i s h the
benefit of sealing the foot of the sail to the deck. I n addition,
it is rarely possible to obtain the o p t i m u m vertical distribution of loading for the existing conditions of vertical 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 foot is not perfectly sealed to the deck. The load d i s t r i b u t i o n for a triangular 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 in u n i f o r m flow with, an optimum load d i s t r i b u t i o n . The aspect ratio of this equivalent
wing is called the "equivalent aspect r a t i o , " AE, and may 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:
Thus, equation (10) can be w r i t t e n :
C„^ = C.^TTAE
Cfl,, = Ct^S/7r62
(13)
(12)
from which i t can be seen t h a t the induced drag is proportional to l i f t coefficient squared and inversely proportional to
the square of the l u f f length or span b.
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 thrust for
most conventional sail configurations w i t h effective aspect
ratios between two and three. To understand this, i t is i n -
• Nomenclature—
A = aspect ratio =
b^/S
AE = effective aspect ratio
b = sail span ( l u f f length)
CR = resultant force
(6)
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)
JULY 1 9 7 4
coefficient,
equation
(1) .
CT = thrust coefficient, equations ( 2 ) and
D
H
h
L
M
iï
S
=
=
=
=
=
=
=
sail drag
heeling force
height of center of effort
sail l i f t
heeling moment
resultant sail force
sail area
T = thrust
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
course
apparent
Sh. = h u l l drag angle = atan
8s = sail drag angle = a t a n
p
wind . and
(H/T)
(L/D)
= air mass density
271
LIFT COEFFICIENT, C|_
Fig. 3
Variation of ttirust coefficient with lift coefficient for various
effective aspect ratios
EFFECTIVE ASPECT R A T I O , AE
Fig. 4
Variation of thrust coefficient with effective aspect ratios
, for various lift coefficients
structive to rewrite equation (6) i n terms of induced and parasite drag:
asite drag is of m u c h less importance than the induced drag
losses.
Figure 4 is a crosspiot of Fig. 3 w h i c h again shows the imCr = CL sin/3 - (CI^/TTAE) COS/J - C^^ cos/3
(14)
portance of aspect ratio. I n viewing this figure i t should he
This equation is plotted in Fig. 3 and 4 for the u p w i n d case kept i n m i n d t h a t the aspect ratio of conventional sloopof /3 = 3 0 deg and no parasite drag. I t can be seen i n Fig. 3 rigged boats usually lies between two and three, while even
that for any effective aspect ratio, a m a x i m u m thrust coeffi- the t a l l narrow rigs of the " C " class catamarans typically
cient, C T , is achieved at some given l i f t coefficient, CL, and have aspect ratios of about four and never exceed values of
that further increasing the l i f t coefficient actually reduces 5.5 for the most extreme designs.
the available thrust. T h i s m a x i m u m thrust coefficient can be
I n reality, a boat w i l l achieve its m a x i m u m speed at l i f t coexpressed as:
efficients somewhat less than those which yield the maximum
thi-ust coefficient. T h i s is because the heeling force also inCr„,,, = \CL* sin/3 - C^^ cos/3
(15)
creases w i t h increasing l i f t coefficient which, i n t u r n , increases
the h u l l resistance. I n addition, the preceding equations apply
where C i * is the l i f t coefficient at Crtmax) and is given by
only to a sail i n an upright position, and heeling w i l l also deC t * = ( 7 r A £ / 2 ) tan/3
(16)
grade the sail's perforrnance.
From equations (15) and (16) i t can be seen t h a t the maxiNonetheless, i t appears t h a t the primary requirement for
mum thrust is proportional to the effective aspect ratio.
improving upwind sailing is to design a sail w i t h the miniTo get an appreciation for the relative importance of the mum possible induced drag. T h i s is more important than eiparasite drag, we note t h a t the parasite drag coefficient ther the reduction of parasite drag or attainment of, high lift
(Cu{p)) m i g h t be between the values of 0.01 for a very clean coefficients.
rig and 0.05 for a rig where little attention has been paid to
Before leaving the requirements for upwind sail design, it
unnecessary windage. This would i n t u r n reduce the avail- is of interest to examine the requirements for m i n i m i z i n g the
able thrust coefficient, Cr, by an amount f r o m 0.00866 to angle /3, t h a t is, m i n i m i z i n g the angle between the apparent
0.0433 respectively. While this is not an insignificant wind and the course of the boat. Looking again at Fig. 1,
amount, i t can be seen by comparing this value w i t h CT can be seen that the angle /3 is equal to the sum of the two
values at typical effective aspect ratios i n Fig. 3 t h a t the par- angles 5s and 5h. The angle 5s is the arctangent of the sail lift"
272
MARINE
TECHNOLOGY
drag ratio and the angle 8h is similarly the arctangent of the
hulls side force-resistance ratio. Thus;
/? = ATAN
( L / D ) + ATAN
{ H / T ) = 5, + 5*
Thin Section
(17)
This relationship is often réferred to as the "course theorem." Stated i n words, i t says that the angle between the apparent wind and the boat's course is equal to the sum of the
drag angles for the sail (6s) and 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 up 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
if a close-winded boat is to result.
Downvi^ind s a i l i n g
Boats which sail straight downwind and depend on aerodynamic drag of the sails for thrust 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 faster, the apparent w i n d over the sails is reduced. Since the
driving 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 which 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 downwind. While the high-performance catamarans 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 downwind and the apparent w i n d is just about abeam; that is, the angle
is about 90
deg. This condition is the same as broad reaching and is the
one of concern i n the design of wing sails.
Sailing downwind is conceptually much simpler than the
upwind problem. Sail drag is of secondary importance as i t
acts normal 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 importance. 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 stall.
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 high 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 high t h a t the flow
can no longer adhere to the low-pressure side and separates
from 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 by selecting
the proper amount of camber and a good leading-edge shape.
Sail camber has probably received more attention than
any other factor i n sail design and therefore w i l l not be discussed further here. However, a good leading edge is very i m portant i n both achieving high l i f t coefficients and low f o r m
drag. The conventional fixed mast provides a very poor leading 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 high 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
JULY 1974
>
Fig. 5
Wing Mast Section
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 would
occur when sailing i n a seaway.
Rotating, a i r f o i l - s h a p é d masts provide improvement. The
large wing 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 mast nearly obsolete on these boats.
Trailing-edge stall is more d i f f i c u l t to deal w i t h . T h i s type
of stall is caused by the i n a b i l i t y of the low-energy air i n the
boundary layer to move f r o m the low-pressure region near
the mid-chord of the lee side to the higher pressure at the
trailing 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 boundarylayer 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 mode m aircraft.
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 feasib i l i t y of using a double-slotted f l a p to achieve high l i f t coefficients on a new wing sail for his " C " class catamaran
Patient
Lady IL T h i s very ingenious wing 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 which serves as the mast, a 15-percent chord central p a n è l , and a 4 0 - p e r c é n t trailing-edge
panel. The after two 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
273
2.6
Z
Z
LU
Ö
O
O
O
u
-0.4
10
20
ANGLE O F A n A C K , a
Fig. 6
30
(degrees)
40
l
0.2
0.4
0.6
0.8
O
0.2
0.4
0.6
0.8
DRAG COEFFICIENT,
Variation of lift coefficient witti angle of attack and lift coefficient versus drag coefficient for ttiln section
The unusual behavior of the highly cambered t h i n section
high-speed water channel i n both a high-camber and lowcamber configuration. For comparison, high- and low-cam- (Fig. 6) is of interest. T h i s behavior is the result of separabered models of a conventional wing mast and a t h i n section tion occurring on b o t h the pressure and suction side at the
similar to a j i b were also tested. Sections of the six models same time—an indication of excessive camber for a section
are shown i n Fig. 5.
w i t h such a t h i n leading edge.
The models have a 6-in. cord and a 15-in. span, giving
However, of greatest interest are the results of the Hubthem an aspect ratio of only 2.5. The results of these tests bard slotted section which exhibited a m a x i m u m l i f t coeffiare presented on Figs. 6 through 8. These results have been cient of 2.4. This is a very high value compared w i t h 1.9 for
corrected for tunnel boundary effects and converted to an as- the wing mast and 1.7 for the t h i n section. Even more enpect ratio of 4, the aspect ratio of the f u l l scale r i g .
couraging is the f a c t t h a t the parasite drag is not greater
Each figure presents l i f t coefficient, Ci, as a f u n c t i o n of t h a n t h a t of the wing mast i n the low-camber configuration.
angle of attack, a, and l i f t coefficient, CL, versus drag coeffi- T h i s means that this section w i l l provide improved downcient, CD, for each f o i l type. The drag coefficient plots also w i n d sailing w i t h no penalty to u p w i n d performance. As a recontain a reference induced drag line for aspect ratio 4 as sult, this section has been adopted for the new wing sail on
given by equation (13). I n principle, the parasite drag is the Patient Lady II.
difference between this reference induced drag line and the
I n order to achieve a high overall l i f t coefficient for the enmeasured drag data. However, i t w i l l be noted that i n Figs. 6
tire sail, the entire sail should be u n i f o r m l y loaded. Referring
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 to Fig. 2(b), i t can be seen that for a triangular sail the top
ratio correction procedure so that, i n reality, these data actu- portion tends to' be overloaded while the foot can never be
ally represent an aspect ratio of slightly greater t h a n 4. 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
However, this does not detract f r o m the relative comparison
prevent the achievement of a high average l i f t coefficient for
of the f o i l types.
274
MARINE
TECHNOLOGY
-0.4!
-10
-0.4
0
10
20
A N G L E OF A T T A C K , a,(degrees)
Fig. 7
30
40
J
I
0.2
0.4
0.6
0.8
0
0.2
DRAG COEFFICIENT,
L
0.4
0.6
0.8
C^
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 the true w i n d . When combined w i t h the true w i n d , only a
area i n a more or less elhptical fashion so t h a t i t tends to small angular twist i n the apparent w i n d occurs even for a
match the load distribution. T h i s w i l l not only provide a re- fairly large difference i n true w i n d speed between the top
and b o t t o m of the mast.
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
However, when broad reaching as i n Fig. 9(b), the w i n d
does a great deal to improve sail area d i s t r i b u t i o n i n the generated by the boat's speed makes an angle of about 135
upper portion of the sail. The wide chord of a wing mast fur- deg w i t h the true w i n d . The geometry works out to cause a
ther helps to provide a good distribution of sail area. How- very large twist i n apparent w i n d direction between the top
and b o t t o m of the sail.
ever, the foot remains a problem unless i t is sealed against
Therefore, to operate efficiently over a wide range of coursthe deck or cut back to a rather small chord.
es, the sail must be capable of operating w i t h b o t h small and
The control of sail twist is also an i m p o r t a n t factor i n oblarge amounts of twist while still m a i n t a i n i n g good cross-sectaining high overall l i f t coefficients. The presence of a verti- tional shape along the entire span. I n the case of the doublecal gradient i n w i n d velocity over the-water surface results i n slotted f l a p section on Patient Lady II, this has been accoma twist to the apparent w i n d approaching the sail. Sailing plished by dividing the flaps into three sections so that the
upwind this twist is very small, while on a board reach or bottom flaps can be set at higher angles of attack than the
tacking downwind the twist i n apparent w i n d may be 20 to upper flaps, thereby effectively creating a twist when sailing
30 deg or more between the top and bottom of the mast for a downwind.
fast boat. The reason for this can be seen by comparing Figs
^(a) and 9(b).
Summary
When sailing to windward, 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 f u t u r e of sail development holds great promise i f we
JULY 1974
275
z
LU
O
u
CO)
io
O
20
30
40
0.2
0.4
A N G L E OF ATTACK, a ( degrees)
Fig. 8
0.6
0.8
0
0.2
0.4
0.6
0.6
DRAG COEFFICIENT, C^
Variation of lift coefficient witti angle of attack and lift coefficient versus drag coefficient for Hubbard double-slotted flap section
ANGULAR TWIST IN
APPARENT WIND
APPARENT WIND ALOFT
TRUE WIND ALOFT
APPARENT WIND ALOFT
APPARENT WIND
NEAR WATER
ANGULAR TV/IST IN
APPARENT WIND
TRUE WIND ALOFT
TRUE WIND NEAR WATER
APPARENT WIND
NEAR WATER
WIND FROM BOAT SPEED
TRUE WIND NEAR WATER
WIND FROM BOAT SPEED
Fig. 9(a)
Velocity diagram showing twist in apparent wind when
going to windward
can advance f r o m the old soft-cloth sails and f i x e d masts.
The technology already exists for major 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 major requirement to improved u p w i n d
sailing is the reduction of induced drag, while for downwind
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 still exists i n
both cases.
276
Fig. S(b)
Velocity diagram showing twist In apparent wind when
broad reaching
Acknowledgment
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 , designer of Patient Lady II for permission to publish the experimental data f r o m their sail tests. T h i s is an especially welcome addition to the available yacht sail data. T h e h willingness to make these data available for use by potential competitors stands i n marked contrast to the general secrecy
found among the designers and owners of highly competitive
development boats.
MARINE TECHNOLOGY