A method of determining the effect of sail characteristics on a yacht’s close hauled performance and of comparing the merits of different rigs

6 t4V. 1976

UNIVERSITY

OF

SO UTHAM PT

ON

department of

aeronautics

and astronautics

ARCHIEF

ADVISORY COMMITTEE FOR YACHT RESEARCH

Lab.

y.

Scheepsbouwkunde

Technische Hogeschool

De!ft

0

S.U.Y.R. REPORT NO.15

A METHOD OF DETERMINING THE EFFECT OF SAIL CHARACTERISTICS ON A

YACHTS CLOSE-HAULED PERFORMANCE

AND OF COMPARING THE MERITS OF DIFFERENT RIGS

SUMMARY

This report describes a procedure whereby, given the hydrodynamic characteristics of a yacht hull, plots may be prepared which enable the windward performance of the yacht to be deduced directly when the lift

and drag coefficients of the rig are known. This method of performance prediction ¡s likely to be useful ¡n cases where it ¡s desired to compare the performance of a given hull under a number of different rigs. Fairly extensive computations are required to present the hull characteristics

in the required form, but these can be carried out quite easily using a digital computer.

Part II _{of the report presents a set of plots of this kind for a}

12.-metre yacht and discusses briefly the inferences which may be drawn from them.

V (knots) mg k (deg) (deg) 9 (deg) y (deg) cp _(deg) 5m (deg) NOMENCLATURE

Fore-and-aft Axis _{Intersection of Centreplane and}

Waterplane of the yacht.

Track _{Line along which the yacht}

moves, (fixed relative to the water").

VT (knots) _{True wind velocity, relative to the water.} VA (knots) Apparent wind velocity, relative _{to the yacht.}

V (knots)

Velocity of the yacht, along the track (relative

to the waterS')

Speed made good, component of the yacht's velocity (relative to the water"), _{in the direction opposite}

to _VT

Leeway Angle, Angle between track _{and fore-and-aft}

ax ¡ s.

Apparent Wind Angle, Angle between the apparent wind vector and the fore-and-aft _axis.

Relative Wind Angle, Angle between the apparent wind vector

(VA) and the track (V5)

Angle between the True wind vector (V1) and the track (V5)

Heel Angle of the yacht.

Angle between main _{Loom and yacht's centreplane,} measured in a plane perpendicular _{to the}

centre-plane.

If these words

are included, this nomenclature and the work in this _report are appi ¡cable even when the water has a velocity relative _{to the earth} due to tide or current.

C1 , C0 Lift and drag coefficients of the rig, including

above water part of the hull. (Lift and drag forces measured in trie horizontal plane, perpen-dicular and parallel to _VA).

C C C Lift and drag coefficients as above, measured with Lb L20 L30 Lcp

CD10 CO20 CD CD

F F (lb) Components, respectively parallel and perpendicular

to the fore and aft axis, of the air and water

Fxa Fya (lb) _{forces on the yacht measured in the horizontal} plane.

C C Coefficients of F and F

X y xa ya

R , H (lb) Components, respectively parallel and perpendicular

to the track, of the water force on the yacht, measured in the horizontal plane.

Mxa (lb ft) Heel ing moment about the fore-and-aft axis due to air forces on the rig including above-water part of the hull

M (lb ft) Righting moment about the fore-and-aft axis due to water and gravity forces on the yacht.

M (lb ft)

xp Value of M when H = O

, V

O

xw

M (lb ft) Value of M , when H O and V = Û

Xo xw S

i.e. Static Righting Moment

SA (sq ft) Sail Area, taken as area of Mainsail (excluding roach) + 100% of Area of Foretriangle.

CEH (ft) Center of Effort Height, defined as M cos

Coefficients of Air Forces ₌

_Force/pA

. VA2 . SA

where _VA ¡s in ft per sec, and _VA = 1.688 _VA

= air density, slugs per cu ft.

o o o

PART

NTRODUCT ON

The recent development of methods of measuring aerodynamic characteristics of sails n the wind tunnel has considerably increased the importance of the

quest on:

''How can one decide from their aerodynamic characteristics whether one rig or another will give the better performance to

windward, on a hull of known hydrodynamic characteristics?.

Clearly this is not the only criterion to be considered when designing a yacht rig. A compromise must be achieved, taking into account performance on other points of sailing, convenience of handling, behaviour in gale con-ditions etc. None-the-less it _{is generally agreed that windward performance} is very important, so much so that the use of tank testing in yacht design has so far been directed mainly to improvement in this respect.

Methods of determining yacht performance to windward for given hull and

sail characteristics were developed by Davidsonh23. _{Procedures more}

appropriate to the use of coefficients for a variety of sails have been

sug-5 6,7

gested by Sainsbury and Crewe . Fundamentally all these methods and the

one described in the present paper are based on three equations expressing the conditions of equilibrium of the yacht, namely:

Air drivirìq force

r-water resistance (in fore and aft direction) Air side force r- water sideforce (in transverse direction)

Air heeling moment = _{Righting moment due to water and gravity forces.} Davidson's procedure involves certain special assumptions concerning the

behaviour of sail forces, while that of Sainsbury is the most general. Both

wind speed for chosen values of V (ship speed through the water), and c.p

(heel angle). These calculations are repeated for several values of V at each of three or more values of cç

Vmg

VT 2 = 30

20'

=10'

The results are then plotted as in the sketch and the envelope to the several curves for different values of p represents the best obtainable

per-formance of the hull and rig configuration under consideration. To determine the effect of any change of hull or rig (for example a change of boom angle) it is necessary to repeat the calculations and determine a new envelope.

Crewe's work includes a study of the way in which sail characteristics affect the performance calculation and he has shown that many, but not all, non-optimum rig configurations may be eliminated at an early stage in the calculations. Even so, with any of these methods, comparison of several Sail configurations on the same hull is liable to involve considerable calculation

for each sail

condition. To perform many such calculations by hand

would

be

an extremely laborious task. On the other hand it is now possible to carry out the calculations on a digital computer, and to arrange for most of the plotting to be done automatically. Thus, if facilities of this kind are

avail-able, calculation of V - V1 envelopes for a number of configurations may in some cases be regarded as a feasible alternative to the procedure described

in the present report.

It will be realised that much of the earlier work on performance calcu-lation was directed at the problem of comparing the merits of different hulls on the basis of tank test results. This purpose can be achieved by manual calculation of V - V envelopes without excessive labour. Fortunately

mg T

used, since any reasonable system will usually give much the same assessment of the relative merits of various hulls of simi lar type. Thus the use of a

simplified representation of sail characteristics, such as Davidson's Gimcrack sail coefficients, is usually acceptable for this purpose. _{However, when the} purpose is _{to study the effect of various rig configurations and to elucidate}

the optimum rig characteristics for sailing to windward, then it is valuable to have at hand a method whereby the performance of a given hull under many different rigs can quickly be examined.

lt is the purpose of Part I of the present report to show how hul I

charac-teristics may be presented in a form which enables the speed made good to

wind-ward to be deduced directly when the lift and drag characteristics of the _sails are known. _{Fairly extensive computations are required for any hull, but these} can be performed quite easily using a digital computer. Thereafter the wind-ward performance of this hull under any rig can be deterniined with very little

calcul at ion.

The procedure to be described makes use of the same basic principles and the same equilibrium equations as the other methods mentioned _above.

Accord-ingly no substantial difference is to be expected in the final results.

However, it is important always to bear in mind that any performance predictiun based on tank and wind tunnel results is subject to various errors and

uncer-tainties. These arise both from difficulties in scal ing-up model results and from differences between test and fullsize conditions, such as the gustiness of real wind and the waves on real water.

A set of plots representing the hull characteristics of a 12-metre yacht has been prepared in accordance with the method discussed and is presented in

Part II of this report.

PRINCIPLES OF THE METHOD

A basic requirement for any performance prediction is knowledge of the hydrodynamic characteristics of the hull, which may be obtained from tank tests, or otherwise (e.g. the characteristics of a notional hull might be arbitrarily specified, or devised by modifying those of a known hull). For

the present purpose it _{is necessary that this data shall be available in a}

form from which the resistance, sideforce and righting moment can be computed for any values of ship speed

(V),

heel angle (cp) and leeway angle (X) within appropriate limits.

Not all tank test results are in the required form, since tests are often made for only a few values of p and V , and results cannot readily be

derived for intermediate values of these variables. Fortunately, however, Crewe6 has given a set of figures for a 12-metre which can be used for the present purpose with a little approximation. Furthermore, it is now the

prac-tice at M.I.T. to present yacht test results in the form of polynomial expressions for resistance and sideforce in terms of V , p and X

. Such

data ¡s well suited for our present purpose, and data for a 12-metre tested at M.I.T. have been used to illustrate the present discussion. More extensive

performance calculations for the same yrht are given in Part I of this report.

Together with the hull characteristics we must specify two parameters con-cerning the rig, namely the Sail Area and Centre of Effort Height (CEH).

Methods of investigating the effects of changes in Sail Area and CEH are des-cribed later. Some knowledge is also needed of the way in which sail lift and drag vary with heel angle; this requirement is also discussed ¡ri greater

detail later.

We now consider Figure 1, which consists of three separate plots, each for a different value of the apparent wind angle,(). The axes represent values of lift and drag coefficients, C and C , for the rig at a

L0

D2O

chosen heel angle, 20 in this case. For convenience the plots were prepared for those o' values for which wind tunnel sail data were usually obtained.

The actual o' values in the tunnel were 17.5, 20 and 22.5 degrees.

However, corrections were introduced to allow for the effect of the tunnel walls, and the results were considered to apply to o' values of approximately 18, 20.5

and 23 degrees ¡n open air. More recently the procedure for calculating wind tunnel corrections has been revised, and results are now obtained for somewhat different values of o' . In any event it is usually desirable to plot wind

tunnel test values of _CL and _CD against o' and faired values can then be

picked off for any desired values of o'.

The lines in Figure I are computed from the hull data, etc., specified

above, and characterise the behaviour of the hull. Their significance is defined thus:

If at the specified heel angle, 200 in this case, and at the o'

value of the plot lift and drag coefficient values C and C

L2O D20

for the rig (including the above-water part of the hull) correspond to any point on one of these hull characteristic lines, then, in a

true wind of 13 knots the yacht will make good to windward the speed indicated alongside this line, when sail ing in calm water at the apparent wind angle specified for the plot.

If the _CL2O and _CD values for the rig correspond to a point falling between the lines of constant V , the appropriate V

mg mg

value may be estimated by interpolation.

It is important to note that the above statement does not imply that the yacht will actually sail at a heel angle of 20°. As will be seen below, the plot is arranged so that _Vmg values at the heel angles which actually occur are obtained from sail tests at a fixed heel angle.

Plots are needed for several o' values, and on each plot it is

conve-nient to mark the point corresponding to the _CL2O and _CD2O values for the rig at the value of o' appropriate to the plot. In Figure I such

points are shown for two different rig settings, with the main boom at angles of 10 _and 30

to the centre line of the hull.

It is now apparent that the greatest speed made good is obtained with

the 10 boom angle at an apparent wind angle (o') near 20.50.

A simple plot of V against o' , as shown in Figure 8, may be used

to arrive at a good estimate of the optimum V and of the o' value at

mg which this occurs.

Since points on the curves of constant V represent the behaviour mg

of the yacht when sail ing under a rig having the indicated values of

CL and C0 , it is possible to indicate as parameters on the curves the

values of any quantities associated with sailing conditions, such as the heel angle (cp) , true wind angle (y) , leeway angle _(x) , ship speed

(V)

, etc. Some of these quantities are indicated in Figure

1 and on the

Although a later section describes n some detail the procedure by which

the hull characteristic lines are computed, a brief explanation is now given, since it may faci i ¡tate understanding of their use.

For any characteristic line, SA, CEH, V , and V

T mg

are fixed. We choose a series of values of the leeway angle X

covering the range in which sailing conditions will lie, and for each value of X we carry out the following procedure.

Since - c' + X

, V , VT

and are known so that

V and

VA may be calculated from the geometry of the vector

triangles (see sketch).

With V X and CEH known, the heel angle (tp) , water

sideforce and resistance are determined from the known hydrodynamic and stability characteristics of the hull.

The air force on the sails is of course equal and opposite

to the water force on the hull, and the apparent wind velocity and direction _(VA and ) being known the air force is resolved

into lift and drag components. These are converted to coefficients

CL and CD based on the known sail area of the rig (SA).

These

CL and CD values clearly refer to the rig heeled

at the angle q, just determined, which is probably not equal to

the heel angle, say 20° , for which the sail characteristics are

known. The next step is to use the known (or assumed) variation

of C and C with q, to find the values, C and C

L D L20 D20

at q, = 20 to which the

CL and CD values just determined

would change if the heel angle were changed from q, to 200

without any other change in the rig. These values, _CL and CD2 , are plotted to define a point on the hull characteristic

1 ¡ne.

Other points on this line are found by repeating the calculation for different values of . The whole procedure has now to be

repeated for the various values of V and mg

Accordingly, ¡f at cp = 200 and at the value of one of the plots, the rig gave C and C values corresponding to a point on one of the hull

L20

characteristic lines, the yacht, with this rig and at this , might well

sail in a 13 knot wind at a heel angle somewhat different from 200. However,

the _{CL and} CD values given by the rig at the actual heel angle would be such as to provide the sail forces necessary to give the indicated V

It is evidently the case that the solid lines in Figure 1, whose func-tion is to represent the hull behaviour, are dependent to some extent on a property of the sails, namely the variation of _CL and _{CD with} p.

For-tunately the experimental evidence at present available suggests that this variation is likely to be fairly consistent so that a single plot, as ¡n Figure 1, can probably be used with adequate accuracy for a variety of sail configurations. However, this is certainly a point to which attention should be paid in future sail testing.

The importance of accurate knowledge of the variation of CL and _CD with p may be minimized by choosing the values of p and V1 for the

plot so that optimum performance is likely to occur at an actual heel angle which does not differ greatly from the heel angle for which the plot is

pre-pared and for which, of course, sail data must be available. Then the necessary corrections to CL and CD are likely to be for relatively small changes of p, in the part of the plot relevant to optimum performance.

In order to study yacht performance under different wind conditions it is desirable to prepare similar plots for several values of _VT , choosing

these values so that the optimum performance occurs at heel angles near

those for which the sail data are available. Suitable values for most displacement yachts are about:

p lO 20 30 degrees

VT 7.5 13 20 knots

For yachts of different types, e.g. Catamarans, quite different values of _p may be required. However, much the same values of _VT should be considered in order to demonstrate the effect of varying sail characteristics when sailing in light, medium and strong winds.

CHANGES OF STABILITY

t is now appropriate to consider how we may examine the effect of

changes of stabil ¡ty on our performance estimates. This is obviously impor-tant if we are interested in the effects of, say, changes in ballast ratio. Furthermore changes of stability have much the same effect in the calculations as changes in centre of effort height (GEH). The latter may be of interest either because we wish to consider performance under a different rig with

different CEH, or because we find, for example, that CEH may change somewhat as we vary boom angle.

The significance of a change of either stability or CEH is that it alters the relation between the sideforce H and heel angle p . Davidson1 adopted

the reasonable approximation that the transverse component of the sail force acts perpendicular to the centre-plane of the yacht. If CEH is the height, above the waterline, at which this force intersects the centreplane, the rela-tion between the air heeling moment M and sideforce F

is:

xa ya

M _{= CEH} . F sec cp

xa ya

Fyw secç

We may with advantage go a step further and define CEFI as

Ma

cos

If this relation is used to calculate GEH from sail test results, the

ques-tion whether the sail force is exactly perpendicular to the centre-plane becomes of little importance in the present work.

The air heeling moment is, of course, equal to the water righting moment,

M . Since the water sideforce acts some

distance below the axis of moments which is taken in the water-plane, increase of sideforce reduces M If

as an approximation we take this distance d as constant, we may write

M - d.H sec p - M = M H sec cp. CEH,

x xw xa whe re H = sideforce and H F y M cos p M cos p

H=

CEH (CEH + d)

Here M depends principally on the heel angle but varies somewhat with the

Xp

yacht's speed through the water.

The values of CEH and d depend on the geometry of hull and rig. As

a rough rule, the centre of effort usually lies near the centre of area of the sailpian, and d is of the order of half the draft. Thus a 25% increase of

stability, i.e. of M , has the same effect, on the important relationship Xçp

between H and p , as a roughly equal percentage decrease of CEH.

The procedure we adopt to cope with variations of stability or CEH is

simply to carry out the computations for two or more different values of the relation between H and p to plot both sets of results. This is done in Figure 2, where the lighter lines correspond to 25% greater sideforce at any heel angle than the heavy lines. Interpolation between the lines for

differ-ent CEH makes it possible to determine V for intermediate values of CEH.

mg

The above discussion is intended to clarify the effects of stability and

CEH. lt is not necessary to assume, in calculating the hull characteristic

lines, that d is constant, since the value of M can usually be taken

directly from test results.

CHANGES OF SAIL AREA

We may readily examine the effect of changes of sail area, since say, a 10% increase of sail area has much the same effect on the sail forces as a 10% increase of the _CL and

CD values for the sails. Approximate

allow-ance can be made for the fact that a part of the total _CD due to the hull, of the order of .02 for a 12-metre rig at r 2U°, will not increase. Thus

the increase of _CL would be 10% and that of C0 , 10% of (C0 - .02). It

may also be necessary to allow for an increase in the height of the rig, for unless all dimensions are increased in proportion it will probably be incorrect to work from the original sail coefficients. Thus it would be appropriate to estimate the performance for the increased sail area by relating the new sail CL - C0 point to hull curves adjusted for 5% increase of CEH. (See also

pp 23-4)

USE 0F C AND C

If it is desired to examine the effect of sail changes expressed in terms of sail driving and sideforce coefficients, _C< and C,, , the hull

charac-teristic lines can readily be plotted on C - C axes. In fact these

characteristic lines are identical in form with those on the _{CL - CD} plot,

and the change only requires drawing C - C axes at an angle to the CL - C0 axes. Figure 3 shows hull characteristic lines identical to those of Figure 1 plotted on C - C areas.

There have been various discussions in the past as to the relative effects of changes in sail driving force _(Cg) and sail sideforce (Cv)

We may now easily obtain some quantitative information on this point. For

instance Figure 3 shows that, in the vicinity of the optimum point (10 boom angle), a rig change will improve _Vmg provided that the resulting increase

of C exceeds approximately 1/6 of the increase of C . This assumes that

the rig change does not involve a significant change of CEH. If such a change does occur it must be allowed for by the procedure described in the previous section. It is also assumed that there is no change in the optimum

value of . Any such change appears likely to have only a small effect but

¡t could ¡f necessary be allowed for. It does not by any means follow that the same relationship between changes of C and C appi ies in other con-ditions or to other yachts. However, more information on this point may be obtained if the present procedure is applied to yachts of other types.

We may note that, given the present procedure for determining _Vmg

plots of _CL and _CD are no less convenient to use than plots involving C

and C

. CL

and _CD plots may often be preferred since _CL and _CD are

fundamental aerodynamic quantities whose behaviour can more readily be fore-seen and understood from general principles than ¡s the case for C and C,,.

METHOD OF COMPUTATION

When we set out to compute _CL and _CD for a point on one of the hull characteristic lines, Sail Area, CEH, V , V and ' are given, and we

choose arbitrarily a value of X . Different X's will give different points

on the line.

Now - ' + X and it can be shown from the geometry of the velocity

triangles that

Sin (2y _- = (1 + 2 V "y ) sin

mg! T

y

=v

/cos

S mg

and _{VA = VT sin}

y/sin

Thus _VA and V are found.

For any value of , sail tests give M and F . The relation

xa ya

between _Fya and _Mxa is conveniently expressed by defining the Centre of Effort Heiqht, CEH , by the equation

M CEH . F

xa ya

It is found in sail tests that _{CEH thus defined varies only slightly} with and cp . Accordingly it is convenient to treat GEH as a parameter

in the present computations.

Now M M and F

=F

xw xa yw ya

so that M = F . CEH . sec cp

xw yw

Also the hydrodynamic characteristics of the hull determine M xw

and F in terms of p , V and X. CEH, V and

X are known, and so

yw s s

we have 3 relations involving the three unknowns p, M and F

.

Unfor-xw yw

tunately M and F are generally complicated functions of V , p

and

X , so that an analytical solution is not possible.

However, no great diffi-culty arises in obtaining the required solutions for p and F by an

iterative process using a digital computer. R can then be computed from

the hydrodynamic characteristics of the hull.

Hull hydrodynamic characteristics are usually given in terms of

R and H rather than F . Since R and H , like F

and F

yw xw yw

are components of the resultant horizontal water force

F R2 +

H2 cos(tanR/H

-yw

or very nearly

F = H - R.X (where X is in radians)

yw

Further, since R. ). is of the order of 2% of H little error results from

tak i ng

F

=H

yw

and this approximation has been used in the computations in the present report. The resultant horizontal force on the yacht having now been found, the lift and drag components of the air force are determined and these are con-verted to coefficient form using the apparent wind angle , the apparent

wind velocity VA , and the sail area of the yacht rig.

(There are various different methods which may be used in calculating sail area as a basis for coefficients, and ¡t ¡s important that the area used here is consistent with the area used in calculating the sail data)

We have now determined the values of sail CL and CD and the heel angle p corresponding to the specified values of Vmg VT

and X

So far no assumptions have been made other than those commonly involved in performance calculations, including the assumption of constant CEFI

However, it is necessary to convert the values of CL and C0

which we have

calculated to those which the same sails would have at the fixed heel angle at which the Sail tests have been performed, say 200 . This conversion

requires knowledge of the variation of sail _CL and

CD with cp and,

strictly speaking, the results are only applicable to those sails for which the variation assumed is correct.

The results of some 12-metre sail tests were found to agree well with the

follo.iing relations:

2 2

C

=C

.cos

20/cos r.p

L20

2

CD = CD . cos 20/cos2

+ .ûûo(

- 20)( - 20)

(' and cp being measured in degrees)

The last terni is chosen empirically to fit an existing set of measurements,

and i t may iel be possible to f md better expressions for general use. If

di ffernt expressions are found to be appropriate to a particular rig under consideration, it is not difficult to make the necessary corrections since only the very last stage of the computation is affected, and this may readily be altered. Furthermore, the results can often be made somewhat insensitive

to the variation of CL and CD with cp , by choosing V1 so that optimum

performance for the hull and rig concerned occurs at a heel angle near to that for which the sail data is available.

The calculations described above are repeated for the same values of V1 and _Vmg with several values of X , giving pairs of values of

CL and CD

all on one hull characteristic line. Then by varying _Vmg and

the

various hull characteristic lines shown in Figure 1 are obtained.

PART II

APPLICATION TO A 12-METRE YACHT

INTRODUCTION

This part of the report presents a set of plots prepared in the form described in Part I , and representing approximately the characteristics of a

12-metre yacht. When values of sail _CL and _CD are known, for a heel angle of 100, 20° or 300, it is possible to read off directly from the plots the

speed that the yacht would make good to windward, sailing in a true wind of 7.5, 13 or 20 knots. Values of heel angle, true wind angle, and leeway angle may be obtained at the same time. The effect of varying the yacht's stability or the sail centre of effort height can also be studied.

To illustrate the use of the plots sail CL and CD values from wind tunnel tests of a 12-metre rig are indicated.

As explained in Part I, the preparation of these plots requires hull data in a form from

which

the resistance and other important characteristics can be derived for any value of the heel angle. The procedures at the M.I.T. tank

differ from those used elsewhere and regularly produce results in this form. Therefore the author has welcomed the opportunity to use data on a 12-metre tested at M.I.T. for a first application of the procedures described in this

report.

It should be noted that the yacht to which the present work refers dif-fers somewhat from other recent yachts of this class and is not entirely

representative of the characteristics of modern 12-metres. Thus, while the plots indicate broadly the characteristics of 12-metres, and to some extent of yachts in general, it should not be supposed that they are exactly

applic-able to all modern 12-metres.

HULL CHARACTERISTICS

Stability

The data concerning the stability of this yacht are in less complete form than is usual, since the effect of speed on the righting moment was not investigated. However, Crewe6 showed that, for another 12-metre, this effect was small.

The information given on the stability of the M. 1.1. 12-metre is that

Static Righting Moment = M0

= 57J

_-

2 in degrees)

= H sec p . (CEH + d)

= H sec cp .

36.5

(for general discussion of this relationship see Part I, page 9.)

Crev'e also showed that an expression of this kind well represented the data for the 12-metre that he studied.

The present report includes plots for the yacht with the stability given

by the above relation, and also for the yacht with the static righting moment, and consequently the sideforce at any heel angle, arbitrarily _{increased by 25/..} These two cases are referred to as 'Normal Stability and '25% Increased

Stability'

Since changes of CEH _{have the same effect in the calculations as changes}

of stability, we may if we wish regard the normal and _{increased stability cases} as representing hulls both having the original stab lity hut with differing centre of effort heights. _{If we assume the same value for} d _{as that obtained}

by Crewe for his 12-metre, namely _{3 ft. approximately, we arrive at the}

follow-ing values:

Normal Stability CEH =

33.5

ft.

25% Increased Stability CEH 26.2 ft.

The significant effect of changes of either hull stability or CEH on

the calculations is to vary the relationship between the sideforce (H) and

heel angle (p) , which for the two cases is given in round figures _{n the}

following table.

o

p=

10 20° 30°

Normal Stability H 1L+S0 2500 3200 lb

25% Increased Stability H = 1800 3153 +000

By interpolation between the plots for the two conditions the performance of the yacht may be obtained for any intermediate values of hull stability or

CEH.

In accordance with the usual M.I.T. practice the value taken for GEH in the stability relation includes allowance for the effect of the velocity gradient of the wind. Wind-Tunnel tests indicate that GEH for a 12-metre rig is approximately 28 ft. without velocity gradient, so that the value of 33.5 ft. taken for the normal stability case implies that GEH ¡s increased by some 20% as a result of the velocity gradient. Although this increase

appears to be a large one rough calculations suggest that an increase of this order is not impossible. However, no reliable data on the appropriate figure

is available and for this reason the velocity gradient is often disregarded in performance calculations.

If the user of the plots in the present report desires to obtain perform-ance estimates assuming a GEH not corrected for velocity gradient, this may readily be done by interpolating for the desired GEH between the

character-istics given for the two different stabil ities. Resistance, Sideforce and Leeway

The tank test results for this yacht are given in the form of 13 term polynomial expressions for the resistance and sideforce expanded to fullsize, in terms of the yacht's speed, heel angle and leeway angle. These po1ynomias are very convenient for the calculations that have to be made, but in order to indicate the hull characteristics in a more easily comprehensible form Figure L+ has been prepared from them. Here resistance is plotted against speed for

o o o . .

zero heel, zero leeway, and for heel angles 10 , 20 and 30 , with fixed

side-force values at each heel angle corresponding to the normal stability and 25% increased stability conditions. Values of the leeway angle have been indicated as parameters on these curves.

At the time when the study of this hull was carried out it was believed at M.I.T. that the relationship between sideforce and leeway was subject to scale effect between tank model tests and the fulisize yacht. A correction was applied for this which had approximately the effect of making the leeway

angles given for the fulls 12e yacht less by some 30% than those measured on the model at the corresponding speed and sideforce. More recently fulisize tests of the 5+ metre Antiope have indicated that the scale effect on side-force is small. Thus the present plots may well be based on somewhat smaller

leeway angles than actually occur with a 12-metre.

SAIL CHARACTERISTICS

The _CL and _CD values marked on the ordinate and abscissa scales of the plots really represent the lift and drag components of the air forces necessary to propel the yacht, divided by V . Sail Area. The sail

area assumed in the preparation of the plots was 1900 square feet (this represents the area of foretriangle and mainsail without roach for a repre-sentative 12-metre rig). Thus, if a rig of different area, or Sail coeffici-ents based on a different nominal area for the rig,are used the _CL and CD values for the rig must be multiplied by the area used divided by 1900

before being applied to the plots.

As pointed out in Part I of this report, preparation of the plots requires

knowledge of the variation of sail _CL and _CD with heel angle. The present plots have been prepared on the basis of the empirical relations given on page 13 of Part I

The sail characteristics indicated on the plots are taken from faired results of tests of a 1/9 scale model of a 12-metre rig in the wind-tunnel. They are intended to indicate the approximate values of the sail coefficients that may be obtained with such a rig but they may well not represent the opti-mum characteristics that can be achieved by adjusting sail trim etc. No

allowance for scale effects between model and fullsize has been included.

As is appropriate in this and most other methods of performance

calcula-t i on calcula-the air forces on calcula-the hul 1 _{are included with the sail forces. n the}

the bare hull gave negligible lift, and thit its drag was sufricient to in-crease the drag coefficient of the rig by an amount increasing roughly

o o

linearly from .015 at = 18 to .03 at r 25.7

The CEH values for these sails measured in the wind tunnel showed

little variation with heel angle or apparent wind angle over the ranges re-quired for the present appl ication, and corresponded to approximately 28 ft

fullsize. This ¡s ¡n the absence of wind gradient. To obtan performance

figures from the plots for this CEH we should relate the sail points with interpolated performance lines of the way from the lines for increased stability (CEH 26.2 ft) toward those for normal stabil ity (CEH = 33.5 ft)

Alternatively if we accept the M.I.T. assumption that the wind gradient causes some 20% increase of CEH we may relate the sail points with the

per-formance lnes for normal stability. It should be noted that the wind gradient will probably have some effect on the _CL and _CD values so that the performance figures thus obtained might not be exactly correct in the presence of a wind gradient.

INTERPRETATION OF THE PLOTS

In order to illustrate the use of the plots we will now consider certain inferences concerning the behaviour of 12-metre yachts which can be drawn

from them. However, it should be borne ¡n mind that we are here more con-cerned to illustrate the use of the plots than to enter into detailed discussion of 12-metre behaviour.

Performance in Light Winds

Consider first the plots (Figure 5) for sailing ¡n a true wind of 7.5 knots, on which have been inserted points representing the behaviour of a

12-metre rig in the wind tunnel at heel angle io', with boom angles 10 and

30

Let us read off _Vm values for boom angles 10 and 3, and plot these against the apparent wind angle

()

as in Figure 8.

We see that an optimum V of about L.7 Kn is achieved with ô = 1°

mg m

and o about 22 . For boom angle 1 , we can take the following approximate

figures from the plots

19 23° 11° 20.50 Ql O "2 y 40 °

and for optimum performance, which occurs about = 220, we find by inter-polation that c 10 and y = -5 approximately.

Although at o' _23°, V for _Orn = 3 is about equal to that for = 10, _{the wider sail trim ¡s inferior at the lower values of} . On the

other hand, ¡f by further reduction of the boom angle, or by other alterations of the sail trim, C could be increased above the value it has for o

= 1,

L m

without the simultaneous increase of _CD exceeding about 1/3 of the increase

of _CL , then the resultant sail point on Figure 5 would come nearer to the

V = +.3 line and the yacht's performance would be improved. This draws attention to the fact that in light winds sails should be trimmed to give

large _CL values provided that the increase of C0 ¡s not excessive. Experience in certain 12-metres has shown that this requirement can be met and optimum performance in light winds achieved by using sails of relatively large camber with the boom approximately amidships.

Another method by which performance ¡n the 7.5 knot wind might be

im-proved is by increasing the sail area. This would result in an increase of lift force proportional to the increase of area, and a somewhat less than proportionate increase of drag, since part of the drag is due to the windage of the

hull.

(see pp. 11 and 17-18) We might estimate the effect of such changes by moving the sail point upward from the o = I point along a line

through

this

point from CL = 0, CD = .02 (.02 being the part of the drag coefficient corresponding approximately to the air drag of the hull.

It

will

be noticed that for the 7.5 knot wind no plots are given for the

25% increased stability. This ¡s because the change of stability ¡s found

to have a barely significant effect on the position of the constant V9

lines. The only effect of this change is to reduce the heel angle by 20%. Values of _Vmg y and . do not change significantly.

Performance in Moderate Winds

For the 13 knot wind (Figure 6) two plots are superimposed, the heavy one for the normal stability case, and the lighter one for the 25% increased stability. Sail points have been inserted for wind-tunnel tests of a 12-metre

rig at heel angie 20°, boom angles 1° and 3.

When we relate the sail points to the normal stability plot we see that

the lo boom angle ¡s rather better than 30 and optimum _Vmg is close to 6.2 knots and occurs with near and slightly above 20.50. t is possible to

read off from the plots values of y and cp for the sailing condition e.g. at = 20.5, ô = 370 and cp = 22°

For this condition it appears that increase of _CL would only ¡rnprove performance if the associated increase of _CD was less than about 1/14.5 of

the increase of _CL

For the increased stability case, optimum V9 is nearly 6.14 knots and ¡s achieved with = 20.5°,

5m

= 10, y

370

and cp = 18°. In this con-dition it seems that some advantage might be gained by increase of sail area,

though, after allowing for the increased centre of effort height, the benefit obtained is likely to be small.

Performance ¡n Strong Winds

For the 18 knot wind, (Figure 7) plots are again shown for normal and increased stability and sail points are given for heel angle 300, boom angles

o o o .

1 , 3 and 5 . The improvement of optimum performance resulting from the

increased stability is now about 0.14 knots compared with about 0.15 knots ¡ri

the 13 knot wind and zero ¡n the 7.5 knot wind.

In the 18 knot wind it appears for the normal stability case that the largest boom angle, 5°, gives the best V , just over 6.4 knots, with

= 21.5 , y = 35 and cp = 30 . It is clear that neither increase of CL

nor of sail area would be beneficial. Indeed some reduction might be advan-tageous if the reduction of drag achieved at the same time exceeded about 1/7 of the reduction of lift. For the increased stability case, it appears that

the boom angle 30 gives the best _Vmg nearly 6.8 knots, with = 210

y 350 and cp = 270. In fact slightly better performance may perhaps be

obtained ¡n the normal stability case with a boom angle somewhat greater

than 50, and ¡n the increased stability case with a boom angle between 30

o and 5

CONCLUDING REMARKS

With the aid of the above examples, and of the discussion ¡n Part I of

the report, it should be apparent that the effect of different sail charac-teristics on the performance of a yacht can readily be deduced from plots of the kind described. However, as there are uncertainties in the expan-sion to fuilsize of model test results for both sails and hulls, it should be recognized that too great reliance must not be placed on the exact results obtained from performance predictions by this method, or indeed by any other method. Attention must also be paid to the fact that the present

calculations refer to yacht behaviour in calm water whereas yachts commonly

sail in a seaway which ¡s likely to have a considerable effect on their performance. Subject to those reservations it is believed that plots of the type presented in the present report will be of value in indicating the general trends to be expected in yacht behaviour and the directions ¡n which improvement may be sought by changes in rig characteristics.

In order that the general behaviour of yachts and the desirable characteristics of sails may be better understood it would be useful to prepare hull characteristic plots in the form described here for a number of representative yachts.

In future experimental and theoretical work on sails, regard should be had to the need for expressions giving the variation of _CL and _CD with heel angle. Such data will evidently be of value in connection with the present method of performance estimation and is likely also to be helpful in other studies of yacht performance.

REFERENCES

DAVIDSON, K. S. M., "Some Experimental Studies of the Sailing Yacht'', T. Soc. Nay. Arch. and Mar. Eng., New York, 1936.

A Review of the Gimcrack Sail Coefficients, DL TM 16, Stevens Institute of Technology, 1935.

Sailing Yacht Testing Technique, DL TM 17, Stevens Institute of Technology, 1936.

+. Investigation of Yacht Sail and Rig Characteristics, DL TM 55, Stevens

Institute of Technology, l9+O.

SAINSBURY, J. C., "4indward Performance Prediction", Southampton University Yacht Research Report 8, 1961.

CREWE, P. R., "Estimation of Effect of Sail Performance on Yacht Closehauled Behaviour", T. R.I.N.A., 196k.

CREWE, P. R., "Methods of Estimating Yacht Performance". Read at a meeting of Southern Joint Branch RINA & I Mar. E, 196k.

HERRESHOFF, H. C., "Hydrodynamics & Aerodynamics of the Sailing Yacht", T. Soc. Nay. Arch & Mar. Eng., New York, 1964.

r

1.

CL2

1.

i

1 0.

o

0.

o

Viz,-'

u 3O

e.10

o

o

01

0.2

_D20

_o

Fig I

_{Plots of 12 metre performance}

_{against CL & CD}

Rig

at heel angle 200

_{rrue wind 13 knots}

0.2 CD

03

Vmg:6.4

/

6.0

₅₆

/

¡

i

I

A.4z37T

As71

y

/

.226 A .34

A.2

25

A-3

A .23 2. J

/

I

.Au2

/

IVs668

( .331

6'lo-4

iji

iliiir

3

)

2

Vu 763

Vmg64 6.0

_5.6

A.3

!

/

/

_1V1667

Az4j1 :32.9

/th//'

e =

1 7

i

_I

_*O

9 :221

D 9 A 2

8

Ï//

A .2

6

/

I

/

A.15

AWA:o218°

/Az2

1

vas'.»

jiii1iii

14

CL20

13

1.2 1 .1

i

o

V1s37

Y 40

0. 0. 0.

Figicont. GJ

12 metre rig CL & CD at e:20,

Çm:1°&3°

Vmgz6A

-V-..-

06e

56

V3=5 1

=4i'21A

e:25o

2

IV,:74$

A:5z415

e237

:.

Az3 2. A=25

/

7 A:151

/

rV=7.17

A:23e.6

Le:123

II

I

01

_D20

1. 1. 1.

0

o

o

0.

o

01

_o2

0.3

D20

o

01

0.2

C

D20

0.3

Fig. 2

Plots of 12 metre performance against

_{CL & CD}

Rig at heel angle 20°.

_{True wind 13 knots.}

Vmg64t

6.0

156

7g

/./

7/,

tì/

///AWA20.5O

11H

I

Hl

r

Vmg 64 6.05.

11/

AWA:18°

Fig.2 cont.

_{Normal stability}

Stability increased 25°/e

02

01

02

01

0.3

02

Cx20

06

08

I

0$

10

cx20

10

10

12

AWA

o.18

:6.4

.-

6.0

AWA :

20.5

cY20

.6.0

Fig.3

Plots of

_{12 metre performance against C & Cy}

True wind 13 knots.

Enter with sail C & C

for heel angle 20°

® 12 metre rig C & C

at O20°, Çm° & 1°

Vrng :6.4

5.6

60

AWA:0.

23°

5.6

Cv20

5.6

Cr20

!I1

III

I Pf8

0.1

1100

1000

900

800f

u, m -J

700

600

500

400

ÇH:

1800-e-1o1

_{z 1450}

300F

-8:30°

60

8:20°

SI D E FORCE

z H z 4,000

Hz 3200

70

'z

H:3,150

/

H: 2,500

Z

Fig.4

12 metre hull characteristics.

Normal stability

Stability increased

25/e

AJ

ti

I

lilt

80

_Vs(KNOTS)

/

ÇHEL

ANGLE :e0

[LEEWAY ANGLE:A:0

i

1

11

o

o

o

06

Vmg4.8

/

4.4

/14.0

/

CL,0

Y:

/.

'/1/

I

/

i

35//e= 7.5

= 34

/

2 I

4'

_',

II

/

/

₇

'I

If

_/

/

/

I

25

y33

/

I

1.I

/

/

/

,

/

m

AWA18°

ABII

C010

-Vmg48

4.4

/.,/

4.c

k'!

15

¡

AWA

205

A

zl5

C010

-i ¡ i i I

ii r

o

01

02

0.3

o

01

02

03

Fig.5

_{Performance plots}

_{for 12 metre}

True wind 75 knots

Erter w;th sad characteristics for

10° heel.

1.

I

i

i

i

o

o

a

Ui

z 15

Fig. 5 con t.

Normal stability

25e1

change of

stability

or CEH changes

e ony

:56

e :13.1

Vrrs .4

/

e:IoK

I

I

I

I

I-I

iv-51.

A :2

2.6/

Aaii

AWA ::25.7'

/

Colo

111I1H

4

3 2

Vmg:4.8

/

Q,

/

4.4

CL,0

i

/

/

/

/

2

.5/

20.

eio

/

/

/

/

/

/

s,

/

46

I

/

/

/

/

/

,//

//

1

_/

/

/

_/

/

_/

/

_/

.9

.8

/

/

_/

/

/

_/

/

I

/

/

/

/

/

/

/

/

/ r AWA:o:23°

A

CD,0

IHI

Liir

0.1

02

0.3

Fig.6

Performance plots for 12 metre.

True wind 13 knots.

14

13

12

i 1

10

09

08

O.

o

o

12 metre rig

CL&CD at

e2o,

1°&3°

Fig.6 cont.

Normal stability, CEH 33.5ft

-

Stability increased

25°/e or CEH reduced to 262ft.

Vm.

6.4

_Q

6.0

.

5.6

CL2O

e2o4

A À. 15.

r-40

r

_/

/

i

e-io

/

'2

/1.5

AWA:o:23°

CD20

»iii itir

0.1 .2

04

o

A2

-

LIItIJ11d

01

02,-'

03

'- D0

V

Eß

64

6.0

Fig.7 Frformance plots for

12 metre

True wind 18 knots.

I

GB

64

₆₀

Vmg:1

¡

168

64

6.

f

1'

11

0.

0

o

o

o

o

12 metre rig CL & CD

at O3O Çm

1°, 3°& 50

0

0.1

0.2 CD30 0.3

Fig. 7 cont.

Norma! stability1

CEH 33-5ft.

Stability increased 25°/e or CEH reduced to 262 ft.

)

\ \

I t

e:31L

¡

/

:39

e=3c t

-j

\\\

e:30

IH

:39

e25

:37

-P

\

e

=2t

=37

e:

25)... 5 2 1 3

AWA:o

230

f

Az2 -

-I i i i I

6.5

6.0

Vmg

/

+

VT 75ka

I

AWA

20

22

AWA

5.5 I 1 5.51 18

20

22

24

18 5.5 18

20

22

AWA

24

26

VT

2Okn.

o o 1

BOOM ANGLE

+ +

3 BOOM ANGLE

X

X 5 BOOM ANGLE

AWA

20

22

24

S.J

I

AWA

24

18

20

22

24

Fig.8

Variation of

frìg with Apparent Wind Angle

for 12 metre

in Calm Water.

STABILITY INCREASED 25/.

NORMAL STABILITY

-X

+ X

60

6.0

F-65

651-

,--I

Vmg