Special Ship Types

College MT524

-

Special Ship lypes

Drir. J.A. Keuning

Parti

Report 171 9-K

Geometry, Resistance and Stability of the Deift Systematic Yacht Eul1 Series Prof.ir. J. Gerritsma, R. Onnink, ing. A. Versluis

SUMMARY

Resistance and stability in upright and ieeled position has been determined for a series of twenty two systematically varied yacht hull forms.

The analysed results of the model exDeriments are given in a form which can. be used for various purposes in sailing yacht design, inclùding velocity prediction.

1. INTRODUCTION

An extensive systematic investigation of the resistance and stability

characteristics of sailing yacht hull forms has been carried out in the Deift Shiphydromechanics Laboratory. The model series includes twenty two different hull

forms, all of which have been derived from one parent form. This parent form is closely related to the "Standfast 43" designed by Fracs Maas.

The variations concerned the length-displacement ratio, the prismatic coefficient, the longitudinal position of the centre of buoancy and the beam- draught ratio. The first part of the program has been carried out with the cooperation of the Department of Ocean Engineering, Massachusetts Institute of Technology. This cooperation concerns the first nine models of the series of which the lines have been generated by M.I.T. The model tests to determine the resistance and

stability have been carried out in Deift. The analysed data of this part of the program have been published in a number of reports and publications [i, 2, 3, _4]

These first results have formed the basis of the Velocity Program for ocean racing yachts for which the research was carried out by M.I.T. under the North American Yacht Racing Union Ocean Race Handicapping Project [3, 4].

The use of the experimental data is of course not restricted to handicapping problems: this data base may be used as well for optimizing the design of cruising yachts and for the comparison with other methods of predicting yacht performance, including analytical approaches. In this paper the experimental results are given in a more or less condensed form. The tabulated original test data will be available in the near future.

For the predïct±on of poiar velocity diagrams using-stndardize&--saiiforce coefficients, reference is made to the work of Kerwin [4] and Nomoto [5] In this paper the emphasis is on the presentation of the experimental data, although a limited analysis of the results is included.

2. GEOMETRY OF THE SERIES

The twenty two hull forms of the series have been derived from the "Standfast 43" a successful 1970 Admiral Cupoer. The hull of this sailing yacht has clean lines, without extreme variations in the curvature of the hull surface.

The main form parameters, prismatic coefficient C, _{length-displacement ratio} longitudinalpositjon of the centre of buoancy LCB and the ratios of lengtti, beam and draught are given in Table 1. Model i _{represents the parent}

form.

The relations between the various parameters for each model is shown in

Figure 1, which also indicates the considered _{ranges of parameters.}

Some of the models have unusual combinations of form parameters,. which have

produced rather extreme hull forms. These models have been included in _{the series} for a better definition of the various relations between resistance and stability, and hull form parameters.

The lines of the twenty two models are given in Figure 2.

Variation in beam and: depth of the models has been obtained by multiplication of the coordinates of the parent förm with a factor which is constant for the

underwater part of the hull. The same scaling in breadth has been used _{for the} above water part of the hull, but in order to obtain the same freeboard for all models, the depth scaling for the above water part of the hull was adjusted in a mathematically smooth manner.

The resulting cross-sections, waterlines and buttocks have been f aired by computer graphics with spline cubic equations, with slight corrections of the profile ends fore and aft, to obtain more or less realistic forms. These

corrections caused minor différences in C _{as is shown in Table i (models} i - 7). D

Variation, of the prismatic coefficient has been accomplished by shifting cross-sections to obtain a curve of cross-sectional areas corresponding to the desired

C and LCB (models 10- 22) [6].

The waterline, length of the "Standfast 43" is 10 .metres. The scale factor of all models has been fixed at a = 6,25, resulting in a model waterline length of

1,.6 metres. Some of the experimental result _{have been scaled to 10 metre}

waterline yachts, but in principle a non-dimensional bresentation _{of the data is} used. Some of the hull data, s.uch as wetted surface S, _{metacentric radius etc.} are given for the canoe body, as well as for the combination canoe body with keel and rudder. It has to be noted that the keelpoint K as used in some of the hydrostatic formulas, is assumed to be on the baseline. which is the horizontal line in the centreolape tangent to the _{canoe body.}

The. main dimensions of the hull forms and _{some other hull data, such as wetted} area, waterp.iane area, theposition of the centre of buoan'cy''and the metacentrum etc. are given in the Tables 2a and 2b assuming _{a waterline length of 10 metres.}

The freeboard in all cases is 1,15 metres.

Because hull form variations and their influence on resistance and

stability

are

the main ourDose of the series, all models have been tested with the same finkeel and rudder. Consequently deep and shallow hulls have different total draughts, although this may not be a common design Dractice. A NACA 632015 airfoil section has been used for the finkeel and a NACA 0012 section for the rudder. The uniform arrangement of keel arid rudder is shown in Figure 3 and. Table 3 gives the areas and volumes of keel and rudder, again assuming a waterline length of 10 metres.

The following empirical relations between formdata have been derived for the

series: _{Wetted surface of canoe body}

0,171

J C

.L

- draught of canoe body

- volume of disolacement of canoe body

The r.m.s. of the difference between the calculated and actual values of the wetted surface is less than

1%

Eleight of metacentre above base line of canoe body B2 KM =

0,664 T

+ 0,111

C c _T C (r.m.s. error is 1,5 %) (1) (2)

The fIrst term in (2) represents the height of the centre of buoancy above the base line KB , whereas the second term stands for the metacentric radius BM

c _c

The influence of keel and rudder on KB, BM and KM is shown in Table 2, where these values are given for the canoe body, as well as for the hull with keel and rudder. The inclusion of keel and rudder reduces B M and KM with respectively 7 % and

cc

c -.

9 % approximately.

The static stability has been computed for heeling angles up to 90 degrees and the so called residuary stability k(th) is given for all models in Table 4 (canoe body only). -49. S C =

[1197 +

where: T c V c

The definition of the dimensionless residuary stability for this particular case is given by:

M N sin4

k (q;) C C

C

BM

_CC

(3)

The meaning of MN in this expression is shown in Figure 4.

For geometrically similar hull forms the static stability may be obtained from the following equations:

KNsin($) = KM sin + k (d)) _{B M} - NN siri4 (4)

C C

CC

C

where NN _{is a correction for the influence of keel and rudder:}

c = KN

-KN

(5) C C KN = V KN - V KB - V KB

cc

k k R R 50 V

Finally the lever of static stability in calm water is obtained from:

GNsinq = KNsin - KGsin (6)

The residuary stability decreases with increasing beam-depth ratio as shown in Figure 5, where kc() is plotted on a base of maximum beam/depth ratio.

The empirical formulas(1) and (2) should not be applied outside the considered range of form parameters. Also the k() values as given in Figure 5 are valid only for the particular cross sectional forms of the seies, in particular at

large angles of heel.

3. RESISTANCE EXPERIMENTS

3.1 Experimental set up

All models have been constructed with a waterline length of 1,6 metres corre-sponding to a liñäi scale ratio a _{6,25 for a full scale waterline length} of 10 metres.

This model size, with an overall length of about 2,1 metres, fits the yacht measuring apparatus of the Deift Ship Hydromechanics Laboratory and gives in combination with the applied turbulence stimulator an adequate guarantee for consistent test results. This turbulence stimulator consists of carborundum strips on hull, keel and rudder, as shown in Figure 6. The carborundum grains with a sandpaper grain size 20 have been applied on the models with a density of approximately 10 grains/cm2.

Upright resistance tests for model speeds of 0,5 rn/s - 1,_8 rn/s

(F _{= 0.13 - 0.45) have been carried out with a "single" and a "double" sand}

strip to enable an extrapolation of the measured resistance values to zero sand strip width. It is assumed that the extra resistance due to the sand strips varies with the speed squared and is proportilonal to the strip width. Mean values of the resistance coefficients of the strips have been determined

in the central part of the considered speed range (V = 1,0 - 1,6 m/s), to avoid influence of laminar flow or wave making of.the turbulence stimulator.

Ail tests have been carried out in tank nô. 2 of the Delft Shiphydromechanics Laboratory, which has a cross-section of 1,22 x 2,75 m, but to study the influence of the blockage, the models 1, 6 and 7 have also been tested in tank

no. _{r, which has a cross-section of 2,55 x 4,22 m.}

The upright resistance values, as measured in tank no. 2, have been corrected for blockage effects, using Landwebers method as given in [7] The comparison with the measured values in tank no. 1 showed a very

satis--factory- agreement, the -speed correction--coefficients being-:- 1-,O07 1,013 and

1,0Ó for the models 1, 6 and 7. Consequently this correction method has been applied to the measured upright resistance values of all models. The speed correction covered a range of 1,005 to 1,013.

The experimental values for side force, induced resistance and leeway angle did not differ significantly in the case o-f models 1, 6 and 7 and no correc-tions have been used- for these values as measured in tank no. 2.

3.2 Upright resistance

The residuary resistance per unit weight of displacement of the canoe body, RR/Ac is given on a base of the Froude number Fn = V/VgL' in the

Tables Sa, Sb and Sc.

For the comparison of the various models the weight of displacement of the canoe body is used for the dimensionless presentation of the results, because the influence of keel and rudder on the upright residuary resistance is quite small. Thus for geometric similar hull forms the total residuary resistance is obtained from:

= RR/AC (7)

where =pgV.

C C

V = F

\JgL

To determine the total upright resistance RT the frictional resistance RF is added to (7), thus:

RT

= RR+RF

For yachts with a separate fin keel and rudder the frictional resistance is obtained by adding the contributions of hull, rudder and keel:

(lO)

=

pV2(ScCFc + SkCFk +

r Fr

where S , S and S. are the wetted areas of the canoe body, the keel and the

C k r

rudder; the coefficients CF CFk and CFr are the corresponding frictional resistance coefficients.

The frictional resistance coeffiáients have been. calculated according to the definition of the International Towing Tank Conference 1957:

0.075

(11)

CF

_(1ogR-2)2

The Reynolds number R is determined for canoe body, keel and rudder separately:

V * 0,7

R nc R = nk R_nk =

V*

V V

V*Cr

and the corresponding forward speed is given by:

52

(9)

with: \)= 1,1413 iO6 for fresh water of 15°C V = 1,1907 * io6 _{for sait water of 15°C}

Ck and C are the average chord lengths of keel and rudder in metres.

The factor 0,7 in the definition of the Reynolds number for the canoe body allows for the particular profile and waterline slope of a yacht and defines a kind of average length.

The results of the resistance tests have been corrected for the effects of the carborundum turbulence stimulator strips, tank blockage and water temperature.

The relative importance of C, LCB and L/V 1/3 with regard to the upright resistance

T is shown in Table 6, where RT is given for three forward speeds (5,1f 6,9; 8,6 knots), assuming a waterline leright of 10 metres,. This example clearly shOws the importance of the slenderness ratio L/V1/3 on the upright resistance. A low prismatic gives a low resistance at low speeds and a high prismatic is better at high Froude numbers.

For a more analytical approach of the influence of the hull geometry on the upright resistance the experimental residuary resistance values have been expressed in a polynomial form, for discrete values of the Froude number with hull geometry coefficients as variables:

RR/

l0

A + A1C + A2C2 + A3LCB + A4(LCE)2 +

C

where A is the weight of water displaced by the canoe body

c

and LCB is the horizontal distance of the centre of buoancy from the mid waterline length, expressed as a percentage of LWL (forward of LWL/2 positive).

The coefficients A - A6 are given in Table 7 for Froude numbers ranging from

F = 0,125 to 0,450.

n

The expression (13) may be used to find optimum values of C and LCB for minimum residuary resistance.

These follow from:

C

= A/2A

p 1 2

53

54

The optimum values according to (14) are plotted on a base of Froude numbers in Figure 7.

The. accuracy of the polynomial expression (13) is satisfactory: for F = 0,35 the r.m.s. error is less than four percent, which corresponds to less than two percent error in the total upright resistance.

The relative importance of the optimum values of C and LCB is shown in the Figures 8 and 9, where the increase of the residuary resistance is given when

C _{ánd LCB diverge from their optimum values. Mean values of the residua_ry}

resistance for all twenty two models at F = 0,30, 0,35 and 0,40 are respect-ively RR/ A0 = 3,8 10, 8,1 * 10, 21,9 * 10 which indicates the

relative importance of the resistance increments as shown in Figures 8 and 9.

4. RESISTANCE., SIDE FORCE AND STABILITY

Extensive model tests with heeling angle and leeway angle have been carried out with the twenty two models for a range of Froude numbers to determine the relations between the heeled resistance R, the side force F8, the heeling angle and the leeway angle. The experimental set up is given in Figure 10. The

horizontal side force on the model in non-symmetric flow conditions is measured by two, stiff strain gauge dynamometers, preventing lateral dispiacèments only: the model is not restricted in vertical displacement, heeling, and pitching. The pivots of the connection between the side force dynamometers and the model are at a distance h above the still waterline (DWL), see' Figure 11. The height of the centre of gravity ZG is not scaled to model values ZGM and also h doés not correspond to the height of the centre of effort of the sails. Therefore at each of the considered forward speeds a range of shifts t of the weight p is included to enable the correction of the measured values for specified positions of the centre of gravity and the centre of effort of the sails for conditions corre-sponding to full scale values.

The heeled tests have been carried out at modelsoeeds 1,0-, 1,-2, 1,-4 and 1,6 m/s,

corresponding to a.Froude number range of 0,25 to 0,40. Additional leeway tests with zero heeling angle have been carried outat F _{= 0,20 and 0,35.}

Forward speed and heeling angle have a certain correlation in conditions other than running. In particular routine experiments to determine the close hauled performance, as carried out in the Deift towing tank, are carried out at

F = 0,25; 0,30 and 0,35 in combination with heeling angles respectively:

= 10, 20 and 30 degrees. During each run the drift angle is varied to find the equilibrium condition corresponding to this combination of forward speeds and heeling angles.

In the present test program this linear dependency has been avoided and each of the three heeling angle conditions has been investigated for a range of forward speeds. In this way abetter definition òf the relations between speeds, heeling angle, side force and resistance could be obtained in some cases.

The experimental data have been used to formulate expressions for the leeway angle, the heeled resistance and the stability as a function of the heeling angle the side force and the forward speed by means of least squares procedures and these expressions are given in this paper. A similar analysis of yacht hull data has been given in [2, 3, 4, 8] to reduce experimental data.

4.. 1 Leeway angle

With a high degree of accuracy the leeway angle 6 is expressed by:

Fcos

H (15)

-

½pv2S

cos q) is the horizontal comporint of the side force,

is the wetted area of the canoe body, and q) in radians.

The constants B and B2 deperd on the hull,, keel and rudder geometry and are given in Table 8 for the twenty two models. The least squares fit resulted

in a mean r.m.s. error of 0,28 degrees.

It should be mentioned here that the wide range of the variables, as discussed above, sometimes resulted in unrealistic combinations of forward speed, heeling angle and leeway angle. A slightly batter fit with (15) is obtained when the test data of selected' runs, as used for the routine performance, are analysed.

In that case the for B and B do

o 2

number of runs.

A typical plot of experimental points in comparison with the relation (15) is given in Figure 12 for model 1.

55

mean r.m.s. error is smaller than 0,2 degrees, but the values not differ very much from those obtained from the total

where. F

s c

4.2 Heeled resistance

The. resistance due to heeling and leeway is given by

Rth - RT, where is the

heeled resistance and is the upright resistance with zero leeway.

The added resistance can be split up in a part due to side force production (induced resistance) and a relatively small part due to heeling and leeway in the zero side force condition. A rather simple expression to reláte the added resistance with side force, heeling angle and forward speed is given by

- RT

½ pV

(C + C )F 2

o H

(½PV2S)2

where: FR - the side force

- the heeling angle in radians

The coefficients C, C2 and _CH depend on hull form, keel- and rudder geometry. The coefficients as obtained from all test runs of the twenty two models by a

least squares fit, are given in Table 9. The mean r.m.s. error of this fit is approximately 0,2 N.

However Table 9 shows that in many cases a negative value for C2 has been found. This would indióate an increase of the effective aspect ratio of the underwater part of the yacht with increasing heeling angle, which is not very likely from a physical point of view.

To study this effect more closely the experimental added resistanee values have been plotted as a function of side foràe and Fròude number, see Figure 13a b

c d. To fit the data the Froude nuner has to be ircluded in the slope of the resistance-side force relation as well as in second term of the expression:

R -pV2 - C

(C1 +

C2p2

+ C F )F 2

_3fl

(½pV2S ) 2 C

Table 10 gives the values of the constants C1 - C4 for all twenty two models (mean r.m.s. error 0,16 N) and the result of (17) is compared with the

measured resistances in the Figures 13.

Although some scatter of the experimentalvalues is observed, the tïeãh f.Í'n.ä. error is close to the exerimental accuracy and a further. refinement of (17) does not seem feasable.

56

(16)

For the selected rm-is the strong relation between the heeling angle and the Fraude number simplifies the matter to a fair degree and equation (16) is therefore preferable..

Table 11 gives the coefficients CO, C2 and C for this particular case, with a mean r.m.s. error of 0,11 N. Figure 14 shows the quality of fit for the case of model 1.

The resistance parts of (16) and (17) which are not induced by. the side force are not easy to relate to the geometry of the underwater part of the various yacht hull forms. Formulation of these parts is therefore not attempted.

4. 3 Stability

The heeled runs allow the determination of the stability at forward speed. For the model experiment the following equation is valid in the equilibrium position, see Figure 11:

AGNsin =

ptcos

_{+ FH.DL}

(18)

where: A is the weight of total displacement

p is a known weight displace athwartship over a distance t from a position in which the model is in upright position

DL

is the lever of heeling moment, caused by the side force FH.

In general the vertical position of the centre of gravity of the model is not on scale but at a known distance under the still water plane, see

-Figure 11.

Also the vertical position of the pivot point S, at a distance h above the still water plane does not correspond with the centre of effort of the

sail-force ZCE..

Therefore equation (18) is rewritten in the following form:

ptcos

--Az

sin

= AONsin4

_{- FH.DL}

(19)

with:

cr4

h

D4 = D

L

p , A _, ZGM and h are known quantities for a given model, whereas , FH, ON

and D4 have to be determined from the model test. To this end _AONsinth is expressed by:

AQNsin

= ACL(Di

+ D F +

2 n

57

The first term reoresents the initial stability for the case = 0, with

GM. = _{LLDl. The second term represents the influence of forward sneed}

on the heeled stability. The third term is included for non-linearity at larqer anqies of heel.

For the reduction of the experimental data is written:

= Dc + D24F

+ T2 -

(21) where: and

k()

= ptcosq _{- IZGMSin} Dd = -WL

The coefficients D are a function of the geometry of _{hull, keel and rudder.} They have been derived with a least squares fit and the results are given in Table 12 for all of the twenty two models.

The exoression (21) fits the data with a mean rm.s. errorof 0,14 Nm. Again, with a selected number of runs the fit is better _{(mean r.m.s. error 0,12 Nm)} but the least .squares procedure does not _{provide reliable coefficients D2 and} D3, because of the strong correlation between F and in this case. A.

coiùputation, assuming D2 _{= O gives a similar fit}

( mean r.m.s. error 0,12 Nm),

but for all runs D2 = O results in a slightly less satisfactory fit (mean r.m.s. error 0,23 Nm).

For an actual yacht, with a given _{centre of gravity ZG and centre of effort} ZCE the stability moment is given by:

Mt = AL(D1

+ D2F

+ D32)

+ AZGsir1 (22)

The heeling moment follows from:

= FH(zcE + D4L) ₍₂₃₎

4.4 The longitudinal position of-the _{centre of lateral resistance}

The longitudinal moment produced by the side force has been measured to determine the location of the òentre d _{lateral resistance in the upright}

Position. Two forward speeds have, been considered: _{F = 0,20 correspoñding with} very moderate wave making and F _{= 0,35 with a rather large bow wave in most}

cases.

Table 13 gives the positions of the centre o lateral resistance, as determined for these conditions. As a reference the draught of the canoe body, the

prismatic coefficient and the longitudinal position of the centre of buoyancy of all models have been included in the Table.

For F = 0,20, a mean value: CLR = 7,7 % of L forward of L /2 has been

n WL WL

found. For F = 0,35 this mean value slightly increases to 9,8 %, which may be due to the influence of the bow wave system. From Table 13 it could be concluded that with increasing draught the CLR moves forward, but apoarently this increase is very small.

It has to be remarked that in all tests the rudder has been fixed in the mid-position. During actual sailing the helmsman corrects for the side wash of the keel and the resulting larger side force of the rudder causes a shift of the CLR. According to Nomoto [s] a three degree rudder angle could result in a 10 % shift of CLR.

5. DISCUSSION OF THE RESULTS

5.1 Upright resistance

A calculation of the upright resistance according to (10) and (13) has been carried out for three hull forms: the oarent form of the systematic series

(model 1), the Netherlands national one design class "Pion" (model 123), and a 1981 Admiral Cupper (model 195) designed by de Pdder.Asshown_in Figures 15, 16 and 17 the calculation agrees satisfactorily with the measured resistance, in particular the good result in case of the Admiral Cupper is noteworthy, because in this case the beam-depth BWL/T = 6,33 is well outside the range considered in the systematic series.

The calculation may be used to study the relative merits of hull changes in a design process..

5.2 Side force

Equation (15) can be written in the following form.:

FHcos s

-

(B + B 2)

(½PV2SE) o 2 SE

(24)

where the arbitrarily chosen wetted hull area Sc for non-dimensioning the side force is retlaced by any effective area SE.

For instance SE can be taken equal to the sum of the keel and rudder areas when extended to the DWL, neglecting the hull area completely.

In combination with an exnression for the liftslope, as used in relation with an isolated lifting surface, the effective aspect ratio of the hull,

keel and rudder configuration, as represented by (24) may be determined. The well known liftslope. formulation, as given in [7] can be used for this purnose:

ac 5.7 AR

L E

-- =

1,8 + cosAV

_ '

where a is the slope of the lift coefficient at an angle of attack a = O

A is the sweep angle of the quarter chord linè a in radians

AR

is

the effective aspect ratio

In Table 14 the effective asoect ratios ARE for side force of the twenty two models have been determined with SE = _AKI where AK

is

the projecd area of the keel, when extended to the DWL. These effective aspect ratios are comnared with twice' the geometric aspect ratio ARG of the extended keels in Figure 18

for = 0, 10, 20 and 30 degrees on a base of BWL/T.

With increasing heel and increasing seam-draught ratio the effective aspect-ratio of the kee-1 is decreasing. The drawn lines in Figure 18 may be used to approximate the side force for a given leeway heeling angle, forward speed and keel geometry only, accepting the scatter of the experimental points.

In [i] the extended keel and rudder concept has been introduced as a design tool to calculate side force. Also in this case the expression (25) has been used, assuming in addition that the effective aspect ratio of the rudder is al-so equal to twice the geometric aspect ratio of the projected rudder area when extended to the DWL. Based on wake measurements on model scale the water

speed at the rudder has been taken as 90 % of the forward speed of the yacht. The influence of side wash, produced by the keel, on the angle of incedence

should be included when comparing calculated side forc with the results of model tests with zero rudder angle (see [1])

(25)

In the present case the influence of side wash is neglected and the calculated side force according to (25) using the extended keel and rudder is directly comoared with the exoerimental values in Figure 19 for Froude numbers F = 0,20 and 0,35 and zero heeling angle. The agreement between-calculation and

experiment is satisfactory taking into account the rather crude assumption that the influence of the hull is included in the extended parts of keel and -rudder. Apparently this is due to the rather large beam-draught ratios of the

considered canoe bodies, which are- not ideal for the Droduction of side force. The method is useful for design ourooses, but is recommended only for modern flat hull forms.

The side wash of the keel diminishes the angle of incidence of the rudder. Because of the relatively large distance between keel and rudder the side-wash is mainly caùsed by the free vortices of the keel.

An estimation for the upright condition as given in [g] shows that the side wash angle is arrnrox-imately 60 % of the leeway angle. In addition to a wake

fraction of 0,1 a total "reduction" factor for the rudder of 0,92 x 0,4 0,324

-is found.

-Assuming the rudder and keel extended to the DWL, neglecting the influence of the canoe body, and using (25) for the determination of the side forces produced by keel and rudder, the CLR is 3,1-%forward o _{LWL/2 for model 1,}

independent of the forward speed of the yacht.

The difference with the exr)erimental value at F = 0,20 is small.

-. n

A similar correlation has been found for the other models.

-5.3 Heeled resistance

A similar exercise has been carried out with the experimental heeled resist-anc-e results as reduced to equations (16) and (17).

It should be remarked that the first term in these equations may be regarded as induced resistance, whereas the second term could reflect the increased resistance due to asymmetry of the underwater part of the hull in the position with leeway and heel but without side force. To study the induced resistance

61 part R1

R1 =

or:

in more detail we write,

(C_o

+ C22)F1

starting from F2 H (16): -(26) ½pS V2 C -S R I = (C_o

+C2q2)!.

,c

(27) ½PSEV2

In view of the well known expression for the induced resistance coefficient CDI of a lifting surface producing a lift coefficient CL:

c (28)

DI _¶ARE

we may write with (27) s C i ARE = lISE C0 + C4) and: F2 i H (3.0) R. _{= wARs ½PSEVZ}

For S5 = AK. the projected extended. keel area the effective aspect ratios for all models have been calculated for = 0, 1,0, 20 and 30 degrees..

These values are expressed in percents of twice the geometric aspect ratio of the extended keel area, as given in Table 14.

In Figure 20 these values are given on a base of beam-draught ratio, showing a decreasing efficiency with increasing heel. There is a slight tendency of the effective aspect ratio to increase with increasing beam-draught ratio at zero and ten degrees heeling angle.

The influence of the second term in (16) and (17) is small but not to be neglected for the larger heeling angles. The mean value of CH from Table 11

is approximately 5 x 10. With 2 = 0,03, 0,12 and 0,27 for 10, 20 and 30 degrees of heel the relative imnortance of the second term may be estimated, for instance by using the mean values given for the residuary resistance in chapter 3.

The C5 values denend weakly on the beam-draught ratio. As a rough guide: CH equals 4, 5 and 6x103 for respectively BWL/T = 3, 4 and 5.

5.4 Stability

The stability according to (21) as measured with the model experiments, has been compared with the result of static

stability

calculations. Three heeling angles and three forward speeds have been considered for this comparison

viz..: = 10, 20 and '30 degrees with resoectively F = 0,30 and 0,35.

Figure 21 gives a typical result (model 1) showing a slightly lower experi-mental stability, due to dynamic effects at forward speed (s'hiD waves). For almost all models a similar picture has been obtained, with differences smaller than 5 %. There are three exceDtions: model 10 has 10 % less

stabil-(29)

ity, model il has 25 % less stability and model 14 has 9 % more stability when comoared with a static stability calculation.

The 25 % reduction in the case of model 11 could not be exnlajned from the geometry of the model; the possibility of an error in the measurement of the heeling moment should not be excluded in this narticular case.

For the determination of the heeling moment., the vertical position of the centre of lateral resistance is imnortant. From D4L (Table 12) and the total draught of the yachts (Table 2a) it could be concluded that the distance of the centre of lateral resistance below the designed waterline is between the extremes 0,31 T and 0,40 T, with a mean value of 0,35 T. Again there is a weak dependency of DL/T with EWL/Tc. Aoproximately: D4L/T = 0,37, 0,35 and 0,34 for respectively BWL/Tc = 3, 4 and 5.

These values are somewhat smaller than 42 % of the draught, which follows from an ellintical side force distribution which could be assumed when the extended keel concept is used for the approximation of the side force.

These lower values cornoensate for the slight loss of stability lever as measured for almost all models and consequently a completely tatic stabil-ity calculation, as commonly used in naval architecture, may be used for the prediction of sailing yacht oerformance.

When D4L is referred to the draught of the canoe body T, a mean value of 0,97 T is found with extreme values 0,77 T and 1,12 T

c c c

For flat hull shapes with a large beam-draught ratio the centre of lateral resistance is locatéd at a small distance under the canoe body.---For--smaller_-beam-draught ratios D4L is smaller than T and consequently the CLR is

within the canoe body.

In general however it may be stated that the centre of lateral resistance is very close to the bottom of the canoe body of the considered yacht models. A similar trend has been found earlier by Nomoto for three very different yachts [5}.

--ooüoo--The analysis of the large amount of exoerimental data, as given in this chapter, is not to be considered as conclusive.

The original experimental däta will be made available in the near future, to allow_additional_studyby those who. are interested in this narticular f ie.ld.

References

[iJ J. Gerritsma, G. Moeyes, R. Onnink

Test results of a systematic yacht hull series 5th Symposium on developments of

interest to yacht architecture.

HISWA Amsterdam 1977

[2] D.S. Jenkins

Analysis of a systematic series of yacht model tests.

M.Sc. Thesis, Department of Ocean Engineering M.I.T. 1977

'[3] J.E. Kerwin, J.N. Newman

A summary of the H. Irving Pratt Ocean Race Handicanoing Project

Chesapeake Sailing Ycht Symoosium S.N.A.M.E. Annapolis 1979

[4] i.E. Kerwin

A velocity prediction program for ocean racing yachts.

New England Sailing Symposium New London, Connecticut 1976

f5] K. Nomoto

Balance of helm of a sailing yacht - a ship hydrodynamic approach of the problem

6th Symposium on developments of interest to yacht architecture HISWA

Amsterdam 1979

A. Versiuis

Computer aided

design of sliipform by affine transformatic

International Shipbuilding Progress 1977

Principles of Naval Architeòture

Soc. of Naval Architects and Marine Engineers 1967

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

Determination of sailforces based on full scale measurements and model tests

4th Symposium on developments of interest to yacht architecture HISWA

Amsterdam 1975

[J J. Gerritsma

Course-keeping qualities and motions in waves of a sailing-yacht

Third A1AA Symposium on the aerodynamics and hydrodynamics

Nomenclature Nomenclature

waterplane area ci. linear scale ratio

maximum sectional area : leeway angle

aspect ratio A : weiqht of displacement

project area of the keel : volume of disolacement

maximum breadth : heeling angle

waterline breadth A : sweep angle of quarter chord li

metacentric radius : kinematic viscosity

chord p specific density

centre of effort

frictional resistance coefficient Subscripts: lift coefficient

c : rerers to canoe body

CLR : centre of lateral resistance

E : refers to erfective

Cci : prismatic coefficient

G refers to geometric D deoth - k refers to keel DWL : design waterline r : refers to rudder Fn : Froude number FH : side force g : gravity acceleration G centre of gravity GM : metacentre height

GNsin : arm of static stability

1T transverse moment of inertia of waterolane 'L longitudinal moment of inertia of waterolane

KB :height of centre of buoyancy above base line height of metacentre above base line

L : length

LWL : waterline length

LCB : longitudinal position centre of buoyancy

LCF : longitudinal position centre of f lotation

MNsin arm .of residuary stability

Rc : total resistance with heel and leeway

RF : frictional resistance

RR residuary resistance

RT : total resistance in upright oosition

R1 induced resistance

R : Reynolds number

S wetted area

S effective area of keel or rudder

65 Ax : AR : AK : Bmax : BWL : BM : C : C : CF : C L

Table i

Main form parameters.

66 Model

nr.

LWL

/BWL

LWL BWL C p LWL/

/1/3

LCB 1

3.17

2.73

3.99

0.568

4.78

-2.3

2

3.64

3.12

3.04

0.569

4.78

-2.3

3

2.76

2.35

5.35

0.565

4. 78

-2.3

4

3.53

3.01

3.95

0.564

5.10

-2.3

5

2.76

2.36

3.9'6

0.574

4.36

-2.4

6

3.15

2.73

2.98

0.568

4.34

-2.4

7

3.17

2.72

4.95

0.562

5.14

-2.3

8

3.32

2.82

3.84

0.585

4.78

-2.4

9

3.07

2.62

4.13

0.546

4.78

-2.2

10

3.15

2.72

3.99

0.565

4.77

0.0

11

3.15

2.72

3.99

0.565

4.77

-5.0

12

3.51

3.03

3.94

0.565

5.10

0.0

13

3.51

3.03

3.94

0.565

5.10

-5.0

14

3.51

3.03

3.69

0.530

5.11

-2.3

15

3.16

2.72

3.68

0.530

4.76

-2.3

16

3.15

2.72

2.81

0.530

4.34

-2.3

17

3.15

2.72

4.24

0.600

4.73

0.0

18

3.15

2.72

4.24

0.600

4.78

-5.0

19

3.15

2.72

.3.75

0.530

4.78

0.0

20

3.15

2.72

3.75

0.530

4.78

-5.0

21

3.51

3.0.3

4.17

0.600

5.10

-2.3

22

2.73

2.36

4.2.3.

0.600.

4.34

-2.3

Table 2 a

Main dimensions and derived quantities.

67 Model nr LWL in m BrL m T m D in V _Sc m2 1 _{10.04 3.67 3.17 0.79 1.94 9.18 25.4 1.62 21.8} 2 10.04 3.21 2.76 0.91 2.06 9.1.8 23.9 1.62 19.1 3 10.06 4.25 3.64 0.68 1.83 9.16 27.6 1.63 25.2 4 10.06 3.32 _{2.85 0.72 1.87 7.55 23.0 1.34 19.8} 5 10.05 4.24 3.64 _{0.92 2.07 12.10 29.1 2.15 25.3} 6 10.00 3.66. 3.17 1.06 2.21 12.24 27.5

216

21.9 7 10.06 3.68 3.17 0.64 1.79 7.35 24.1 1.31 21..8 8 10.15 3.54 3.05 0.79 1.94 9.18 25.4 1.57 22.1 9 10.07 3.81 3.28 0.79 1.94 9.18 25.0 1.68 21.5 10 10.00 3.68 3.17 0.79 1.94 9.19 25.6 1.62 22.0 11 10.00 3.68 3.17 0.79 1.94 9.19 25.3 1.62 21.6 12 10.00 3.3Ò 2.85 0.72 1.87 7.52 23.0 1.33 19.8 13 10.00 3.30 2.85 0-72 1.87 7.52 22.8 1.33 19.4 14 10.00 3.30 2.85 0.77 1.92 7.5.2 22.4 1.42 18.7 15 10.00 3.67 3.16 0.86 2.01 9.29 24.9 1.76 20.8 16 10.00 3.68 3.17 1.1,3 2.28 12.23 27.3 2.32 20.9 17 10.00 3.68 3.17 0.75 1.90 9.17 26.3 1.53 23.0 18 10.00 3.68 3.17 0.75 1.90 9.17 26.0 1.53 22.6 19 10.00 3.68 3.17 0.84 1.99 9.17 24.8 1.73 21.0 20 10.00 3.68 3.17 0.84 1.99 9.17 24.6 1,73 20.6 .21 10.00 3.30 _{2.85 0.68 1.83 7.54 23.6 1.26 20.5} 22 10.00 4.24 3.66 0.86 2.01 12.26 30.2 2.05 1 26.3

68

Table 2 b

Main dimensions and derived quantities.

Table 3

Volume and wetted area of keel and rudder Model nr. 'T m 'L LCF % LOE % KB m BM m KM rn KB m BM in KM m 1 12.89 113.2 -3.3 -2.3 H 0.53 1.40 1.93 0.45 1.30 1.75 2 8.64 99.2 -3.3 -2.3 0.60 0.94 1.54 0.56 0.87 1.43 3 19.88 131.1 -3.3 -2.3 0.45 2J7 2.62 0.38 2.02. 2.40 4 9.60 102.8 -3.3 -2.3 0.48 1.27 1.75 0.39 1.16 1.55 5 19.99 131.2 -3.3 -2.4 0.61 1.60 2.21 0.55 1.51 2.06 6 12.85 113.2 -3.3 -2.4 0.71 1.05 1.76 0.64 0.99 1.63 7 12.85 109.8 -3.3 -2.3 0.43 1.75 2.18 0.34 1.60 1.94 8 12.66 120.6 -3.4 -2.4 0.53 1.38 1.91 0.45 1.28 1.73 9 . 13.21 105.3 -3.1 -2.2 0.52 1.43 1.95 0.45 1.33 1.78 10 13.06115.0 -1.6 0.0 0.52,1.42 1.95 0.45 1.32 1.77 1.1 12.66 113.6 -5.0 -5.0 0.52 .138 1.90 0.45 1.28 1.73 12 9.47 103.3 -1.9 0.0 0.4.8 1.26 1.74 0.39 1.15 1.54 13 9.17 102.1 -5.0 -5.0 0.48 1:22 1.70 0.39 1.12 1.51 14 8.69 92.3 -3.5 -2.3 0.52 1.16 1.67 0.43 1.07 1.50 15 11.92. 102.6 -3.5 -2.3 0.57 1.28 1.85 0.49 1.19 1.68 .16 11.99 102.7 -3.5 -2.3 0.75 0.98

173

0.68 0.93 1.61 17 13. 94 127.2 -1.8 0.0 0.49 1.52 2.01 0.42 1.41 1.83 18 13.53 125.8 -4.9 -5.0 Ò.4.9 1.48 1.96 0.42 1.37

179

19 12.18 104.0 -2.0 0.0 0.56 1.33 1.89 0.49 1.24 1.72 20 11.77 102.5 -5.1 -5.0 0.56 1.28 1.84 0.48 1.19 1,68 21 9.96 113.1 -3.3 -2.3 0.45 1.32 1.77 0.37 1.21 1.58 22 21.12 . 145.3 -3.2 -2.3 0.57 1.72 2.29 ' 0.61 1.63 2.24 keel . . rudder volume m3 wetted area in2 0.639 ' 0.055 6.01 2.15 total _{0.694 8.16}

Table 4

Dimensionless residuary stability (canoe body)

k()

= MN sin th /BM.103 C Cc cc 69 Model _{loo 200} 30° 40° 50° 60° 70° 80° 90° 1 0 - 6 -25 -. 56 -101 -182 -272 -384 -479 2 o + 5 +16 + 34 + 29 - 2 - 55 -133 -225 3 0 -30 -74 -141 -236 -348 -463 -573 -668 4 -12 -27 - 47 - 88 -14.9 -244 -340 -436 5. 0 - 8 -19 - 57 -134 -229 -336 -446 -544 6 0 + 7 +20 + 30 + 41 - 4.2 -110 -193 -294 7 _{-3 -27 -66 -117 -188 -287 -396 -504 -600} 8 -5 - 9 -26 - 43 - 92 -162 -258 -363 -4.68 9 0 -10 -27 - 62 -119 -2Oi -301 4O4 -507 10 -6 -1]. -27 - 56 -116 -199 -296 -4.02 : -509 11 -4 - 8 -24 - 47 -101 -175 -273 -377 -475 12 -1 -10 -25 - 4.2 - 80 -145 -232 -335 -435 13 -1 -. 9 -22 - 37 -. 74 -139 -232 -329 -430 14 -i - 6 -i4 - 28... 9 -. -l79 . -.17.5.. -3.71.. 15 -1 - 6 -13 - 29 - 71 -148 -236 -337 -437 16 +2 + 5 +.7 + 16 -. 3 - 45 -107 -185 -266 17 -3 -16 -40 76 -137 -221 -32.4 -431 -532 18 -2 -12 -34 - 69 . -132 -215 -316 -414 -521 19 . -1 - 8 -18 - 37 - 85 -157 -248 -351 -4.52 20 -1 - 5 -13 - 31 -. 79 -14.8 -238 -337 -438 21 -3 -13 -35 - 65 -110 -181 -274 -374 -471 22 -2 -14 -37 . - 91 -177 -278 -389 -499 -598

Table 5 a.

Residuary resistance Der unit weight of displacement of canoe body.

RR/.

Table 5b

Residuary resistance per unit weight of disolacernent (canoe body only)

R/A 70 rodel F n 1 2 H 3 4 5 6 7. 8 0.125 0.11 0.04 0.09 0.20 0.16 0.12 0.28 . 0.20 0.150 . 0,27 0.17 0.29 0.35 0.23 0.26 0.44 0.38 0.175 0.47 0.37 0.56 0.65 0.35 0.43 0.70 0.64 0.200 0.78 0.66 0.86 0.93 0.54 0.69. 1.07 0.97 0.225 1.18 1.06 1.31 1.37 0.85 1.09 1.57 1.36 0.250 1.82

i.9

1.99 1.97 1.31 1.67 2.23 1.98 0.275 2.61 2.33 2.94 2.83 2.08 2.46 3.09 2.91 0.300 3.76 3.29 4.21 3.99 3.06 3.43 4.09 4.35 0.325 4.99 4.61

554

5.19 4.49 4.62 5.8.2 5.79 0.350 7.16 7.11 . 8.215 8.03 6.69 6.86 8.28 8.04 0.375 11.93 11.99 13.08 12.86 11.53 11.56 12.80 12.15 0.400 20.11 21.09 21.40 21.51 19.55 20.63 2.0.41 19.18 0.425 32.75 35.01 33.14 33.97 32.90 34.50 32.34 30.09 0.450 49.49 51.80 50.14 50.36 50.45 54.23 47.29 4.4.38 Model F n 9 10 11 - . 12 : 13 - 14 15. 0.125 . 0.15 0.11 0.07 0.08 0.08 0.08 0.10 0.150 0.32 0.24 0.18 0.26 0.24 0,25 0.23 0.175 0.55 0.49 0.40 0.50 0.45 0.46 0.47 0.2.00 0.86 0.79 0.70 0.83 0.77 0.75 0.76 0.225 1.24 1.28 1.14 1.28 1.19 1.11 1.15 0.25e 1.76 1.96 1.83 1.90

1.6

1.57 1.65 0.275 2.49 2.88 2.77 2.68 2.59 2.17 2.28 0.300 3.45 4.14 4.12 3.76 3.85 2.98 3.09 0.325 4.83 5.96 5.41 5.27 4.4.2 .4.41 0.350

737

9.07 7..87 8.76 7.74 7.84 7.51 0.375 12.76 14.93 12.71 14.24 12.40 14.11 13.77 0.400 21.99 24.13 21.02 23.05 20.91 24.14 23.96 0.425 35.64 38.12 34.58 35.46 33.23 37.95 37.39 0.450 53.07 55.44 51.77 51.99 49.14 55.17 56.46

Table 5c

Residuary resistance per unit weight of

displacement -RR/A. i0 71 F n MOd el 16 1 18 19 20 21 22 0.125 0.05 0.03 0.06 0.16 0.09 0.01 0.04 0.150 0.17 O.lb 0.15 0.32 0.24 0.16 0.17 0.175 0.3.5 0.40 0.34 0.59 0.47 0.39 0.36 0.200 0.63 0.73 0.63 .0.92 0.78

O73

0.64 0.225 1.01

1.O

1.13 1.37 1.21 1.24 1.02 0.2.50 1.43 2.16 1.85 1.94 1.85 1.96 1.62 0.275 2.05 3.35 2.84 2.62 2.62 3.04 2.63 0.300 2.73 5.06 4.34 3.70 3.69 4.46 4.15 0.325 3.87 7.14 6.20 5.45 5.07 6.31 6.00 0.350 7.19 10.36 8.62 9.45 7.95 8.68 8.47 0.375 13.96 15.25 12.49 16.31 13.73 12.39 12.27 0.400 25.18 23.15 20.41 27.34 23.55 20.14 19.59 0.42.5 41.34 34.62 32.46 41.77 37.14 31.77 30.48 0.4.50 62.42 51.50 50.94 60.85 55.87 47.13 46.66

Table .6

Total upright resistance for three speeds.

72 Model nr. C

L/r

LCB _RT IN NEWTONS 5.1 kn 6.9 kn 8.6 kn i 0.568 4.78 -2.3 56.1 1310 5021 2 0.569 4.78 -2.3 518 1284 5199 3 0.565 4.78 -2.3 600 1453 5115 4 0.564 5.10 H _{-2.3 509 1200 4246} 5 0.574 4.34 -2.3 605 1594 6695 6 .0.568 4.34 -2..3 635 1594 7142 7 0.562 5.14 -2.3 541 1220 4029 8 0.585 4.78 -2.4 581 1381 4604 9 0.546 4.78 -2.2 54.6 1333 5307 10 0.565 4.77 0.0 581 1510 5554 11 0.565 4.77 -5.0 568 1373 5208 12. 0.565 5.10 0.0 499 1265 4354 13 0.565 5.10 -5.0 489 . 1170 4147 14 0.530 5.11 -2.3 465 1193 4564 15 0.530 4.76 -2.3 534. 1374 5644 16 0.530 4.34 -2.3 595 1712 3095 17 0.600 4.78 0.0 622 1626 5209 18 0.600 4.78 -5.0 581 1445 5117 19 0.530 4.78 0.0 558 1548 5980 20 0.530 4.78 -5.0 553 1386 5536 21 0.600 5.Si0 -2.3 524 1243 4043 22 0.600 4.34 -2.3 677 1813 6355

Table 7

Residuary Resistance polynomical coefficients.

73 Fn A0 A1 A2 A3 A4 A5 A6 0.125 -13.01 ±46.84 -42.34 -0.0190 -0.0046 +0.0341 +0.0085. 0.150 -14.00 +50.15 -45.53 _0.0214 -0.0062 ±0.04.81 +0.0585

0175

-13.11 +46.58 -42.76 -0.0153 -00062 +0.0674 +0.1425

0200

-10.26 +36.06 -33.41 -0.0021 -0.0043 ±0.0757 +0.2246

0225

-4.151 +13.68 -12.81 +0.0478 +0.0041 +0.0967 ±0.2965

0250

-0.15.6 -2.106 +3.196 +0.1211 ±0.0176 ±0.1504 +0.3532 0.275 +6.203 -27.30 ±29.88 +0.1711 +0.0273 +0.2240 ±0.3408

0300

-24.87 -98.55 ±100.1 +0.3168 +0.0570 -1-0.33:65, +0.3313 0.325 +85.16 -315.2 296.8 +0.5725 +0.0930 +0.4526 +0.4662 0.. 350

+195.6

-687.8

6I 7.0

±1; 009

-0 .

1476 +0 ..4.6.40., +06774

0375

+272.8

-901.2

+777.1

+1.540

±OE.2142

+0.3431

+0.3463

0.400 +414.0 -1321 +1117 ±1.934 ±0.2690 -0.1746 +0.0872. 0.425 +379.3 -1085 ±877.8 +2.265 ±0.326.6 -1.064 -1.053 0.450 ±588.1 -166.6 -4-1362 ±2.871 +0.4519 -1.501 -4.4.17

Table 8

Leeway versus sideforce.

74 Model nr. B1 B2 1 2.087 4.453 2 1.742 3.661 3 2.441 7.160 4 2.003 5.402 5 2.229 4.777 6 1.822 3.157 7 2.158 6.659 8 1.972 4.575 9 2.008 4.338 10 2.082 4.888 11 2.014 4.2S6 12 1.951 5.117 13 1.869 4.406 14 1.815 4.980 15 1.929 4.293 16 1.816 2.285 17 2.247 4.507 18 2.101 3.337 19 1.936 4.096 20 1.882 3.260 21 2.156 4.462 22 2.322 4.639

75

Table 9

Heeled Resistance coefficients.

Model nr. C 0 C2 C..103H 1 1.2138 -1.1431 10.200 2 1.0970 -0.8800 5.874 3 1.4516 0.1141 11.043 4 1.2710 0.2168 8.098 5 1.3257 -o.04i5 4.902 6 1.0779 -0.7065 6.194 7 1.2299 0.7666 13.493 8 1,1452 0.3167 6.439 9 1,1695 -1.6059 13.330 10 1,3252 -1.2624 7.863 11 1,2:649 0.2059 4.944 12 1,3893 -0.6143 6.502 13 1,1602 1.1137 5.507 14 1,0598 . 0.5758 6.752 15 1,1537 -0.6889 9.076 16 1,0900 -1.8796 7.490 17 1,3617 -1.2660 7.2.64 18 1,3977 0.5058 2.925 19 1,1697 -0.5552 10.048 20 1,1257 0.6875 4.602 21 1,329.3 -0.0457 5.848 22 1,3024 0.7547 3.594

Table 10

Heeled Resistance coefficients. Froude number included

76 C1 C2 C3 C4.103 1 0.1698 0.5989 3.24.11 21.131 2 -0.0307 0.4617 3.6538 13.261 3 H -0.4433 _{1,7611 6.2263 22.990} 4 0.0862 1.8361 3.8100 19.069 5 0.742.3 0.4217 1.9915 12.499 6 0.4665 -0.3763 2.5414 13.520 7 0.3412 2.7756 2.3673 31.498 8 0.5612 1.1014 2.0077 13.612 9 0.3289 0.4359 2.7142 _31.119 10 0.7358 -0.5321 2.1077 19.175 11 0.6017 1.000,2 2.3956 11.427 12 0.2870 0.2239 3.6438 . 17.632 13 0.9854 . 1.9973 0.6282 14.121 14 0.9632 2.0991 0.2466 18.128 15 0.3596 0.4563 3.1478 19.383 16 0.5100 -0.3393 2.1075 17.055 17 1.1619 0.0693 0.3359 19.615 18 0.4427 0.1666 3.9578 1.531 19 0.5195 0.1126 2.4796 23.992 20 0.4919 0.3386 2.699.8 7.240 21. 0.8265 C.8856 _1.7453. 14.427 22 0.3713 0.8853 2.9768 7.154

Table 11

Heeled Resistance Coefficients

(selected runs) 77 Model nr. C o C2 C..103H 1 1.2370 2.6198 5.772 2 1.1898 2.0259 3.709 3 1.5429 5.3097 6.339 4 1.3443 3.9076 5.363 5 1.2956 3.1894 2.357 6 1.2065 1.8437 3.623 7 1.146. 5.12&7 10.083 8 1.1198 3.0482 3373 9 1.2285 2.2096 8.9.25 10 1.4313 1.3333 5.485 11 1.2948 2.5980 3.020 12. 1.4972 2.3810 4.976 13 .1953 3. 1922 3. 925--14 1.1122 2.4273 5.604 15. 1.2875 1.8152 6.597 16 1.1305 3.1478 3.587 17 1.4308 0.4758 5.169 18 1.7597 1.3760 -0.3.39 19 1.2261 2.2881 6.618 20 1.1952 2.6571 1.440 21 1.4448 1.64.80 4.570 22 1.3819 1.9687 1.592

Table 12

Stability coefficients

78 Model

nr.

D1 D2. 102 D3. 102 D D4 1

0.10841

-1.5855

-3.1892

0.2367

0.0773

2

0.05094

-0.4732

0.0838

0.2424

0.0849

3

0.20197

-4.5588

-9.9022

0.2265

0.0685

4

0.09574

-1.4240

-3.1054

0.2333

0.0733

5

0.13238

-2.0356

-3.1371

0.2332

0.0707

6

0.05773

0.5227

0.0446

0.2464

0.0870

7

0.15570

-3.5306

-7.3639

0.2290

0.0714

8

0.11634

-0.7350

-3.4314

_0.2275

_0.074.4 9 0.1074.8

-3.7040

-2.1738

0.2301

0.0711

10

_0.10364

_-2.8469

_-2.3324

_0.2195

_0.0776

11

_0.07824

_-0.8111

_-2.8353

_0.2433

_0.0839

12

0.09452

-1.4.898

-2.81.6:8

0.2181

0.0750

13

0.08501

-0.8194

-1.9409

0.2317

0.0748

14

0.09217

-1.4733

-1.4758

0.2381

0.0756

15

0.08667

-1.2210

-1.9385

0.2478

0.0809

16

_0.04888

_0.1413

_0.0890

_0.2602

_0.0971

17

_0.12679

_-3.1679

_-4.0696

_0.2514

_0.0758

.18 .

0.11759

-1.3.193

-4.1053

0.2544

0.0838

19

0.09874

-2.7554

-1.8924

0.2317

0.0761

20

0.08725

-0.7916

-1.1414

0.234

0.0802

21

_0.10381

_-1.9703

_-3.2891

_0.2269

_0.0757

22

_0.14526

_-3.0122

_-4.4078

_0.2262

_0.0681

Table 13

Centre of Lateral Resistance.

CLR is expressed as a percentage of LWL. Forward of LWL/2 is positive. 7g Model nr. CLR T C C_p LCB F =0.20:F n n=0.35 ni

i

6.9 9.0 0.79 0.568 -2.3 2 9.1 12.1 0.91 0.569 -2.3 3 4.1 6.9 0.68 0.565 -2.3 4 7.1 9.9 0.72 0.564 -2.3 5 7.9 9.6 0.92 0.574 6 11.6 13.3 1.06 0.568 -2.4 7 8.0 11.0 0.64 0.562 -2.3 8 6.5 7.1 0.79 0.585 -2.4 9 7.4 9.3 0.79 0.546 -2.2 10 0.0 11.1 0.79 0.565 0.0 11 9.2 11.4 0.79 0.565 -5.0 12 7.3 9.7 0.72 0.565 0.0 13 6.4 9.8 0.72 0.565 14 5.5 10.1 0.77 0.530 -2.3 15 8.2 10.2 0.06 0.530 -2.3 16 11.5 13.2 1.13 0.530 -2.3--17 6.1 11.0 0.75 0.600 0.0 18 6.8 5.3 0.75 0.600 -5.0 19 11.1 11.2 0.84 0.530 0.0 20 12.6 12.4 0.84 0.530 =5.0 21 4.7 8.3 0.68 0.6;00 -2.3 22 3.3 2.8 0.86 0.600 -2.3

Table 14

Effective aspect ratios for side force _{and induced resistance}

ART/2ARG * loo

80

Model

nr

SIDE FORCE _{INDUCED RESISTANCE}

=O =lO° =2O0 3Q0 q=o HJ=lO° =2O0 =3O0

1 117 103 77 55 70 66 56 44 2 126 110 80 57 62 59 51 34 3 111 94 65 44 68 61 48 35 4 116 99 71 49 63 58 46 39 5 118 104 77 H _{55 69 64 53 41} 6 123 110 84 61 61 59 52 43 7 126 _{105 72 48} . 83 73 54 37 8 133 114 82 57 77 71 58 45 9 123 108 _{79 56 70 66} 57 47 10 120 104 75 53 61 59 55 49 11 125 109 81 57 66 63 54 43 12 123 105 75 51 56 54 47 39 13 132 114 81 5.6 69 64 53 40 14 124 . 105 73 50 70 66 55 39 15 118 103 76 54 62 59 52 44 16 110 102 83 64 62 57 46 35 1.7 134 _{102 77 56 65 64} 62 59 18 130 117 91 . 68 53 51 48 43 19 120 106 78 55 66 6.2 54 42 20 1.26 112 86 63 67 62 53 41 2,1 113 _{100 75 55 62 59} . 54 47 22 121 106 80 57 70 67 59 5Ó mean 122 106 78 . 56 66 62 53 43

1 L C.B 0 -2 4. 8 LWL /

/Y

46 4.4

-.

s

I

SO

_.

81

I

s

sa

s

s

5 0.54 Cp 056 0.58 0.60

s

s

-s

s

_s

'I

4 -I

s

s

s

s

B 3

s

s

s--6 5.0

s

s

I I I I

s

0.54 0.56

C p

--05.B 060

s

a

I

2.8 3.0 3.2 3.4 3.6 LWL/BWL

o 6

k-JI,,r

IACA NACA 012 PARENT MODEL i

FIGURE 2 LINES OF SYSTEMATIC SERIES. 82

±

2 3

1

PARENT MODEL 1

FIGURE 2 LINES OF SYSTEMATIC SERIES (CONTINUED)..

83 =

iìî

8 g io 11 12 13 NACA NACA 0012 632A015

NACA

0012

PARENT MODEL 1

FIGURE 2 LINES OF SYSTEMATIC SERIFS (CONTINUED). 84

15

16 17

N.CA 0012

20

2Z

PARENT MODEL i

FIGURE 2 LINES OF SYSTEMATIC SERIES (CONTINUED).

85

u-111w',

A

60rn

(1

FIGURE 3 FIN KEEL AND RUDDER ARRANGEMENT.

I .l26m

1.64m

kr()

MN sìn

BM

FIGURE 4 DEFINITION OF RESIDUARY STABILITY.

87

/

Bmax

D

1.6 1.8 2.0 2.2.

Brna.x

1,6 1.8 2.0 2,2

FIGURE 5 _{RESIDUARY STABILITY AS A FUNCTION OF HEELING}

ANGLE AND BEAM-DRAUGHT RATIO.

"10mm

single 10mm

double 20mm

FIGURE 6 TURBULENCE SIMULATION.

single 20mm

double 40mm

strips of carborundurn sand (grain size 20)

density 10 grains/cm2

-J

10 to 15mm

single 15 mm

LEB

60

Cp

.50

Fn

FIGURE 7 OPTIMUM VALUES FOR LCE AND C

p

90

Cp

range of series

LCB

FIGURE 8 INFLUENCE OF LCB ON RESISTANCE.

Cp

FIGURE 9 INFLUENCE OF C ON RESISTANCE.

p

FIGURE 10 TEST ARMNGErIENT.

93

FIGURE 11 DEFINITION OF SYMBOLS USED IN STABILITY TESTS.

1

4

FM

cos4/*p v2sc

1

6

4

I t

Modet.1

O0

Experiment

-

Catcutation according to formuLa 17

2

FH2/(4PV2Sc

)

3

FIGURE 13a _{HEELED RESISTANCE VERSUS SIDE FORCE SQUARED.}

-3

5i0

L)

>

6

2

Calcutafon

according fo forrnul.a 17

® Fn. 0.30

Fn.0.35.

_0.45

Fn. 0.40

_0.40

_0.35

D Fn. 0.45

i

2

F2/(

'/ (D

V2S

3

FIGURE 13c _{HEELED RESISTANCE VERSUS}

6

O

Model i

.p10

Calculation

according. to formula 17

O

Fn. 0.25

®

Fn. 0.30

Fn. 0.35

Experiment

A

Fn. 0.40

D

_{Fn. 0.45}

0.25

2 3 EH

P

V2

Sc

6

4

Li

I >

2 2 3

4

FHa,/(pVlSC)2

I.

Catcutafion according t

FIGURE 14 HEELED RESISTANCE VERSUS SIDE FORCE SQUARED.

-3

5000 4000 3000 200.0 1000 MOOEL i O = EXPERIMENT = CALCULATION I I I loo LWL =

10.04 m

B =

3.17m

WL p LCB =

2.3%

=

4.78

=

9.18rn3

C I 6 V

=

KNOTS

FIGURE 15 COMPARISON OF EXPERIMENTAL AND CALCULATED UPRIGHT

RESISTANCE; 4ODEL 1.

T =

O.79m

3WL/T =

4.01 m

2500

2000 1500 1000 500 t MODEL. 123 O _EXPERIMENT

-

CALCULATION

'Uil)

L/vy =

4.88 V = 3.24 ni3 C 0 2 4 6 KNOTS

FIGURE 16 COMPARISON OF EXPERIMENTAL AND CALCULATED UPRIGHT

RESISTANCE; MODEL. 123. 101 J I I L = 7.10 in B = 2.34 in T =

0.52 in

BWL/T = 4.5Ö CP =

.556

LCB =

-3.5%

N 3000

Rî

5000 4000 2000 1000 MODEL 195

O = EXPERIMENT

- CALCULATION

LVJi

WY

C 102 L =

9.73m

= 3.10 m T =

0.49m

BWI/T = 6.33 C C p = .550 LOE = -4.5% = 5.34 V 6.05m3 o 2 6 8 V KNOTS

FIGURE 17 COMPARISON OF EXPEflIMENTAL AND CALCULATED UPRIGHT

150

loo

100

sa

o

A R E/2

AR

_G

*

s'

T

.1

.

4

FIGURE 18 EFFECTIVE ASPECT PATIO WITH REGARD TO SIDEFORCE.

103

00

.

,+ 1(\

104

0.4 0.5 0.6 0.4 0.5 0.6

1//2 PV2Scca(c. Fw/Y2 P V2Scca[c.

FIGURE 19 CALCULATED AND MEASURED SIDEFORCE.

02

A.3

0.5

+7

viO

A 14 .15

v21

X 22 X 11 12 0 13 0 16

i 17

18 ® 19 20

60

i 05

BWL/1

1.2

io

0.8

04

b 0.2 o

Model i

x According to formula 22

I I I I _I

L

L

10

₂₀

₃₀

₄₀

₅₀

₆₀

_7O

₈₀

90

degrees

FIGURE 21 _{EXPERIMENTAL AND CALCULATED}

Il Simposio internacional de diseño y producción de yates de motor y vela. Il International Symposium on yacht design and production.

An Approximation Method for the Added

Resistance in Waves

of a Sailing Yacht

J.A. Keuning1

K.J. Vermeulen2

H.P. ten Have3

Abstract

For the use in a VPP environment an easy

to use calculation method for the

assessment of the added resistance of a sailing yacht, when sailing in waves, is essential to be able to compare a large

number of designs in the early design stage.

The method used should be able to take

into account the primary design parameters

of interest as far as added resistance in

waves is concerned. Also the trends should be predicted correctly because these play an important role when comparing different design alternatives. In many cases these

are more important than the absolute values. On the other hand in the

assessment of the added resistance

calculations the actual environmental

conditions, i.e. the shape of the wave spectrum, may play an important role. Therefore the calculation method preferably

should be capable of taking into account

user defined (wind generated) wave

conditions.

Different methods are available. The

method presented here makes use of a polynomial expression derived from an extensive data base containing all the relevant hull data to approximate the

Response Amplitude Operator (RAO) of the added resistance in waves of an arbitrary

yacht. In the VPP environment this RAO can be combined with an arbitrary wave

spectrum to yield the added resistance at

any speed at any heading between head wind (180 degrees) and beam seas (90

degrees).

The method is described and presented in this paper. Some results are shown and the

advantages over the traditional method

shown.

r

'Associate Professor Shiphydromectianics Department Deift University of Technology

2Rssea Officer Shiphydiomechanics Department DeC University of Technology

3Master student Deift Potytechnical Institute Inholland

1. Introduction.

Since the introduction of the influence of

the seakeeping behavior of a sailing yacht

in the velocity prediction in the 70's

considerable attention has been paid to the subject. In particular the added resistance

in the wind generated waves, which are

inevitably present when sailing with wind on

exposed waters, drew a lot of attention. Both the designers and the "operators"

found that there were considerable gains in

speed and performance to be made by

proper design and operation of the sailing

yacht. Noticeable papers on the subject

were, amongst others, presented by

Gerritsma -in 1974 Ref [1] showing the

influence of Length Displacement ratio and Longitudinal radius of Gyration and by

Gerritsma and Keuning in 1994 Ref [2] showing also the influence of the heel and

the leeway on the added resistance.

Both the experiments in the towing tanks with sailing yacht models in waves and the

calculation methods for the added

resistance of a sailing yacht in waves

howeier contain deficiencies. The towing

tank tests

are hampered by the difficulty of towing the yacht in the proper equilibrium condition (at

reasonable cost) and the absence of the

sail

forces. The calculation methods generally

used in the Shiphydromechanics field for

commercial ships are also not fully

applicable. The influence of the heel

causing asymmetry in the geometry of the hull, the influence of the instationaire lift on

the appendages, the influence of the

damping of the motions by the presence of the sails and the influence of the relatively high Froude numbers at which the yachts

are sailing causes problems for the more traditional methods methods. These may also be overcome by more sophisticated

methods now available, but again at

considerable cost and time.

To increase the chaIlenge also the environmental conditions in which the

An Approximation Method for the Added Resistance in Waves of a Sailing Yacht

M DY'06

D-

Il Simposio Internacional de diseño y producción de yates de_{motar y vela.} II International Symposium on yacht design and production. yachts are sailing are most of the time _not

precisely known. These however have a

considerable influence on the result.

Parameters like the exact shape of the

(wave) energy _{distribution over the}

frequency range, the_{directional spreading} in the wave spectrum and for instance _the effect of the wave-cuent interaction have a large influence on the final _{outcome and}

are commonly not available.

So, in general this _{implies that there is a}

strong tendency in the design and

evaluation process to put the most attention

on the comparison between _{various design}

options and so the trend of the relation

between the _{performance and the}

parameters of interest should be properly

predicted.

In addition, this _{implies that a method}

should be available which is capable of

assessing the added_{resistance in waves in}

a _{generic Velocity Prediction}

Program

(VPP) "environment"

The most straight forward approach is the

one being used in _{the VPP of the}

International Measurement System (IMS) from the Offshore Racing _{Congress (ORC).} This method ¡s based on the calculation of the added resistance _{using a 3-D potential} theory panel method_{with forward speed}

on

a small series of 5 _{sYstematically varied}

hulls. The _{added resistance}

is

approximated _{with the}

Length/Displacement the Beam/Draft and the Longitudinal Radius of Gyration (k»)as

prime parameters. In this assessment, a

fixed relationship between the wind speed and the generated_{waves is assumed. The} shape of _{the, wave spectrum and the} energy distribution _{is kept constant and} only the significant wave height is varied with wind speed. This_{relationship is based}

on a limited amount of real scale

measurements on one or two of _{the larger}

lakes in _{the USA. This is an obvious}

restriction of the general_{applicability of the} method when _{more or all of the (major)} sailing areas of the_{world are considered.}

This _{brought Gerijtsma, Keuning and} Verslujs Ref 131 in 1993 _{to the introduction}

of a more elaborate _{assessment method.}

This method was based on the results of

calculations using _{the, in}

Shiphydromechanica widely used method

known as the "ordinary _{2-D strip theory"}

and the well proven "GerritsrnaBeukelman»

method for the determination of the added

resistance, on a series of 8 different _hulls,

all part of the extensive DeIft _Systematic Yacht Hull Series (DSYHS). _{The, added}

resistance of all hulls was calculated _with

three variations in the _{k» value, for a range}

of forward speeds and headings _between

135 and 90 degrees. The parameters of the hulls taken into the final _assessment

method for the added resistance were the

Length/Displacement ratio and k».

To obtain mean values in a realistic seaway

these calculations _{were carried Out in a} number of wave spectra for_{fully developed}

seas _{according to the well}

known Bretschnejder formulation:

S

Aw_5e°

inwhich: _A=173L.i3

with:

S _{wave energy spectral densfty}

[m2s]

co0 _{encounter frequency of the}

wave [rad/s]

significant wave height

[mJ

T1 _{average period of the spectrum}

[s]

By doing so they enabled the introduction of both the mean wave period T1 and the significant wave height H113 _{as an input}

parameter for the assessment method.

A Systematical _{analysis of. the results} obtained for the added resistance by these calculations showed that for_{constant wave} direction, wave height, _{wave period and}

forward speed the added _reÎstance depends for the greater part on the factor:

V1"3_{,/Lwl * k» /Lwl}

A typical result is presented in Figure 1 for

T1 4 sec. H113 _{1.5 meter, Fn = 0.35 and}

waterline length Lwl 10 meters.

H113

691

and B=

An Approximation Method for

the Added Resistance in Waves of a Sailing Yacht 60