Upright resistance of sailing yacht hull forms

(1)

Upright resistance of sailing yacht hull forms.

Prof. ir.. J. Cerr.itsrna,

I.r. J.A. Keuning and Ing. A. Verslu.is Rep ortnr. 8 36

(2)

The Deift Systematic Yacht Hull Form Series has

_{been extended} with six light displacement models in view of modern trend!s in yacht design.

Because of the higher speed potential of the ligt'h. displacement

yachts the existing polynomial expression for the upright

resis-tance, as used for velocity predictions s:houl.d now include a

speed range exceeding Fn = 0.45, which corresponds to the speed limit of the original series.

In this report. a new regression model _{is given which covers a} speed range up to Fn 0.60.

Determination of regression models for the. residuary resistance.

The .ge'ometrt.c data and the analysis of the' _{experimental results}

of

the

.22

models

of

the

.o!ri;gi.nal

'Deift

Systematic

Series

in'cl.udi:ng. a. .re:gre:s.si.on..m'odei.fo.r..the...resjdua.,ry resistance

_{up to}

Fn

0 . 4.5 was given in

_{[ 1]}

The experimental data., of al,l :'r.uns''i.nc:l.u:d.in'g

_{.t'h'e. condition's with}

keel and leeway are'.summarized :in

[.2],.

Th'e re:siduary resistance _{R'R. co.uld be expressed with satisfactory}

accuracy by:

RR

*

l0 - A0 + A1C + A,2'C + A3 LCB + A4 ('LCB)2

+ A5 BWL/Tc + A6

_LWL/V/3.

The coefficients A0 - A6 are given in Table 1 _{fo.r .Fr.ou.de numbers}

Fn 0.125 - 0.450.

Tab i.e 1

-

1-Residuary resistance, .poi-yno.m.ical coefficients

Fn A0 A1 ₂ A3 ' A A5 A6

0.125 -13.01+46.84

-42.3.4

'0.019O

0.'00.46

+0.0341

+0.0085

0.150 -14.00+50.15

-45.5.3

-'0.0214

-0..006.2

'+0'.0481l

+0.0585

0.175 -.I3.i1 +46.58'. -.4.2.76 -0.0153 -0.00612

+0.0674

+0.1425

0.200 -'iO.26.36...06 -33.41 -0.00.21 -0.0043 +0.0757 +0.2:246 0.225. 4.15i '+13.68 _-1,2.81 _+0.0478 _+0.0041 _+0.0967 _+0.2965 '0.2,50 -0.156 -2.106 +3.196 +0.121.1 +0.0176 +0.1504 +0.3532 0.2.75. +6.203 -27.30 .+29.88 _+0.1711 _+0.0273

₊₀₂₂₄₀

_+0.3408 0.300+24.87 -98.5.5 +100.1 '+0.3168 '+0.0570 40.3365 +0.3313 0.325 +85.16 -315.2 +296.8 +0.5725 +00'930 +0.4526 +0.466.2 '0.350 +195.6 -.687.8 +617.0 +1.0:09 . +0.1.476 +0.4640 0.6.776 0.375 +272.8 -901.2

+7771

+1.540 +0,2142 +0.3431 '+0.3463 :040'O +414.0

-1321

+1117'

+1.934

: +0.2:690 0.I746 +0.0872

0.425 :3793 -1085

+877.8 +2.2:65 +'032,66 -1.064 -1.053 0.450 +588.1 -1666 ±13612 +2.871 +0.4519 -1.501 -4.417

(3)

The residuary resistance in this case is defined as the differ-ence b;e'tween the tota.l resistance in calm w.ater and a "frictional

resistance" RF:

RF ½pV2(S: CFC + SK CFK + SR CFR) (2)

where: S, SK and SR are respectively the wetted

areas of the canoe body, the keel and the ru'dder _{The coefficients CFC, CFK} and CFR are the corresponding frictional resistance coefficients. The coefficients CF were calculated according to the ITTC 1957 extrapolator:

CF = O.075/(1og R - 2)2

(3)

The Reynolds number Rn is

_{seperately determined for the canoe}

body, the keel and the rudder.,

For the canoe, body the effective length is taken as 70% of the waterline

length and for

the keel and rudder the mean chord

lengths are used to define the Reynolds number.

The. fit of expression [1] to the experimental resistance is

satisfactory for speeds up to Fn 0.45 also, in some cases, for hull forms outside the ranges indicated above _['1,3].

With the addition of the six light displacement _{models the ranges} for LWL/VC1/3 and BWL/TC have been extended to:

LWL/VC'/3

BWL/TC 12.50

Froude numbers up to Fn 0.6 have been considered In this case. The main dimensions of the twenty-eight models _{are given in Table} 2 for a waterline length LWL 10 meters.

In Figure 1 the lines of the l.ight-displacement hull forms _are

given. The models 'have been tested with the same keel and rudder as used in the original Series. The main particulars of keel and rudder are given in Figure 2. . . .

Fo.r all twenty-eight models _{a new expression for the residuary}

resistance for speeds up to .Fn = 0.4.5 has been derived.

In addition for the speed range Fn 0.45 w 0.60 a se;parate expression for the s1x light-displacement hulls has been _deduced from the experim'ents

The 2.2 models of the form parameters:

Series I cover the following range of main

LWL/BWL 2.73 - 3.64

BW.L/Tc 2.81 5.35

C _0.53 _0.60

LwL/Vc'/3 4.34 - 5. 11

(4)

Fn = 0.125 - 0.450

RR/AC * l0'

= A0 + A1 C + A'2 L'CB + A3 BWL/TC + + A4 * LWL/Vc"/3 + A5 * C. + + A6 * Cp * LWL/VC1/3 + A7 * (LCB.)2 + + A8 * '(LwL/Vc-/3).2 + Ag * (LwL/Vc-/3)3 ₍₄₎ Fn = 0.45 - 0.60 * io _{= C0 + C.1.* LWL'/'BWL + C2 * 'AW/V/3 +} + C3 * (LwL/BWL)2 +C4 * (LWijBWL)(AW/V/3)3 ₍₅₎ Table 2 - 3' -.LWL m BWL m Tc. rn C _LCB .DIS'P.Lc _SC rn2 SY.SSER 1

10.04,

3.17 0.790 .568 -2.30 9.180 25.40 21.8 SYSSER 2 10.04 2.76 0.910 .56.9 -2.30, 9.180 2:3.90: 19.1 SYSSER 3 10.06:3.6,4 0.680 .565 -2.30 9.160 27.60 25.2 SYSSER 4 10.06 2.85 0.720 .564 -2.30 7.550 23.00 19.8 'SYSSER 5 _{10.05 3.64 0.920 .574 -2.40 12.100} _29.10 _25.3 SYSSER 6

10.00

_{3.17 1.06:0 .568 -2.40 12.240} _27.50 _21.9 SYSS.'ER 7 _{1.0.063.17 0.640 .562 -2.30} _7.350 _24.10 _21.8 SYSSER 8 _{10.15 3.05 0.790 .585 -2.40} _9.180 _25.40 22.1 SYSSER 9 1:0.07'3.28 0.79:0 _{.5.46 -2.20: 9.180} _25.00 _21.5

SYSSER .10 10.00

3.17 0.79.0 .565: 0.00 9.190 25.60 22.0

SYSSER 11 :iooo

3.17 0.79:0 .565 -5.00 9.19.0 25.30 21.6 SYSSE'R 12,10.00 2.85 0.72:0 .565 0.00 7.520 23.00 19.8 SYSSER 13 10.00. 2.85 '0.720 .565 -500 _{.7.520 .22.80} _19.4 SYSS'ER 14

1.0.00

_{2.85 0.770 .530 -2.30} _{7.. 520} _.22.40 _18.7

SYSS:ER. 1510.00.

.3.1.6 0.860 .530 -2.30 .9.290 24.90 20.8 SYSSER 16

10. 003

.17 1.130 .530. -2 :30. .12 .:230 : 27 30 .20.9 SYSS:ER 17:

10.00,

3.17 '0.750 .600 .0.00 9.1.70 26.30 '23.0 SYSS:ER 18

1.0.00

_{3.17 0.750 .600}

500

_9.170 _26.00 _22.6 SYSSER .19,

10.00

3.17 0.840 .530 '0:0.0 9.170 24.80 21.0 SYSSER 20'

10.00.

3.17 0.840 .530 5.00: _9.170 _24.60 _20.6 SYSSER 21

10.00

_{2.85 0.680 .600 -2.30} _7.540 _23.60 _20.5 SYS:SER 22

10.0:0

_{3.66 0.860 .600 -2.3.0 12.2,60} _30.20 _26.3 SYSSER 23 SYSSER 24

10.00,

10 00

2.862 86 0.740 0 261 548 .548-1.90 -2 07 7.974 2 995 23.32 19 85 19.3 19 0 SYS:S;E'R 25

10.00

_{2.50 0.464 .548} i.94 _4.618 _18.98 _16.7 SYSSER 26

10 00

2 50 0 194 545 -2 10 1 972 17 30 16 7 SYS;S,ER 27 :10.00 2.22, 0.904 _{48, -189} _7.915 _21.73 _14.9 SYS:S,ER 28

10.0:0

_{222: 0.329 .546-1.89} _2.922 _16.17 _14.6

(5)

The coefficients A and C of thes.e _{polynomial expressions are} given in tables 3 and 4.

Table 3.

Residuary resistance polynomial coffi.cients

Fn = 0.125 - 0.450

-4-Fn A0. A5 A1 A6 A2 A7 A3 A.8 A.4 A9 0.125 -12.45884 +41.96056 -0.015664 +0.054216 +0.172104 -3564266 -0.557162 -0.003683 +0.063850 -0.006880 0 150 -16 63653 +49 04490 -0 014415 +0 022791 +0 732430 -30.52534-3.193774 -0.004341 +0.268158 -0.019881 0.175 -5.440638+27.47384+0.006670 +0.065666 -1.074351 -29.80142 +1.073305 -0.001053 +0.133609 -0:010561 0.200 +11.6732.4 -14.97679 +0.047823 --0.085.557 -2.774123 -11.59.52:0 +5.792069 +0.0071:54 -0.093147 +0.006347 0.225 +27.6260!8 _{5:2.72783+O.O93:2O2 +0,15l86: -4.915521} +4.128:0:28 +10.06:511 +0.014441-0.13.5946+O.O,O!862O 0.250 +41.57053. -84.10490+0.173:649+O.I9O69.6.9'218O5. +15.232:34 +14.54537 +0.029416 -0.256058+0.017730 0.275H.54,774l5 -123.9609+0.225905 +0.2.54739 -8.10142.5 +45.43005 1-16.84450 +0.039728 -0.267875 +0.017628

0.300,+76.66O922O2.8173 +0.396418 +03419

-8.068824 +114.7038! +18.79237 +0.074764 -0.521396 +0.034366

o;325+137.9o19 -417.2575 0.676a86 0.46G0'46-8.171168

+302.6570+20.40:0040.116017 -0.684892 +0.044301 0.350 +26.6.8098 -830.7'063 +1.154643 +0.541289 _-I07'2063 +636.3.422 +2:5.85:210+0.1800:37 -0.767488 +0.047520 0.375 +358.9669 -1O95.O62+1671016o.53:o:5o8: -10.70230 +817.6215 +31.45530 +0244i.67 .-1.378868 +0.08:2385, 04.0O +537.5.134 -1598.655i-i,.982948+O.27O.975 -16.79936 +1171.654 +4.5.01871 +0.2814.34 0.425+606.39'43 -1647.52.:4+2.,273537.+O.02:5498 24.2:08S4

+1018.761 +8367038 +0.332559 -4.570643+0277169

0.450+943.9:2022651.32o +2.913360HI-0.296555-22.67869: +1643.984 +138,.8056 +0.469272 -11.37453 +0.693914

(6)

Residuary resistance polynomial coefficients Fn = 0.45 - 0.60

The goodness of fit of a total resistance prediction based on [4] and [5] and the ITTC 1957 extrapolator has been carried _{out for}

all twenty - eight models.

Th:e results are depicted in the figures _{indicated by} Sysser

numbers I to 28 for ,a waterline length of 1.0 meters.

in these figures the drawn line _{represents the experimental data} and the centered symbols represent the calculated values.

The correlation between the measured values and the regression models Is satisfactory. _{In. particular in the speed range Fn} ₌

0.45 - 0.60 the prediction, as based on only two form p:aramet:ers

i.e. _{Lwl/BwL and A./V:/3,} _is _{very close} _to _the _experimental values..

As shown in Table 2 models 23 - 28 have almost the same LCB. _A

variation in LCB could influence the goodness of _{fi.t based on [3]}

and [4]

The influence of .LCB variation wiLl. b:e investigated in the near future.

Acknowledgement

The testing of the mo;dels 2,3 28 has been carried out by

R. Onnln.k.

Re ferences

'[I] .J. _{Gerritsma, R. Onn.ink and A. Versluis,}

Geometry, Resistance and Stability of the Delft _Systematic

Yacht Hui.l Series, 7th H.IS'WA-Symposium, 1981, Anis;t'erdam. 5 Fn C0 C;1 _C3 _C4 0.45 111.4237 18.61l20 -4.0.00404 1.667833 0.0033438 0.475. _{177.7123 -35.02741 -6.845442} _{3.290199 0.0057676} 0.50 _{328.9239 -88.22548 -11.63294} _{9.258911 0.010760} 0.1525 354.14.05 -87.10124-13.6789:0 8..638060 .0.012453 0.55 428.1995 -111.7306-15.83484 _{.11.29797 0.0145:84} 0.575 446..7'202 -113.0711 -16.86441 1.1.21449 0.015.553 0.60 .4:51. 8:8,231 -109.3.091 _{17,. 5,390.9} . 1,0 .55:4.25 0.0160189

(7)

J. Cerritsma and R. Onnink,

The Experimental Results of the Deift _{Systematic Yacht Hull}

Series,

Re.portnr. 595., 1983, Deift Ship Hydromechani.c.s Laboratory.

J. Cerritsma and J.A. Keuning,

Performance of Light and Heavy displacement _{sailing yachts in}

waves,

(8)

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(9)

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Figure 2. Fin keel and rudder arrangement and position of the dynathometers.

(12)

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Upright resistance of sailing yacht hull forms

The Deift Systematic Yacht Hull Form Series has

Because of the higher speed potential of the ligt'h. displacement

yachts the existing polynomial expression for the upright

of

the

models

of

the

.o!ri;gi.nal

'Deift

Systematic

Series

in'cl.udi:ng. a. .re:gre:s.si.on..m'odei.fo.r..the...resjdua.,ry resistance

up to

0 . 4.5 was given in

The experimental data., of al,l :'r.uns''i.nc:l.u:d.in'g

.t'h'e. condition's with

keel and leeway are'.summarized :in

*

LWL/V/3.

1-Residuary resistance, .poi-yno.m.ical coefficients

0.125 -13.01+46.84

-42.3.4

'0.019O

0.'00.46

+0.0341

+0.0085

0.150 -14.00+50.15

-45.5.3

-'0.0214

-0..006.2

'+0'.0481l

+0.0585

+0.0674

+0.1425

+02240

+7771

-1321

+1117'

+1.934

0.425 :3793 -1085

where: S, SK and SR are respectively the wetted

The Reynolds number Rn is

length and for

RR/AC * l0'

10.04,

10.00

SYSSER .10 10.00

SYSSER 11 :iooo

1.0.00

SYSS:ER. 1510.00.

10. 003

10.00,

1.0.00

500

10.00

10.00.

10.00

10.0:0

10.00,

10 00

10.00

10 00

10.0:0

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+1018.761 +8367038 +0.332559 -4.570643+0277169

un.

,w.ii

sysser 24

Figure ia;

*1--I-,-.

-I

sysser

sysser

Figure lb.

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_LWL/V/3.

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