Determination of sailforces based on full scale measurements and model tests

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TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSI4YDROMECHANICA

Rapport No. 444.

DETERMINATION OF SAILFORCES BASED ON FULL SCALE

MEASUREMENTS AND MODEL TESTS.

Symposium Yacht Architecture HISWA 1975

J.Gerritsma, J.E.Kerwin and G.Moeyes

november 1975

Deift University of Technology Ship Hydromechanics Laboratory Mekelweg 2

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ABSTRACT

Following Davidson's method full scale sail forces of the Admiral's cup. yacht

8 "Standfast" have been determined by combining full scale measurements and

9

corresponding modeltests.

As an êxtension of Davidson's method the rudder angle was included as a

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variable to define the situation of the yacht. Other conditions than sailing

to windward have been considered too.

Delft University of Technology

Massachusetts Institute of Technology

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J. Gerritsma , J.E. Kerwin , G. Moeyes

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3 Determination of sailforces based on full scale measurements and model tests

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1. INTRODUCTION

In hi classic paper on the prediction of sailing performance based on model

tests, Davidson described a method to determine full scale sail forces from actual sailing tests and corresponding model tests [i]

The method is based on the fact that in a stationary condition the

aero-dynamic forces on the sails are equal in magnitude to the hydroaero-dynamic forces acting on hull, keel and rudder, but of opposite sign.

In particular it follows, as shown in Figure -1,

the longitudinaL driving force FD is equal to the résistance RT of the yacht in the direction of travel

the aerodynamic sideforce FH cos is equal to the hydrodynamic side

force acting on hull, keel and rudder

the heeling moment due to the sailforces is equal to the stability

moment of the yacht.

Davidson assumed that the aerodynamic forces on the sails could be reduced to one resultant force vector acting through the centre of-effort of the

total rig. The determination of the center of effort was based on geometrics only, but included different weight factors for mainsail and foresails.

The assumption of one resultant sail force implies that there is no

irreducible aerodynamic couple. in addition he assumed that the resultant

sail forcevector lies in a plane perpendicular to the mast.

The condition of the yacht during the full scale trials is characterized by the heel angle , the forward speed through the water V, the rudder

angle S _{, the relative wind speed}

aw' relative wind direction

and is assumed to be stationary. Davidson neglected as a first approximation the rudder angle. As this condition is to be imitated on model scale it is desirable to carry out the full scale tests in calm water, because the measurements and reproduction on model scale of the encountered wave spectrum for this particular purpose is almost impossible. In addition there should not be too much variation in wind velocity.

The ideal circumstances for full scale yacht tests are hard to find. For instance in the case of "Gimcrack"trials some runs at higher wind:speêds

may have suffered from seawaves, as reported by Davidson himself [i]

Model testsare carried out to correspond to the full scale trials.

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The, towing force of the model is equal to the resistance of the yacht in the direction of' travel and the sideforce and leeway angle for the condition

under consideration can be measured during the run, using the equilibrium

of hydrodynamic and aerodynamic forces.

The sailforces can be calculated and related to the sailarea. In this

way Davidson obtained sailforce coefficients from "Gimcrack" trials.

Davidson's assumptions look very reasonable. Although the sails cannot be considered as parallel flat surfaces, neglecting tangential forces, there is no strong indication that the direction of the resultant sail

force is not perpendicular to the mast.

The assumed vertical position of the center of effort of the sail force,

based on geometry of the sailpian only seems doubtful, but measurements on a set of stainless steel model sails of "Standfast" did ndt show a

marked deviation from the assumptions for the close-hauled condition [2].

The "Gimcrack" coefficients are in fact sailförces per unit area and

can be 'used for other configurations when it is assumed that form and size of the sail plan have no influence on the sailforce coefficients.

In the past 1O years the Gimcrack sailforce coefficients have been used to predict the performance of sailing yachts, in combination with model

tests of the hulls.

To this end the speed-made-good V-and the corresponding true wind spe'ed are determind for combinations of yacht speed V5 and heel angles (for instance 410 , 20 and 30 ).

The optimum values of the speed-made-good determine the optimum performance

in the close-hauled condition.

In the Deift Shipbuilding Laboratory this procedure is computerized and extended to an analysis of the model data combined with various sail plans and positions of.the centre of gravity of the yacht;

In Davidson's öriginal method the rudder of the model is always at the centre line. For routine yacht model testing the influence of rudder angle on the pérformance is not considered, partly because of finÑìcial reasons:

the inclusion of ì'udder angle variations should bhsiderably-incréase time

needed for the experiments and costs involved.. However, leeway angles

predicted from standrd tests are considered too high in sailing practice. In general rudder angles are used during sailing and it may be questioned wether model tests ith zero rudder angle are sufficiently representative

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In order to review the "Gimcrack" coefficients and the performance

prediction method derived by Davidson., the Deift Shipbuilding Laboratory

has directed an extensive full scale and model test program with the

Admiral's cup yacht "Standfast".

The full scale trials were carried out in deep and calm water to avoid added- resistance due to restricted water depth and seawaves. All parameters which are relevant to the ships condition in wind and water were measured. and averaged over a period of five minutes for carefully

selected runs during the 19714 racing season.

Contrary to the "Gimcrack" trials not only close hauled courses ;are

considered., but all headings, These data might provide a welcome addition

to published results of windtunnel tests, such as presented in [3] and [14],

because full scale data are scarce-.

The full scale measurements are the basis for the sail force determination,

büt in addition they may be of interest to show the performance in various wind conditions as well as the resulting heeling angle and applied

rudder angles with appropriate choices of sail configuration.

The yacht hull model tests for the sail force determination are extensive because the range of - heel angle, rudder angle and forward speeds has

to coverall full scale measurements.

To interpolate in the selected ranges of variables olynomial expressions

have been matched to the model results, to give resistance and side

force for any combintion of forward speed, h6e...angle and rudder angle,

as described èarlier by Kerwin in the case of "BAIBA" -

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. In

combination with the sail configuration for each of the considered full scale runs, the resistance and side force and thus the driving sail force

and heeling sail force cari be related to sail area tö arrive at sailforce coefficients.

Next to this, the full scale close hauled results can be compared with

the standard model predicition, based on the "Gimcrack" sail coefficients,

to check their validity. .

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2. FULL SCALE TESTS

The Standfast full scale trials have been carried out during the racing

season in 19714.

The main partuculars of the yacht in trial condition are summarized in

table 1. The displacement includes the weight of eight crew members, their luggage, drinking water and fuel oil to a total of 1200 kgf.

These weights are taken into account for the calculation of the center

of- gravity's vertical position.

The- following parameters., which define the yachts position with respect

to wind and water, have beén measured

yacht speed V

apparent wind speed

aw 3-. apparent wind angle

aw

heeling angle rudder angle

The measurements of apparent wind speed and direction, as well as the speed

of t-he yacht through the water were- carried ut with standàrd Brookes and

Gatehouse transducers. The windspeed meter has been carefully calibrated

in one of the, windtunnels of- the Deift University of Technolor and the

speedometers have been calibrated on the yacht -in the canal;through

-Walcheren. The -starboard and port speedometers were situated aft of the

main section and due to the potential flow along the hull an appreciable

correction factor was needed for calibrating the speed measuring system.

The calibration trials were carried out in upright. osition

using the auxiliary motor. Excellent linearity has been found up t-o

a speed of six knots. The electronic equipment included a potentiometer

to measure the rudder an'gle and a rroscope to measure the heeling angie.

A block diagram- of the measuring system is given in Figure 2..

Each of the five- measured sgna1s was integrated over a period of five minutes to average short period fluctuations and thus to approximate

stationary conditions.

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Stationary conditions with regard to wind are hard to find : there is

alvays turbulence in the air causing gusts and shifts.. After preliminary

continious records of wind speed and direction the five minutes period

has been selected as showing relatively minor deviations from the average. The integrated signals vere presented digitally for ease of reading..

For each run the crew completed a form which contained the results of the five measured signals as well as the sail configuration, waterdepth

and wave conditions.

The apparent and true wind, as well as the apparenL. and. true wind angle could

be determined with the readings-of th heeling angle, the components of the wind speed and wind direction, as measured. It should be

realized that wind speed and direction are.measured in a plane perpendicular

to the mast (respectively V.and

'aw Therefore a reduction of the

original readings of these variables usi.ng the heeling angle,, was necessary.

it follows from Figure ,14a. and b that

y' sin cos 4 tg = av = tg cos 4 av

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The results of' the runs are tabulated in tables 2a,2b,2c and 2d, for

four sectors of' true wind direction respectively. The various sail

configurations are defined in table 3, whereas in figure 3 the main

dimensions of the sails are summarized.

it should be realised that the results depend strongly on the trim of

sails and on the way the yacht is steered.

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To a certain extend it may be assumed that an optimum condition has been obtained during the Standfast trials because most of the measurements

have been carried out during races in coastal waters of Zeeland, which

are sufficiently deep and more or less -sheltered.

-As a first analysis of the data the yacht's speed, -heeling angle and

rudder angle are plotted on a base of true windspee,see Figures 5..

Four sectors of the true- wind direction with regard to the course of the

boat have been considered. For sec4or 1, where : I5°the average

apparent wind angle is approximately 2Î° with extremeva]Lues of 30 and

15 degrees. The average true wind- angle is 38 -

-It should -be noted that for this set of data, as for the- other sec-tors,

the sail configuration is not the same for all runs. In fact the sails

1200, 1300 and i600 where used to cope with the various -wind velocities.

The area's where the three sail configurations are used are quite

clearly defined in Figure 5a. Apparently the choice of the sails is made to limit the average heeling and rudder angles to approximately 30 and

15 degrees. In the sectors where

_{5°<t90°, and 9O°<t}

135° the data

points scatter considerable-, as could be expected (figure 5h,c). It remains of interest to -note that very large variations of yacht speed

at constant true wind velocity can be expected for this conditions. For

the running condition, more or lessrepresented by the- last sector,

whére 18O°<ß 135° the attainable speed is more clearly related to true wind speed, see Figure 5d.

It is not suggested that Figure 5 -analyses the sailing performance-to

its full extend. The figure should be regarded as a first view at the

full scale- runs. For a closer look -at-- the results Figure 5 should be

studied in relation with Table 3 and Figure 3.-

-As a first and rough judgement of "Gimcrack" coefficients the performance

predicted from model tests with their values, can be compared to t-he full scale results on beating -legs. From figure 5a it appears that ship

speed isr w'1l predicted. Though this may be attributed to the right

values of "Gimcrack" driving forc,e coefficients, it must be remarked

that in the,consideredspeed range, 5 to ₇ knots, the ship operates

airead-y on t-he steeper part of its resistance curve. For example, a speed increase from .5.5.knots to-6.3 knots, which is a-bout the difference

between predicted and measured curve in medium winds, causes a resistance, and thus a driving force- increase of about .60%.

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Only at highçr wind speeds (about 20 knots true wind) the measured speed i somewha1 lower than predicted, possibly due to waves and ship motions. Also the Gimcrack method to represent all foresails of different sizes by the

same. value of foretriangle area might be a source of the mentioned deviation.

The genoa area at 20 knots wind is approximately two third of the areas

used at lower wind speeds.

When actual and predicted heeling angles are compared (figure 5a) it can be remarked that in medium and lower wind speeds measured values are much

"hi1ier. than values obtained with the "Gimcrack" coefficients.

The matching of both curves at higher wind speeds must be explained by the use of an unreefed rig for the predictions, while in reality the ship

sails with reefed mainsail and small genoa.

Combining the conclusions with respect to driving and heeling sail force

it can be said that "Gimcrack" coefficients underestimate the total sail

force t quite some extent. This could be expe6ted .

of the evaluation of modern sail clothes, sail plans and rig design.

The representation of force sails by 85% of force triangle area used in the

Gimcrack method, should, also be takèn into account...

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3. MODEL EXPERIMENTS

As mentioned before, the full scale data have to be matched with the results

of model experiments to determine the sail force coefficients.

For large variations of the relevant parameters: fôrward speed, heel

angle: and rudder angle, resistance and side force has been measured with a 1:6.5 scale polyester model of "Standfast". The test conditions included

heel angles of zero, 10, 2C,, and 30 degrees, rudder angles of O, 5, 10, 15

and 20 degrees and forward speeds up to a corresponding yacht speed of

approximately 9 knots.

Systematic combinations of the variables were considered, rather than

realistic conibiñations.to be matched directly with the full'scaie-runs. At each combination of speed,. heel angle and rudder angle three leeway angles were, chosen,, resulting in three. different measured side-force

values... Therefore the data can be used tó study the influence of yacht stability as well as sail dimensions on the performance. A

typical example of the model test results is shown in Figures 6-8, where the leeway angle, the excess resistance. RmRtm (= resistance with heel and leeway minus total upright resistance), and the side force as -.

measured are plotted on a base of model speed.

Figure 9 shows the influence of rudder angle on the magnitude of the

leeway angle for one heel angle only. The figure illustrates the

rnportant influence of rudder angle on leeway. To study this effect in

somewhat more detal a standard speed-made-good prediction for sailing to windward has been made using the "Gimcrack" coefficients for five

constant rudder angles; . iS=0,5,lO,15 and 20 degrees. The.results are

given in Table 4, where a relatively large influence of the rudder

angle is observed. However it is not realistic to combine for instance

a heel angle of 10 degrees with a 20 degree rudder deflection,

when optimum conditions are.considered.

For more suitable combinations,, which can be obtained by the sailor

with sail trim and by the designer with fin keel and and, rudder location,

the influence on speed-made-good can still be observed but is not

alarming.. At least for comparison of various designs the standard

prediction method using zero rudder angle could be regarded: as' satisfactory, except fór the leeway 'angles., which 'have' very high predicted values.

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-9-However, as can be derived.from table 4, the overestimation of leeway might

be caused by the zéro rudder angle dur.ing tests.. When more realistic rudder

angles are applied leeway will be reduced to values acceptable in practice.

The expei-irnental results are reduced to mathematical expressions to calculate reistance:and side force. and leeway. for any combination of heel angle,

forward speed and rudder angle, with the considered ranges of

the

variables. The immediate objective of this analysis is to provide a means of estimating.

the hydrodynamic forces for the.fuli scale "STANDFÄST" under the specific

conditions, of the sailing trials. Höwevet, the functions which have been

derived are sufficiently general to permit arbitrary specification of the scale, position of the center of gravity, sali area and height of the center

of ef.fort of the full-scale yacht. An analysis of the effect of such

vriations .on boat speed is o.f particular interest in the development of

cean race handicapping systems.. In the. following sections we will discuss

the mathematical representation of .pright resistance, excess resistance,

stability and leeway.

3a. UPRIGHT RESISTANCE

An. upright resistance test consists.oÍ a series of measurements of model

teistance, Rtm, at a sequence of speeds., Vm. Following the usual Froude

method of extrapolation

R ₌ _4PSV

_2{c

(F) + CF(R) + _CF(.Rfl)} (5)

where .p is the fluid mass. density, .S

is.

the wettEd surface of the model,

CR is the bare-hull residuary resistance coefficient, ."ÓCF.FS the 'fric.tfon'ai

esistance coefficient caused by the tubuIence stimulating .sand strips

located on the. model.. The residuar,y resIstance., :by assumption, is 'a

function only o.f Froude number .

V,

m

(6)

/gL

while the frictional resistance is a specific fu'ict'ion o.f Reynolds Number

in ccord'ance with the ITTC formulation

C 0.075.

F - _{(log R-2)2} (7)

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-where

0.7 Vm LNI

The factor 0.7 in (8) is customarily used in sailboat test extrapolation to account for the reduction in effective length due to the keel.

The results of upright resistance tests of the "STANDFAST" model are given

in dimensional f drm in Fig.. 10, and In the non_dImensional form of equation

(5) in Fig. li. The two sets of symbols represent tests with single and:

double width sand strips. If we can assume that CF is directly

propor-tional to the width of the sand strips, these two tests permit extrapolation

to zero width to obtain the bare-hull CR.

The test values of CR + CF for both sand strip tests were next approxi-mated by a least-squares spline-cubic function with Vm2 as the independent

variable. The degree of smoothing provided by this procedure can be

varied until the resulting curve passes close enough to the test points

without responding to the minor irregularities due to experimental error.

The result of this procedure is a: table of coefficients of a sequence of

cubics which can be readily evaluated to obtain CR at any speed with

CF extrapolated to zero. This procedure also provides a check on test

accuracy by computing the root-mean-square deviation between the test

data and the approximating function. For the results, shown in Fig.. 11,

the rms error for the double sand strip test is 0.9%, while the corresponding

error for the single sand strip tests is 1.5%. The spline-cubic function

therefóre appears to be extremely accurate.

3b. EXCESS RESISTAIsICE

We define heeled resistance., R$-Rt, as the difference between the total resistance of a yacht with some combination of heel., leeway and rudder

angle and the corresponding upright resistance at the same speed,. This

rsi.stance is predominately the induced drag associated with the generation

of side force by the keel, hull and rudder. However, it also contains the

change in hull resistance, not associated with side force, resulting from the change in underwater hull shape due to heel.

The formulation of the equation for excess resistance was developed by solving for the coefficients in a series expansion in the principal

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parameters .least squares. A computer program was developed which first. obtained the upright resistance function.as described in section

3a, u'btracted this. f röm each of the 295 heeled. test values,, solved for

the coefficients of the prescribed functions by least squares and then

evaluated the difference between .the measured and predicted model reÂjs-tance at each of the têst pOints..

T.he following table summarizes the resulting, rms .error in predicted model resistance obtained bynThe different combinations of terms.

RNS :error - kgf .047 .045 :04.2 .040 .03.9. .037 .045 .045 .042

The first term can. beidentified as the inauced drag at. zero heel in the

absence of a free surface. The next two terms., which include even powers

of the heel angle, , provide for the dependence of induced drag on heel,.

Terms 4 and 5 represent the drag increase in the absence of side force..

Term 6 is the primary contribution of the rudder to induced drag, while

term 7 provides fOr heel dependence on r.udder drag. _{Term 8 can be thought}

o.f as an adjustment to induced' drag related to the proportion of the side

force provided by the rudder. The combination of 8 and' 6 is essential

.f or the mathematical formulation to yield an optimum rudder angle for

12 -Term l

F./-pSV

2 F112q2/pSV2 3 4 pSV 5 6 pSV2S2 i

4pSVsq2

it is evident from the table that the rms error can not significantly be reduced below the value of .047 kgf obtained with the simple five

term series in column a. This tends to confirm a similar conclusion

reached in [5] in the analysis of the "BAYBEA" tank data.

Another way of approaching this problem is by exarnining in detail the

differences between the measured and predicted values of resistance as

a function of the primary variables. This is facilitated by the cmputer

generated plots given in Figs. 12a-d corresponding to the five-term series. It is clear that there is no obvious systematic trend in the error which

would suggest the need for an 'additional term. It can be concluded from

these plots that the errors are least at high speeds and greatest at combinations of low speeds and large leeway angles. it is also evident

that the distribution of errors Is Independent of heel angle.

Some of the largest errors can be traced back to occasional errors in the

original test data which under. the normal manual system of data reduction

would be corrected or discarded.. The remaining error is due t some

combination of inadequacy of the mathematical model and inherent random

errors assocIated with the tests:. The rms percent error of the data as

presented in Fig. 12 is 4.7%, which is about three times the value

cor-responding to the single sand strip upright resistance tests:. Since the

heeled tests involve simultaneous reading and adj;ustment of several times

as many instruments, some increase in error is not surprising from a

statistical point of view. In addition, the tests at the lowest speeds

and largest leeway angles are probably influenced by some degree of flow

instability. It seems probable., therefore, that a significant part of

the 4.7% rms error is an inherent: model testing error, and that the five term series for excess resistance, combined with the spline-cubic formula for the upright resistance is quite satisfactory for full-scale prediction.

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-The fInal equation for the excess resistanc is therefore

-F2

R_Rt=

H pSV 1.6551 - 6.7869 X IOTk +; psv2{35348 x l0_642 + 73Il3 X io_6t52}. - .0017194 FH

where. the heel angle, , is expressed in degrees.

3c. STABILITY

A similar analysis vas made to determine a suitable expression for the ydrodynsmic righting moment of the hull. The primary term is, of course,

the linear hydrostatic righting moment obtained by inclining experiments.

However, there is a significant reduction. in stability with speed, which

is immediately evident from the: tank data. In addition, the righting

moment deviates somewhat from a linear function of , and the side force,, acting at a point below the hull tends to reduce the net righting moment;.

A: satisfactory equation for the righting moment, K, with origin at TWL is

K() = AT4f1.l802

X

10- 3.4684

X

lÖ'F

6.9943 X

iø_61

8.. 0159 X

_l02LT

FH + AC sin' (10)

II'he Inclusion of the second and third terms in (.]i0.) reduces the nns error

by about a factor of three.. Additional terms, including products of Froude

Number and heel angle, and higher powers of heel angle resulted in negligible reductions in the error.

The fourth term in (10) indicates that the locatiön of the center of effort

of the heeling force is about 0.8m below the waterline, which corresponds.

to 35Z of the draft. This is a smaller value than one would expect, and

at f irs:t the result vas thought to be in error. However,. if we consider qualitatively the pressure field of a keel attached: to. a relatively wide

hull, we see that the pressure distribution on the bottom of the hull produces a moment in the opposite direction to that produced by the keel.

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The effective center of effort, in this case, would be higher than the

center of lift of the keel. The last term in (10) accounts for the

difference in the vertical position of the center of gravity of the

full-size yacht and the model,, GsGm. This correction is, of course, exact,.

LEEWAY

The preceding formulations for excess resistance and stability have inten-tionally used heeling force rather than leeway as an independent variable

since this simplifies subsequent solutions for equilibrium under sail..

However, it is necessary to estimate leeway angles in order to correct wind direction measurements made in a coordinate system fixed on the yacht

to coordinates aligned with the direction of motion, and to correct

compass headings for navigational purposes.

The following equation, derived by least squares in a similar manner,

results in an rius error of 0.3 degrees

F cos

H

{134.28 + .l104742} - .1l884S - 1.2531 X 10'5&12 (11)

--pSv2

Since measurement of wind or course angles contain errors well in excess

of 0.3 degrees, further refinement of this equation was considered unnecessary.

PREDICTION 0F FULL-SCALE RESISTANCE AND LEEWAY

With the equations developed in the preceding sections,, full scale resistance

and leeway can be readily computed for a given speed, heel angle, rudder

angle and side force. If we now prescribe the position of the center of

gravity and the height of the center of effort of the full size yacht, we can use the moment equation (10) to eliminate side force. Resistance and leeway are then functions of speed, heél angle and rudder angle. Computer

calculations have been made of these quantities for the full size "STANDFÄST" for a center of gravity position of 0.24m below the waterline, corresponding to a value of CsGm of 0.491m relative to the tank model. The height of the center of effort above the waterline, Zce is 7.07m. The computer

'generated plots,, shown in Figs. 13 and 14, are obtained by solving the

resistance and leeway equations for each angle of heel and rudder angle

at 100 values of speed. These finely spaced points are then connected by

straight lines to give the appearance of smooth curves.

(17)

-The resistance curves clearly demonstrate the existance' of a speed for minimum' drag of 'about 4.5 knOts, at:30° heel,, as seen also in the _{raw model}

data plotted in Fig.. 7.. In principie, it woúld be possible to sail at

either 3 knots òr 6.5 knots wIth the same driving force! The practical

consequences of this have long been recognized by experienced sailors. If temporarily slowed down by a bad tack or an unusual sea, a yacht can easily by "captured" ori the wrOng side of the resistance curve.. T'be only

way to escape is' to ease sheets' to' reduce the heel angle until the yacht

finds itself 'on an upward 'sloping, curve. Once the yacht accelôra'tespas:t

the minimum drag speed, sheets may be brought back in and the optimum

sailing cOndition' is reachéd.

(18)

-4. DETERMINATION OF SAIL FORCE COEFFICIENTS

The equations developed in the preceding, section enable us to estimate full

scale upright resistance, total resistance, side force and leeway for any

speed, heel angie and rudder angle. This can be done either by entering

the appropriate values in Figs. 13 and 14 or 'by direct computation. The

saine computer program which generated these graphs has been used to compute

these quantities for each of the trial runs given in Table 2. This is

more accurate than the graphs, since the computed center of effort height

is used in each case, depending on the particular sail's set. if we assume

that the sea was sufficiently calm for calm water resistance values to be applicable, the tabulated forces then represent the forces developed by the

sails to provide equilibrium.

These results all appear reasonable except for run 146 in table. 2a which

has been retained for the amusement of those who may be suspicious of

anything coming out of a computer. For the measured heel angle of 3 degrees,

the predicted side force is 91 kgf, which is quite correct. To develop

this force at the measured speed of 0.6 knots would require an impossibly

high lift coefficient. Nothing is impossible, of course, for the computerized

"STANDFAST", which simply sails to windward broadsid'e with a leeway angle

of 68 degrees!

With the forces estimated, and the relative wind velocities and directions obtained as described in Section 2, the driving force coefficient,

C=

_R

1 ₂

p S V

2 a a aw

and the side force coefficient,

F cos

C-

_H ₁

2

vp

S V

2 a a aw

can be computed. In this case

a is the mass density of air and Sa is an

appropriate sail area. The particular area to use depends on the intended

application. For yacht handicapping purposes, a fixed sail area is

appro-priate since we can then see how fast a yacht will go in different wind speeds and points of sailing with a given rated sail area.

FD

(19)

On the other hand,, to evaluate the effectiveness of particular sails, it

Is. more logical to vary the sail area depending on the particular sails

set,. _{While there are an endless number of possibilities:, we have ca]iculatéd}

sail cöèfficjents on twO bases:

I) A f Ixed sail area equal.to the actual fore triangle. and

maIn triangle areas,

i/2(i

X J + PE X E) = 76.88m2.

2) A variable, area equal to the total area of all salis set

in accordance with Fig. 3.

Values. of these coefficients aregivem.fn Table 2,, and.are plotted in .Figs.

15-18 as a function of .the angle. between the relative wind and the direction of motion of' the yacht

aw + . Fo:r comparison, the salI coefficient

derived from Log data. recorded on "BAYBEA" during -the 1975 SORC races off Florida [5] ar.e superimposed, on Figs. 15 and 16.

The trend of the "STANDFÄST" data follows the "BAYBEA" _{averaged curvés}

remarkably well. _{Points which lie well below the cûrve probably represent}

adverse conditions. The large driving force coefficients at a relative

wind angle of 160 degrees are obtained at high wind velocities, where speeds

may be. increased somewhat due to surfing.

The entirely different character of Figs. 15 and 16 and _{Figs1 .17 and 18}

is a consequence of the tremendous difference be:tween windward _{and off}

wind sail area for a modern ocean racing yacht..

(20)

-L

:3 (J 7 u , a :3 5 7 (J h1 o bI .1

CIk

fl''::,

I I J( :(

;flai°' (iifl3fl

onceyb)k2'

ACKNOWLEDGEMENT

-, criLN:r:a (op

The authors want to thank Frans Maas and Piet Vroon and their crew for carrying out the extensive full scale measurement program on board

"Standfast".

The electronic measuring equipment was designed and constructed by Maarten Búitenhek and Hans Oôms and the extensive model tests were carried outby Aad van Strien at the Deift Shipbuilding Laboratory;

their enthiousiastic cooperation is much appreciated.

The reduction and computer analysis of the modeltests and full scale data was done at M.I.T. under the North merican Yacht Racing Union

Ocean Race Handicapping Project.

The generous support of the individual donors to this program is

gratefully acknowledged.

The authors wish to thank Mr. Anthony Zolotas and Mr. Douglas Jenkins, graduate students at MIT, for their help in computer program development.

CiJubbely ijdi

((flkU1Z1 jd i )

G

f

n

(21)

-REFERENCES

1 Davidson, K.S.M.

Some experimental studies on the sailing yacht

Transactions Society of Naval Architects and Marine Engineers 1936

Manen B. van

Thesis work Deift University of Technology 19T5 (not published)

Marchaj, C.A.

Sailing theory and practice 196)4

G±anada Publishing Limited, London 196)4 )4. Wagner, B. and Bese, P.

Windkanaluntersuchingen einer Segeljacht

Schiff und Hafen, Vol. 20, no. 9,1968

-5 Kerwin, J.E. Oppenheim, B.W. Mays, J.H.

A procedure for sailing performance analysis based on full scale

log entries and towing tank data

MIT report no. )4-i, 197)4.

(22)

j '-j 3 r) h

bneo

eij fer

TABLE i

Main particulars of "Standfast" in trial conditions

Length over all L 12.20 m

Length over waterline 10.03 ni

Maximum beam B 14.00 ni max Width of waterline 3.145 ni Measured beam :393 ni Draught of hull 0.96 ni Total draught 2.93 m Total displacement 121498 kgf LCB aft _0.385m

Total wetted surface 36.214 ni2

Vertical position of center of gravity under TWL 0.214 ni

Moment of stability at i degree 216 kgfm

I 10.00 m

J

_5.25m

E _)4.25ni

15.18 m

distance of boom above deck i.14ï m

freeboard at mast position 1.08 m

(club b el z i j di g)

- 21

-(nl'izi jdic)

(23)

NOTE: ANGLES IN DEGREES SPEEDS IN KNOTS FORCES IN KGF

CR,CH BASED ON TOTAL SAIL AREA

CR*,CH* BASED ON FORE AND MAIN TRIANGLE AREA

Run ô

aw .

tw Vs Vaw

BLE 2a: STANDFAST.FtJLL SCALE TRIAL..

00 < 450 BEATING V SAIL S z R R ew a ce t F co H ' t C R CH C *R C *H 13 :31

15

24

32 5,4

20.0

15.3 1300

9414

_7.1

_{79.: 176.... 681.}

_9.2

_0.28

_1.09

_0.35

1.314

14

27 '12

24

35

6.3

19.9 14,4

1300

9144

_7.1

_{120... 207.}

6214. .

5.2

0.33

1.01

0.141

1.214

15

26

10

27

41

6.4

18.3

12.9 1300

9l414

7.1

127.

206.

.

609.

4.9

0.39

1.17

0.148

1.143

16

26

.11 214 314

6.2

19.8

114.4 ₁₃₀₀ 94.14

7.1

114.

193.

610.

5.2

0.32

1.00

0.39

1.23

30

29

14

29

140

6.0

20.1

15.1 1300

911.14

7.1

104.

199.

653.

.

6.4

0.32

1.014

0.39

1.27

31

27

.

12

32

45

6.4

19.2

14.2 1300

94.4

7.1

127.

215.

_6214.

5.0

0.37

1.09

0.46

1.33

45

10

3

21

35

4.8

11.5

7.3 1200 100.4

7.1

60. 74.. 280.

3.2

0.314

1.28

0.144

1.67

46 .9

2 19 3.3

4.6

10.9

6.7 1200 1.00.4

7.1 54..

67. 2514.

3.2

0.34

1.29

0.44

1.69.

¿48

14

5

27

¿13

5.3

12.8

8.14

1200 100.4

7.1

76.

101.

.

378.

3.6

0.37

1.39

0.149

1.82

50

20

8

29

¿15

6.7

16.9

11.6 1200 100.4

7.1

152.

205. 501....

3..0

0.143

1.06

0.56

1.38

51

23

9

26

38

5.8

16.7

11.8 1200 100.4

7.1 95.. 155.

561..

5.3

0.34

1.21

0.44

1.59

82

31

14

22

30

7.2

24.2 17,7

1300

94.14 _7.1

_227.

_358.

_668.

_4.3,

_0.39

_0.73

_0.48

_0.90

85

28

.

11

29

37

5.6

24.1

19.7 1600

.

73.9

7.2

87.

167.

631.

7.4

0.23

0.87

0.22

0.84

86

27

11 2g

36 .5.4

214.9

20.3 1600

73.9

7.2

79. 155.. 619.

7.7

0.20

0.82

0.20

0.79

87

29

13

29

37

5.4

24.7

20.2 1600

73.9

7.2

79. 165.. 645.

8.3

0.22

0.87

0.21

0.83

88 .32

15

32

40

5.4

25.6

21.2 1600

73.9

7.2 79....

178.

679.

9.5

0.22

0.85

0.21

0.82

115

211 : .6 31

43

5.8

19.9

15.0 1300

914,14

7.1

95.

157.

581.

6.0

0.26

0.94 0.31 1.16

146

:.3

.1

:27

,:38

0.6

1.9

1.5 1200.100.4

7.1 1..

77...

91... 68.2 12.79 15.22 16.70 19.88

(24)

Run c

aw tw V V

TABLE 2b: STANDFAST FULL SCALE TRIALS

450 < _{< 900 CLOSE-REACHING} tw -V SAIL _Sa Z _Rt R _FHcos CR CH CR* 9

32

14

111

55

6.6

21.2

16.7 1370 112.4

6.9

142.

263.

693.

6.0

0.32 _0.83

_0.146

_1.22

lo

30

18

39

54

6.5 _20.3

_15.8

_{1370 112.4}

_6.9

_134.

_257.

_672.

_5.1

_0.34

_0.88

_O.L9

_1.29

11

26

10

50

72

7.5

18.8

15.2 1370 112.4

6.9

304.

400.

611.

3.2

0.61

0.93

0.89

1.36

12

22

10

63

87 7L

18.1

16.1 1370 112.4

6.9

276.

349. 5L6.

2.5

0.58

0.90

0.84

1.31

26

12

5

52

86

6.7 _12.0

_9.4

_{1203 100.L4}

_7.1

_152.

_172.

_325.

_1.6

_0.72

_1.36

_O.9L4

_1.78

42

4

0 414

₆₇

3.3

7.7

5.8 _{12C0 100.0}

7.1 _26.

_30.

_118.

_2.9

_0.31

_1.20

_0.40

1.57

49

- g 2

29

51

1.8

10.1 6.Li

1200 100.L4

7.1

60.

72. _2514.

2.9

0.43

1.50

0.56 _1.96

53

24

12

56

87

6.5

12.9

10.7 1790 194.9

9.9

134.

203. 42L1.

2.4

0.38

0.79 _0.96

_2.01

63

24

3

57

80

7.7 _19.6

16.7 1670

91.9

7.0

371.

447.

572. 3L4

_0.77

_0.98

_0.92

_1.17

64

26

3

48

68

7.3

19.14

15.5 1670

91.9

7.0

250.

333.

606.

11.3

0.58

1.06

0.70

1.27

80

24

12

L0

57

6.5

19.0

14.7 1300

9414

_7.1

_134.

_210.

_577.

_3.9

_0.37

_1.03

_0.46

_1.26

81

25

13

£43

₅₃

6.4 _2O.4

16.3 ₁₃₀₀

94L

_7.1

_127.

_209.

_594.

_.2

_0.32

_0.92

_0.40

1.12

83

22

10

32

46

5.6

16.7

12.3 1303

9L4L

_7.1

_87.

_144.

_547.

_5.3

_0.33

_1.26

_0.L1

_1.55

814

28

1I

40

54

5.6

19.11

15.6 1300

94.1$

_7.1

_87.

_173.

_643.

_7.2

_0.30

_1.10

_0.36

_1.35

105

1L ₈

₆₃

₈₈

5.8

13.7

12.2 _{1FGO 118.14}

7.0 _95.

_123.

_382.

_2.6

_0.311

_1.011

_0.52

_1.60

106

20

6 6L$

₅

6.8

18.7

16.8 1PGO 118.4

7.0

163.

214. _509.

3.2 _0.31

_0.71i

_0.48

_1.15

107

19

7

66

88

6.7

18.3

16.8 1PG0 118.14

7.0

152.

199. '489.

2.9

0.30

0.75 Ø.L7

_1.15

108

19

7

66

88

6.7

17.7

16.2 1FGO 118.4

7.0

152.

199.

489.

2.9

0.33

0.80

0.50

1.23

109

21

6

64

85

6.7

18.1

16.3 1FGO 118.L4

7.0

152.

206.

528.

3.5

0.32

0.83

0.50

1.27 11t

25

7 (15

59

5.8

21.0

17.3 ₁₃₀₀

94.4

7.1

95. _162.

_597.

6.3 _0.214

_0.87

_0.29

_1.07

116

8 4

30

57

14,9

8.9 5.L

1370 112.t4

6.9 _63.

_73.

_232.

_2.2

_0.50

_1.58

_0.72

2.31

123

10 II 6L&

95

8.0

15.14

13.8 1370 112.14

6.9

494.

511.

277.

0.8

1.16

0.63

1.70

0.92

125

21

6

17

77

8.0

15.6 1-1.7

1370 112.0

6.9

49L4

560.

524.

2.2 _1.24

_1.16

_1.81

_1.70

126

23

7

59

88

8.14

_17.5

_15.0

_{1370 112.4}

_6.9

_697.

_782.

_558.

_2.2

_1.38

_0.98

_2.01

_1.44

127

24

7

53

80

8.4

18.3

15.0 1373 112.4

6.9

697.

788.

574.

2.3

1.27

0.92

1.86

1.35

145

3 0

43

71 1.14

2.6

1.9 _{1200 100.4}

_7.1

_4.

_18.

_90.

_12.4

_1.61

_8.07

_{2.10 10.54}

147

5 1 '46

₈₄

3.1

5.1

3.7 12CC 100.4

7.1

22. _30.

_1147.

_4.1

_0.70

_3.41

_0.91

_4.45

(25)

Run

aw tw Vs V

LE 2c: STANDFAST FULL SCALE

TRIALÒ

9O°<

<135°

tw--SAIL z 'R R a ce t F cos4 H CR . CH CR* CH*

21

14

22

18

2.3

12

24

10

28

13

29

11

52

15

57 '21

58

21

59

17

61 :12

62

12

76

5

78

15

79 rlj

97

12 loo

'11

101 '11

102 ₁₂

103

14

1Q14

14

110

10

111

7

112

12

113

14

120 _:15

121

16

128 ¿ 6

134

24

1143

:7

144

6 1118 4

149 '6

'8

5 5 6 'L4 :T7

12

8 6

6 '.2

8

7

6 7 7 8 8

:4

H1 :3

(:4

8 9 4

13

4 ¿4 2 3

97

80

93

90

69

108

86

80

85

88

92

96

93

66

73

111

106

91

107 ;102

67'

90

103

73

75

,83

'85

100 '70

.74 ':79

53

71

127

125

119

107

135

125

116

117

118

122 .125

118

93

98

135

132

123

133

124

93

119

129

108

108 T122

.:123

129 1O2

120 '123

99

108 8. 3

7.7

8.1

7.9

7.0

8.0 7. 9

7.8

8.0 8. 1

7. 9

6.0

7. ¿4

6.8

7.2

6.6 .6.3

6.9

7.2

6.6

6.8

8.0 8. 2

8.2

7.5 7. 6

6.6

7.8

5.6

2.9

2.7

13. ¿4

8.9

15.8

14.5

10.6

12.3

10.5

12.0

13.6

14.4

13.6 1 3. 6

12.2 16 3

15. 8

12. 5

11.2 10. 1

11.1

16.0

14.9

12.4

14.1.

13.8 14. 4

10.1

10.3

10.5

14.4

6.8

4.1

4.5

16.6

10.8

18.1

16.5

10.14

16.6

12.7

13

1

15.2

16.3

16.0

16.4

13.9

14.9

15.4

16.5

114.14

12.0

14.7

18.8

13.7

111.2

17.7

13.9

114.6 11 .9

12.14

13.2

13.8

7.6 8. 0

3.3

14.5

171E

171:E

1370

1790

i 7B0

18E0

1717E

171E

1600

1370

179E

1600

1370

179E

1300

170 i 8C0

1780

1200

253.9

253.9 112.1$

112.14 1914.9

162.1$

109.3

253.9

73.9

112.14

112.4

253.9

253.9 253 9

73.9

112.4

253.9

253.9 9!44

162.4 16244

162 .14

100.11

100.4

9.3

6.9

9.9

8.5

7.4

9.3

7.2

6.9

9.3

93

7.2

6.9

9.3

7.1

8.5

1.1

7.1 6183.

371.

.

5141.

276. 163.:

227...

142.

120.

176.

.

227. 142..

163.

.

494.

591.

591. 304..

336.

1q42.

409. 87..

87.

19.

.

17.

677.

421. -566.

469.

20.

285. 355..

327.

277.

257.

253.

376. 400...

399. .338.

250.

141. ¿101.

356..

252. 2314..

235.

252.

289. 290..

271.

191.

327.

375.

306.

322.

170. 1483.

169..

1146.

118.

89.

0.6

1.0

2 1.

0.7

0.9

0.7

1.1

0.9

0.8

0.7

0.5

0.8 1 .3

1 5

0.6

0.9 o .9

0.7

0.8

1.1

1.2 o'4

1.1 i .2

0.7

0.6

1.5

1.0

0.8

3.6

2.9

0.90

1.27

1.22

1.20

0.59

1.27

.

2.146

081

0.74

0.68

0.61

0.59

0.64

0.41

0.38

0.30

0.32

0.38

0.214

0.18

0.94

2.08

1.74

1.62

0.80

.

0.86.

0.87

0.92

0.75 Ø7L4

0.89 0.60,

0.38

1.07

071

0.71.

0.71

0.62

1.89 0.66..

0.52

0.39

0.32

0.78

0.81

0.77

0.38

0.45

0.55

0.149

0.27

0.31

1.45

0.79

0.93

0.97

0.71

0.73

0.99

0.87

1.37

1.18

4.25

2.66

2.97

4.19

1.79

1.76

1.50

2.67

3.50

2.67

2.46

2.25

2.02

0.57

0.93

0.60

1.26

1.00

1.06

1.26 O 80

0.60

0.91

2.00

2.514

2.36

2.64

2.82

1.06

1

93

1.58

1.56

1.16

0.78

1.25

3.53

1.03

1.04

1.80

1.32 '2. 69

2.19

1.70

1.28

1.06

0.75

1.19

1.12

1.27

1.47

1.81

1.61

0.89

1.03

139

0.76

1.35

1.42

2.36

2.40

1.22

1.84

2.89

2.49

5.55

3.48

(26)

TABLE 2d: STANDFAST FULL SCALE TRIALS

135° <_-

_tw-

< 180° BROAD REACHING AND RUNNING

Run q o

aw ew y V V SAIL Sa Zce R R FHcos I) CR CH CR* CH*

17

3

2

157

167

7.9

10.5

18.0 1AOO 176.9

10.2

450.

452.

61.

0.0

1.40

0.19

3.23

0.43

18

2 2

160

168

8.1

11.7

19.5 1AOO 176.9

10.2

541.

543.

41. -0.1

1.36

0.10

3.12

0.23

19

2 2

151

162

8.3

13.14

21.0 1AOO 176.9

10.2

643.

644.

41. -0.1

1.23

0.08

2.83

0.18

20

2 1

137

153

7.9

12.3

18.8 1AEO 235.9

9.6

450.

451.

43.

0.3

0.77

0.07

2.35

0.23

27

1

0

153

165

5.5

7.3

12.5 1900 176.9

10.2

83.

21.

0.2

0.53

0.13

1.23

0.31

35 0

0

178

179

5.6

6.5

12.1 1900 176.9

10.2

87.

0.

0.0

0.70

0.0

1.61

0.0

36

0

169

174

5.8

6.7

12.5 1903 176.9

10.2

95.

0.

0.0

0.72

0.0

1.66

0.0

37

1

3

120

1143

8.3 12.L

18.0 19!0 235.9

9.6

643.

645.

22. -0.3

1.08 _0.014

3.31

0.11

54

1 0

146

163

6.3

6.5

12.3 19E0 235.9

9.6 _120..

120.

22.

0.1

0.73

0.13

2.24

0.41

55

1

0

158

169

6.0

11.8 19E0 235.9

9.6

104. _1014.

22.

0.2

0.74

0.16

2.28

0.49

65

2 2 1.38

146

7.5

27.1

33.0 1600

73.9

7.2

334.

395.

605.

4.3 Ø4L4

_0.68

_0.142

_0.65

67

3

16

179

8.1

12.8

20.9 17AE 253.9

9.3

541.

602.

66.

2.2

0.88

0.10

2.90

0.32

68

5

23

159

167

8.8

14.4

22.8 179E 253.9

9.3 929. 1079.

108. -2.4

1.24

0.12

4.10

0.41

69

4

17

158

167

8.6

13.3

21.5 179B 253.9

9.3

811.

889.

87. -1.7

1.20

0.12

3.96

0.39

70

4

15

161

168

8.6

13.3

21.6 179E 253.9

9.3

811.

872.

87. -1.5

1.18

0.12 3,89

0.39

71

3

13

159

168

8.3

11.7

19.7 179E 253.9

9.3

643.

685.

66. -1.3

1.19

0.12

3.95

0.38

72

¿4 ₈

160

168

8.5

12.3

20.5 179E 253.9

9.3

753.

771.

87. -0.6

1.22

0.14

4.02 _0.146

77

15

8 1149

158

6.9

16.2

22.4 1370 112.4

6.9

176.

211.

403.

1.7

0.43

0.83

0.63 _1.21

89

2 1

180

5.8

7.8

13.6 19B0 235.9

9.6

95. 95..

44.

0.2

0.40

0.19

1.23

0.57

90

3

2

175

177

6.5

8.2

14.7 19!O 235.9

9.6 _134.

135.

66.

0.2

0.52

0.25

1.59

0.77

91

2 1

166

172 '4.8

6.2

10.9 19W 235.9

9.6

60.

45.

0.6

0.40

0.30

1.24

0.92

92

2 0

174

177

6.1

8.5

114.6 _{19x0 235.9}

_9.6

_139.

_109.

_44.

_0.3

_0.39

_0.16

_1.19

_0.48

93

3 1 1714

177

6.1

8.3

114.4 19E0 235.9

9.6

109.

110.

66.

0.4

0.41

0.25 _1.26

0.75

94

3 1

170

1714

6.0

8.3

111.2 iSEO 235.9

9.6

1014.

105.

66.

0.4

0.39

0.25 _1.20

_0.75

95

8 5

116

139

7.0

11.8

16.1 179E 253.9

9.3

190.

201.

173.

0.11

0.34

0.30

1.114

0.98

96

10

5

113

137

7.2

12.2

16.14 j79

253.9

9.3

227.

242.

213.

0.6

0.39

0.34

1.28

1.13

98

10

5

116

139

7.2

12.0

16.5 179E 253.9

9.3

227.

242.

213.

0.6

0.40

0.35

1.33

1.17

99

12

7 1114

137

6.9

11.7

15.8 17SE 253.9

9.3

176.

198.

252.

0.7

0.34

0.44 _1.14

_1.45

117

0

165

172

119

145

7.6

10.1

15.14 179E 253.9

9.3

336.

345.

131.

0.0

0.81

0.31

2.67

1.01

130

3 1

116

1140

7.0

11.0

15.4 1300

94.4

7.1

190.

192.

86.

0.4

1.02

0.46

1.25

0.56

131

2 1

112

137

6.8

10.9

15.0 1303

94.4

7.1

163.

164.

58.

0.2

0.88

0.31

1.09

0.38

132

₂ 1

110

136

7.0

11.1

15.0 1300

94.4

7.1

190.

191.

58.

0.2

1.00

0.30

1.22

0.37

133

2 1

115

139

6.6

10.9

15.0 1300

94Z4

7.1

_1142.

143.

58.

0.2

0.77

0.31

0.95

0.38

(27)

b

TABLE 3

'J

Sailconfigurations Standfast

26

(duhbelzijdi g)

_{(enk«tzi Jrii}

Sail Naine Geometric

C.E.

code

number

sail area above TWL1

Máin sail

32.3

1.71

2 Genoa I

68.1 6.77'

3 Genoa II

62.1

6.68

Genoa III

_57.3

6.)46

6 Genoa II High dewed

1-i.6

_6.75

T Tall boy

i8.O

6.29

9 Spinnaker 0.75 ONZ

iii.I.6

(effective area)

10.80

A Spinnaker 1.50 ONZ iII.6 (effective area)

10.80

B Spinnaker star cut

1.50

ONZ

112.1

(effective area)

9.00

E Tall staysail

_59.0

F Reacher Genua see code nr. 2

68.i

6.77'

G Reacher Staysail see code nr. ₇

18.0

6.29

(28)

9

3

b

f

c:;n-i

))ii (i12b

TABLE 14

Performance prediction '!Standfast" with different rudder angles.

-2-(dubhelzijclig)

((I1kO

IZI jiLl

-27

/ i C) degr. y tw kn y s kn y mg kn $ degr. degr. aw degr. tw degr. 6.148 14.314 3.314

_7.1

-

_23.9

_39..6 0

_12.96

_5.92

11.78

17.0 _5.9

25.0

36.2

'j .1

_18.52

6.20 _5.17

25.5

_7.14

253 _33.5

S 6.148 14,1414

_3.51

7.3

2.3

22.6 _37.8

5

12.96

5.914 14.80

17.0

314 214.9

36.1

18.52 6.i

5.08

25.14

5.2

26.1

314.6 6.148

_1i.ly

3.22

6.9

2.1

214.2

_39.5

10

12.96

5.87

14.63

16.8

2.8

26.3

37.9

18.52

6.22

5.09

25.5

14.6

26.5 _35.1

.7

6.148

3.99

2.98

6.5

0.9

26.0

15

12.96

5.71

14.1414 16.14

2.3

27.2

38.8

9 1:8.52

6.17

14.98

25.2 14.î

27.14

36.2

ç.; 6.118

3.78

2.86

6.2

0.7

26.0

110.8 20

12.96

5.66

11.38

16.2

1.7

27.7

39.14

18.52

6.22

11.911

_25.1

3.5

28.2

37.14 (7 13 z) i l 'J -7 8 50

i

9 :3 E.; 7 8 9 b1 co

bi

.R;O C.i t'(fl'.

(29)

(30)

RUDDER ANGLE

HEELING ANGLE

V

YACHT SPEED

piw

r

'io

I NTEG RATO RS

E1/1

,i

L---____j_,

I---'

_{____,}

)

FIGURE 2: SCHEMATIC PRESENTATION OF MEASURING SYSTEM

_.,STANDFAST"

'RESET

H

i

'

HOLD

DIGITAL

READ

OUT

(31)

SAIL 9: 0.75 ONZ. SPI.

SAIL 7: TALL BOY

(MAX.SIZE)

AREA18.0M2

*AREA14L.6M2

CE.6.29M ABOVE TWL.

CE.ABT 10.80M ABOVE

STANDFAST 40: SAIL CONFIGURATIL.1S

SAIL 1:MAINSAIL SAIL 2: GENOA I SAIL 3: GENOA E SAIL 4: GENOA

AREA 32.25 M2

AREA 68.12M2

AREA 62.1 M2

_{AREA 57.3 M2}

CE 777M ABOVE TWL CE 677M ABOVE TWL CE 668M ABOVE TWL

CE.6 46M ABOVE TWL

SAIL A:1.50 ONZ.SPI.

(MAX.SIZE)

* AREA 144.6

M2

CE.ABT 10.80 M ABOVE

SAIL B:i50

ONZ.STAR-CUT SPL(75 a80%

MAX.-*AREA112.1M2

SIZE)

CE.ABT 9.00 M ABOVE WL.

* EFFECTIVE ESTIMATED AREA. (=1.62 x IxJ)

FIGURE 3: DEFINITION 0F SAIL CONFIGURATIONS. (DIMENSIONS IÑ METERS.)

SAIL6:GENOA]I HIGH

CLE WED

AREA 416 M2

CE.675 M ABOVE TWL

SAIL E:TALL STAYSAIL

(SPI.=STAYSAIL)

AREA 59.ÙM2

(32)

VAW sin

f3