Some experimental studies of the sailing yacht

ARCHIEF

N4i'-fL-

/cl3C

Lab.

v Scheepsbouwkunde

Tedrniscke Hog schooI

Deift

SOME EXPERiMENTAL STUDIES OF THE SAILING YACHT

By

KENNETH S. M. DAvIDsoN, MEMBEII*

Last year, in a paper 011 the cup defense

yachts (1) t, Burgess suggested that an investi-gation of the relation between the longitudinal and lateral resistances of sailing yacht hulls might prove interesting. In a discussion of his paper (2) I mentioned that such an

investiga-288

Watson as he watched Columbia beating

Sham-rock II in 1901, ''I wish Herreshoff had a

tow-ing tank"

(1).

On the Qther hand it was

extremely difficult to believe that an experimerl-tal method which had been successfully applied to steamship and aircraft problems for many years could be inherently unsuited to the study of such closely related problems as those of the sailing yacht. One or other of two con-clusions seemed inescapable either the earlie tests had been unreliable or they had not

evin-a ted those chevin-arevin-acteristics

of the hull which

really control the ability of a boat when under

sail.

rj

_{very few' published accounts were}

any-hung hut speiIic

(3). They indicated of

coluise that tJie eatlitu' tests had been made iii Owing tanks designed primarily for steamship

work. As that implied limited facilities for

measuring anything but the longitudinal resist-anees, it seemed reasonable to infer that many of the tests had been limited in scope. There

was evidence of another thing, however, which appeared,. to have an even more basic

sigiiifie-ance.

At a time whenwithout the modern

ideas regarding turbulent

skin frictionthe

erratic behavior of short steamship models had definitely discouraged their use, comparatively short yacht models seemed to have been the rule. Since nothing was advanced to show that a short yacht model was likely

to be more

reliable than a short steamship model, it fol-lowed that there was no real assurance that the tests had correctly evaluated even those factors which they had considered.

Compared with most steamships, a racing yacht has a rather higher displacemellt-length ratio, together with a rather higher maximulil

'-length ratio (both ratiosbeing based

on the

load waterline length). An average 20-foot load waterline steamship model weighs from one to

two toiis and requires a maximum towing speed

of about 5 knots.

A 20-foot load waterline yacht model would be almost as large as a

full-size six-meter boat. Because such a model

FIG. 1.YACHT Monm. UNDER TEST AT THE STEVENS

ToWING TANK

tien had already been started at the ,Stevens towing tank. II is the purpose of the present paper to eonsider the progress of this project, and to review' briefly the studies which led us to

undertake it.

It was clear enough in

1932, when these

studies were begun, that previous model tests of

yacht hulls had failed on the whole to produce

useful design information-. rrhiere _{was for} instance tile classic remark atttibuted to G. L.

* 10 rector. Ixpirimen to I Towing 'l'ank, St cw'ns Inst tote of Tfchn(logy, I lolioken. N. .1.

t }'lgure in parentheses refer to the bibliography at the end of th' paper.

Voul(1 weigh nearly four tons and would have to be tested up to at least 7 knots, a towing tank built for 20-foot steamship models could not, in most eases, handle it. Apparently then the short models of the earlier yacht tests had been a matter of necessity rather than of choicea point of view which led very naturally to the toitcinsion that the future of yacht model tests depended on either the availability of a towing tank larger titan any then in operation in this country, or the development of some means of getting reliable data from comparatively small

models.

SMALL MODELS

Following this conclusion, early in 1932, a general investigation of the behavior of small

models was undertaken. From the start there

WUS reason to believe that the difficulties were itot basic and unavoidable.

A good deal of

fundamental research,

chiefly in the field of

a eroclynamics, during the preceding thirty yea rs, had gradually brought the understanding of skin friction phenomena to a point where it

ciiiiicl be said with sonic confidence that the Principal source of the difficulties was an

in-stability of the flow pattern in the boundiiiy

ioii layer

(4))iOre recently,

various experiments tiad suggested that, provided the Reynolds' number was not altogfTier too low, stable turbulent flow might be established in the boundary layer by introducing a suitable disturbance of the stream into which the model moved (5). On the other hand, there had never been a clear-cut demonstration that the flow pattern could be completely stabilized or that,

if this were accomplished, the small model would become a reliable experimental tool. Accordingly our first investigation was directed to these ends.

The results of this investigation have been described elsewhere (6). But they are so per-tinent to the present discussion that they are summarized in Appendix 1 of this paper.

Briefly, it was found that, probably because of

the extremely easy charter of the

the shortns ofthe lower parts of the keel

the siyaeht form is ratherJBe

induce its own turbulence than__t_erge

steamshipYorm. 'l'liëretore, to ensure complete

turbulence, strong measures are necessary. Of the various shemeffIed, the application of a Strip oI coarse sand, extending along the stem from the waterline to the bottom of the keel, was the most successful.

Su1i a strip had an

250 200 i-Iso 00 so 0

Fir.. 2. - ConrAlusox OF UPIUGIIT RESISTANCES OF

'Gnicii'ci" AS PREDICTED FROSt TESTS OF 3-Foor LOAD \VATERLINE MODEL, AND AS DIRECTLY MEASURED

cxi -a resistanre of its own, to be sure, but this ipsisi a iiee was Joitud to be proportional to Ihe sfivare of the speil. and siisoeptihle if' ,opurq1-i

eva Ii at ion Lv nbscrv I nu' the _jffeet of altering

lie Si _P yitlth. The eneral philosophy was

established that failure to achieve complete

turbulence rendered a test useless whereas the magnitude of an extra resistance introduced for the purpose of ensuring turbulence could always be evaluated, and was therefore im-material. As a final step, the resistance curves

predicted from tests of three-foot load waterline models were compared, in two eases, with actual measured resistances of the full-size yachts.* In Figs. 2 and 3, which show these comparisons,

the curves represent the predictions, the spots

the individual full-size measurements. Although the latter, as in similar attempts to measure resistances in open water, are less accurate than might be desired, it is clear that the predicted curves represent them as well as any reasonable mean curves which might be drawn through them without reference to the model tests.

In all of this work, the forms were tow'ed in the upright position, through substantially still water.

In the full-size tests the yachts were towed, a little

to one side of the wake of the towing hont, by a long light line attached to a specially built spring dynamometer.

Speed was measured by a pitot tube mounted on a

frame-work which brought the measuring point about 8 feet ahead

of the forward end of th(' load waterline.

A L,ne Prethc from 'lodel Tests ---fed --. Measured Full-Size Resl5tances --:

--ai11

4 5 6 Speed , Knots

EXPERIMENTAL STUDIES OF THE SAILING YACHT

300 350 5o I0 5 Speed, Kro 5

FIG. 3.COMPARISON OF UPRIGHT RESISTANCES o F

tJ-METEI Bovr "JACK' AS PREDICTEI) FROSt fESTS o

3-FooT MODEL, AND DIRECTLY MEASUREI)

UPRIGHT REStSTANCE COMPARISONS

In as highly developed a class of yachts as the six-meters, it is often very difficult to judge the relative abilities of two boats. If they are nearly alike, the accidents of racing may so affect the final results that the true abilities are

masked, and even a whole season of racing may not show anything conclusive.

During the

summer of 1934. however, the newer six-meter

boat Jack proved to be distinctly inferior to the older boat Jill, which had a good record behind her. At the close of the season, it was generally

agreed that the failure of the newer boat could not be attributed to faulty sails or to incom-petent handling; a number of different sails had been tried and various experienced sailors had raced her. Therefore, the difference must lie in the hulls.

The upright resistance curve of one of the hulls had already been determined. It is shown in Fig. 3.

It was a simple matter to build

and test a model of the other. The two predicted curves are compared in Fig. 4.

Although this is only one case, it is so striking

that, for practical purposes, it seems to dispose at once of any idea that the upright resistances

are a sufficient measure of the general ability of a yacht hull under sail. When the poorer of

two boats has slightly more sail areaas in

this caseand appreciably lower upright resist-ances over much of the useful speed range, it is evident that other factors must be at least as important as the upright resistances.

It is an old saying, to which most modern designers subscribe, that yacht races are lost or won on the windward leg. When close-hauled, a yacht never sails in the upright position and she rarely moves through still water. Under these circumstances it would be surprising indeed

if the upright resistances were a sufficient mea-sure of the hull ability. What is so interesting about the comparison of Jill and Jack is the indication that a hull which has lower upright resistances may be lcs.s desirable than one with higher upright resistances. The upright resist-ances are probably a good measure ol running

ability, andTn fact tile poorer of these two boats

L,ne Predicted from Model Tests ... o MeourQd FullSize P'sJsfa,vces 0 8 4 5 7 Boot Speed-Knots

FIn. 4.CosTpursoN OF UPICIGTIT RESISTANCES OF THE

6-ME'I'IIt Bous "JILL" AND "JACK"

2 C 7

- ₂₀₀

q)

C

4-EXP.I RL\IENTAL ST IJDIES

mu well. But they uiiay evidently be worse

han useless as a measure o1 what serums to h of rumore I inporta flee, iianiely, the mlose-liauled abmi ity. Thus pouuit is eiuiphiasized because it

clear t iiiTsonme at least of the earlier tests

tailed to consider other factors than the upright

rcssta flees.

ieom additional factors which suggest

themselves as having a possible bearing on the

close-hauled ability can be considered to be com-pletely independent of the others. Nevertheless,

in undertaking to investigate the importance of some of these factors, it has seemed reasonable, as a workin" hypothesis, to assume

that the

effects of encountered waves can be separated from the effects of such things as stability, heel

and leeway. The latter are quite obviously

inter-i1d7They are presumably functions of the

hull form only, and they can be treated as

problems in steady motion. In the studies with which this paper is primarily concerned, the effects of encountered waves are not directly considered.

FORCE ANALYSIS

Mechanically, a sailing yacht in steady motion is a rigid body in equilibrium under the corn-bined action of three systems of forces:

Gravity forces (weights)

Air forces Water forces

The individual gravity forces are parallel, and reduce at once to a vertical resultant force acting at the center of gravity.

If the sails were parallel plane surfaces, and if tangential air friction did not exist, the local

air forces would be parallel and, like the gravity

forces, would reduce to a single resultant force

normal to the sail planes. Actually, because the sails are not plane surfaces, and because tangen-tial friction is present, the air forces are not necessarily reducible to

a force without an

irreducible resultant couple. On the other hand rio direct evidence of the existence of an

irre-ducible air couple has been found and, at least in

the sloop rig, no reason for suspectiig....the existence of very important air couples suggests

itself.

The local water forces are not ordinarily even

roughly parallel. Hence, except in the special

eases when the flow pattern is

symmetrical,

there is every possibility that irreducible water couples of important magnitude may exist. In

fact, the ability of a rudder to turn a boat is

sufficient evidence that they do exist.

OF TilE SAILNG YACHT

9i

If it be assumed that irreducible air couples can be neglected, the condition for equilibrium

system miiust ufTsct the conmUiumed resultant of time separato air and gravity resultant forces,

it follows that an

irreducible water couple Occurs whenever the

separate air aiidgravity resultant forces fajl

to lie in the same 1ane.

Consider the simple cases of equilibrium

shown in Fig. 5. Here, as in the more general ease to follow, the moving yacht is referred to a set of rectangular coordinate axes which has its origin at the center of gravity, the x axis being horizontal in space and parallel with the course, the y axis being horizontal in space and normal to the course, and the z axis being

verti-cal in space.

Case 1. A yacht running dead free with spin-naker, the sail trim such that the resultant air force is horizontal, and in the xz plane. Under these conditions the air force F and the gravity

force TV, because they lie in the same plane, can be reduced at once to a single force, with no

resultant couple. TIme force lies in the xz plane and has a line of action which, with a slope from

time vertical of F/W, passes through the inter-section of the hues ol: action of F and W. Its

point of a pplicatiomm is iiumiuiaterial.

For cqnilibriiummm, the opposing water force

must have the same magnitude and line

of action, and there must be no water couple. The couple is avoided ifthe rudder being central the plane of symmetry coincides with the xz plane; under these conditions y components of all local water forces cancel, and x and z com-ponents reduce to a single force in the plane of

symmetry. The force evidently has a vertical component equal to W, it will have a horizontal component equal to F when the equilibrium speed is attained, and its line of action can come

into coincidence with that of the combined air and gravity forces by virtue of the freedom of the hull to alter its trim.

Case 2. The same yacht running dead free as before, but without spinnaker, the sail trim and wind speed such that the resultant air force is identical with that for Case 1 in all respects

except that it

lies to leeward a distance o.

Under these conditions F and V/ are not in the same plane, and they cannot be reduced to a single force without a resultant couple.

If opposing horizontal forces, equal to F, be

introduced at point 1 in the xz plane, the system

as a whole is unaltered, but F' can then be

com-bined with W to form the same comcom-bined

4

EXPE1TIMENTA.L STUDIES OF THE SAILING

YACHT

<

1. 5LProjection 0 V xy Projecion yz. Projec+iOn

Case 1.Iiunning dead free with spinnaker

FIG. 5.ANALYSES OF FoRcEs

ant force as for Case 1 while F", with F, forms

the horizontal resultant couple F o.

The opposing water couple required for equi-librium is formed by inequalities in the y com-ponents of the local water forces which occur when, with weather helm, the plane of symme-try is made to lie at an angle with the xz plane,

as shown in the xy projection.

The fact that, under the conditions assumed,

the resultant water force is identical in all

respects with that for Case 1 does not imply that the speeds are necessarily the same for both eases. The asymmetry of the flow pattern in Case 2 may very welT mean that the hull resistances have been incrcaséd so that the same

force F is balanced at a lower speed.

In the more general case of a yacht sailing on the wind, Fig. 6, the resultant air force F can he resolved immediately into components F, F.. cos 0, and F11sin 0 parallel, respectively,

to the three axes. Then the projections of the line o1 action of the combined resultant of the

air and gravity forces on the xz, yz, and zy

planes pass through the points 1,

2, and 3,

respectively, and the magnitude of the resultant horizontal couple is indicated in the xy pro-jection. e5uIi11n+ Fore

I

xl. Projection Resuonty I.CDUI5 ___.__a...___ .Sk . ... .._. . - _&___s. Rudder (I) y. Projection x Boat 4 V xy Projec±ioo

Case 2.Running dead free without spinnaker Ac-r:rwo ox A BoAr UNOELt SArL

As in Case 2 of Fig. 5, the water

couple

required for equilibrium is formed by

inequali-ties in the y components of the local water

forces. In addition, however, these components

must be generally greater on the lee side than on the weather side to balance the lateral force

F11. This implies that the hull makes leeway.

GENERAL TEST PROCEDURE

Given the necessary test ecLuipment, enougli

sail data and a sufficient knowledge of the laws

of similitude, it would be possible to test a hull model by the direct method of scaling down any desired resultant air force, applying its three components to the model, and measuring the

resulting speed, heel angle, and leeway. The necessary equipment has been developed at the Stevens tank (see Appendix 2), but the sail data available at the present time are much too in-complete to make this straightforward procedure practicable. Consequently an indirect

pro-cedure, more or less

direct, has been adopted.

Under the indirect procedure, the model is tested at given speeds and attitudes (i.e., given heel, .leeway, and trim), and the required air

x X

EXPER1MINTAL STUDIES OF THE SAILING YACHT

293

Irreducible air couples may be neglected

The line of action of the full-size resul ant air toree lies in a l

noa1 to th

and passes through a predictable center of effort.

5l Reynolds' number affects the

tude of the longitudinal resistance coefficient,

Ti't i fThit of the lateral resistance coefficitt.

'T1ji:srrmese assumptions has already

been discussed.

The second is somewhat less arbitrary than it

sounds. Although it cannot be said to rest on experimental evidence, a study of existing sail data (7) indicates that it is reasonable, and it is at least simple.

The third is the usual assumption of aero-dynamics, that, under ordinary conditions, the lift coefficient is practically independent of the

Reynolds' number. The lateral resistance of a yacht hull corresponds exactly to the lift of an airfoil, and this assumption relates the lateral resistances of model and full-size yacht hulls in just the same way as the customary procedure

of aerodynamics relates the lifts of model and

full-size airplanes (8). The only difference between the two cases is that the yacht forms can be compared only at corresponding speeds; i.e., at constant V/\/1T

Consider geometrically similar hulls at the same attitudes to the stream, and at

correspond-ing speeds. With these restrictions the angles of attack (considering the hulls as airfoils) will

be alike and the wave patterns geometrically simi-lar. But identical angles of attack imply identical

lift (lateral resistance) coefficients, _Apu'' and

geometrically similar wave patterns imply iden-tical residual longitudinal, resistance coefficients,

Apv2

It may be concluded then that the

Ia teral, and the resid nal longitudinal resistances behave in time same wa.y and that, since A

and v2 1, thus making A u2 1V, both are

uroportional to the displacement.

in the yz imloiection (the cud view of Fig. 6)

the slope of the line of action of the resultant

water force is . It follows that, if

w + ,, sin 0

F11

W, the slope of this line is the same

for model and ship. Further, since the line must pass through the point 2, which is fixed only by the geometry of the full-size boat, its geometrical l)OSitiOn is the same for both sizes. Now it makes no difference, mechanically,

wilether the resultant water force is opposed by F11 and 1V, or by (F11 cos 0)

and (1V +

F,1 sin 0), nor does it matter where along the line of action of their resultant the latter forces

are applied. The two lateral dynamometers of the Stevens tank e ui ment a spI F11 cos 0 at a height considerably below that of the normal center of effort. The leeway is ajusted until the model supports the force (F,,

eos 0) for

which the test is to be made, and the model cen-ter of gravity is shifted lacen-terally until eqilb-rium is established at the desired heel angle 0. (F,1 sin 0) is applied by adding ballast. From the test data the point 4 and the slope of the resultant line of action can be determined. The

particular value of F1, which will put this line of action through the point 2 can then be fixed by repeating the test for various values, and interpolating. r1,1115 _{value corresponds to the}

actual lateral force which must occur in the full-size boat whenever she sails at th heel angle

in question, and at the speed corresponding to that at which the model was tested.

Assump-tionsotherwise necessaryregarding the reli-abi i y o t e usua static stasi ity calculations when important wave-making is present ar thereby entirely avoided.

Under sail, speed through the water is not a unique function of heel aiigle. With appropri-ate variations in the speed of the relative wind, the heel angle can remain fixed while the speed increases from a minimum when the boat is sailed as close to the wind as is practicable, to a maximum when the relative wind is brought roughly abeam. . It is a matter of everyday

experience, however, that the best speeds "made

good''

against the wind

(Viig = Vs cos y,

see Fig. 12) are associated with actual speeds nearer the minimum than the maximum. hence in any study of windward ability, model t in t ie vicinity of the minimum full-size sailiig speeds are of more interest than tests at other fspeeds. But there is no way in which the model

tests themselves can be used to determine these

speeds. More specifically, there is no necessary

relation between any hull characteristic and the

m.lriving component of the sail force FR, analo.

forces determined by measuring the equal and

opposite water forces which aredeveloped. r1 advantage of this approach is not oiiiy that it relieves hull investigations of complete

depend-ence on sail data, but also that, as will be seen preserttft, it may even be used to extetid the kiiowledge of sail behavior. It considers the sails without requiring predetermined air force

marnitudes.

In a)plyuig this procedure at the present

time, three assumptions are made. They are:

294

EX ['ERIMENTAL STUDIES OF THE SAILING YACHT

ye

+

z Projection

C. E

gous to the necessary relation between the stabil-ity and the lateral component F11.

FIRST TESTS

The first model tested by the procedure just described was that of a small boat Gimcrack, which had about the length of a normal six-meter boat, but rather less weight and sail area.

In this case the selection of test speeds for

Resu+or,t

-/J Y#

y (3) xy Projection yz. Project)on 4.

Ne4e Ookfecl Linc ore Model Forces

FIG. (LANALYSIS ov FORCES ACTING ON A BOAT SAIrIxa C1.osE-HAuT.En ON THE PORT Tcic

the model was governed by a curve, Fig. 7, of

speed against heel angle, measured in the course of a series of tests of the full-size boat under sail.

During these

tests the boat was kept

close-hauled, and she was carefuli sailed

experienced helmsman.

Fig. 8 shows the heeled resistances of the hull, as developed from the model tests, j

short ranges of speed which include ttual

sail ing speed at each heel angle. The curve of

45 40 35 IC 0 0 0 0 8 0 0 00 0

laI.jrai force ii-ecessariito cause

it. maybe

Ensib1e And it immediately suggested that the relative close-hauled abilities

of the

six-meter boats Jill andJack, for which the upright resistances had offered no explanation, might

TABLE 1.-GIMCRACK 'I, -U, a) a:: Z5 20 50 I) 0 C 0 . 100 50 SAa COEFFICIENTS

S The values shown in this line are the values read from Fig. 9. corrected for the relative heights of the point at rade (9 feet), and of the center of effort tlS.75 feet), according to the relationship (V4)=O.464 (h)"5 (V1)i, where

in feet, (Vi),. = wind speed at height h. in kn1ote. and (l's) i = wind eed at heieht of 100 feet. in knots.

which the measurements were h = height above water surface

Byextrapolation.

---.

t From Fig. 7. Heel 35 30°

/

5/

Speeds from Fig 7

IS1 /

from Fig.Z

_7,/

Curve 5 10 15 20 25 30 35 6.22 9.33 11.87 14.33 16.97 19.70 22.51) 87.6 172 248 317 383 444 496 5.22 4.57 4.00 3.50 3.07 2.64 2.26 3.32 4.50 5.18 5.60 5.87 5.97 5.97 26.0 53.4 78.5 103 130 154 175 1.55 1.42 1.29 1.16 1.03 0.912 0.795 26.1 26.5 27.0 27.6 28.6 29.7 31.0 Heel angle, 0 0

Relative wind, VA, knots5 Lateral force, PH, pounds

Lateral coefficient KR = 'H ,104X. _6.00f (.Sit)

VA-Speed, knots

Driving force, Fft, = R, pounds

Driving coefficient KR- , 104X 1.68t

(SA) V1r

Angle between the course and the relative wind, $. _25.8f

EXPERIMENTAL STUDIES OF THE SAILING YACHT

293

0

3 4 5 7

Speed - Krot5

Fio. S-HEELED RESISTANCES OF "GIMCRACK" AS i'IIEI)ICTEI) IROM MODEL TESTS \VITIE LEEWAY

1)OSsiblv be acconnte(l for oi the basis of the total heeled resistances. The models of these boats were available, and it was not difficult to

guess, with the Gimcrack curve as a guide, the proper speed ranges for the model tests. But a direct quantitative comparison could not be made until some relation between boat speeds

and wind speeds had been established.

The sailing tests of Gimcrack had included measurements of relative wind speeds, Fig. 9,

and some comparatively rough measurements of the angles $ between the course and the relative wind. With the wind speeds, the known hull

0 2 3 4 5 t 7

Boot Speed-l<no+s

Fi. 7.-RELATION riErwi:x B(A'L' S['El.:n AND flEET. .N(;LI 2IIEASt1{EI) IN '1IE I'rr.I.-SIzE BOAr "GrlcuAcr"

\VIIEN SAII.TNG CLOSE-HAULED

upright resistance (which is that of Fig. 2) is included for comparison. This chart showed us

for the first time the vr

lar.e increase. f

forces and tie sail (l ) = 4:t4 51111a1e

I04

feet. it hera tie possible to eiileiilate i set

itt ciii (0(tti(iotltS aS itinctiotis iti: t;lie heel iiii.le.

'1lit (rtleIiiali(tls ale ciVelt ill fable 1, and Fig. 5r0

it) sliiivs the tiliviS. 'fiihlL I iiicliide. ils(),

ia iri'tl va I u's of

With these ciiiilie ienls it became possible to 4

reverse the proceihitre used fur (iimcliic/:. that is, to work forward Iroiti known hull forces, to

wind a iid boat speeds. rather tim ii backward to 4.0

the coefficients t hieniselves. Thins a mechaiiisin

VLS provided for coitipleting the CompariSon between ,1iii and Jec1 by straightforward steps.

For a given heel angle

'I-w28 Since I",, is fixed by the model tests, time 8

equation F,, = K (SA) VA2 fixes the relative 24

wind VA.

The analogous equation

F = R =

(Sit) VA2 then fixes the driving component F, e

(i.e., the resistance R which the sails will

balance).

The spee(1 through the water is then read from the en rves of total, heeled resistatire ( l'i. Ii shows I hiese curves for .1 iii).

(ii) Fituahlv, with t lie angle of: colt rse to

rein-five wind / a vector diagram (Fig. 12) gives flue

liiue wait! L, liii' nile of course to trite winch y

and the sio'etl uii;ide gitoil lnq.

hhie result; is l"ig. 1.1 \VliL('hI ShtO\VS sliced

dir-feieties ill the siunie uhireetwit, and of the sante

FX i>1 R I t I N'l'A T Sr.I UI) I IS (1)I'

TIlE Si\ILTNG YACIIT

2.0 i2 Driving

r

Lolerat CoefiCi2nf KH oefficient 1( 0 5 0 5 20 25 30 35 40 45

Reel Angie - e-oegrees

tic. jli.---4,ij, (,,i:iitii:si's lIi:iiirlEi, 1iOr,t SA1F,TNO

i,,, lm;i.i.-Sizi: lloicr ''(iiici\cu'' %Ni) 3i,ucr.

'Ii;srs UI Ilium C o,ilij ll.uir= K c,'iiiIu,il, X

order of magnitude, as those observed in the

a e t.0 a 1 1 oats.

Wit Ii this result the broader aspects of the

q nest it til. not alone of the reliability of Tno(1e1 tests as such, bitt. of their almil itv to be of direct use in actual prflblei)15 of sailing yacht design,

o'ut rod to have been a nsweied. r1hiere was

little Ieisoii to suppose that details of both tile

test amid calculation procedures might not have to lie not, titled, or t hat; I lie (i,uiciack sail eneiti-('ieiuts Niuhl he eoIuSu( broil more titan a first

aj)pruxiitual iou. But, with no indication of a

hiasie Fallacy iii the approach, critical studies of

flue various factors and of i:hie implications of the whole method could be unchertaken with

some confidence. Accordingly the emphasis was

shifted to such studies. These have not yet

advanced to the stage whore a detailed discus-siomi is warranted, lmiit one or two of them may

be uitentioned briefly.

"Gt1cRAc1"SAIL COEFFIC1NTS

The most striking feature of the Gime rack sail

eoeflic ieiils is the very pronounced droops of both

. _,_.1__.__. - __

-.-n

8 0 IZ 4 6 8 2.0 2.2 24

R&Gtive Wind 5peed-t(not5

Fin. 9.Rlf.ATtON flEiwEEr RELATEVE WINI) AND

11J:rL ANGt,J .\IEASUIIFI) IN 'rilE FtJlj.SuzE BOAT

"C 1MCTIACli" Wit EN SAIll NO Cuosi:-1T, IILEI) 45 40 35 O25 a, aa '5 z l0 5

300 aso o0 00 50 0

EXPERIMENTAL STU1)iFS ()I

TILE SATLIN(J YACI-IT 297

Fro. 12.Vj:c'ron DIAGRAM

FOR DETERMINING V, y, AND

Vmg WHEN V, VA, AND

Aiu KNOWN

has sometimes been supposed in the 'ast but, since ie oat speed rea.c ics a definite ItIaXirnhIIrl Fig. 'T) while the wind speed does riot (Fig ti),

there is no way 01 avoiding the conclusion that increasing heel angle musLbe accompanied by

either an enormous reduction in the driving force

cffkient or an enormous increase of hull

resist-hnce. The huTI resistance wiIl be discussed In the meantime, it is interesting to investigate the sail coefficients from a purely aerodynamic point of view.

TABLE 2

ANALYSIS OF SAIL COEFFICIENTS

Line (a) in Table 2, and Fig. 14, show the ratios between the coefficients at 10-degree steps of heel angle. These ratios are seen to increase moderately with the aughe, so that while the resultant coefficient ItT [(see line (h) and Fig.

14)] decreases materially, the effectiveness of the

rig increases. Now any contention that this is a

false in d icJat ion is eq UIVa I cutbecause the lateral are probably the more reliable of the two sets of

forces from which the coefficients were

calcu-So.ed Soeed 3,50/

/

/

esistoncesat Colculoked Speed 330 as° ao°

I,

Mode God.V,,,5 Throuh Water,\'5 350 3S 35I 3O0HeeI 300 3Q0 3O. Jill 050 _Jock 050 Jock I5 Jill 250 20. I5Heel Ii IO0__ Ii 50 50 I00 50 50 Heel AngIe, 8 0 10 20 30

(a) K,,/K,, from Table 1 0.280 0.310 0.331 0.345

(b) KT, 1O' x 6.23 4.77 3.70 2.80 (e) CT (= K7. X 294.5) 1.835 1.405 1.090 0.825 (d) C, 1.807 1.389 1.079 0.819 (e) CD 0.324 0.218 0.149 0.105 (f) CL/CD 5.58 6.30 7.25 7.84 2 3 4 5 7 Speed -XflOt5

Fio. 13.00SIPARE50N OF CALCULATED CLOSE-HAILED SPEEDS OF TIi.E 6-Mu.:TER Botrs "Jrr,r," AND "JACK"

Vmg V COR y

Book Speed -Knots

FIG. ILHEELED RESISTANCES OF 6-METER BoAT

"JILL" AS PBEDTCTED FUOM MODEL TES'rs WETII LEEWAY

the curves in Fig 10 with increase of heee.

liependent evidence has been discovered which throws any real light on the reliability of the droops indicated. They are rather more than

3 4 .7 0'eO w IS U -o a, '4 0 JO a, 0 C a, a

]4 XI' E RI \I ENTAL srr 111 ).1 !S ( )F1 lZlIt'(ltO a COiit('ill iOu that the driving eoefficien t

euirvt' çFig. 10) does not, droop enough. But t here is rat her more reason for supposing tlia t it droops to,m much. .[tdeiives from model tests

run in still water, whei'eas the boat act miii Ily

sailed (at the higher heel angles) into sonic chop. aflTmouiii resistances from this source were probably not great. but they certainly cannot have beeii negative.

'sVIicui they were first calculated, the coefficients for low heel angles, where reasonably direct corn-parisom is with airfoil characteristics are possible, seemed large, even allowing for the possible 'slot'' effect of the jib. It was then discovered that the extrapolated values for 0 degree heel

were in almost perfect agreement with

the values measured by Warner (7)

for a metal

plate cambered to approximate the draft of a sail and tested without jib or slot in a wind

tunnel. Taking Warner's camber No. 4 at the

angle of course to relative wind /3 deduced from time Gimcracic tests. 25.8 degrees (Table 1). and recalculating to put the wind speed in knots, his values, compared with the Gimcrack values, are

Varner C imerack

No. 4 eamber 0 heel angle

KR 0.00171 0.00165

It,1 0.00605 L410600

The aerodyuanm ic lift-drag rati( showii in Table 2 depend omi the angles o course to rela-tive wind /3 as well as on time coefficients them-selves. Their general order of magnitude is low

compared with those of ordinary airfoils work-ing at the angles of attack estimated for the Girncrack tests.* _{But low lift-drag ratios are} not surprising in themselves nor are they

incon-sistent with Warner's data. The fact that they

increase slightly with the heel angle is of course

due primarily to the way in which the angle /3

widens out. There is an interesting check on this. It can be shown by geometric construction

that th nungouhTëh appeared to occur

is just about that necessary, with constant sail trim, to cause a constant angle of aflack at all heel angles. Now the boat was sailed largI

'by the luff of the mainsail during the

tests,

so that the angle of attack must have remained

roughly constant. Thus, while there may be

in-stinctive objections to the idea that the lift-drag ratio increases with the heel angle, it is diffi-cult to find tangible evidence against it.

The aerodynamic comparisons which have just

The angle between the mean wall and the coumre waR eMii,n,IIC(I to be about 2 _{degree,, which, with an angle of}

25.8 degr, between the relative wirni find the eouree. leaveR about 3 degreeR for the mean angle of attack.

riiii E SAILING YAChT

F'm. 14.ANI,ysIs OF "C.ii!CIiACK" SAil. Co-El-FICIENTS ShOWING RESULTANT COEFFICIENTS.

LIFT AND DIIAG C0ErFIcIENTs. AND TUE ANGLES BETVIN TIlE COURSE AND THE RELATIVE

WIND (K CoEFFIcIENTS CAN BE REPLACED BY C COEFFICIENTS WITHOUTALTERING THE

RELA-TIVE LENGThS OF THE VECTORS 1

been discussed are largely qualitative. This is

inevitable. Few direct tests of sails appear to have been made and the rig of a yacht is dif-ferent enough from an airfoil, or even from Warner's metal plates, to render accurate

quan-titative comparisons practically impossible.

How-ever, the fact that the qualitative comparisons do not present difficulties is important, and in any ease the usefulness of the coefficients in studies of hull behavior is influenced more by the reliability of the droop with heel angle than

by anything else.

Perhaps the most interesting check on the coefficients which has yet been obtained is a very good agreement between the curve of speed

against heel angle calculated for the J-boat

Weetamoc (by the same procedure as that used

for Jill and Jack) with

the actual measured speeds of boats of this class. This check tends

to confirm not only the absolute magnitudes of

-j 800 700 r000 x LI. 500 .4-a 4-.-_{, _.J} '.- 400 0) a I. a) 4-a -J 00 I 00

EXPERIMENTAL STUDIES OF

THE SAILING YACIIT

299

Dro CQLJ5d by

30 Heel atone

'V

Parabolae orcolculg

ratio -.

ipply1fl' 11mm to stOol) rigs of very different sizes.

There is nothing final about the Gimeruck sail coefficients, but they have been used to calculate

the speeds of a number of boats, and there has lmcn un indication of any essential inaccuracy.

IIULL RESISTANCE

Fig .15 shows a separate study of J11's

resist-ances at a speed of 6.03 knots. This chart for the huh corresponds to the so-called polar dia-gram toe COmpIPI C 3 irl)IaIICS commonly used in aerodynamic analyses, and it has beeti given the

1 to S rat in of scales customary in that work. The upright resistance, and the lateral resist-ances corresponding to the etual stabilities of

the hull, are indicated

It will be noted that, at either

of the heel angles shown, the "drag" added by heeling alone is very much less than the"induced drag,"

and that the latter, as for an

airplane, is ap-proximately proportional to the square of the

''lift.''

The inference seems reasonable that the extra

resistance caused by heeling alone is primarily

FH Corresponding to stabitifies otbot -0° 10 Induced Drag at 30° Heel --/ / 0 _{' /} 30 / // I

0/

00 0 .0JeeIed Resis-ione plotted in Fig.11

\

V

Angles of Leeway lJprght

0,"

Resiskance-.. , 0 50 lOG I50 W0 250 Longitudinal Re&tsianCe - R - Lbs. (Drag)

Vie.. 15.PoI,All ]).C;ILtn ion nULL OF G.METF:R BOAT ".T1d." AT 2O-1)niiEE

AND 30-I)KOI{EF- hEEL ANGLES,

AND AT 6.03 KNOTS SrEn

the result of having altered the wave-making characteristics of the form. This inference is

strenthened b

the ra it

rowing i ,rt-amice of the resistance as

the lied ane0Pd

20 degrees. Insofar as

invali ate.s the old impression that ''1engthene afting Iines,"or some other supposed peculiarity. of the conventional yacht form, reduces the heeled resistances What seems more probable

is t iat the yacht form is relatively successful in avoiding large additions to the wave-making resistance as the heel increases.

From the approximately parabolic shape of the induced drag curves, and the fact that the

curves

for the two heel

angles are nearly

parallel, it may he reasoned that, for analytical purposes, the induced drag can be considered to be practically independent of the wave-making resistance, and that it can be studied from a purely aerodynamic point of view. Table

3 gives the calculations for the effective aspect

ratios which correspond to the parabolae drawn on Fig. 15. It shows also the geometric aspect ratio, calculated for the lateral

plane in the

upright position in still water. For this calcu-lation, the lateral plane has been

taken as a

-v--300

_{EXPERIMENTAL STUDIES OF THE SAILING YACHT}

hali-aitfoil. with its axis in the waterplanc. The

Iil 110 bet Wi'eii the t\vo aSl)'.'Ct 11ItiOS wli iehi is

esst'lII ial lv _{Oswald's airplane} efIicit'iiev lac-ror. (1)) is seen to be about ,O per cent, or

eoiisiderablv less than I hat of most airplanes. IAIII.E NOUCtII) D1Lc CLcu LATIONS ion "JILL"

.T ii. 03 1'NOTS

heel tuigle I), degrees 20 30

Actual F11 of hoat,* pounds 496 713

I at actual F11 ,' pounds 161.0 206.6

R at I' = O, pounds 136.0 149.8

Induced drag R1 , pounds 25.0 56.8

Effective aspect ratio f 0.437 0.396

Oconietric aspect ratio ff 0.826 0.826

Ef!icicnev factor, per cent 52.9 47.9

From Fig. 15,

t In aerodynamic symbols (AR) CL2 L2

Cm -ir _S

F2

For the yacht hull, effective (AR)

-irJI (LA) 2 (2 )< dra 102

tt Geometric (AR)

2 X (LA) where

(L.4 ) = projected lateral area in the upright poi1inn, draft 5.39 feet, and (L.4) = 70.4 square fue'.

The geometric aspect ratio is governed by the

draft Ii mitatioits imposed by the measurement rules. The low efficiency factor is another !llilttCl. _{It eati p('l'lIapS he explained in a} gen-eral vav 011 _{1 he ground that. \vllile the lower}

Fig. 16 is a comparison of the total resistance coefficients of a series of six-meter yacht forms of varying size, with well-known plank friction

coefficients.

In the tests on which these

co-efficients are based, no attempt was made to induce turbulent flow and the surfaces were in all cases very smooth.

The lower speed ends of the model curves, where wave-making is negligible, _{appear to form} parts of a continuous curve having much the same shape characteristics as those of tile com-bined plank curves. The indication that the transition from laminar to turbulent flow begins at about tile same Reynolds' number as that at

S Digest of paper previously publIshed (0).

APPENDIX 1

INvESTIGATIoN OF SMALL MODEL BEHAvI0R*

portions of the keel are fairly effective airfoil

sectiulls. tin' ma in body o the hull is certainly

a very ineffective a ii'I'oil. A along other things,

limo hict that reducing the leeway to zero does not clmninate lateral resistance is an indication

that the hull proper makes jill) mrtant eon

tm'ibu-tions to the lateral resistance.,

Fig. 13 shows that the speed selected for the Fig. 15 tests is fairly representative of the ac-tual sailing speeds at both of the heel angles investigated. Now it is clear that, at speeds in this vicinity, the stabilities are nothing like large enough to bring about the maximum

lift-drag ratios of the forum. Thus, since the driv-ing force of the sails is roughly proportional to the lateral force [line (a) Table 2], independent increases of stability (by lowering the center of gravity, for example) might be expected to im-prove the speed. Jack has lower stabilities than Jill, which partially explains her generally poorer close-hauled ability. But the fact that she has lower efficiency factors is needed to make this explanation convincing. Although they have not yet completely clarified the matter, other studies have mdicatecl that increased stabil-it.v may not always improve the speeds made good at moderate heel angles. One reason for this is that, at mnoileitite lied angles. the boat speeds anti Ihe relative wind speeds become so

ni'ar]v alike that a small increase in boat speed

widens the sailing angle y very appreciably.

which the plank transition usually starts

sug-gests that yacht models have little tendency to

induce their own turbulence.

It was thought at first that the residual co-efficients for all the models of this series might be considered to be the differences between the

total coefficients and a base curve such as that for model D. _{It was then observed that this} did not result in identical residual coefficients

at constant speed-length ratio, and that the

vertical differences between the curve for model

D and the plank coefficient curves were very much greater in the laminar region than in tile turbulent region. Reasoning that tile latter

c oo

ii

1.1/ 0 00S C.007 11 0,005 0 o, 0.004 C 0.003 II, 0002

of a sphere, that is. to an important alteration

in the point of separation of the hoiiiidary

layer, it was concluded that, at least for full-bodied forms, the basic differences ol behavior

between

I he laminar and turbulent

regions a iiiounled to more than a mere difference in I he

skiii friction coefficient, and that tests iii the laminar region could nut he used to predict

resistances in the turbulent region.

In Fig. 17, the coefficients for a 3-foot load waterline model, tested with and without

in-0010 0.009 o0o 0.007 0.00E 0.00 5 0.004 0.00 3

EXPERiMlNTAL STUDIES OF THE SAILiNG YACHT

0.00

v1/V ReynoId3 Number

Fiu. I7.COMI'AiusoN OF TESTS OF 3-FooT MODEL OF 6-METER BOAT MADE WIT!! ANDWITnOIJ'r

INDUCED TURBULENCE

9 -3

Reynolcs Number

Fic. 1(;.COMPATUSON OF TOTAL RESISTANCE COIFFIC1ENTS OF (i-METER BOAT FoRMs OF VARIoUs SIZES WITH PLANK FIuCTI0N COEFFICIENTS. Ar TESTS \VI'rLIOUT INDUCE!) TURbULENCE

dueed turbulence, are compared with the same

plank friction data and with the curve for model

1) of tile pre\'ious figure.

It is clear that the

induced tiIrbilleIlCe has very materially altered the coefficients, and there is evidence that the trim usi tiot to turbulent flow has been completed

at it Beytiolds' )llllflbCF of about 6 )< 1O. Figs. iS and 11) show the resistance coefficients

for two models tested with different widths of sand strip to determine the added resistance of

the sand. In each ease the curves for the

dii-'. /,?c-CF

-Rough 2 Widths ningof fougbened-'

IP

Piqin Mu/I Id'

C-forO7/,/

U

p

Model Refercncc prC' D included from Fig I I I '

---j----

fl5;/-.''3

b-1ft

e.:s,tC. j8/-433i '.I.L._t L.WL.l C L.IVLI) V 3

4'5-'7 B

3 4 b 0 I

EXPERIMENTAL STUDIES OF TILE SAILING YACHT

0007 0 LI 0OO( 0.01 0.0 0.00 0.004 0.003 0.002 0.001 0

Fxo. 18.EFFECT OF VARYING SAND WIDTH ON THE RESISTANCE COEFFICIENTS OF A 3-FOOT MODEL

C 0.00 0.006 o 0.005 '-I 0.004 0.003 0.001 8 0.00) 0 3 0 'vl/ ,.' Reynolos Number

FIG. 19.EFFECT 01' VARYING SNn WIoTIE ON IIE

RESISTANCE COEFFICTENTS OF A 3-FOOT MODEL OF

"C IMCRACK" 0.00 0.00 0.00 4-I) 0 U 0.001 0 4 0.7 0 II 5 6 7 5, Reynolds Number..0.7--- 0

iireiit widths have I,lie same shape, will, verl:i'a I

displaeenients as ri'qiiired by the test data. \s this procedure cannot be sai(1 to have abusi the' data, it is clear that altering the sand width

merely altered the magnitude of a constant

add,-ton to alt total eoeficients. lit other words, I IC

sand strip caused au additional eddy resistall(e. proportional to the square of the speed. rrhIe auxiliary charts in these figures show that, for narrow widths, the constant addition to all coefficients is practically proportional

to the

width (the length being held constant).

Fig. 20 shows the method employed to

investi-gate the correlation between the tests shown in Fig 19 and direct measurements of the full-size resistances. There is no essential difference between this method and that ordinarily em-ployed in predicting the resistances of full-size vessels from tests of large models. Assuming

no basic change of behavior, the important

thing is to find out by how much the total co-efficient (at constant speed-length ratio) drops off as the size of the form is increased. _If

Froude's major assumption of the

additive nature of skin and residual resistances holds, then the change of total coefficient produced _by a change of speed-length ratio is independent of the size, and the drop with increase _{of size} is a function of the Reynolds' number _only. Schoenherr's plank coefficients were used in this

comparison, and were subsequently adopted _as the standard of the Stevens tank, because they

a S I it3,.₁₈₈ 1W'uthof Ofl :1 a..-L.ItI 317/7d '8

-SIr,,

Curl-es Drawr, with

Cnstnf O,ftererice : 07 0.8 0,9 1.0 1.1 I.? 1.3 1.4

___RUIU

U

W 0 _J 9thof -POU9hfl Curves

Con5tantDrawn withDifference..

-V - ...-Correctec,' Curve 0.7 0.8 0.9 1.0 1.1 /.2 1.3 /.

I

Coefficient iigi9 (Correctea'

am.

11111

Moc/e/'esJstc,,oce.. Curve-) Curve -.

'

Fu/A5/ze Prea',ctea' 2cient

__

V 0.6 0.7 0.8 0.9/01/12/31.4

IIii

ill

. 6 7 8 9 10 0.? Reynolds Nurnber0.7.

Fzo. 20.CoEazr.ATrozq OF MODEL AND FULL-SIZE RESISTANCE COEFFICIENTS _{OF "GIMCRACK"}

U0. 000

Dead Weight pan

EXPERIMENTAL STUDIES OF THE SAILING YACHT

303

are based on a very comprehensive correlation of most of the reliable, completely turbulent

plank tests which have been made.

In designing the apparatus for making model tests with heel and leeway, the principal prob-lem was to control the leeway, and to measure

Carriage Rail Track - _Roller YZView Fixture in Model XZ View Auxiliary Leaf Spring Da5hpot Slot for Rote r"j XY VICW

Fin. 2I.LTERAr. DYNAMOMETER ARRANGEMENT

the lateral force, without restraining the model in any other way. It was apparent that the heel angle could be adjusted by shifting the ballast

APPENDIX 2

SPECIAL TEST APPARATUS

XZView

BIBLIOGRAPHY

(1) C. P. Burgess. ''The America's Cup De- Architects and Marine Engineers. Volume 43, fenders," Transactions of The Society of Naval 1935.

Fig. 2 of the paper shows the correlation ob-tained for this ease, in the more usual form of

resistance vs. speed.

laterally, and that the vertical component of the sail force could be applied by adding ballast. It was necessary, however, to apply the lateral component F,1 cos 0 of the sail force, without restraining natural trim changes, and without interfering with the measurement of the longi-tudinal resistance.

Fig. 21 shows the general scheme adopted. To eliminate yawing, and to provide for locat-ing the fore and aft position of the resultant, two lateral dynamometers are used. They are of

the deadweight type with a

light auxiliary spring. The total motion of the lower end of the vertical arm, through which the force is applied to the model, has been kept as small as possible so that lateral motion at this point will not cause an appreciable alteration of the lee-way setting. The small motion is multiplied optically.

Longitudinal slots on the dynamometer arms bear against rollers attached to rotating fixtures mounted near the ends of the model. The

lee-way is adjusted b moving the lateral dynamo-meters bodily on cross tracks attached to the regular towing carriage of the tank.

In the actual test procedure, the heel angle is made the independent variable. Thus, at the beginning of a test, the fixtures in the model are rotated and clamped so that the rollers will have vertical axes when the model is at the

desired heel angle. The model is towed entirely

by the regular longitudinal dynamometer of the tank equipment, the slots in the arms of the lateral dynamometers allowing the freedom of longitudinal movement necessary to the proper functioning of the longitudinal dynamometer.

:.04

EXPERIMENTAL STUi)IiS OF THE SAILING YACHT

() K.

-A I. I)avidsitti. ilisetissioti of

refer-citee (1.).

iiiitt',it/ittn. otl'

lit' Oeit't.v of Naval _\tcltiteets otiti i\liiriiie .Etigiiieeis. Volume -13,

1935.

S. l3ut-gess iii 1'luc Sportsman, May, 1927.

C. B. Mill ikmi. ' The Boundary Layer and

Skimi Frici len for a Figure of Revolution,''

i)'tlTh-eICIiO)iS of the American Society of Me-chanical Enoineers, Volume 54, 1932.

K. E. Schoenlierr. "Resistance of Flat Surfaces Moving Through a Fluid,'' Trans-actions of Time Society of Naval Architects and Marine Engineers, Volume 40, 1932.

K. S. M. Davidson, ''An Experimental

MR. \V. W. SMITH, Vicc-Prendcnt: Referring to Figs. 16 to 19, turbulent flow is clearly iicees-sary and important for accurate results. rfite method of inducing tmmrhttleuee. anti of ('litItiltilt-i112 flue error tmmst'tt I IteiPb\', appears to he

mtriiimtt' amid mt'lUmI)lt'. It vomuld be d('si lute fit

adopt tins hid hod for all intidel tests to cmi-Bate the errors \Vitich are frequently iij)[)tit'Ht

at low sl)eCt15.

Referriimg to Fig. 20. it appears that time

surfaces of tIme model and of time boat are equally smooth. and they are the same as that of time varmi ished plank. This is not time of Ships, where time rougiiiiess is considerably more thaii

that of the model.

At time lowest speed-length ratio in Figs. 19 and 20, it appears that the wave resistance is practically zero; that form resistance coefficiemit

for the model and for the boat is the saute;

that its value is 4/] 0 ; and, that the form

resist-ance varies as the square of the speed.

accord-ing to general theory. More iii formation on time

forimi resistance of various forms of hulls is

desirable.

It has become common practice to use the form of. prescmtt.atiomi in Fig. 20. This form

shows clearly the laws of frictional, form and

wave, resistance, anti the scale effect.

Tue amzreemnemit between the model and the

boat tests shown mm Figs. 2, 3 and 20 is very

good.

it

is much better than that of model

propulsion tests and, ship trials. Other model tanks shmoimbl take note of this.

DISCUSSION

'I'tuing 'l'mnk for mtiall Models,'' Tiautsue/tie. of. the A.ititriciii tcitty of. Meeli;tnical Eni-utters, (.Jonr'iutti of A pplicd 31fcI,.anu:x ) , .Jtitle, 1936.

E. P. \Vam'ncr immi Shatswelh Olmr, ' ititttlima niles of Vat:lit sails.'' 7'iunnteIion. if

'Flie Societ- of Naval A rcltitccl.s and Ma Hoc Eimgimmeers, \Tolunme 33, 1925.

T. von 1.arman and C. B. Millikan, ''The Uses of the Wind Tunnel in Connection with Aircraft-Design Problems,'' Transactions of the

American Society of Mechanical Engineers, Volume 56, 1934.

W. B. Oswald. ''General Formulas and Charts for the Calculation of Airplane Perform-auice," N.A.C.A. Technical Report No. 408.

The author deserves much credit for

obtain-ing such (on1h)lete aimti accurate resm.ilts with sumdt liuttited t't1tmipmnemtt and staff; and, par-tii'tmlarly. fctm' provimt2 that his imiotlel tests

prt'tltt aet'ura.It'Iv I lie perfoi'mmiaiite of the boat. I wish to comtLrrimttmlate hint oil his very

inter-esti mm a itti val tiable om per.

1)u. G. KEMI'F, ,41etnbcr: The method of

testing a sailing yacht developed by the author at flue Stevens towing tank is very ingenious

a]ld the results show that it

is also effective and reliable, at least to a certain degree.

Cer-tainly it is one of the most difficult things to do iii tank work to test a model of a sailing yacht in a sufficiently accurate manner. I say this from my own experience, because I have tried to do similar work some twenty-five

years ago.

The model was towed by two

falling weights, one for the drag the other for

the lift

as components to the relative wind force which was kept constant tom' a set of

tests. Time model was pulled fm'outm a certain point above the waterl inc where time center

of wind pressure was supposed to be. This

point of attack was shifted after each iuii

over the whole field where the center might have been. Under that force, time model took a certain heel, leeway and speed

and it was

a relatively easy method to compare time

behavior of two different models under time force of time sonic relative wind.

EXi.EltiMENTAL STUI)1ES

gear wliieh al lol the Jilollel to titove ir('t'ly,

bitt I iited it otilv OlieP and I iiever had the

0Pluit (iii IV ((I _{lest ing iirhI foinis ag;Liii.} .1

ani coil viiicetl that the iiiel 110(1 i(lOpt ('d by

I lit' a Ut lior is inutli inoit' retiihle.

In Ilit' inca ut tue tIn' kuuowle 121' has advanced 50 ltIiltIi I hat ii is possible

to rely even on

test i i. snia II models. if certa iii precautions have

been taken to assu it' lii rhiilent flow. This is a very iiiiportaiit result: of the author's work.

iegardiiig the results, we can compare the

effectiveness of yacht hulls with an airfoil.

The keel itself has fairly effective airfoil

see-tiotis. but in one vav it is acting badly. This

is because the lift coinpoiieut of the keel tends

to increase the heel of the boat and to

de-crease the effective wind pressure. Perhaps

it would be an interesting study, if it is not

possible to reduce the ]ift of the keel by turning

it to a lower angle of attack. Then the

lee-way might increase, but the heel will decrease and the wind might give a greater effect.

I think we must be indebted to the author

for the development of a small tank with a

very effective measuring device and for his

iIiUT'liiOiTS \VOPk (IL testitig 1iiO(l('ls of sai!!li!4

yachts.

Dn. Furnr:nicm S. .1 )T:1ii:Niiuc!t. Jn., li .4/or:

it

is

an jnteresting fact

that experimental mel boils which have proven thueinsel yes invalu-able, accurate amid necessary in one field of en gilleering are f req i ientl y treated with suspi-cion, disdain or even ridicule when applied to analogous investigations. At present treat-ment by analogy seems to be the ray of hope in

overcoming thi e increasi ii g requirements of

specialization. Thus many problems of a

physical nature dealiiig with

boats can be

treated by methods and analyzed by results obtained from general liydroclvnamic and

aero-(lylia Iii IC investigations, particularly those

dealing with airpiaiies. Professor ljovgaard,

from Ii is masterly mathematical treatment o.f

submarines, was nub to become almost at once an authority on Zeppelin-type dirigibles by merely changing the physical data of the

medium in which the shiq) operated.

_{In the}

case of floating ships au added difficulty arises clue to the ship operating iii a boundary between two fluids

of very different

characteristics,

namely water and air. Among other difficulties

wave motion set up by this boundary have

* Reesirrh Asocinte, M,uss:Lc!I1I,ati,4 I!u(lIiute of

Tech-noiogy, Camhriig., Masu.

OF THE SAILING YACHT

305 made model tests hard to interpret. As this pa per so clearly shows, deductions must be t.ui'ittel with care, and 1:ests iuiiude to fit actual

(oml(litiohIs. Iii all cases observations of any

tests covet' 1 Tel i aviol' tl at mu ust be co rr et, sill cc the test itself lotlows phiysica I laws. But the observations may not be applicable to the ease being studied, or the test may be set up

ihucor-rectly or the accuracy possible in making observations may be inadequate to separate the feature controlling ultimate behavior of the device.

The problem of sailing yachts, and partieli-]arly racing ones, is intriguing because it deals

with very small differences. The average

differ-ence of speed between the two leading Class Q boats racing at Marblehead for every race all one summer was 0.03 knot. In sailing 5.7

degrees, or about i/2 point, means 0.1 mile to windward for every mile sailed.

This is of

course due to the fact that 5.7 degrees is 10 per cent of a radian. A difference of 1 degree in windward ability therefore means 100 feet more made good to windward for every nautical

mile sailed. The usual cup defence 10-mile wiul(lwar(l leg on a triangular course would meahu a un iii of 1000 feet to windward for each 1 degree red i u(tioii iii angii' of attack req uiireil to (uppose leeward forces. This is no small advantage, and yet gaimueci from a very small

di thereuce. i'm fessor 1)avidson is, therefore,

to be greatly commended iii developing model tests, both from the technique of performance and the interpretation of results, that are lead-big to definite facts covering design dealing accurately with even smaller differences than

those mentioned. While sailing yachts are not

commercial in the sense of the mercantile marine, and therefore the famous question of ''what good is it" may arise, nevertheless the financial investment in sailing yachts is large enough to iuiake it taxable, and so subject to government, and supposedly also, popular. imuter-est. Furthermore, investigations of this type invariably lead

to further application of the

knowledge gained iii matters further and

further afield,

so that its importance is far

greater than the possible first impression of ''something to do with sail boats" would imply. Vince' investigated forces on inclined flat planes in water in 1.798. llayleighi2 worked out

the first mathematical analysis of pressures on

plates with inclined fluid flow in 1876. Langley3

diii further work on airfoils in 1899. Tavlor ii ivesti gated rudders of symmetrieal camber

:.of ; CL

to

.8 .4 .0 .o1 .0

.1X I:l RI l.lNTA.L STI iI)T IS OF THE iTL I MG YAChT

/

3öt.429 A N. A. C. A. 99 + Fta+ Plote Rudder Rudder Free V Keels NPo __________ CL - \(' ₀ V

£4

\e:'

_\

AV2i_

_r

V AVAYAY

dr i

A

V

4/

V

40 _{ç0 8° 10° 2.0°} Angle of Aftc*ck

-Flu. 22.Co1rRrsoN Cii ART FOR SURFACES OF Di FIERENT ASPECT RATIOS

The plotted points show the fits o various staioinrd forms as well as preseit heeled boat and keel..

development has been full of aerodynamic. absolute coefficients (or any other

non-irnen-results applicable to hly(lrodynamie problems sional system) are used. Thus this paper marks almost without change,

if the N. A. C. A.

the 138th anniversary of the start of

investiga-.100

tioiis on keels, a iiil at

last we are getting

soiiiewliire

flie tout rihiut iou (If. iiiost. iuiterest. to nie lies n Ilit' ('Elect, of lice! a uiLrle and Ilie yen

itl

aiwic (it attack of keels, cmisitlernug this

dis-crete paper, and not uiiiiiiniiziuig the able work prior to it. lii tIns couuuueel,ioR I wolul(1 like to

show a chart

( Pig. 22) br plottiii

results

Vhiicli _{gives iuiterestiiutr eOuiiparisouis. By using}

logaritliiiiic coordiuiales the plotted results _are

Op91e(l out. Iluis (lepeui(ls Upon the relation

XaCL/7r.IIL. (I)

\\iior. a _{ijiti ilgi Iii} iIo of _{II I ttik}

corrt,1a)iii1-ilig to .111. .1 R = asl)ect ratio.

C, = cotfllc en t of _{1 ft oil absolti to .eit] e.}

The ordinates are absolute coefficients of lift anti correspond to the author's nomenclature

for the ''C coefficients.''

The abscissae are

au i gl es of attack am I iii uust I)e iii terp rete(1 as the

total a ogle troni the val tie where C,.

= 0

t.litt

is, wit Ii flat plates or svuuiiui(l;rical (aI.uuiluer,

= () iIIIiI (L 0' _{(i II} ci tililitIc. _{hi it} vloii

(i = (I

itt ito clv _ 2° viI Ii I lii' :uuil iou's

l'i. l.

0-hgp-t

lii!. hun

I his aiiioiiiil utilisi 1)11 SO hJ}IiI,it Is;i!W;l\s Iii Intil

jiititii

III iiI2I('. 'l'Ii

ItilItiui.

iuiufilil

a U Ill I,(( I

\IIII

...

I1 lit

_{I:. I.:i:}

_(fl.

AR- (Span/Aren .080 .060 .040 E 020 .016 .012 .010 .2 .3 .4 .5 .6 .8 l.a 2

Aspect Rto -AR

Fin. 2t.i.oi'i.: or Lrrr Cor:rricii;NT TN

.Asii:;i U,ti to

Illiiilt

i(Ii.! ii

Iiuii,Iiii (i)

1 iiiiiihtr

...iF,r,i,. (I;).

:ti

lvf,riiit.

liii Itir,,

'l'hie Eiiiijtiutjouis oh this t:liart uisisI; of

(I) C, 1es.. t.ita ii i).S(i ) a nit iiater I liii ] ()0

:1)

', -roil-

ittiforint _{ivitli airfoil}

The wing sections, being all designed for ;l if = 0, fall on the same straight line. ]!t

is _{interesting the way flue parameters of _1.11}

get. closer to2ethier as A If gets Lriiat(r.

e!iul)liii-sized still ]iiore, indirectly, by the fait, that, the

;uuigles of attack are spreading out. it tim Same tunic iluic to Jig siiIe. lii:riEnri'. siiiiih! inipinvi'-nietits in effective A if of keel, or efficieiuev

of airfoil stirface as given iii the author's Table

3, wilt have a marked effect; upon the windward

ability of the boat.

The curves on

Taylor's rudders are

par-ticularly interesting. These cover one ease

with _{the rudder immediately under the bottom}

of. l,he boat, and the other, case with the rudder

1/ _{depth below the bottom. Aspect ratio is}

really a measure of the slipping of fluid off the ends of a surface. The rudder shape being square, AR = I by itself. _{Where free of the}

'I..

V

EXI!.'

I.M lN'l\ L ST tJi)IlS OF rJITJ. SATL1Na YACHT

₃₀₇

3 4 6 0

20 Tinus eu.

30S

_{EXPEIHM.ENTAL STUDiES OF TIlE SAILiNG YACHT}

bottom, Fig. 22 results in coincidence with this AR line. H the rudder were fastened to the bottom with no leakage, and no peculiar streamline flow in(llIce(1 by the bottom shape,

theii water eould only slide

off the bottom.

end, and in I rror image would be illel uded

giv-SIDE EIEs'ivrroN

11:Iri, one half under surface, other half top uiface.

Fio. 24 (I)) .Suini:is;s:o PAWI- OF BOAT AND MIRROE IMAGE AS EFFECTIVE HYDRoFOIL; ANGLE OF HEEL. 30 J)E;IIEI:s; ANuL: OF ATTACK, 10 1)EGREEs (ANGLES AND SCALES PUItl'OSEIX EXADDERATED TO

KEEP LINES CLER)

I0

a

ing AR = 2. ITowever; there is some chance to slip as the rudder isn't tight, and Fig 22 gives AR = 1.5, a compronhise between ru(lder free, and with its mirror image. As figured by Professor Davidson, the mirror image method is used fOr keels as tile closest assumpi ion.. This s:&;fl:Sd5OOn

:

5tois

a"4 LWL3OOHI Sco I: increased other dimensions 5O0/ on

.iuk&

Stations sJeW

Irdi

' Vj S

EXPERJI\l l'NTAL STUDIES OF THE SAILiNG YACHT

309 will III (((1050 Ia'

ifh'lI I)v

\VliVe-iti(LkiIi!Z at

i lie IIt'l

stub'. and

SI pa it ol tie a pint reiitiv

('t 'liielt'litV ((I 1 he keel is a tiiil ler of

tiefliti-loll 2000101 lien I ;ts1)eet ruut in.

Ii oider II) !1Ot it tlear IIIOIIIiJI ('011ei'l)tiOil of_

wilult tltt 2e011letrV oL aspett ratio looks like

by no't tot! of illIines. l"ii.r. 24 mis been drawn

sliowi tig Ilit' proJec't ((11 td. net ual suhtiiergecl boat

iiies am! I heir images. drawii about an assumed flat waterline plane. rFlIe boat lines can be seen by lIoldiII2 the bow elevation of l"ig. 24 (a) hotizonta liv. The waterliuies have not been

repeated in image to avon! coidusion and save

labor. 'l'his now beroines a parasol monoplane with narrow wing span, very long chord and a great big buigy fuselage. In addition there is an extreme lateral dihedral angle. hJnfortu-tiately few data have been found on tests of wings with such large dihedrals. In the author's Table 3 tue effect of dihedral oti aspect ratio has been neglected and this seems wise at the present state of knowledge. It is included in

the ''efficiency'' of the ''wing.''

To understand this a little better it is prob-ably necessary to analyze the lileaning of the

CXI)ression

.4)? C-L/rC,)z (see Davidson Table 3) (II

This is generally ati ribiuted to Prandtl and was initial lv a itietliod of deteriiu liii iig total drag. The profile drag eoeffieient remains substantially constant for any AR. But the induced drag (Reference to footnote.) depends

upon the AR in accordance with

(II) for the

assumed conditions. Reference (9), pages

185-213, gives the derivation, which goes soinetliiiig

like this. Miuiulc (see footnote reference (9),

J)agc 204) showed that the airfoil with mininiuiri iiidiieed drag would have an elliptic lift dis-tlih)lll oil along the wing. This is shown iii Fig. 25 (_4t ) . On tIl is assumption expression

(El) was (Ion ved inn thieiivat icahly, written

= (Cj.;'(tr ii)?) (III)

Tile least drag that au airfoil emi have (for a given tR) is thins determined by (C01 + C00),

where (], = profile drag at any AR.

The ir

enters through the integration of an ellipse, the area of the semi-ellipse in Fig. 25 (A) of course iuig irbG/4. This relation therefore can be used as a measure of efficiency, as in the author's

;oak In of ii n a logies. I 'ra mill 0 uitt ri bitt es the term

iti,iui,,.,l (lrflg" I,, Mii,ik H ii,I $;I.Vs. 'This ,Iesigiititlon is used

II (11(0 l'ii.y wi ii, ,,f elect r',uiitug,ii'tic induct ion.

whil, ar' quit. similar to I tins, of livitr,ilynaniic vortex fields.'' tiff hatuil i Wouulil seottu :i far crc froiji itiagnet isin ii)

boat perforinaiiceiuriicss lii referelice to the compass

b -- b

a

(A) Elliptic. Lift Distribution

b a (B) Two EllipsesOb5±ruction on Sum. CD. = - [l.u.kr2.] /3p b a

(C) Sum Ellipse ond Non-Ellipse

Ftc. 25--ENAMPI.ES Ol LIFT l)ISTILI1IUTION Ai.osc

Si''N : (A ) Ei.t.iL'TIlA I Li F'!', (II) Ni;nI- Er_r.tI'SES.

(() UM OF J':i.LIrr[cAr.AND Nos-EI,r.Ii'TIctr Cuavi;s

(Titus IS I'RoIIABLY NEAREST TO DAVIDSON Fifl. 15)

Table 3. For analytical purposes with lift

dis-tribution iii Fig. 24 beiiig very

far from

assutlie(l elliptic form, Prandtl° suggests the use of other distributions based on eli iptie torni, which are possible to handle inathematieailv. From r.nahysis of one such forni a possible developed foniuutila becomes

c,0 =

.i[i

+ 16

Whichi may be written

7r.AR (1 ± 16r2) (IV)

Where,

C coefficients are as in the paper. AR aspect ratio asbefore.

r = (G,,/b) = ratioof"amplitude" of lift curve to span of wing.

b wing span.

"amplitude" of lift curve on wing (see

below). 7 N N \

'I

Wing 2. C 1. i-tAR 2. L

C.'.

_t i-tAR

310

EXPERIMENTAL STUDIES OF THE SAILING

YACHT

Lf1 Dskrbutort .40

e 3QO

Submerged Partof Hull

cx l00

e _300

1-l(.. 2._TIj.'l' I)Istl:Ilit'I'1i,N ui' Fto. 20 (C) .&ND

i)r-I'l.INI: ui' ffyuiw,Il. }'lII. 24. 'l'iris iIows

1)15-JLA(:EMKN'I' ut' Lii'!' rltuu (EN'tI'I{ I)ut': ru LARGE II U IL I x'rERi'l:)S(;!

If the lift at the center of the ''wing'' Fig.

24 were zero and elliptic distribution assumed

on both sides, then equation (II) would become

= 2CL2/1rCD! (V)

This type of distribution is shown in Fig. 25 (B). It is more likely nearer fact than the most efficient wing. It has the effect of doubling Davidson's figures giving ''effective aspect ratio" of Table 3 as 0.874 arid 0.792 for 20 degrees and 30 degrees heel respectively. These are very close to ''geometrical'' AR = 0.826. It is shown below that from test data of Fig. 15 the best fit is given when the correction term

from (IV)

(1 + 16r) = (1 + 0 0) = 1.9

This checks the roughly assumed value of 2 in

equation (V). Fig. 25 (C) shows the type of lift distribution titus obtained, the ellipse being the I)trt obtained by the straight formula and the other curve, zero ami(lships, being the cor-rection term for hull interference. The

amp11-800

00 0

0 50 00 150 ?00

Drag- Pounds

FIG. 27.PoLuc PLOT OF BOAT LIFT AND DRAG This is Davidson Fig. 10 replotted to semi-square-root clii ri I show oil ye nI, 1 interpo1 tilig with straight

lines.

Z50 300

tude of both eutves must, of course, be adjusted

so that the total a rca gives the total lift.

Fig. i shows the lift distribution compared to I he hull and image as in Fig. 24.

It at least

looks reasonable. Actual tests of this curve on wings ate well shown in reference (5), pages

85-90.

In plotting data straight lines are always

advantageous for averaging observations. In Davidson's Fig. 15 t.he

lift comes in as the

square of its value as in (V) above.

There-fore, if 'semi-square root'' coordinate paper is used, the curves will be straight lines if the parabolic relation holds. This is shown replotted this way in Fig. 27.

In sllmnlary, therefore. I would like to (1) Commend the author of this paper for:

The past development of small model technique producing accurate results.

The presentation of valuable data upon

effects of angle of attic-k and heel, with adequate

accuracy to be of practical use.

(C) The general application

of aero and

hydrodynamics towar(l the solution of a prob-leIn on which the first recorded tests seem to have been made 138 years ago.

(2) hope that this discussion has

(A) helped to confirm analogies between

other data and the behavior of sailing yachts.

5' 0 o Pa ra bolos 0 700 800 0 0 500 400 300