Geometry, resistance and stability of the Delft Systematic Yacht hull series

Reprinted from

International Shipbuilding Progress Volume 28, No 328 December 1981

S2o- r

GEOMETRY, RESISTANCE AND STABILITY OF THE

DELFT SYSTEMATIC YACHT HULL SERIES

by

Prof.ir. J. Gerritsma, R. Onnmk and ing. A. Versluis

Deift University of Technology Ship Hydromechanics Laboratory

-2628 CD DELFT

The Netherlands Phone015-786882

GEOMETRY, RESISTANCE AND STABILITY OF THE

DELFT SYSTEMATIC YACHT HULL SERIES

by

Prof.ir. J. Gerritsma, R. Onnink and ing. A. Versluis

Deift University of Technology Ship Hydromechanics Laboratory Mekelweg 2

Reprinted from 2628 CD DELFT

International Shipbufldingfrogress The Netherlands

276

GEOMETRY, RESISTANCE AND STABILITY OF THE DELFT SYSTEMATIC YACHT HULL SERIES *)

by

Prof.ir. J. Gerritsma, R. Onniñk, and ing. A. Versluis

Summary

Resistance and stability in upright and heeled position has been determined for a series of twenty two sys-tematically varied yacht hull forms.

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

I. Introduction

An extensive systematic investigation of the resis-tance and stability characteristics of sailing yacht hull forms has been carrind out in the Delft Shiphydro-mechanics 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

Frans Maas.

The variations concerned the length-displacement ratio, the prismatic coefficient, the longitudinal posi-tion of the centre of buoyancy 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 Delft. The analysed data of this part of the program have been published

in a number of reports and publications [1,2,3,4].

These first results have formed the basis of the Velo-city 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 Handi-capping Project [3,41.

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 prediction of polar velocity diagrams using standardized sailforce coefficients, reference is made to the work of KerWin [44 and Nomoto [5].

In this paper the emphasis is on the presentatjon of

the experimental data, although a limited analysis

of the results is included.

5)_{Report Technological University Deift, Deift, The Netherlands.}

2. Geometry of the series

The twenty two hull forms of the series have been

derived from the 'Standfast 43' a successful 1970

Admiral Cupper. The hull of this sailing yacht has

clean lines, without extreme variations in the

cur-vature of the hull surface.

The main form parameters, prismatic coefficient CL! length-displacement ratio L/v"3, longitudinal

po-sition of the centre of buoyancy LCB and the ratios of length, beam and draught are givien in Table I. Model

1 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.

Table I Main form parameters

Model LWL LWL BWL

LWL LGB %

BWL Bmax T

V 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 5l0 -2.3

5 2.76 2.36

3.96 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

10 3.15 2.72

3.99 0.565

4.77 0.0 II 3.15 2.72

3.99 0.565 437 -5.0

12 3.51 3.03

3.94 0.565

5.10 0.0 13

35l

3.03 3.94 0365 5J0 -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

232 2.81

0.530 4.34 -2.3

17 3.15

2.72 4.24 0.600 4.78

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

3.03 4.17 0.600 5.10 -2.3

22 2.73

2.36 4.23 0600 4.34 -2.3

Lw

'LCB

.

S S S

of the hull was adjusted in a mathematically smooth manner.

The resulting cross-sections, waterlines and buttocks have been faired 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 differences in

C is shown in Table I (models 1-7).

Variation of the prismatic coefficient has been ac-complished 'by 'shifting cross-sections tO obtain a curve of cross-sectional areas corresponding tO the desired

and LCB (models 10-22) [61.

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 results have

been scaled to 10 metres. waterline yachts; but in

principle a non-dimensional presentation of the data is used. Some of the hull data, such as wetted surface S,, rnetàcentric 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 asused in some of the hydrostatic formulas, is assumed to be on the baseline' which is the 'horizontal 'line' in the centreplane tangent to the canoe body.

The main dimensions of 'the hull forms and some other hull data, such as wetted area, waterplane area, the position of the 'centre of buoyancy and the meta-centre etc. are given in the Tables' 2a and 2b assuming a waterline length of 10 metres. The freeboard in all

cases is I ,l 5 metres.'

Because hull form variations and their influence on resistance and stability are the main purpose of the series, all models have been tested with the same fin-keel 'and rudder. Consequently deep and 'shallow' hulls have different total draughts, although this may not be a common design practice. A NACA 632-015 airfoil section has been used' for the finkeel andi 'a NACA 0012 section for the rudder. The uniform arrangement of keel and rudder 'is shown' in Figure 3 and Table' 3 gives the areas and volumes of keel and rudder, again

assumirig:a waterline length of 10 metres.

The following empirical relations between formdata have been derived for the series:

Wetted surface of canoe body

The lines of the twenty two models are given in Fi-

S =

[l97

+

0171] ,I

VJ

LJ,,

gure 2. Variation in beam and depth of the models has '

'

been obtained by multiplication of the coordinates of where:

the parent form with a factor which is constant for the - draught of canoe body

underwater part of the hull. The same scaling in

V

c

-

volume of displacement"of canoe body breadth has' been. used for the above water part of the _{The r.m.s. of the difference between the calculated}

hull,, but in order to obtain the same freeboard for

_{and actualvahies-of-the-wettedsurfaceisiessthan} all 'models, the depth scaling for the abovewater part

1%. 277 -4 S S S -6 I I 0.56 056 0.56 0.60 op -0.54 0.56 0.58 0.60

cp,_-28 3.0 3.2 34 3.6 LWL/BWL

Figure 1. Form parameters of the systematic series.

0 .

S WL Tc I I I

.

.

.

_S S

.

S

S S

.

.

I I I

278 2 1, NACA 0012 .6

I

NACA 632A015 PARENT MODEL I

!1IL'!IL1!!r

8

I1LJIJr

Figure 2 Linesof systematic séries(coñtinUed).

279 NACA NACA 0012 632A015 PARENT MODEL 1 10

_ii

12 13

280 16

!U.LWi1)IlUV

18

1iilIIiA

r

NACAI NACA 0012 632A015 PARENT MODEL 1

Figure 2. Lines of systematic series (continued).

17

1 9

NACA

0012

22

Figure 2. IJnes of systematic series.(cofltiOued).

NACA, 32A015

PARENT MODEL 1

Table 2a

Main dimensions and derived quantities

281 Model LWL no. m Bmax BwL T rn m m D m m3 Sc m2 A m2 A rn2' 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

0.91 206

9.18 239 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';O 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 2.16 21.9

7

10.06 3.68 3A7 064 1.79

735 24.1

1.31 2L8 8 10.15

3.54 3.05

0.79 1.94

9.18 25.4

1.57 22.1 9

10.07 381 3.28 0.79

1.94 ' 9.18

25.0 L68 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 2L6

12'

10.00 3.30 2.85 072 1.87

7.52 230 1.33

19.8 13

10.00 3.30 2.85 0.72

1.87

7.52 22.8

1.33 19.4 14 1OMO 330 2.85 0.17 1.92

7.52 224 L42 18.7

15

1000 3.67 3.16 '0.86

2.01 9.29 24.9 1.76 2th8 16

100O 368 3.17

1.13 2.28 12.23 .27.3' 2.32 2th9

17

10.00 3.68 3.17 0.75

1.90 9.17 26.3 1.53 23.0 18 1.0.00

3.68 3.17 '0.7.5

1.90

9.17' 260 1.53

22.6 19

10.00 168 3.17 084 1.99

9.17' 24.8 '1.73 '21.0 20

1000 3.68 3.17 0.84 L99

9.17 24.6

1.73 20:6 21

F000 3.30

2.85 068 1.83

7.514 23.6 1.26 20.5 '22

10.00 424 3.66 0.86

2.0.1

12.26 30.2 2.05

26.3 20 ₂₁

282

Table 2b

Main dimensions and derived quantities

Figure 3. Fin keel'and rudderarrangement.

Height of'metacentre above base line of canoe body

B.L

.KM=0,664T+0,111--__

(r:m.s. error is 1,5%).

The first term in (.2) represents the height of the centre of buoyancy above the base line KB, whereas

the second term stands .for the metacentric radius

BM.

The influence of keel and: rudder on KB, BM and KM is shown in Table 2b, 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 BCMC and KM with respectively 7% and 9%

approx-imately.

The static stability 'has been. computed for heeling angles up to 90 degrees and the so called residuary stability k() 'is given for all models in Table 4 (canoe

body on1y) (2)

k (')-

McNcslncP C -UC I.lC 'N

The definition of .the dimensionless residuary stab-ility for this particular case is given by:

MN.sin

k ()

C

_BM

Cc

The meaning of MN in. this expression is shown in

Figure 4.'

For geometrically similar hull forms. the static stability may beobtained from the following equations:

KNsin =KMsin

k() BM - NNsin

(4)

where NN is a correction for the influence of keel

:MN sirit

VK

Figure 4.,Definition.of residuary stability.

(3) Model I nr. m4 'L m4

LCF LCB KB

% % m

BM

m KM rn KB m BM m KM m 12.89

113.2, -3.3 -2.3

0.53 1.40 1.93 0.45 1.30 1.75 2 &64

992

-3.3 -2.3 0.60 0.94

1.54 056 087 1.43

3

l988 131.1

-3.3 -2.3 0.45.

2.17

2.62 0.38

2.02 2.40

4

960 102.8

-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 1 13.2

-3.3 -2.4 071

1.05

1.76 064 099 '1.63

7 12.85

l098 -3.3 -2.3 0.43

1.75 2.1.8 0.34.

1.60 L94

8.

12.66 1206 -3.4 -2.4 0.53

1.38 1.91 0.45 1.28 1.73 '9 13.21 105.3

-3.1 -2.2 052 1.43

1.95 0.45 I:.33 1.78 10 13M6 1 15,O' -1.6

00 032 1.42

1.95 0.45 1.32 1.77 11 12.66

113.6 -5.0 -5.0 0.52

1.38 1.90 0.45 1.28 .1.73. 12 9.47

103.3 -L9

OM 48 '1.26

1.74 0.39

1.1.5 1.54 13 9.17 102.1

-5.0 -5.0 0.48

1.22 1.70 0.39 1.12 1.51 _{Table 3} 14 15 16 . 8.69 =1 1.92 11.99 92.3 102.6 102.7

-3.5

-33

-3.5

-2.3 0.52

-2.3'. Q57

-23 0.75

1.16 1.28 0.98 1.67 L85 1.73 0.43 0.49 0.68 1.07 1.19 0.93 1.5.0 1.68 1.61

Volume and wetted area of keel and rudder

17

134 1.27.2 -L8

00 0.49

1.52

2Oi 0.42

141 1.83 _{volume wetted area}

18 13.53

125.8 -4.9 -5.0. 0.49

1.48 1.96 0.42 1.37 1.79 _{m3 m2}

19

12.18 l040 -2.0

0.0 0.56

'1.33

1.89 0.49

1.24 1.7.2

20 1.1;.77 102.5

-5.1 -5.0 0.56

1.28

L84 0.48

1.19 L68 keel 0.639 6.01

21 9.96 113.1

-3.3 -2.3 0.45

1.32

1.77 0.37

1.21 1.58

rudder 0.055

2.15

and rudder:

NN =

-

(5)

' _{kKBk - '7R "BR}

V

Finally the lever of static stability in calm water is

obtained from:

GNsin =KNsin KGsinc6 (6)

The residuary stability decreases with increasing beam-depth. ratio as shown in Figure 5, where k(Ø) is plotted on a. base of maximum beam/depth ratio. The empirical formulas (1) and (2) should not be ap-plied outside the considered range of form parameters. Also the k(Ø) values as given in Figure 5 are valid

only for the particular cross sectional forms of the

series, in particular at large angles of heel. 3. Resistanceexperiments

3.1. Experimental set up

All models 'have 'been. constructed with a waterline '

-20 length of 1,6 metres corresponding to a linear scale k(*) ratio a '= 6,25 for a full scale waterline length of 110

4,

-.40

metres.

This model size, with an overall length Of about 2,1 metres, fits the yacht measuring apparatus of the

Delft Ship Hydromechanics Laboratory and gives _{Figure 5 Resithiary stability as a fuirctlon'nf heeling angle and} combination with 'the applied turbulence stimulator :beamdepth ratio.

Table 4

Dimensionless residuary stability (canoe body)

iO3 k(4)

I

.20 .t6 1.8 21) 12 0 - .20 0 k(c) -.20

I

- .60 1.6 1.8 2.0 22 283 41 r20° 111o60° 90 Model nr. 100 200 300 _40° 500 _60° 700 _80° 900 1 0

6 25 - 5.6 101 182 272 384 479

2 0 + '5 +16 + 34

29 -

2' - 55. 1.33 225

3

0 30 74 141 '-236 348 463 573 668

4

0 12 27 -. 47 - 88 149 244 340 436.

5

0 - 8 19 -. 57 134 229 336 446 544

6 0 +

7 +20

+. 30 + 4.1

- 42 110 1193 294

7

3 27 '-66 117 188 287' 396 504 600

8

5'' 9' 26 - 43 - 92 162 258 363----468

9 '

'0 10 27

62 119 201 301 404 507

10

6

27 - 56

1.16. 199 296 402 509

11

4

'8' 24 - 47 101 _175 273 377 -475

12

1 10 25

42

80 145 232 335 --43'5

13

- 9 22

37 74.

1.39

-232 329 430 :

14

1

6 14 - 28

43

99 179 275. 371

15'

1 - 6 13

29

71 148 236 337 437

16 +2 + 5' +17

+ 16

3

-

45

107 185, 266

17

3 16 40

76 137 221 324 431' 532'

18

2 1.2 34 -

69

132. 215 316 414 521

19 1

8 18

37 85

157 248 35.1

452

20

-. 5

13'

31

- 79 148. 238 337 438

21

3 '13 35

65 110 181 274 374 471

22

2 14 37

91 177 278 '-389 L499 98

284

smngie 20,,,, doubt,

Figure 6. Turbulence simulation.

an adequate quarantee 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 ap-proximately 10 grains/cm2.

Upright resistance tests for model speeds of 0,5

rn/s - 1,8 rn/s (F = 0,13 - O,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 proportional to the strip width. Mean values of the resistance coefficients of the strips have been determined in the central.partof the considered speed range (V = I ,O - 1,6 m/s), to avoid influence of laminar flow or wave making of the turbulence stimu-lator.

All tests have been carried out in tank no. 2 of the Deift Shiphydromechanics Laboratory, which has a cross-section of 1,22 x 2,75 m, but to study the in-fluence of the blockage, the models 1, 6 and 7 have also been tested in tank no. 1, which has a cross-sec-tion of 2,55 x 4,22 m.

(grain n.2a) Strips at carborta,dum sand

density 10 gramns/cm'

tOt, 10,,,, sin9Le to Cnn, doobte 30 nun

Table5a

Residuary resistance per unit weight of displacement of canoe body

RR/LC' iø

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. I showed a very satisfactory agreement, the speed correction coeffi-cients being: 1,007, 1,013 and 1 COOS 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

l,005.'to 1,013.

The experimental values for side force, induced re-sistance and leeway angle did not differ significantly in the case of models 1, 6 and 7 and no corrections have been used for these values as measured in tank no. 2.

3.2. Upright resistance

The residuary resistance per unit weight of displace-ment of the canoe body, RR / is given on a base of the Froude number = V/.S/gL in the Tables 5a,

'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 residu-ary resistance isquite small. Thus for geometric similar hull forms the total residuary resistance is obtained from:

RR=RR/ACXLC (7)

where

= pg

and the corresponding forward

speed is given by:

V = F X -s,JgL_WL (8')

To determine the total upright resistance R the

F

Model 1 2 3 4 5 6 7 8 0.125 0.11

.. 004

0.09 0.20 0.16 0.12 0.28 0.20 0.150 0.27 0.17 '0.29

035

0.23 0.26 Q44

038

0.175 0.47 0.37 0.56 65 0.35 0.43 0.70, '0.64 0.200 0.78' O66 0.86 0.93 0.54 0.69 lO7 0.97 0.225 1.18 1.06 1.31 1.37 0.85 1.09 1.57 1.36 0.250' 1.82 1.59 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 4.6.1 5.54 5.19

449

4.62 5.82 5.79 0.350 7.16 7.11 8.25 8.03 6.69 6.86 8.28 8.04 0.3.75 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 .2063 20:41 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 44,38

.11

"glur

.10rnno

-s,ngle ton.,. doubLe 20mm

/

Table Sb

Residuary resistance per unit weight of displacement of canoe body

RR/tC

Model

Table 5,c

Residuary resistance per unit weight of displacement of canoe body

RR/L,c 10

0.075

(IogR,, 2)2

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

VXO,7LWL knc = I) (1 '1)

vx

Rflk= Vx Cr (12) Rflk= with:

v 1,1413X 106 for fresh water of 15°C

v = 1,1907 X i0 for salt water of 15°C

Ck and C'r 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 cor-rected for the effects of the carborundum turbulence stimulator strips, tank blockage and water tempera-ture.

The relative importance of C',,, LCB and with regard to the upright resistance R is shown in Table 6, where RT is given for three forward speeds '(5,1; 6,9; 8,6 knots), 'assuming a waterline length of 10

Table 6

Total upright resistance forthree speeds

285 F,, 9 10 '11 1.2 13 14 1,5 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 0.200 0.86 0.79 0.70 0.83 0.77 0.75 0.76 0.225 1.24 1.28 1.14 1.28 9 1.11 1.15 0.250 1.76 1.96 1.83 1.90 1.76 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 5.57 5.27 4.42 4.41 0.350 7.37 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 2196

0.425

35.64 38.12 34.58 35.46 33.23

37.95 37.38

0.450 53.07

55.44 51.77 51.99 49.14 55.17 56.46

Model C,, ,

L/V LCB

nr. ' RT inNeWtons

5i kn 69 kn

8.6 kn 0.568

4.78' -2.3

561 1310 5021 2 '

0.569 4.78 -2.3

51,8 1284 5199 3

0.565 4.78 -2.3

600' 1453 51.15 4

0.564 5.10 -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

546 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 8095 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 243

524-1

4043' 2L___O 600-5-.-L0---2.3 22

'0.600 4.34 -2.3

677 1813 6355 F,, Model 16 17 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 0.18 0.15 0.32 0.24 0.16

017

0.175 0.35 0.40 0.34 0.59 0.47 0.39 0.36 0.200 0.63 0.73 0.63 0.92 0.78 0.73 0.64 0.225 1.01 1.30 1.13 1.37 1.21 1.24 1.02 0.250 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 0.37,5 13.96 15.25 12.49 16.31 13.73 1.2.39 12.27

0.400 25A8 23.15

20.41

27.34 23.55 20.14 19.59

0.425 41.34 34.62 32A6 41.77 37.14 31.77

30.48

0.450 62.42 51.50 50.94 60.85

55.87 47.13' 46:66

frictional resistance RF is added to (7), thus:

RT=RR +RF

(9)

For yachts with a separate finkeel and rudder the

frictional resistance is obtained by adding the contribu-tions of hull, ruddernd keel:

RF = '/2p V2(SCCFC + SkCFk + SrCFr) (10) where S, Sk and S, are the wetted areas of the canoe body, the keel and the rudder; the coefficients c'Fc. CFk and CFr are the corresponding frictional resistance coefficients.

The frictional resistance coefficients have been cal culated according to the definition of the InternationaL Towing Tank Conference 1957:

286

metres. This example clearly shows the importance of the slenderness ratio L/v/"3 on the upright resis-tance A low prismatic gives a low resisresis-tance 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 perimental residuary resistance values have been ex-pressed ih. a polynomial form, for discrete values of the Froude nUmber with hull geometry coefficients asvariables:

RR/ACx

1O =A0+A1C +A2C +A3LCB+

+A4(LcB)2 +ASBwL/TC +A'6LwL/v"3 (13)

where . is the weight of waterdisplaced by the canoe body and LCB is the horizontal distance of the centre of buoyancy from the mid waterline length, expressed

as a percentage of LWL (forward of LwL,2 is positive).

The coefficients A0 - A6 are given in Table 7 for

Froude numbersranging from F =0,125 to 0,450. The expression (13) may be used to find optimum values of C, and LCB for minimum residuary

resis-tance.

These follow from:

C,,

=-A1/2A2

LCB =-A3/2A4 (14)

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 per-cent 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

Table 7

Residuary resistance polynomical coefficients

range of series p.

F

A0 A1, A2 A3 A4 A5 A6 0.1 2-5 _13.01: + 46.84

-42.34

-0.0 190 -0:0046 + 0.0341 +0.0085

0.150 -14:00

50.15

-45.53

-002l4

-0:0062 + 0.048.1: +i00585 0.175 -13.1.1

+4638

-42.76

-0.0153 -0:0062 + 00674 + 0:1425

0.200 -10.26

+ 36.06 -33.4.1 -0.0021 -0:0043

+00757

+0:2246 0.225 -4.15.1 + 13.68 -12.81 +0.0478

+0004l

+ 0.0967 +0.2965

0.250 -0.156

-2.106

+3.196 +0.1211 +0:0176 + 0.1504

+03532

0.275 + 6.203

-27.30

+ 29.88 +0.1711 +0:0273 + 0.2240 +0.3408

0.300 +24.87

-98.55

+100.1 +0.3168 +0:0570 + 0:3365 + 0.33113

0325

l-85.16 -31 5.2 + 296.8

+03725

+0i0930 0.4526 + 0.4662 0.350 +195.6

-6878

+ 617.0 +1.009 +0.1476 + 0A640 +0.6776

0.375 +272.8

-90! .2 + 777.1 +15401 +0:2142 +0:3431 + 0.3463 0.400 414.0 -1321 + 111:7 _{+ 1.934}

₊₀₂₆₉₀

_-Ol746

_{+ 0O872} 0.425 +3793 -1085 + 877.8 +2.265 +0.3266 -1.064

-1.053

0.450 + 588.1

-1666

+ 1362 +2.87l +0.4519 -1.501 -4.41 7 30 .35 .60 .45 Fn

Figure 7. Optimum valuesfor LGE andce,.

the increase of the residuary resistance is given when C, and LCB diverge from their optimum values. Mean values of the residuary resistance for all twenty two models at F = 0330, 0,35 and 0,40 are respectively

RR/LC =338X 8,1 X

103,21,9X 10

which

indicates the relative importance of the resistance in-crementsas shown in Figures 8 and 9.

4. Resistance, side force and stability

Extensive model tests with heeling angle and leeway angle l have been carried out with the twenty two models for a range of Froude numbers to deter-mine the relations between the heeled resistance R4, the side force FH, the heeling angle and the leeway

0/

LCB

$

1.0 0 -5 I I I I Fn.4O Fn=.35 Fn.30 LCB -3 0/₍₀ Cp

Figure 9. Influence of C on resistance.

angle. The experimental set up is given in Figure 10. The horizontal side force on the model m non-sym-metric flow conditions is measured by two stiff strain gauge dynamometers, preventing lateral displacements only:

the model is not restricted

in vertical dis-placement, 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 does 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 con-ditions corresponding to full scale values.

The heeled tests have been carried out at model speeds 1,0, 1,2, 1 ,4 and 1,6 mis, corresponding to a

Froude number range of 0,25 to 0,40. Additional.

leeway tests with zero heeling angle have been carried

-2 0 Figure 8.Influence ofLCBon

resistance.

Figure 10. Testarrangement.

287

288

Forward speed and heeling angle have a certain cor-relation m 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 combina-tion with heeling angles.respéctively: = 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 con-ditions has been investigated for a range of forward speed. In this way a better definition of 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. Leewayangle

With a high degree of accuracy the leeway angle f3

is expressed by:' FHcosØ

gl= ,(B0+B202) (15)

'/zpV2S where

FHcos

is the horizontal component of the side

force,

S is the wetted area of the canoe body; j3 and in radians.

The constants B0 and B2 depend 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.

10-f 15 d3O D2i° lIodel 1 flJO 'ExperimeAt Calculation according tO formula15 2 8 F..cos/j-PV'Sc

-Figure 12. Side force versus leeway angle.

10 . 10

It should be mentioned here that the wide range of

the variables, as discussed above, sometimesresulted in unrealistic combinations of forward speed, heeling angle and leeway angle. A slightly better fit with (15) is obtained when the test data of selected runs, as used for the routine performance, are analysed. In that case the mean r.m.s error is smaller than 0,2 degrees, but the values for B and B2 do not differ very much from those obtained from the total number of runs.

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

4.2. Heeled resistance

The resistance due to heeling and leeway is given by

- RT,

where R1, 'is the heeled resistance and RT 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 relate the

added resistance with side force, heeling angle and for-ward speed is given by:

R -R

(C0±Ccb2)F

'

-

' +C11çb2 (16)

.Y2PV2Sc ('/2pV2S)2 where: '

- the side force

- the heeling angle in radians. Table 8' Leeway versus sideforce Model B0 nr. 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

II

2.014 4.25'6 12 1.951' 5.117 13 1.869 4.406 14 1.8i5 4.980 15 L929 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

The coefficients CO3 C2 and C11 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 indicate.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 resistance values have been plotted as 'a function of side force and Froude number, see Figure 13a b, 'c, d. To fit the data the Froude number has to be

in-I I

Modell ø0° Experiment

- 'CaLculaion according to formula 17

Figure 13a. Heeled resistance versus side force squared.

0

0

0

6

Model.1 t'10°

- Calcutation according to formula 17

- 0

Fn0.'25 ® Fn. 030 Fn. 0.35 Experiment A Fn.0.40

- 0

Fn.0.65 0.25 FuYl/xPV'Sc 1°

Figure 13b. Heeled resistanceversus side force squared.

ModeL I 't'=20°

- Calculation according to formula 17

Fn. 0.30

Fn. °'35LE '0.45

A Fn 0.40[ 0.40 O35 0.

0 Fh.0.45J

F'/l..4pV°S, 2

Figure 13c. Heeled resistance versus side force squared..

3 4 Model I

-

Calculation,according

-

to formula 17 Fri 0.301 Fn,0.35Exp. A 'Fn. 0.60 0.40 0.35 .. 0.30

cluded in the. slope of the resistance-side force relation as well asin second term of the expression:

R -.R

_{4, =}

(C1+C2cb2+C3F)F

+CF2

½pv2S (½p.V2'S.)2

'

(17) 289 5 .100 Table 9

Heeled resistance coefficients

' 6 MOdel C'0 C2

CH iø

2 1.2138 1.0970

-0.8800

-1.1431 1'O2005.874

f4

3 1.4516 0.1141 11.043

4 1.2710 0.2168 &098' _elc-I>

5

1.3257 -0.0415

4902' c b4! 6

L0779 -01065

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 1.2649 0.2059

4944

12

13893 -06143

_6.502 13 1.1602 1.1137 5.507 14 L0598 0:5758

6352

15

1. 153.7 -06889

9076' 16

L0900 -L8796

_7.490 17'

1.3617 -1.2660

_'7.264 18 1.3977 0.5058 2.925 6 19

1.1697 -0.5552

10.048 20 1.1257 0.6875 4.602 21

_{1.3293 -0.0457}

₅₈₄₈ 22' 1.3024 0.7547 3.594 6 I-I .. io 1 .2 FY( 4 (DV0Sc I'

:290

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 its the Figures 13.

Although some scatter of the experimental values is observed, the mean rrn.s. error is close to the experi-mental accuracy and a further refinement of (17) does not seem feasible.

For theselected runs the strong relation between the heeling angle and the Froude number simplifies the matter to a fair degree and equation (16) is there-fore preferable.

6

4 1>

Table 10

Heeled resistance coefficients Froude number included

ModeL 1 - Calculation according .t S U 0 Experiment formula 17 43O0 _42O° I I. I 1 2 a, a a

F,/(hpVSL

-Figure 14. Heeled resistance versus side force squared.

4 5 .10-'

Table 11

Heeled resistance coefficients (selected runs)

Table 11 gives the coefficients C'0, C2 and C11 for this particular case, with a mean r.ms. error of 0,1 1 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 stab-ility at forward speed. For the model experiment the followmg equation is valid in the equilibrium position, see Figure 11:

AGNsin =ptcos +FH DL

(18)

where;

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

D,L

is

the lever of heeling moment, caused by

the side forceFH.

In general the vertical position of thecentre of grav-ity of. the model is not on scale but at a known dis-tance ZGM under the still water plane, see Figure 11. Also the vertical position of the pivot S. at a distance

Model C1 C2 C3

,C4103

nr. 01698 0.5989 3.2411 21.131 2 -0.0307 0.4617 3.6538 13.261 3 -0.4433 1.7611 6.2263 22.990 4 0.0862 1.8361 3.8100 119069 5 0.7423 0.4217 1.9915 12.499 6 0.4665 -0.3763 2.5414 13.520 7 0.3412 2.7756 2.8673 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

060l7

1.0002 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 -0.3893 2.1075 17.055 17 1.1619 0.0693 03359 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 26998 7.240 21 0.8265 0;8856 1.7453 14.427 22 0.3713 0.8853 2.9768 7.154 Model C'0 C2 C,,, 1 1.2370 2.6198 5.772 2. 1.1898 2.0259 3.709 3 1.5429 5.3097

6339

4 1.3443 .3.9076 5.363 5 1.2956 3.1894 2.357 6 1.2065 1.8437 3.623 7 1.1465 5.1287

l0083

8. 1.1198 3.0482 3.373 9 1.2285 2.2096 8.925 10 1.4313 1.3333 5.485 11 1.2948 2.5980 3.020 12 1.4972 2.3810 4.976 13 1.1953 3.1i922 .3.925 14 1.11.22 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

-0.339

19 1.2261 2.2881 6.618 20 1.1952 2.6571 1.440 21 1.4448 1.6480 4.570 22 1.3819 1.9687 1.592

h above the still water plane dOes not correspond with the centre of effort of the sailforce Z.

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

ptcos - 1 Zfsrn4 = 1ONsinçb - FH DLWL

(19) with:

D =D' -

h WL

p',. , ZGM

and h are known quantities for a given

model, whereas p, F,,, ON and D4 have to be deter-mined from the model test. To this end AONsinø is expressed by:

L\ONsincb =tCLwL(Dl +D2çbF,, +D3Ø2) (20) The first term represents the initial stability foi the

case zG

= 0, with GM =-- L

WL1D-. The second term

represents the influence of forward speed on the

heeled stability. The third term is included for, non-linearity at larger angles of heel..

For the reduction of the experimental data is writ-ten: CLWL

=Db+D2ØF,, +D32 -

D (21) where: k(Ø)=ptcosçb -LzGMsrnp Table 12 Stability coefficients and h D4 =D4 L_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 expression (21,) fits the data with a mean r.m.s. error of 0,14 Nm. Again, with a' selected' number of runs the fit is better (mean r.ms. error 0,12 Nm) but the least squares procedure does not provide reliable coefficients D2 and D3,, because of the strong correla-tion. between F,, and 0 in this case. A computation, assuming D2 = 0 gives a similar fit (mean r.m.s. error 0,12 Nm), but for all runs D2 = 0 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:

M, ='LCLWL(Do +D2cbF +D302) +AZGsifl0

The heeling moment follows from:

MH =FH(zcE +D4LWL) (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 centre of lateral resistance in the upright 'position. Two forward speeds have, been considered: F,, = 0,20 corresponding' with very moderate wave making and F,, = 0,35 with a rather large .bow wave in most cases.

Table 13 gries the positions of the centre of 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 LWL for-ward of LwL/2 has been 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 apparently 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 [5] a three

degree rudder angle could result in a '10% shift of

CLR. 291 H Model nr. D1

D2102

D3l02

D D4. 1' 0.10841

-1.5855

-3.1892 0.2367 0.0733

'2

0;05094 -0.4,732 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

02464 0.0870

7 0.15570

-3.5306

-7.3639 0.2290 0.0714 8 0.1 1634

-0.7350

-3.4314

0.2275 00144

9 _0.10748

_-3.7040

_{-2.1738 0.2301 0.0711} 10 0.10364

-2.8469

-2.3324

0.2195 00776

11 0.07824 -0.81 11 -2.8353'

02433 0.0839

12

009452

-1.4898

-2.8168 0.2181 0.0750 '13 008501

-0.8194

_-1.9409

0.2317 00748

14 0.09217

-1.4733

-1.4758

0.2381 00756

15

008667

_-1.2210

_-1.9385

_{02478 0.0809}

16 '0M4888 0.1413 0.0890 0.2602 0.0971 17 0.12679

-3.1679

-4.0696 0.2514 0.0758 18 OA1759

-1.3193

-4.1053 '0.2544 0.0838 19 0.09874

-2.7554

-1.8924

023l7 0.0761

20 0.08725

-0.7916

-1.. 1414 0.2364 0.0802 21 0.10381

-1.9703

-3.2891

0.2269 00757

22 0.14526

-3.0122

-4.4078. 0.2262 '0.0681

292

CLR is expressed as a percentage of LWL.

Forward of LwL/2 is positive.

5. Discussion of the results 5.1. Upright resistance

A calculation of the upright resistance according to

(10) mid (13) has been carried out for three hull

forms: the parent 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 Ridder. As shown in Figures 15, 16 and 17 the calculation agrees satisfactorily with the measured resistahce. In particular the good result in case of the Admiral Cupper is noteworthy, because in this casethe beam-depth BWL/TC = 6,33 is:well out-side the range conout-sidered in the systematic series.

The calculation may be used to study the relative

meritsof hull changes in a design process; 5.2. Side force

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

: _FHcos

. . .- 1.Sc

(B +B2Ø2 . (24)

Ø(Y2pV2SE) .

. S

where the arbitrarily chosen wetted hull area S for non-dimensioning the side force is., replaced by any

effective area SE.

For instance SE can be taken equal to the sum of the Table 13

Centre of lateral resistance

T5 5000 4 3000 2000 V5 - KNOTS

Figure 15. Comparison of experimental and calculated upright resistance; model 1. 2500 2000 1500 1000 500 MODEL 1 o B EXPERIMENT - rCALCULATION,

L%P1JJ

0 0 0 0 0 2 2 6 6 6

V - KNOTS

Figure 16; Comparison of experimental and calculated upright resistance; model 123. 8 MODEL 123 0 EXPERIMENT

-

- o CALCULATION 0 Model nr. CLR m C,, LCB

F=0.20

F=0.35

1 6.9 9.0 0.79 0.568

-2.3

2 9.1 12.1 0.91

0569 --2.3

3 4.1 6.9 0.68 0.565

-2.3

4 7.1

99

032

0564 -2.3

.5 7.9 .

96

0.92

0.574 -2.4

6 . 11.6 13.3

106

0568 -2.4

7 _8.0 11.0 0.64 0.562

-2.3

8 6.5 7.1 0.79 0.585 9

74

.9,3 0.79

0.546 -2.2

10 8.0 11.1

.

0.79 0.565 0.0o '11 9.2 11.4 0.79

0.565 -5.0

12 7.3 . 9.7 0.72 0;565

00

13 6.4 9.8 0.72

0.565 -5.0

14 . 5.5 10.1 0.77

0.530 -2.3

15 8.2 10.2

086

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

0530

00

20 f2.6 12.4 0.84

0.530 --50

21 4.7 8.3

068

0600 -2.3

22 3.3 2.8 0.86

0.600 -2.3

I = I 0 0.04 m B WL P = 0.19 m 5WL/T = 401 m C p = . 56B LCB = -2.3% = 4.78 Lwti0 9.18 & Lw - 7.40 rn = 2.34 P 0WL P = 0.52rn = 4.50 Rot/P Cp - .556 LCB -3.5% = 4.88 = 3.24 U

R5 MODEL 195 o EXPERIMENT - CALCULATION 5000- 4000-3000 2000-U

1000-keel and rudder areas when extended to the DWL, neglecting the hull area completely.

In combination with an' expression for the liftslope, as used in relation with an isolated lifting surface, the effective aspect ratio of the hull, keel and rudder con-figuration, as represented by (24) may be determined; The well known liftslope formulation, as given in [71 can be used for this purpose:

5.7 ARE

-

(25) aa

_/AR

l,8+cosAl/

+4

' _cos where

ac

___! _{is the slope of the lift coefficient at an angle}

of attack a = 0

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

ARE is the effective aspect ratio.

In' Table '14' the effective aspect ratios ARE for side force of the twenty two models have been determined with SE = AK, where AK is the projected area of the keel, when extended to the DWL. These effective as-pect ratios are compared with twice the geometric aspect ratio AIG of the extended keels in Figure 18 forØ = 1, 10,20 and 30 degrees on a base of BWL/TC.

Table 14

Effective aspect ratios for side force and induced resistance ARE/2ARG X 100%

293

Model

nr

side force induced resistance

çb=O l0° =20° 30° =0 'l0 =20° =30° 117 103 77 55 .70 66 .56 44 2 126 110 80 5.7 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 55 69 64 53 41 6 123 1 10 _{. 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 56 69 64 53 40 14 124 105 73 50 70 66 55' 39 15 118 1:03 76 54 62 59 52 44 16 110 102 83 64 62 57 46 35 17 134 102 77 56 65 64 62 59 18 130 117 91 68. 53 51 48 43 19 120 1:06 78 '55 66 62 54 42 20 126 112 86 63 67 62 53 41 21 113 100 75 55 62 59 54 47 22 l-2-l--l06 80 57 70 67 59 50 mean 122 106 78 56 66 62 53 43 LWL = S.73m wr. = 3.10 m T. WL/T = 0.49 , 6.33 = .550 LCB = -4.5% = 5.34 = 6.05 & 4 6 8 vs KNOTS

Figure 17. Comparison of experimental and calculated upright resistance; model 195.

294

100

013

4

BwL/1

Figure 18. Effective aspect ratio with regard to side force.

.

ARE/2AR . 100% S 5 0.4 0.5 0.6 Fi.i/'/aPV2Sca(c. S 0°

Figure 19. Calculated and measured sideforce.

With increasing heel and increasing beam-draught ratio the effective aspect ratios of the keel is decreas-ing. The drawn lines in Figure 18 may be used to ap-proximate the side force for a given leeway heeling angle, forward speed and keel geometry only, accept-ing the scatter of the experimental points.

In [1] 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 also equal to twice the geomet-ric aspect ratio of the projected rudder area when ex-tended 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 incidence should be included when comparing

0.6 0.4 0.5 0.6 FH/YaPV2SccaLc.

Si

02

£3

05

6

12

0 13

£14

15

0 16

17

+ 18

® 19 20

v 21

x 22

150 I I

calculated side force with the results of model tests with zero rudder angle (see [II ]).

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 compared with the experimental values in Figure 19 for Froude number F,, = 0,20 and 0,35 andzero heel-ing angle. The agreement between calculation and ex-periment is satisfactory taking intb'account the rather crude assumption that the influence of the hull is in-cIuded in the extended parts of keel and rudder. Ap-parently this is due to the rather large beam-draught ratios of the considered canoe bodies, which are not

ideal for the production of side force; The method

is useful for design purposes, but is recommended only for modem fiat 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 caused by the free vortices of the keel.

An estimation for the, upright condition as given in [9] shoWs that the side wash angle is approximately 60% of the leeway angle. 'In addition to a wake'

frac-tion of 0,1 a total "reducfrac-tion' 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 of

L WL/2 for model 1, independent of the forward speed of the yacht;

The difference with the experimental value at. F =

0,20 is small.

A similar correlation has been found. for the other

models.

.5.3. Heeled resistance

A similar exercise has been carried out with the ex-perimental heeled resistance results

as reduced to

equations (16) arid (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 part R1 in' more detail we write, starting from (1!6):

(C0 + C2

F

'/2pS v2

_CO

+C202)SE F, S _'/2PSV2

In view of the well known expression for the' in-duced resistance coefficient CDI of a lifting surface producing a lift coefficient CL:

c2

CDI

- AE

. (28)

we may write with (27)

ARE--0 3 Sc ''E

C0+C22

Sap

40 S I

--4.

BWL/T

Figure 20. Effective aspect ratio with regard to induced re-sistance. 295 and H irAR 'APSE V2

For SE = AK, the projected extended keel area the effective aspect ratios for all models have been cal-culated for 0 = 0, 10, 20 'and' 30 degrees. These values are expressed' in percent 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 ef-fective aspect ratio to incréasë with increasing beam-draught ratio at zero and ten degrees heeling angle'.'

5 6

60

= 3° R1 =

296

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

ap-proximately 5 x l0-. With

2 _{=0,03, 0,12 and 0,27} for 10, 20 and 30 degrees of heel the relative

import-ance of the second term may be estimated, for

in-stance by using the mean values given for the residuary resistance in chapter 3.

The Cfl values depend weakly on the beam-draught ratio. As a rough guide: CH equals 4, 5 and 6 X l0-for respectively BWL/TC = 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 respectively F = 0,30 and 0,35.

Figure 21 gives a typical result (model 1) showing a slightly lower experimental stability, due to dynamic effects at forward speed (ship waves). For almost all models a similar picture has been obtained, with dif-ferences smaller than 5%. There are three exceptions: model 10 has 10% less stability, model 11 has 25% less stability and model 14 has 9% more stability when compared with a static stability calculation.

The 25% reduction in the case of model 11 could not

be explained from the geometry of the model; the

possibility of an error in the measurement of the

heeling moment should not be excluded in this

par-ticular case.

For the determination of the heeling moment, the vertical position of the centre of lateral resistance is important. 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

Model 1

x According to formula 22

I I I I I I I I

10 20 30 40 50 60 70 80 90

degrees

Figure 21. Experimental and calculated stability.

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 D4L/T with BWL/TC. Approx-imately: 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 elliptical side force

distribution which could be assumed when the

ex-tended keel concept is used for the approximation of the side force.

These lower values compensate for the slight loss of stability lever as measured for almost all models

and consequently a completely static stability

cal-culation, as commonly used in naval architecture, may be used for the prediction of sailing yacht

performan-ce.

When D4L is referred to the draught of the canoe

body T, a mean value of 0,97 T is found with

ex-treme values 0,77 T and 1,12 T.

For flat hull shapes with a large beam-draught ratio

the centre of lateral resistance is located at a small

distance under the canoe body. For smaller

beam-draught ratios D4L is smaller than T and consequent-ly 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 [51.

The analysis of the large amount of experimental data, as given in this chapter, is not to be considered

as conclusive.

The original experimental data will be made available in the near future, to allow additional study by those who are interested in this particular field.

References

Gerritsma, J., Moeyes, G., and Onnink, R., 'Test results of a systematic yacht hull series', 5th Symposium on develop. ments of interest to yacht architecture, HISWA Amsterdam 1977.

Jenkins, D.S., 'Analysis of a systematic series of yacht model tests', M.Sc. Thesis, Department of Ocean Engineering, M.I.T. 1977.

Kerwin, J.E., and Newman, J.N., 'A summary of the H. Irving Pratt ocean race handicapping project', Chesapeake Sailing Yacht Symposium S.N.A.M.E., Annapolis 1979. Kerwin, J.E., 'A velocity prediction program for ocean racing yachts', New England Sailing Symposium, New London, Connecticut 1976.

Nomoto, K., 'Balance of helm of a sailing yacht - a ship hydrodynaniic approach of the problem', 6th Symposium on developments of interest to yacht architecture H1SWA Amsterdam 1979. t2 10 e 08 0.6 0.4 z 02

Versluis, A., 'Computer aided design of shipform by affIne transformation', International Shipbuilding Progress, Vol. 24. No. 274, 1977.

'Principles of naval architecture', Society of Naval Archi-tects and Marine Engineers, 1967.

Gerritsma, J., Kerwiñ, i.E., and Moeyes, G., 'Determination of sailforces based on full scale measurements and model tests', 4th Symposium on developments of interest to yacht architecture HISWA Amsterdam 1975.

Gerritsma, J., 'Course-keeping qualities and motions in waves of a sailing-yacht', Third AIAA Symposium on the aerodyna-mics and hydrodynaaerodyna-mics.

Nomenclature

waterplane area

Ax maximum sectional area

AR aspect ratio

AK project area of the keel

B maximum breadth

BWL waterline breadth

BM metacentric radius

C chord

CE centre of effort

CF frictional resistance coefficient CL lift coefficient

CLR centre of lateral resistance Cp prismatic coefficient D depth DWL design waterline F,1 Froude number FH side force g gravity acceleration G centre of gravity GM metacentric height

GNsin arm of static stability

297

IT transverse moment of inertia of waterplane

longitudinal moment of inertia of waterplane

KB height of centre of buoyancy above base line

KM _{height of metacentre above base line} L length

LWL waterline length

LCB longitudinal position centre of buoyancy LCF longitudinal position centre of flotation

MNsmn 0 arm of residuary stability

R0 total resistance with heel and leeway RF frictional resistance

RR residuary resistance

RT total resistance in upright position

R1 induced resistance R Reynolds number

S wetted area

SE effective area of keel or rudder

a linear scale ratio

leeway angle

weight of displacement

V volume of displacement 0 heeling angle

A sweep angle of quarter chord line V _{kinematic viscosity}

p specific density

Subscripts

c refers to canoe body E refers to effective

G refers to geometric k refers to keel

Geometry, Resistance and Stability of the Deift Systematic Yacht Hull Series

Prof.ir. J. Gerritsma,. R. Onnink, ing. A. Versluis

SUMMARY

Resistance and stability in upright and heeled 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, including velocity

orediction.

SQO

INTRODUCTION

An extensive systematic investigation of the resistance and stability

characteristics, of sailing yacht hull forms has been carried out in the Deift

Shinhydromechanics Laboratory. The model series includes twenty two different hull forms, all of which have been derived from one parent form. This oarent form is closely related to the "Standfast 43" designed by Frans Maas.

The variations concerned the length-disolacement 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 Delft. 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 optitnizing the design of

cruising yachts thd or the comparison with other methods of predicting yacht

performance, inc'1tiding analytical approaches. In this paper the experimenal

results are given in a more or less condensed form. The tabulated original test data will be available in the near future.

For the prediction of polar velocity diagrams using st-andardized sailforce

coefficients, reference is made to the work of Kerwin [4] and Nomoto [s] In this paoer the emphasis is on the presentation of the experimental data, although a limited analysis of the results is included.

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}

L/v 1/3 , longitudinal position of the centre of buoancy LCB and the ratios _of

length, beam and draught are given in Table 1. Model 1 reoresents 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 form 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 faired 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 differences in C as is shown in Table 1 (models 1 - 7)

0

Variation of the prisnatic 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].

p

The waterline length of the StandIast 43U is 10 metres. The scale factor of all

models has been fixed at ci. _{= 6,25, resulting in a model waterline length of}

1,6 metres. Some of the experimental results have been scaled to 10 metre

water line yachts, but in principle a non-dimensional presentation of the data is

used. Some of the hull data, such 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 centreolae tangent to the canoe body.

The main dimensions of the hull forms and some other hull data, such as wetted

area, waterplane area, the position of the centre of buoancy 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 andy stability are

the main nurose 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 practice. A NACA 632_015 airfoil section has been used for the finkeel and a NACA 0012 section for the rudder. The uniform

arrangement of keel and 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}

-where: T - drauoht of canoe body

V - voLume of disolacement of canoe body

c

The r.m.s. of the difference between the calculated

and actual values of the wetted surface is less than

1%

Height of metacentre above base line of canoe body B2

KM =

0,664 T

+ 0,111

c

c

T

(r.m.s.

error is 1,5 %)

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, EM 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 1Q4 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(Ô) is given for all models in Table 4 (canoe body

only).

C

The definition of the dimensionless residuary stability for this particular case is given by:: k (cb) = C

M N sinP

CC

EM

_CC

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

₌

k() BM

- NNsin

(4)

where NN is a correction for the influence, of keel and rudder:

c NN = KN

- KN

(5) C C

KN

=

V KN - V KB

- V KB

c c k k R R 50 (3) V

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

GNsinq

=

KNin4 - KGsin

(6)

The tesivary stability decreases with increasing beam-depth ratio as shown in

Figure 5, where k() 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. Als.O the k() values as given in Figure 5 are valid only for the particular cross sectional forms of the series, in particular at

large angles of heel.

3. RESISTANCE. EXPERIMENTS

3.1 Experimental set up

All models have been constructed with a waterline ienqth of 1,6 metres

cOrre-sponding to a linear scale ratio a = 6,25 for a full scale waterline length

51

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 carbor.undum 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 m/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 proportional 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 rn/s), to avoid influence of laminar flow or wave making of the turbulence stimulator.

All tests have been carried out in tank no. 2 of the Deift Shiphydromechanics

Laboratory, which has a cross-section of 1,22 x 2,75 rn, but to study the

influence of the: blockage, the models 1., 6 and 7 have also been tested iP tank

no. I, 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: 1,007, 1,013 and

1,005 for the models 1, 6 and 7. Consequently this correction method has been

applied to the measured uoright 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 of models 1, 6 and 7 and no

correc-tioris 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/c

is given on a base of the Froude number

Fn = V/VgL'

in the

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

=

RR/Ac

A

(7)

where A = and the corresponding forward speed is given by:

R

nc

R

=

nk

_V

V*Cr

R =

nk

v V

v*

52

(12)

V

=

gL

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:

=

½pV2(ScCF

+ SkCFk + SrCFr)

(in)

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

c k

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

The frictional resistance coefficients have been. calculated according to the

definition of the International Towing Tank Conference 1957:

0.075

= (1ogR-2)2

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