The influence of heel on the bare hull resistance of a sailing yacht

Date July 2010

Author Keuning, J.A. and M. Katgert Address Deift University of Techpoiogy

Ship 1-lydromechanics Laboratory

Mekelweg 2, 2628 CD Deift

TUDeift

Delft University of Techno'ogy

Page /of 1/1

The influence of heel on the bare hull

Resistance of a sailing yacht

by

iA. Keuning and M. Katgert

Report No. 1684-P

2010

Published in: Proceedings of the 2Md International

Conference on Innovation in High Performance Sailing Yachts, 30 June 1 July 2010, Lorient, France, Royal Institution of Naval Architects, RINA, ISBN: 978-1-905040-72-8

THE SECOND INTERNATIONAL CONFERENCE ON

INNOVATION IN HIGH PERFORMANCE SAILING

YACHTS

30 June - 1 July 2010, Lorient, France

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THE ROYAL iNSTITUTION OF NAVAL ARCHITECTS

THE SECOND INTERNATIONAL

CONFERENCE ON INNOVATION IN HIGH

PERFORMANCE SAILING YACHTS

30 June - 1 July 2010

© 2010: The Royal InstitutionofNaval Architects

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opinionsexpressed by the individual authors or

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RINA

The Second International Conference on Innovation in High Performance Sailing Yachts, Lorient, France

CONTENTS

.SUPPLENESS-AEROELASTIC CONSIDERATIONS IN RIG DESIGN

*

P. Heppel, Peter Heppel Associates, UK

SLAMMING COMPUTATION ON THE MULTIHIJLL GROUPAMA 3

1

1'. Roux, Company K-Epsilon, France

J. Wackers, Ecole Centrale de Nantes, France

L. Dorez, Team Groupama, France

NUMERICAL MODELLING OF SAIL AERODYNAMIC BEHAVIOR IN

7

DYNAMIC CONDITIONS

F.Fossati, and S. Muggiasca, Politecnico di Milano, Milan, Italy

EXPERIMENTAL VALIDATION OF UNSTEADY MODELS FOR WIND! SAILS!

23

RIGGING FLUID SRUCTURE INTERACTION

B Augier, P Bot and F Hauville, Research Institute of the French Naval Academy,

France

MDurand K-epsilon, France

THE USE OF SHELL ELEMENTS TO CAPTURE SAIL WRINKLES, AND THEIR

33

INFLUENCE ON AERODYNAMIC LOADS

D. Trimarchi, S. R. Turnock andD. J. Taunton, School of Engineering Sciences,

University of Southampton, UK

D. Chapelle, INRL4, MACS team, France

FLUID STRUCTURE INTERACTION SIMULATION OF SPINNAKERS -

47

GETTING CLOSER TO REALITY

H F Renzsch, TU Delfi, The Netherlands

K U Graf University of Applied Sciences Kiel, Germany

UNSTEADY NUMERICAL SIMULATIONS OF DOWNWIND SAiLS

57

M Durand, Company K-Epsilon, Ecole Centrale de Nantes, France

F. Hauville, P. Bot, and B. Augier, Research Institute of the French Naval Academy,

France

Y. Roux Company K-Epsilon, France

A. Leroyer, and M Visonneau, Ecole Centrale de Nantes, France

OFF-WIND SAIL PERFORMANCE PREDICTION AND OPTIMISATION

65

A M Wright and A R Claughton, University of Southampton, UK

JPaton andR Lewis, TotalSim, UK

PERFORMANCE OPTIMIZATION OF INTERACTING SAILS THROUGH FLUID

75

STRUCTURE COUPLING

V.G. Chapin and N. de Carlan, Université de Toulouse, France

P.

Heppel, Peter Heppel & Associates, Port-Louis, France

The Second International _{onferece on'1ñfl"oat,onzn zidë Sailing Yachts, Lorient, France}

© 2010 The Royal Institution of Naval Architects

AUTOMATIC SAILSETS CREATION

_{AND OPTSATI}

Phi hppe Cousin, CEREALOG, France.

Julien Valette, TENSYL, France

OD

PERFORJVIMCE PREDICTION OF TIlE PLANING YACHT HUTI

L A le Clercq andD A Hudson, University ofSouthampton, UK

THE INFLUENCE OF HEEL ON THE BARE HULL RESISTANCE OF A SAILING

99

YACHT

J. A. Keuning, and M Katgert. Delfi University of Technology, The Netherlands

PREDICTION OF FORCES AND FLOW AROUND A YACHT KEEL BASED ON

109

LESANDDES

D. Mylonas, P. Sayer and A. Day, University of Strathclyde,

_UK

COUPLING OF RANSE-CFD WITH VPP METHODS: FROM THE NUMERICAL

₁₁₉

TANK TO VIRTUAL BOAT TESTING

CBoehm, Delfi University of Technology, NL

K Graj University ofApplied Sciences Kiel, GER

L'HYDROPTERE: HOW MULTIDISCIPLINARY SCIENTIFIC RESEARCH MAY

131

HELP BREAK THE SAILING SPEED RECORD

M Calmon, MFarhat, P Fua, K Startchev, G Bonnier,

_{J-A Mânson, VMichaud, A}

Sigg, M Oggier, MO Deville, 0 Braun, ML Sawley, L Blecha, J Cugnoni, Ecole

Polytechnique Fédérale de Lausanne (EPFL), CH

JMBourgeon, S Dyen, D Moyon, D Schmäh, R Amacher, D Colegrave,

_Hydroptère

Design Team

A NOVEL TOOL TO COMPUTE THE NON-LINEAR DYNAMIC BEHAVIOR OF

143

AN HYDROFOIL SAILING YACHT

L D Blecha, Almatech, Switzerland

J Cugnoni, Ecole Polytechnique Fédérale de Lausanne, Switzerland

D Moyon, and S Dyen, Hydroptère SA Suisse, Switzerland

PERFORMANCE MODELLING AN) ANALYSIS OF OLYMPIC

_CLASS

₁₄₉

SAILING BOATS AND CREWS WITH NEURAL NETWORKS

A. Reid, Newcastle University, UK

GLOBAL OPTIMISATION OF A VOLVO OPEN 70 RACING YACHT

₁₅₇

J Cuzon, A Douglas, D Gorraiz, I Nicholls and T St Olive, Strathclyde University, UK

STRUCTURAL OPTIMIZATION OF AN AMERICA'S CUP 90 RACiNG YACHT:

171

THE INFLUENCE OF DEFLECTIONS ON UPWIND PERFORMANCE

T Tison, France

P Stocking, Cranfield University, UK

*

The Second International Conference on Innovation in High Performance Sailing Yachts, Lorient, France

SIMULATION BASED DESIGN FOR HIGH PERFORMANCE COMPOSITE

*

SAILING BOATS

P. Groenenboom, ESI Group Netherlands

B. Cartwright and D. McGuckin, Pacflc Engineering Systems International Ply Ltd,

Australia

P. de Luca and A. Kamoulakos, ESI Group France

SAIL AERODYNAMICS: FULL-SCALE PRESSURE MEASUREMENTS ON A 24-

181

FEET SAILING YACHT

I.M Viola & R.G.J. Flay The University of Auckland, New Zealand

A FAULT TREE BASED INVESTIGATION OF THE RELIABILITY OF OCEAN

191

RACING YACHTS INCORPORATING HUMAN PERFORMANCE AND

CANTING KEEL IMPACTS

MJ.Streeter, L Auboin, C.E.Rigg, WD.Robinson, DJ. Taunton, S.R. Turnock, and

J.I.R.Blake, University of Southampton, School of Engineering Sciences, Ship Science,

UK

A FULLY INTEGRATED SAIL-RIG ANALYSIS METHOD

203

S Malpede, and F Nasato, SMAR-Azure Lid, UK

AUTOMATIC SHAPE OPTIMIZATION OF SAIL PLANS IN UPWIND

*

CONDITION

G. Vernengo and S. Brizzolara, University of Genova

EASY-TO-USE ADVANCED PERFORMANCE PREDICTION ANALYSIS FOR

211

YACHT RACING TEAMS

JD Gapdeville, KNE, France

D Nicolopoulos, K1'JE, Spain

H Hansen, FutureS/zip GmbH, Germany

PRELIMINARY ASSESSMENT OF HYDRODYNAMICS FOR AC"33" CLASS

*

RULE MONOHULL BY CFD AND ANALYTICAL FORMULATION

R. Laval-Jeantet and Vincent Jacob, Fluxyz Engineering

6 DEGREE OF FREEDOM CFD APPLIED TO THE DESIGN OF AN IMOCA

221

OPEN 60

R Azcueta and R Schutt, Cape Horn Engineering, Spain

VISCOELATOPLASTIC CYCLIC BEHAVIOUR OF SAIL MATERIALS

227

W. Dib, and A. Tourabi, University of Grenoble, France.

G. Bles, Engineering School ENSIETAlUniversity of Brest/ENIB - Laboratory LBMS,

France.

*

_{- Not available at time of printing}

THE INFLUENCE OF HEEL ON THE BARE HULL RESISTANCE OF A SAILING YACHT

J. A. Keuning, Deift University of Technology

M. Katgert. DeIft Universityof Technology NOMENCLATIJRE

Lwl Waterline length

Bwl Beam on waterline

Tc Draft of canoe body

LCB Longitudinal centerof buoyancy

Cm Midship section coefficient

Sc Wettedarea canoe body

Vc Volume of displacement canoe body Heel angle

Rr.

Residuary resistance

Ri Induced resistance

FH Sideforce

Cv Coefficient of viscous drag

Cf Coefficient of frictional drag

k Form factor p Specific gravity

g Gravitational acceleration

Rn Reynolds number

1. INTRODUCTION

For the useful prediction of the performance of a sailing yacht using a generic Velocity Prediction Program (VPP)

an accurate assessment of the hydrodynamic and

aerodynamic forces and moments involved is essential. In

a socalled "generic VPP", which yields an easy to runand rapid performance prediction of an arbitrary sailing yacht using its main dimensions only, this assessment is even

more complicated due to the limited data of the yacht

available in that case.

Extensive research has been carried out over the last

decades by numerous parties to find general applicable expressions for sail forces, upright resistance, appendage

resistance, side force, induced resistance, added resistance

in waves etcetera etcetera. With the transition from expressions yielding the forces and moments on the

complete yacht, as was the case in the beginning of the DSYHS, to generic expressions for hull, keel and rudder

separately all contributions of the various parts of the yacht

on the overall forces and moments had to be formulated. One of the more difficult components in this assessment

scheme turned out to be the change in resistance due to the

stationary heel of the sailing yacht. Various attempts to "capture" this change have been made but they seem to

lack either general applicability or accuracy. Yet this heeled resistance and more in particular the change in

residuary resistance due to heel, has formed an important item for a long time on the research agenda of, amongst

others, the International Technical Committee of the ORC.

And in some respect it certainly has been a driver for the

hull shapes of new designs.

in the present paper an attempt will be made to present an overview of what has been done in this respect over the last decade using the data of the Delft Systematic Yacht

Hull Series (DSYHS) and, using the same data, try to gain

some insight on the absolute contribution of the heeled resistance on the overall performance and the physical

effects driving it.

2. WHAT CHANGES UNDER HEEL?

If we consider the difference between an upright sailing

yacht hull and the same hull under 20 degrees of heel,

which are the obvious differences?

From a geometric point of view the shape of the

underwater body changes considerably. The waterlines

become highly asymmetric and the section shape changes accordingly. The amount to which thesechanges take place

appears to be dependent on a number of the shape

parameters of the hull under consideration.

This change of geometry of the hull under heel is to some

extent demonstrated in the next figures, in which for a

small, but illustrative, number of models of the DSYHS both the waterlines upright and under 20 degrees of heel

are compared.

The differences between the various models that areshown

are:

Figure 1.1. Waterlines Sysser 1

I) Sysser 1, being the parent model of the Series I of

the DSYHS has a typical wine glass shaped cross section as customary in the 1970's with a modest Beam to Draft (B/T) ratio. In addition the fore and aft body are rather identical leading to a symmetrical hull and rather steep

buttocks aft. Under heel the "windward" waterlines

become quite narrow and stretched and the "leeward" lines bulk-out with increasing Waterline entrance angle fore and

a blunt aft body. There is a decrease in waterline length

under heel, which appears to be symptomatic for all

'FIgure 1.2. 'WaterlInes Sysser 25

Sysser 25, being the parent model of Series 2 of

the DSYHS, has the more customary shape ofthe yachts of

the l98O's The cross sections are much more U' shaped

with' a higherCm value when compared with Sysser 1. The

LIB ratio is smaller than Sysser 1, the BIT ratio is almost similar however there is a considerable asymmetry in the fore and aft lines leading to a much fuller shape of the waterlines and smaller buttock angles aft. Under heel the

most striking feature of this type of hull shape is the

apparent change in centreline of the hull: aft it shifts to

leeward or it "rotates". The asymmetry between windward and leeward is less than with Sysser I and compared' with

the shifted centreline the leeward side now becomes

slightly more stretched and the windward side more bulky. The length of the "shifted" or "rotated" water-(centre-) line

increasesconsiderably when under heel and this shows to

be consistent for all models denved from this parent

Figure '13: Waierlines Sysser 27

Figure.1.4: Waterlines Sysser 29

These effects become smaller with decreasingBIT'

ratio as is shown with the lines of Sysser 27 which is a very low BIT ratib hull derived from' the same lines as Sysser 25, and they increase with increasing B/T ratio as

shown' with the'lines 'from Sysser 29, whiáh is a very 1high

B/T ratio hull again also derived from Sysser 25 as a

parent. Also the waterline separation at the leeward side decreases strongly with increasing B/T ratio as becomes obvious from comparison between #27, #25 and #29 with

increasing B/T ratio. Also a trend for increasing curvature

in the'shiftedcentrelinebecornesapparent.

Figure 1.5: Waterlines Sysser 44

With the lines of Sysser 44, which is the parent of

Series 4 of the DSHS, the largest difference' with the

earliereffects appears to be in the more rounded end of 'the

waterlines aft and the smaller difference in shape between the windward and the leeward waterlines 'The parent of Series 4 has again a somewhat higherCin'than the parent 'ofSeries 2anda' lOwer LengthtoBamratio

Figure L6: Waterlines Sysser47

The lines of Sysser 47, which' is a high B/T derivative

of Sysser 44 show a larger rotation of the centre line and an even larger increase in length under heel'. The effect of'

more rounded waterlines' aft under heel disappears

however completely with this Sysser 47, due to the high

Figure 1.7: Waterlines Sysser 81

6) Finally Sysser 81. This is a modem and recent hull

designed for gaining extra length underheel, appropriately

nicknamed "the Boxy". It has a very high Cm and almost

vertical sides. The change of shape is obvious fromthe plot above.

Table 1: Hull parameters upright and heeled

These changes of hull geometry under heel provoke a

number of changes in the hydrodynamics involved:

A) First of all the waterline length under heel is changed. It is interesting to note that all the models of

Series 1 experience a reduction in waterline length under

heel while in the other Series the waterline length increases. When the changes in waterline length were calculated for a typical heeling angle of 20 degrees it became obvious that those hulls that have the biggest

decrease (i.e. change) of the mid ship sectional coefficient

Cm when heeled do have the largest increase in waterline length. This also holds true the other way around. This

dependency is derived from the results as presented in

Table l in which the principal hull parameters upright and

under 20 degrees of heel are

presented; A second

dependency was found with the change in the B/T ratio of

the hull when heeled yielding a larger increase in length

When the change in the B/T ratio is larger when Cm is the unchanged. Only the more illustrative examples within the DSYHS are presented in the Table 1.

This result was used to formulate the parameters of

importance for the change in waterline length when heeled and by means of regression the following relation has been

foUnd for the waterline, length change as function of the

change in mid ship sectional coefficient Cm and the Beam to Draft ratio Lw/co

Bwl

a0+a1i\Cm+a2

L-Lw! Tc with: ACm= CmqCm ABwI Bwlço Bwl Tc Tcço Tc

With the followingcoefficients:

Table 2. Coefficients heeled waterline length regression

The goodness of fit of this polynomial With the data is

shown in the next figure:

Sys Cm BwlITc 0° 20° 0° 20° 1 0646 0.733 399

4l6

25 0.727 0.695 5.39 4.33 27 0.724 0.718 2.46 . 235 29 0;75u1 0.636 10.87 5.04 44 ,: 0.712 0.703 442 3.98 47 0.749 0.658 604 4.56 81 0;783 th679 5.82 4.11 82 0.770 0.685 6.19 4.19 Sys Lwl '0° 20° 1 10 9.735 25 10 10.267 27 10 10.174 29 10 10.306 44 10 10.142 47 10 10.708 81 10 10.703 82 10 10.770 a0 a2 9.6 '9.8 10 10.2 10.4 10.6 10.8 Lw14 measured Em]

Figure 2: Waterline length under heel measured and

calculated

How this change in waterline length may be incorporated

in dealing with the resistance under heel will be discussed later.

B) Secondly the magnitude of the wetted area of the hull when she heels over is 'changed. Since the frictional resistance is assumed to be directly proportional to the

wetted area, every change in wetted area leads to a

proportional change in the frictional resistance. To

visualize this in Figure 3 the change in wetted area is

depicted of some representative models of the DSYHS.

24

+ 25

V27

29 o 81 Caic.

From these results it may be concluded that there is a

strong relationship between the change in wetted area and the beam to draft ratio BIT of the hull and Cm.

In 1998 Keuning and Sonnenberg Ref [1] presented a

polynomial expression for the wetted area of the hull under

heel, which is found to be still rather accurate also when

applied on the new designs. It reads: B 1' "O65 Sc=I

l.97+0.l71--

----

I (Vc.Lwl)

Tc)Cm)

Bwl

(Bwl\2'('

S0 +51 --f-s

Tc

C) When considered appropriate a form factor k can

be applied to get from the frictional resistance to the

viscous resistance. The general applied formulation of the ITFC can be applied in this respect. According to:

Cv=(l+k).Cf

Cf=

0.075

(log(Rn) - 2)2

The usual procedure from either Prohaska or ITTC can be

applied to obtain the form factor k from the experimental

results at the lower speeds. Because the shape of the

underwater part of the hull changes considerably when the

hull is heeled it may be expected that this form factor k will change also under heel. It has been proven to be

however quite difficult to derive a reliable form factor k from the measurements with the heeled bare hull. This is due to the fact that the heeled hull through its asymmetry

delivers also some side force. In addition due to the

"rotation" of the centre line when heeled as demonstrated

in the lines plans also an "effective" leeway angle is

introduced even with zero geometrical leeway for the

model, which was demonstrated by Keuning and Verwerfi

in Ref [3]. Although the overall side force on the heeled

hull may be small there is a considerable yaw moment, due

to the positive side force on the fore part and the negative

side force on the aft part of the heeled hull. This particular

side force distribution over the length of the heeled hull with relative small leeway angles is generally known as "the Munk moment" and results in a small total side force but introduces a large yaw moment. This has been shown by Keuning and Vermeulen in Ref [2]. This side force generation causes vorticity, which will be considerable because the hull is a highly inefficient wing, and so there will be an induced resistance component. This should not

be included in the determination of the form factor k but is

difficult if not impossible to separate. So generally the

form factor obtained in the upright condition will be used instead. However the often quite large change in wetted

area when heeled will generally dominate the small change

in viscous resistance and therefore possible errors in the

changes of the form factor of the heeled hull will have less influence.

So the change in viscous resistance can reasonably

accurate be predicted and therefore the emphasis in the

following parts will be on the determination of the change in residuary resistance under heel.

To establish some insight in the absolute and relative

magnitude of the change in residuary resistance of a heeled

hull for a limited number of the models of the DSYHS for some speeds in the speed range from Fn = 0.25 to Fn =

0.45

in the next figure

the following quantities are

presented: the frictional resistance under heel, the

residuary resistance upright and the change in residuary

resistance due to heel. Sys 1 ISO 60

T::.< L

t --20 0.25 0.3 0.35 0.4 Ff1-I 0.45 Rt Rr sRr4(

- Rt4

+s3.Cm ₁₁ 10 15 20 25 30

Heel angle Ideffi

Figure 3: wetted area canoe body under heel

Scço

= Sc(0).

_1+T.

40

20

0 CO Ca a, U C Ca Ca a) 100 80 60 40 20 0 060

:

-20 0.25 100 L

I:

I-0-4 20I 0.25 0.3 Sys 25 0.3 0.35 0.4 Fn [-] Sys 27 0.45 0.4 0.45 1 0.35 0.4 0.45 Fn [-J Rf Rr aRr4 Rt Rf Rr oRr4i

- Rt

0 80

:

100 80 0 -20 0.25 100 80 20 0

:

-20 0.25 100 80 0 I I I * -'S I 1

--- --- '1 t -t 'I 0.25 Sys 44 0.3 0.35 0.4 FnF-) Sys47 0.45 RI4 Rr 6Rr4 Rt Rr aRrd?

- Rt$

The data presented here is representative for the entire

series of model's in the DSYHS database. From these plots it is obvious that the change in residuary resistance due to

heel is a small quantity when compared to the other

components.

In addition it should be noted that the change in the

residuary resistance due to heel has to be determined from the measurements by subtracting two rather large

quantities, i.e. the resistance upright and the resistance

1 -

060 r

1 Rf Rr Rf Rr 'S....

,/

-oRr4

-r

- oRr4,

- Rt

Rt4 -20 160 80 060 0 0.25 0.3 0.35 Fn [-] Sys 29 -I 0.3 0.35 0.4 0.45 En[-1

Figure 4: Relative contribution of resistance components

to heeled bare hull resistance

60 40 - r

-r

-0,4 0.45 0.35 Fn [-] Sys 81 0.3

under heel, to find the (small) difference. Small errors in either of these two large quantities will inevitably lead to

large errors in their "delta": the change in residuaiy

resistance due to heel. This may lead to all kind of

irregularities in the "measured" change of residuary

resistance dueto heel.

En Ref [2] and [3] it is also shown that depending on the

BIT ratio of the hull there is also a considerable side force production of the sailing yacht at zero leeway angle which generates an even larger induced resistance component on the actual sailing yacht. This is shown in Figure 4 in which

for two different BIT ratios the induced resistance due to heel and side force is depicted. This effect will make the importance of the change of residuary resistance of the

bare hull due to heel on the overall resistance of the actual sailing yacht even smaller.

ASys 24 (BiT=11)Fn0.36

DSys 27 (BIT25) Fn0.36

J L

Figure 6: Change in residuary resistance under heel

measured and calculatedfrom Refill

Based on these results in the database available at that time

they formulated the following expression for the specific

change in residuary resistance due to 20 degrees of heel:

ARrh20. Lw! Bwl

(Bwl

-uo+u. .-+u2.---+u3

Vc.pg

'

Bw! Tc

+u4 .LCB+u .LCB2

With a dependency on the heeling angle to yield a similar result for any arbitrary heeling angle between zero and 30

degrees of heel according to:

EtRrhç = Mrh20. .6.0.q'7

This is a speed independent polynomial expression with

coefficients presented for a fixed series of Froude numbers.

This is similar to the approach followed with the upright

residuary polynomial expression derived from the DSYHS.

The coefficients of this polynomial expression, i.e. u0 till

u5, are presented in Table 3.

Table 3: coefficients regression delta residual resistance

under heel Keuning & Sonnen berg Ref[l]

These formulations, when checked against the DSYHS database, showed reasonable results. When validated

against models not belonging to the database the results still showed satisfactory agreement at least when care is taken not to be outside the parameters space spanned by

the DSYHS. Coefficients multiplied by 1000 Fn 0.25 0.3 0.35 0.4 0.45 0.5 0.55 uO -0.0268 0.6628 1.6433 -0.8659 -3.2715 -0.1976 1.5873 ul -0.0014 -0.0632 -0.2144 -0.0354 0.1372 -0.148 -0.3749 u2 -0.0057 -0.0699 -0.164 0.2226 0.5547 -0.6593 -0.7105 u3 0.0016 0.0069 0.0199 0.0188 0.0268 0.1862 0.2146 u4 -0.007 0.0459 -0.054 -0.58 -1.0064 -0.7489 -0.4818 u5 .0.0017 -0.0004 -0.0268 -0.1133 -0.2026 -0.1648 -0.1174 0 5 10 15 20 25 FH2[kN2]

Figure 5: Induced resistance Ri due to sideforce for

various BIT

3. VARIOUS APPROACHES FOR THE CHANGE IN RESIDUARY RESISTANCE UNDER HEEL

In 1998 Keuning and Sonnenberg Ref [I] formulated an expression for the change in resistance due to heel based on the results of about 25 models out of the total of 50

models of the DSYHS tested at that time. These tests were

carried out using the unappended models of the DSYHS.

The heel angle tested was restricted toone heel angle only, i.e. 20 degrees ofheel. The database where they based their

regression on was the raw database from the DSYHS available at that moment. This database contained 50

models of which only 25 had been tested as bare hulls at 20 degrees of heeL Using the raw database results means that no "fairing" or "smoothing" has been performed on

any of the resistance data, nOt upright nor under heel. This

implied that, as explained before, quite some humps and hollows appear in the small differential of these two large quantities that is the change in resistance due to heel. A

typical example of this isdepicted in Figure 6.

1000 750

z

- 500 250 0

Quite another approach is followed by the ORC in their

VPP used for handicapping purposes. Here a multiplier on the upright residuary resistance is formulateddepending on the pnncipal hull parameters such as length to beam beam

to draft and change of waterplane area upright and under

heel. Their approach is explained in the ORC VPP

documentation 2009 Ref [4]. This formulation obviously has some flaws also because the LTC is seriously looking for anotherapproach.

4. THE PRESENT APPROACH

In the framework of the present study two new attempts

have been made to improve on the assessment of the

change in residuary resistance due to heelof the bare hull: First it has been investigated if fairing the results from the

measurements and so reducing the abnormalities in the

data had any effect on the derived coefficients for the polynomial expression as presented by Keuning and

SOnnenberg Ref [ii] and if so if the results wereimproved Two approaches regarding this fairing procedure have been

followed in this respect. The first one was faking the

residuary resistance curves both upright and heeled. The

change in resistance was then determined from the

difference between these two faired curves at fixed Froude

numbers. The other approach was that the difference as originally determined by Keuning and Sonnenberg was faired directly. It turned out that both procedures did not yield very different results, so fairing the original deltas

was chosen as the method to fair the data. A typical

example of this later procedure is depicted in Figure 7.

10 0 -2

1+1

- V 29

A 44

0 81

- Smooth

-4 0.15 0.2 0.25 0.3 0.35 Fn[-)

Figure 7: measured and smootheddeltas

As may be seen from this figure the overall magnitude of the delta resistance does not change much but the trend in

the lines in particular over the Froude range is much more consistent.

New coefficients have been determined for the same polynomial expression as formulated by Keuning and

Sonnenberg Ref [1] using these new results for the delta

residuary. However this did not improve the results of the assessment formulation significantly.

The second attempt was focussed at gaining new insights

in what or which hull shape characteristics drives this

change in residuary resistance due to heel of the bare hull. If new parameters and dependencies could be found then it

would be possible to formulate an appropriate expression

todeal with those.

Analyzing the results obtained for the change in residuary resistance after fairing these data revealed that there was a

strong dependency on the change in waterline length and on top of that on the change of the Cm and the BIT ratio

again. Soa new formulation was set up using the change in

waterline length under heel, Cm and the B/T ratio. Once

again a speed independent formulation was used with

Froude number dependent coefficients. After some

attempts the best formulation read:

Bwl Lwlço

=b0+b1 A+b2 LCm+b3

pgV

Tc Lw! In which: Tc Tcço Tc ECm= Cmç,Cm with coefficients:

Table 3: coefficients regression delta res dual resistance

under heel Keuning & Katgert 2010

When applied on the results of the database the results as depicted in the following Figure 8 were obtained. In this

Figure only a limited number of the 38 models

is

presented. Those models are selected which show

diverging behaviour with respect to the change in residuary

resistance at heel. They are representative for the general

result and show the general goodness of fit. Coefficients muIt1pFedby 1000 Ffl 0.15 0.2 0.25 0.3 0.35 0.4 0.45 hO -1.850 -1.032 2.061 10.881 26.984 48.633 73.015 hi -0.032 0.000 -0.024 -0.163 -0.494 -1.062 -1.795 b2, 1.037 0.731 0.451 -0.431 -2.208 -4.344 -6.432 b3 1.781 0.996 -2.046 -10773 -26.780 -48.397 -72.799 a 6 0)

0

0

0

4 2 0.4 0.45

60 50 0 60 50 40 0 -10 o i 015 0.2 0.25 0.3 0.35 Fn [-Sysi 8 0.15 0.2 -10 0 1 0.15 0.2 0.25 0.3 0.35 FnF] Sys2 Sysi - Calculated Rr - A _Measured Rr4) Measured Rr.o -- -Measured Rr30-- Calculated ARr - A _{Measured ARr4} Measured Rr0 -- Measured Rr.20 - Calculated Rr4 - _{A Measured Rr4} Measured RrHj -- Measured

a-0

0

0

60 50 40 30 20 10 0 10 01 60 50 4° 10 0 10 0.4 0.45 05 0 1 0.15 0.2 0.25 0.3 0.35 Fn [-Sys27 60 50 40 10 0 10 01 Sys24 - Calculated Rr4 Measured aRr4 Measured Rr0 - Measured Rr =20 0.15 0.2 0.25 0.3 0.35 0.4 Fn[-] Sys25 - Calculated ARr4 Measured aRr4 Measured Rr00 - -Measured Rr420- L r 0.4 0.45 05 - Calculated ARr4 A Measured ARr Measured Rr+o. -- Measured 0.15 0.2 0.25 0.3 0.35 0,4 0.45 0 5 Fn[-] 0,25 0.3 0.35 0.4 0.45 05 Fn[-J 0.4 0.45 05 0.45 05 60 00 40

12:

0

50 10 -10 01 60 50 40 a. 20 0 0 10 -10 60 50 40 > 030 a. 20 10 -10 01 0.15 0.2 Sys29 - Calculated Rr -

'

_MeasuredARr4 MeasUredIRr,... -- MeasuredRr.30. L 0.15 0.2 0.25 0.3 0.35 Fn(-J Sys39 - Calculated - _MeasuredRr4 Measured!Rr0 r_{- -Measured)Rr20.} - Calculated.Rr4 - _{Measured Rr4} Measured Rr0. -- Measured Rrr, 0.25 0.3 0.35 0.4 0.45 05 Ff1-I 60 0₀ 50 0 10 a 30 a. 20 ' 10 0 10 0 1 0.15 0.2 0.25 0.3 0.35 Fn[-] SysBi 80 50 40 o30 a. -Calculated Rr4 Measured Rr Measured Rr+0. - Measured Rr20 01 Sys47 0.4 0.45 05 - Calculated Rr4 - _{Measured.ARr$} Measured Rr+0 -- MeasuredRr+2o. -10 0 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 05 Fn[-] 60 - Calculated ARr 50 _{Measured ARr+} Measured Rr00 L 40 - Measured Rr L_ __L ___L 0.4 0.45 05 0I 0.15 0.2 0.25 0.3 0.35 Fn[-J Sys44 0.4 0.45 05 0.4 0.45 05 0.25 0.3 0.35 Ff1-I Sys49 0.15 0.2

0

Sys82

Keu fling, J. A. and Verwerft, B.

A new Method for the Prediction of the Side Force on Keel and Rudder of a Sailing Yacht based on the Results of the Delft Systematic Yacht Hull Series

Chesapeake Sailing Yacht Symposium, 2009

ORC VPP Documentation 2009

Published by theOffshore Racing Congress

Teeters,J., Pallard, H. and Muselet, C

Analysis of Hull Shape Effects on Hydrodynamic Drag in

Offshore Handicap Racing Rules

Chesapeake Sailing Yacht Symposium, 2003

7. AUTHORS' BIOGRAPHIES

Lex Keuning is associate professor at the Ship

Hydromechanics Laboratory of the Deift University of Technology. He has been responsible for research on the

DelfI Systematic Yacht Hull Series and he is also research advisor of the ITC of the Ocean Racing Congress.

Michiel Katgert is member of the research staff of the

Ship Hydromechanics Laboratory of the Deift University of Technology. He is responsible for carrying out towing

tank research. 60 - CaTculated Rr4 50 MeasuredARr Measured Rr,0. 40 L L _ L - Measured Rr20. 0 I 0.15 0.2 0.25 0.3 0.35 0.4 045 05 Fn I-] Figure 8: results present regression

From these plots it may be concluded that in an overall

view both the trend and the absolute magnitude of the

change in the residuary due to heel is quite satisfactory captured. This certainly also holds true for the sign of the

added resistance, i.e. positive or negative.

In comparison with the earlier assessment method there is

a significant improvement which justifies the use of the

new method.

5. CONCLUSIONS AND RECOMMENDATIONS

Based on the results presented above it may be concluded

that a more reliable method for assessing the change in residuary resistance of the bare hull under heel has been

found. It seems topredict both thequantity and the trend of

this change with reasonable accuracy for the range of the

DSYHS.

In the near future additional tests will be carried out to be able to extend the database were it is based on in those

areas were we still lack information, and to be able to

validate the

results on models not belonging to the

database of the DSYHS.

6. REFERENCES [I]

Keunlng,J.A. andSonnenberg, U.B.

Approximation of the Hydrodynamic Forces on a Sailing

Yachtsbased on the Delfi Systematic Yacht Hull Series

Iternational HISWA Symposium on Yacht Design and

Construction

Amsterdam, November 1998

[2]

Keuning, J. A. and Vermeulen, K. J.

The yaw balance of sailing yachts upright and heeled Chesapeake Sailing Yacht Symposium, 2003