Approximation of the hydrodynamic forces on a sailing yacht based on the Delft Systematic Yacht Hull Series

Approximation of the

Hydrody-namic Forces on a Sailing Yacht

based on the 'Deift Systematic

Yacht Hull Séries'

J.A. Keuning and U.B. Sonnenberg

Report 1175-P Projectnr. SMO 961128

16 November 1998

Published in: 15th International Symposium on

"Yacht Design and Yacht Construction ".

Amsterdam, 16 November 1998, The Netherlands.

ISBN 90 370 01 71-8

TU Deift

Faculty of Mechanical Engineering and MarineTechnology

Ship Hydromechanics Laboratory

1.

15th International Symposium

on

"Yacht Design and Yacht Construction"

Amsterdam, 16 November 1998

PROCEEDINGS

Organized by HISWA - National Association of Watersport Industries in The Netherlands, the International Trade Show for Marine Equipment METS 98

and the Deift University of Technology

EUROPFS ZXUBON FOR ThR

NTERNAflONAL LEISURE CRAFT TRADE AlIO INDUSTRY

C

TU Deift

0 'IP l-__l_.I.

Approximation of the Hydrodynarnic Forces

on a Saiiirg Yacht based on the

'Deift Systematic Yacht Hull Series'

by

JA Keuning ¡

UBSonnenberg'

Abstract

Over the past years a considerable extension hasP been given to the DeIft Systematic Yacht Hull Series (DSYHS) The DSYHS data set now contains information about both the bare hull and appended hull resistance in the upright and the heeled condition, the resistance increase due to the longitudinal trimming moment of the sails, the sideforce production and induced resistance due to sideforce at various combinations of forward speeds, leeway angles and heeling angles. New formulations for the relevant hydrodynamic forces as function of the hull geometry parameters have been derived to be able to deal with a larger variety of yacht hull shapes and appendage designs. During the past two years. some results of this research have already been published. In the present paper an almost complete picture of the relevant expressions which may be used in a Velocity Prediction Program (VPP) will be presented.

I

Shiphydromechanics Laboratory Delft University of Technology

i - INTRODUCTION

The Deift Systematic Yacht Hull Series is a very extensive series of systematic yacht hulls

consisting of some 50 models by now, all of which have been tested at the Delft

Shiphydromechanks Laboratory of the Deift University of TechnolOgy over the last 25 years.

The aim ofthese investigations which léd to the testing of these 50 models of the DSYHS was the develòprnents of equations that could be used as an approximation method for the assessment of the most important hydrodynamic forces acting on a sailing yacht. The shape of the yacht designs has changed considerably over these 25 years which necessitated the change in the shapes of the hulls tested as well as in the approach and/or method of analysis

of the measured data of the DSYHS. Therefore over the total span (in time) of the DSYHS three different parent models have been used. In it's sort the DSYHS is probably the largest

systematic series with such a high degree of consistency in both the model shapes and measurement techniques, procedures and analysis.

Based on the equations derjved from the results of the DSYHS a Velocity Prediction

Program was to be developed, Which should enable designers of sailing yachts to evaluate their designs and the possiblé design variations on their performance in an early dèSign

stage.

In conjunction with this DSYHS a number of smaller systematic series have been tested aimed at solving specific problems not (filly), covered by the DSYHS. In this respect the research on appendage drag and sidefòrce production should be mentioned. Due to the rather large development in the appendage design and layout in the last decades the standard

appendages of the DSYHS did no longer do justice to these new design trends. This

research was aimed to derive formulations for the forces on the appendages separately, so

that a larger variety of designs coUld be dealt with and was based on a series model

experiments containing sorne 13 different kçel configuration placed underneath one

particular yacht hull and on a series of experiments with 6 different keels underneath two systematically different hulls.

The growing interest in the behaviour of the yachts in waves and in particular the added resistance due to these waves has led to research specifically aimed at the calculation of this added resistance suitable for the use in a VPP environment.

Inevitably also the approach towards the assessment of the forces involved has changed over the past 25 years, which led to additional tests with all the models, also with those already previously tested,, for instance to measure bare hull resistance and the change in resistance due to trim and heeling alone.

All these changes mentioned above have led to a substantial new set of polynomial

expressions suitable for the approximation' of the hydrodynamic forces involved in the sailing yacht equilibrium..

During the last decades a considerable number of publications on the these subject of

calculating the hydrodynamic forces on the 'sailing yacht 'have been published by Gerritsma et al , all of which may be found in the List of References at the end of this paper A part of

'the newly deny ed formulations have' already been presented in' some recent publications of the Deift Shiphydromechanics Laboratory. In the present paper 'however the new calculàtion

schedule and the complete set of'equatións that goes with this schedUle will be presented.

The method by which the hydrodynamic forces have been decomposed in separate cómponents is presented in Figure 1 as a kind of flow chart. The decomposition is as

follOws.:

Figure 1 Graphic Representation of Resistance Components

The upright resistance of the bare hull is the starting pOint of the calculation scheme. In this condition the frictional resistance and the residuary resistance are calculated. Then the resistance of keel and rudder are determined in the same condition also as the summation of a viscous and a residuary part. In this upright condition the added resistance of the hull due to wind waves is calculated and added when applicable, i.e. in the upwind courses from close hauled to beam reach. Then the yacht is heeled over and the 'deltas' of the frictional resistance of the hull and the residuary resistance of the hull, the keel and the rudder are determined. Subsequently the yacht assumes leeway and the induced resistance due to the side force is calculated as a function of heeling angle. Finally the change in resistance due to the trimming moment of the crew, adjusting its longitudinal position along the length of the yacht to ccunteract the bow down trimniing moment caused! by driving force of the sails in particular at the running and reaching courses, will be brought into the calculation. Finally thé summatiOn of all these components yields the total resistance of the yacht. For each of these components expressions will be presented in the following, paragraphs.

'In fórmula the total resistance as a sum of the various components can be written as:

(1)

Rtq4 = RJhp± Rvkr + Rrh+ ARrhO + ARriup + Rrk ± ARrkp ± Ri

To give an impression of the magnitude and the contribution of all these different resistance components to the total resistance of a sailing yacht with a waterline length of 10 m, under

Upright Resistance Resistance of Hull Resistance of Hull with

of Hull with Keel

_=Rt

with Keel and

_=Rtç

Keel and Rudder with _=Rtp13

and Rudder Rudder with Heel Heel and Leeway

Frictional! _{Upright Resistance} Resistance of Hull Resistance

Hull

Rih of Hull with Keel and Rudder

with Keel and Rudder with Heel

Residuary Delta Delta

Resistance Hull

= Rrh Frict Resistance

due tolleel =ARfh(p

Resistance

due to Sidé Force = ARrpÍ Hull Hulland Keel!

Viscous Resistance _{= Rvk} Delta Keel Resistance duetoHeel = ARrhp Viscous Resistance Rudder = Rvr Hull = A RiO Delta Resistance. due to Delta Resistance

due to Heel = ARr1«p Trimming MOment Residuary

Resistance _{= Rrk Keel} Keel

loo heel, _{a leeway angle of 3° and with a 4 men crew sitting in the cockpit aft, the relative} contributions to the total resistance for Sysser models i and 25 are presented in Figure 2. Each line adds the component as labelled in the legend:

Resistance 0.15 0.20 025 0.30 0.35 0.40 0.45 0.50 Fn 0:55 0.60

e-Rihphi %

--Rvk %

o-Rvr%

o-Rrti %

-e-dRrtiphi %

o-Rrtiim%

o-Rrk % -M-dRrkphl %

o-Ri % Model i 100 80 60 40 20 0.15 0.20 025 0.30 Resistance 0.35 0.40 0.45 Fn 0.50 0.55 0.60

e-Rfhphl %

-o-Rvk %

o-Rvr %

o-Rrh % -M-dRrhphi %

o-Rrthm %

o-Rrk % -N-dRrkphi %

o-Ri % Model 25

Figure 2 Relative Resistance Contributions

Noticeable is the different influence of the resistance caused by the trimming moment. For model 25 the total resistance decreases when the crew compensates the forward trimming

moment of the sail force. While for model i

this influence is limited to an resistance

increase in the middle speed range only.

2 - DESCRIPTION OF TH'E DSYHS

The original parent model chosen for the Delft Systematic Yacht Hull Séries in 1974 was the well known "Standfàst 43" designed: by Frans Maas at Breskens, The Netherlands. The Standfast 43 was a typical contemporary racing yacht design. From this parent modél (model 1), 21 other systematically varied designs have !been derived (model 2 to model 22) using,, as far as feasible, an affine transformation technique. All models were consequently tested in the towing tank over a period: of 1:0 years. This sub-series of the DSYHS is known as "DSYHS Series I ".

After 10 years the typical yacht designs started to differ considerably from the lines of this original parent and therefore it was decided in 1983 t introduce a new parent model into the.DSYHS according to the lines presented to the Delft Shiphydromechanics Laboratory by Van der Stadt Design at Wormerveer, The Netherlands. From this second parent hull, model 25, another 6 new variations were derived known as subseries "DSYHS Series 2" (model 23 through model 28) and later another 12 models based on the same parent with special emphasis on very light displacement and higher Length to Beam ratios (model 29 through model 40; "DSYHS Series 3"). Finally in '1995 yet another parent model was

introduced into the DSYHS according to the lines presented to the Deift

Shiphydromechanics Laboratory by Sparkman and Stephens from New York, United States

of America, known as the "IMS 40" especially designed for research and which was

intended as some "average" International Measurement System (l'MS) design From this third parent model, modél 44 another 9 variatións 'have been tested sofar and is now known as sub-series "DSYHS Series 4" (modél 42 through model 50).

In general it is believed that by this significant variety in hull shapes a sufficiently large area

of possible yacht designs is being covered by the DSYHS to make its results and the

derivations therefrom applicable to a large diversity of yacht designs.

Nevertheless new additions to the DSYHS in the future may still be necessary to keep up with (inevitable) developments in yacht design.

To give an impression of the hull 'shapes, the bodyplan of the three parent model's are presented in Figure 3 on the next page.

Sysser i

Sysser 25

vij

Sysser 44

Figure 3 The Parent Hull Forms of the DSYHS

Table i The Range of Hull Parameters Tested in the DSYHS

The principal hull parameters varied within DSYHS are presented in Table 1.

A complete oversight of the hull shape parameters of each of the 50 models of the Deift

Systematic Yacht Hull Series is presented in Table2.

This Table is of particular interest because it illustrates the range of values of the various hull shape parameters (and parameter combinations) that have been varied and tested within

the Series which yields an indication of the range of applicability of the formulations

derived from these data.

15th International HISWA Symposium 1998 ₇

Ranges

Length - Beam Ratio

Lw!

2.73 to 5.00

Bwl

Beam - Draft Ratio

Bwl

2.46 to 19.38

Tc

Length - Displacement Ratio

Lwl

4.34 to 8.5ff

Vc

Longitudinal Centre of Buoyancy LCB 0.0 '% to -8.2 %

Longitudinal Centre of Floatation LGF -1.8 % to -9.5 %

Prismatic Coefficient Gp _{0.52 to} 0.60

Midship Area Coefficient Cm 0.65 to 0.78

Loading Factor

Aw

3.78 to 12.67

Table 2 Hull Form Parameters of DSYHS Sysser LwI/BwI Bwl/Tc LwI I VOLc'1/3 LCB LCF Cb Cp Cw Cm Awl VOLc"2/3 % % i 3.155 3.992 4.775 -2.29 -3.33 0.365 0.564 0.688 0.646 4.976 2 3.623 3.043 4.776 -2.30 -3.34 0.367 0.567 0.691 0.646 4.349 3 2.747 5.345 4.779 -2.30 -3.32 0.370 0.572 0.695 0.647 5.776 4 3.509 3.947 5.097 -2.29 -3.33 0.367 0.568 0.691 0.646 5.119 5 2.747 3.957 4.356 -2.41 -3.43 0.361 0.559 0.683 0.647 4.719 6 3.155 2.979 4.339 -2.40 -3.42 0.363 0.561 0.685 0.646 4.091 7 3.155 4.953 5.143 -2.29 -3.35 0.362 0.561 0.685 0.646 5.743 8 3.279 3.841 4.775 -2.40 -3.32 0.379 0.586 0.707 0.647 4.921 9 3.049 4.131 4.776 -2.20 -3.34 0.353 0.546 0.672 0.646 5.026 10 3.155 3.992 4.775 :D 00 -1.91 0.365 0.564 0.694 0.646 5.017 11 3.155 3.992 4.775 -4.98 -4.97 0.365 0.565 0.682 0.646 4.928 12 3.509 3.936 5.104 -0.01 -1.93 0.364 0.564 0.693 0.647 5.149 13 3.509 3.936 5.104 -5.01 -5.01 0.364 0.564 0.681 0.646 5.057 14 3.509 3.692 5.104 -2.30 -3.47 0.342 0.529 0.657 0.646 4.879 15 3.165 3.683 4.757 -2.29 -3.45 0.343 0.530 0.658 0.646 4.708 16 3.155 2.810 4.340 -2.30 -3.48 0.342 0.529 0.657 0.646 3.926 17 3.155 4.244 4.778 -0.01 -1.79 0.387 0.598 0.724 0.647 5.241 18 3.155 4.244 4.778 -5.00 -4.89 0.387 0.599 0.712 0.647 5.152 19 3.155 3.751 4.777 0.01 -2.06 0.342 0.530 0.664 0.646 4.802 20 3.155 3.751 4.778 -4.99 -5.09 0.342 0.530 0.651 0.646 4.712 21 3.509 4.167 5.099 -2.29 -3.22 0.387 0.598 0.718 0.647 5.322 22 2.732 4.231 4.337 -2.29 -3.22 0.387 0.599 0.719 0.647 4.947 23 3.472 4.091 5.001 -1.85 -5.29 0.394 0.547 0.673 0.721 4.850 24 3.497 10.958 6.935 -2.09 -5.84 0.402 0.543 0.670 0.739 9.215 25 4.000 5.388 6.003 -1.99 -5.54 0.399 0.548 0.671 0.727 6.048 26 3.994 12.907 7.970 -2.05 -6.33 0.407 0.543 0.678 0.749 10.791 27 4.496 2.460 5.011 -1.88 -5.24 0.395 0.546 0.677 0.724 3.780 28 4.500 6.754 6.992 -2.05 -5.95 0.400 0.544 0.672 0.736 7.305 29 4.000 10.870 7.498 -4.59 -7.63 0.413 0.549 0.671 0.751 9.437 30 4.000 7.082 6.500 -4.56 -7.66 0.413 0.549 0.672 0.751 7.096 31 4.000 15.823 8.499 -4.53 -7.81 0.412 0.548 0.674 0.752 12.172 32 4.000 10.870 7.498 -2.14 -6.22 0.413 0.549 0.687 0.751 9.651 33 4.000 10.870 7.498 -6.55 -8.73 0.413 0.549 0.859 0.751 9.266 34 4.000 10.373 7.491 -4.37 -7.55 0.395 0.522 0.649 0.757 9.106 35 4.000 11.468 7.472 -4.49 -7.58 0.440 0.580 0.694 0.758 9.686 36 4.000 10.163 7.470 -4.36 -7.29 0.390 0.551 0.663 0.707 9.249 37 4.000 9.434 7.469 -4.42 -6.93 0.362 0.552 0.654 0.657 9.117 38 3.000 19.378 7.503 -4.53 -7.86 0.413 0.547 0.675 0.755 12.666 39 5.000 6.969 7.499 -4.55 -7.54 0.413 0.549 0.670 0.753 7.534 41 4.000 5.208 5.927 -8.16 -9.51 0.400 0.540 0.652 0.741 5.722 42 3.319 3.711 4.699 -3.28 -6.41 0.394 0.554 0.670 0.711 4.460 43 2.784 6.291 4.983 -3.28 -6.49 0.394 0.553 0.672 0.712 5.991 44 3.319 4.424 4.982 -3.29 -6.25 0.394 0.554 0.868 0.712 4.996 45 4.175 2.795 4.982 -3.28 -6.24 0.394 0.554 0.668 0.711 3.969 46 3.319 5.569 5.379 -3.29 -6.26 0.394 0.553 0.668 0.712 5.825 47 3.337 6.042 5.474 -6.02 -8.40 0.410 0.548 0.699 0.749 6.278 48 3.337 5.797 5.426 -0.65 -5.03 0.404 0.557 0.690 0.725 6.084 49 3.352 6.307 5.523 -6.34 -8.43 0.421 0.566 0.699 0.743 6.359 50 3.333 6.342 5.521 -7.90 -9.14 0.419 0.539 0.688 0.777 6.291

2-1

TEST SETUP

All models have been tested in the #1 towing tank of the Deift Shiphydromechanics

Laboratory with a length of 145 meter, width of 4.5 meter and depth of 2.5 meter. The model size within the DSYHS ranges between 1.6 meter waterline length for Series i to 2.00 meter waterline length for the other models (Series 2, 3 and 4).

All models have been tested as bare hulls (unappended) in the speed range from Fn = 0.10 to Fn = 0.60 to measure resistance, sinkage and trim in the following conditions:

- upright with no trim correction for the driving sail forces - upright with trim correction for the driving sail forces

- heeled to 20 degrees heel with no correction for trim due to sail forces

In addition the majority of the models have been fitted with a keel and rudder, identical for all models and according to the plan as presented in Figure 4. For the sake of consistency throughout the series all these models have been fitted with physical the same keel and rudder. This implies that the relative magnitude of the keel and rudder on the full scale yachts with 10 meter waterline length is dependent on the model size and the scale factor

used.

Figure 4 DSYHS Keel and Rudder Configuration Table 3 DSYHS Keel and Rudder Model Dimensions

All these appended models have been tested in the following conditions:

- upright with no trim correction for driving sail forces (Fn = 0.10... .0.60)

- heeled, yawed and trimmed condition in a matrix consisting of all combinations of

- 4 heeling angles (i.e. 0, 10, 20 and 30 degrees)

- at least three different speeds (i.e. ranging from Fn = 0.25 to 0.45) - 4 different leeway angles (i.e. ranging from O to 12 degrees)

symbol unit Keel Rudder

Profile NACA 632A015 0012

Root Chord ckroot cr100 m 0.414 0.124

Tip Chord

ck,

cr1 m 0.262 0.096

Span bk br m 0.219 0.266

Volume Vk Vr m3 0.00262 0.00023

Wetted Area Sk Sr m2 0.1539 0.0550

Sweepback Angle Ak Ar 0 45

54

15th _{International HISWA Symposium 1998}

During the experiments the following values were measured: - forward speed of the model

- resistance force

- heeling angle - heeling moment - leeway angle

- side force and yawing moment sinkage and trim (at speed) - trimming moment

The standard measurement technique

developed for sailing yachts experiments at the Delft Shiphydromechanics Laboratory fias been used throughout the whole series.

This technique implies that the model is

conflected to the towing carriage in such a way that it is free to heave, roll and: pitch but restrained in all other modes of motion.

The connection to the towing carriage is

established by means of two balanced arms

situated at equal distances fore and aft of

the longitudinal position of the Centre of

Gravity of the model' at deck level. A

schematic presentation of the measurement

setup is presented in Figure 5. _{Figure 5 Test Set-up under Towing Carriage}

During the measurements the model is

fitted with carborundum strips for turbulence stimulation, both on the hull and the appendages. On the hull three strips are placed which are 4.0 cm wide each and placed at equal separatiön with the 'first strip at the forward end of the waterline and the after most one approximately 'at station 6½ just forward of the leading. edge of the keel:. On the 'keel and rudder one single strip is placed close to the' leading edge of the appendages and these have a width of 3.0' cm for the keel and for the rudder 2.0 cm.

To correct for the extra resistance originating from' the presence of the strip itself all

resistance tests are carried out twice: once with half width and once with full width of the strips. The difference in resistance between' these two conditions is used to determine the resistance of the strips. The model resistance is obtained by subtracting the extra resistance from the strips from the measured model resistance.

All model' data are extrapolated 'to

a fill

scale 10 m waterline length yacht. The

extrapolation is carried out according to Froude's extrapolation technique.

15th International HISWA Symposium 1998 ₁₁

For the determination of the frictional resistance 'Rf' use is made of the following

expression:

Rf = -pV2 SCf

where:

p density of water kg/rn3

V the forward: velöcity of the yacht mis

S the wetted area at zero speed m2

Cf friction coefficient

In the determination of the frictional resistance use is being made of the well known ITTC-57 extrapolation line, according to:

0.075

(log(Rn) 2)2

in which the hull Reynolds number Rn is determined by:

Rn=

V 0.7. Lwl V in which:

Lw! waterline length m

V kinematic viscosity _m2/s

As may be seen from this

expression for

the reference length necessary for

the

determination of the Reynolds Number 'Rn' 70% of the waterline lèngth is taken. For the appendages the average chord length is used for the determination of the Reynolds Number.

For the upright conditions a so-called Prohaska plot is made to determine the formfactor of the hull. As a typical example of such a Prohaska plOt of the DSYHS in Figure 6 the plots

are presented for the three parent models of the Series. From these figures it may be

concluded that the formfactor is generally small. In general the forrnfactor using this

described turbulence stimulation technique and derived from the Prohaska plots has been found to be in the rañge from 'k' = 0.03 to

'k'

0.07 in most cases and only in one or two exceptional cases 'k' exceeded these values.

Plot for Sysser 44

Figure 6 Prohaska Plots for the Parent Model Hull Measurements

Since no well based or generally accepted formulation is ktiown (nor could it be derived from the results with the DSYHS) determining the formfactor 'k' as function of the hull geometry parameters of any arbitrary hull, it was decided, from the beginning of the series, not to use a formfactor for the calculation of the viscous resistance in the extrapolation procedure. This would make such a calculation method of 'k' necessary in order to be able

to calculate the resistance of a specific yacht under consideration.

151h International HISWA Symposium 1998 ₁₂

3 - CALM WATER RESISTANCE

3.-1 CANOEBODY RESISTANCE

As shown in the flow component chart for the definition of the various resistance

components (Figure 1) the first resistance to be assessed is the bare hull canoe body

resistance.

3-1-1 UPRIGHT RESISTANCE

First the resistance in the upright sailing condition will be calculated. Two separate parts of the resistance in the upright condition will be considered: i.e. the frictional (or viscous) resistance and the residuary resistance.

3-1-i-1 VISCOUS RESISTANCE

The frictional resistance of the bare hull is determined using the following expressiÓn

RJh=-pV2.Sc.Cf in which:

p density of water kg/rn3

V the forward velocity of the yacht mis

Sc the wetted area' of the hull at zero speed m2

Cf friction coefficient

The wetted area of the hull is considered to be known from the hydrostatic calculations. If this is not the case the wetted area of the hull in the upright and zero speed' condition may be approximated by the following expression derived from regression using the hydrostatic calculations carried out for all the models of the DSYHS:

Sc = 11.97

0.17l

('ì

.(Vc. Lw1)

Tc)Cm}

in which:

Bwl beam of waterline m

Tc draft of canoe body m

Cm midship section coefficient

-Vc volume of displacement of canoe m3

Lw! length of waterline m

Fully turbulent flow along the 'hull both during the experiments as in real life is assumed and therefore the friction coefficient Cf is determined using the ITTC-57 extrapolation line. Although the choice of 70% of the waterline length as the reference length in the 'Reynolds Number, as shown before, is quite justifiable for the hull geometry's of Series 1 the choice remains debatable. Particularly for the more contemporary shapes of Series 2, 3 and 4, 90% of the waterline length would appear more appropriate. For the sake of consistency however

151h_{International HISWA Symposium 1998}

70% of Lwl has been used throughout the whole DSYHS for the determination of the frictional resistance. It should be noted that this therefore effects also the magnitude of the residuary resistance part.

As explained before no "form" factor 'k' is used in the DSYHS for the transformation of the frictional into the viscous resistance of the hull. This decision is based on the absence of a generally accepted formulation of the form factor as a function of hull parameters for an arbitrary hull. Such a formulation could also not be derived from the results of the DSYHS.

This implied that 'k'

O was the best approach leaving any differences in the viscous resistance due to hull shape in the residuary resistance.

3-1-1-2 RESIDUARY RESISTANCE

Based on the experience gained with previous expressions for the determination of the

residuary resistance of the hull of a sailing yacht, see Ref. 1, Ref. 2 and Ref. 3, the

following expression for the residuary resistance of a yacht hull in the upright condition at

one specific Froude number has been found to yield sufficient accuracy as well as

(

Vc LCBJ

(LCBJ2

₂ Vc

+1 a5 +a6. +a7 F +a8 C'p i

Sc LCFJ

_{Lwl )}

)

Lwl in which:

Rrh residuary resistance of canoe body N

Vc volume of displacement of canoe body m3

p density of water kg/rn3

g acceleration of gravity rn/s2

Lwl length of waterline

Bwl beam of waterline m

LCBI longitudinal position centre of buoyancy to fpp m LCF longitudinal position centre of flotation to fpp rn

fpp forward perpendicular (ordinate 10) Cp prismatic coefficient

Aw waterplane area at zero speed rn2

Sc wetted surface canoe body at zero speed rn2

"robustness": Rrh

(

LCBJJ,J, _{Vc Bwl}

+a4I

_Lw!) VcX +

(7)

=a0+Ia«

Vcpg

Lwl +a2 Cp+a3 Aw Lw!

Some principal considerations which led to the presented shape of the parametric terms contained in the polynomial are:

The parameters in the terms are coupled with the displacement length ratio to make them. dependent on displacement. The terms are composed in such a way that their supposed contribution to the residuary resistance has a similar trend as the displacement length ratio.

The beam to length ratio is introduced for all speeds involved as an contributing factor 3:. The beam to draft ratio is replaced by the ratio between the displacement and the wetted

area of the hull, Which term is considered to yièld more robustness and less sensitivity to small changes in midship sectión shape.

The LCB-LCF separation is introduced as a possible measure of hull distortion.

Higher order terms of both Cp and LCB are introduced to yield optimum values of Cp and LCB as function of speed within the range covered by the polynomial.

The coefficients of this polynomial expression have been determined at constant forward speeds and are presented for a number of different Froude numbers using a least square fit through the measured data Since the origmal presentation of this expression m 1996, Ref

3, the number of models tested within the DSYHS has increased therefore leading to

differences in the coefficients compared to those presented before. Also this time not all models of the DSYHS have been inckided in the regression but only 39 out of the total of 50 models available have been used, leaving some of the more extreme or highly distorted models out.

The coefficients 'a0' to 'a8' are presented in Table 4 for 11 different Froude numbers from

Fn = 0.10 to Fn = 60.

Table 4 Coefficients for Polynomial: Residuary Resistance of Bare Hull

The resistance curves obtained for the models within the DSYHS using this polynomial expression all showed quite satisfactory correlation with the measured data and they do so over the entire speed. range. As a demonstration of this fit, the measured and calculated residüary resistance curves of the three parent models of the series, some additional models of Series 2 and four models not belonging to the DSYHS are presented in Figure 7.

15th International HISWA Symposium 1998 ₁₅

Fn 0.10 0.15 0.20 0.25 0.30 0.35

40

0.45 0.50 0.55 0.60 a0

-00014: 00004 00014 00027' 00056 00032 -00064 -00171 -00201

00495 00808

a1 00403' -0 1808 -0 1071 00463 -08005 -0 1011 23095 34017 7 1576 1 5618 -5 3233 a2 0.0470. 0.1793 0.0637 : 0.1263.: 0.4891 -0.0813 -1 .5'l52 -1.9862 -6.3304 -6.0661' -1.1513 a3 t0.0227 -0.0004

0.0090: 0.0150. 0.0269 -0382 0751

0.3242 05829 0.8641 09663 a4

-00119 00097 00153

002741 00519 00320 -00858 -01450

0 1630! 11702 16084 a5 00061

00118 00011-002991-00313 -01481 -05349 -08043 -03966 17610 27459

a6 . -0.0086 -0.0055 0.0012 0.0iI0 0.0292. 0.0837 0.1715 0.2952 0.5023 0.9176 0.8491 a7 -0.0307 0.1721, 0.1021 -0.0595 0.7314 0;0223 -2.4550 -3.5284 7..1579' 2.1191 4.7129 a8 -0 0553 -0 1728! -0 0648 0 1220' -0 3619 0 1587 11865 1 3575 5 2534 5 4281 11089

Reslduary:Resietance Bare HúlI Measured & Calculated 10 mLwI

meas: 10000 8000 6000 z 4000 2000

ResIduary Reeletance Bare Hull Measured & Calculeted lo m Lwl

42 0.55 0.6 D meas: 23 V 24 26 27 calc: 23 24 26 27

Parent DSYHS Models

Models of Series 2

Non DSYHS Models

Figure 7 Comparison Hull Residuary Resistance Measured and Approximated

15th_{International HISWA Symposium 1998}

16 10000 8000 6000 z = 4000 2000 o

Residuary Resistance Bare Hull Measured & Calculated 10m Lwl

/

/,-'

A'''

--

s---/

/

-D meas: 329 V 366 232 117 calc. 329 366 232 117 0.2 0.25 0.3 0.35 0.4 0.45 Fn 0.5 0.55 0.6 0.2 0.25 0.3 0:35 0.4 0.45 0.5 0.55 0.6 Fn 0.2 0.25 0.3 0.4 Fn 0.35 0.45 0.5

3-1-2 CHANGE IN RESISTANCE DUE TO HEEL

When the yacht heels over there will be a change in the resistance of the yacht. In real circumstances this heeling will be caused by the arthwarth forces on the sails. This implies lift forces on the hull and its appendages also and:_{therefor the induced resistance component}

will be a large part of the change in total resistance. However to be able to calculate this induced resistance more accurately first an attempt has been made to assess the change in resistance due to heel alone,, i.e. no sideforce involved. This resistance change is split in a viscous and a residuary part, each being, treated separately.

3-1-2-1 CHANGE IN VISCOUS RESISTANCE

The change. in viscous resistance due to heel of the canoe body is solely attributed to a change in wetted area of the yacht hull. This implies no change in viscous resistance, i.e. no change in formfactor, is taken into account. This approach originates, from two considerations:

I. A formfactor is not taken into account in the upright condition as well.

2. A change in form factor due to heel alone can hardly be established based on towing tank measurements alone. The model cOuld be towed with heel and without total sideforce (possibly implying a small drift angle) but this does not mean that there is no sideforce distribution along the length of the model which sums up to zero. This implies a possible "mix up" between a complicated induced resistance component and a possible change m formfactor.

Based on the hydrostatic calculations which have been carried out for all models of the DSYHS the change in wetted area of he hulls with heeling angle has been determined.. This change in Wetted area of the yachts could be approximated with a high degree of accuracy by the following expression:

(8)

I

I

f L _{Bwl Bwl}

SC2=SC(0)il±.iSO+SI.

+s2.(____J

±s3Cn,

Tc Tc in which: Bwl beam of waterline m

Tc draft of canoe body m

Cm midship section coefficient

With the coefficients 's0' to 's3' being determined using a least square fit regression analysis in Table 5:

i5th_{International HISWA Symposium 1998}

Table 5 Coefficients for Polynomial: Wetted Surface under Heel

A typical result of this expression is shown in Figure 8 for one "average" and two "more

extreme" models of the DSYHS. Both the accuracy of the fit using the polynomial

expression for such widely different hulls as the significant difference in the magnitude of the change of wetted area itself is clearly demonstrated.

o

(1) 18 -'

Measured and Calculated Wetted Surface

30 28 26 24 -t I I I i i lt F I t I_ I I I I I t 5 10 15: 20 25 30 35

Heeling Angle PHI [DEG]

V

calculated

Figure 8 Calculation of Wetted Surface

34-2-2

CHANGE IN RESIDUARY RESISTANCE

Due to the asymmetry of the hull when heeled and a corresponding change in the

distribution of displaced volume alöng the length a change in residuary resistance will most probably occur.

To asses this change in resistance two possible approaches have been tried:

To use the same polynomial expression as used for the upright resistance of the çanoe body but determine new coefficients based on the measured data under heel. The result is not a change in residuary resistance but the changed residuary resistance due to heel. The change of residuary resistance due to heel is determined from the measured data and a simplified polynomial expression is formulated for just this delta resistance alone. Both approaches have their pro's and con's. The results of the first approach have been published in Ref. 5 but predicting the total residuary resistance of the heeled hull with the upright geometrical properties of the upright hull seems less justifiable than predicting the

( 5 10 15 20 25 30 35

s0 -4.1l2 -4.522 -3.291 l.850 6.510 12.334 14:.648

s1 0.O54 -0.132 -0.389 -l.200 -2.305 -3.911 -5.182

s2 _{-0.027Y -0.077} -0..1i8 -0.109 -0.066 0.024 0.102

s3 6.329 8338 8.949' 5.364 3.443: 1.767 3.497

151h International HISWA Sympositim 1998 ₁₈

model 26

- 20-model 16 D model 25

upright resistance with the upright parameters and using only some of these to predict the generally small change (delta) due to heel. So the second approach is presented and used throughout this report, althóugh the differences with the first approach are generally small for the cases investigated.

The change in residuary resistance of the canoe body due to heel is derived from the

measurements at zero and 20 degrees of heel with all models used for the upright condition polynomial by determining the viscous resistance upright and heeled and subtracting these from the total resistance of the hull upright and heeled respectively. According to:

(9)

ARrhço(,,,a.) Rrhço,,,)

_{- Rrh(,)}

The delta residuary resistance at 20 degrees of heel (as an average sailing angle) could then be approximated by a polynomial expression given by:

(b)

ARrh200 Lwl Bwl (Bwl

S\2

2

=u0+u1

+u2-+u3I

I +u4LCB+u5LCB

Vc.p.g

Bwl Tc ¼. Tc)

with the coefficients for u0 through u5

Table 6 Coefficients for Polynomial: Delta Resistance Hull due to 20° Heel

The dependency on the heeling angle which is necessary to obtain values of the resistance increase due to heel for any other angle of heel has been determined using a much smaller database of measurement data. In general a good fit was obtained using a dependency of the delta resistance on the heeling angle., The change is calculated to be equivalent with the heeling angle to the power 1.7, according to:

ARrh, = ARrh200 . 6.Q.

with the heel angle 'p' in radians. The fit through the experimental data for a few DSYHS models is shown in Figure 9 and Figure 10 and demonstrates to !be quite satisfactory.

it should be noticed in Figure 9 and Figure 10 that the delta part is small compared with the upright resistance. The scale of the vertical axes in the graphs differ with factor l'o.

Coefficients are multiplied by 1000

Fn 0.25 0.30 0.35 0.40 0.45 0.50 0.55 u0 -0.0268 0.6628 1.6433 -0.8659 -3.2715 -0.1976 1.5873 u1 -0.0014 -0.0632 -0.2144 -0.0354 0.1372 -0.1480 -0.3749: u2 -0.0057 -0.0699 -0.1640' 0.2226 0.5547 -0.6593 -0.7105 u3 0.0016 0.0069: 0M199 0.0188 0.0268 0.1862

2146.

u4 -0.0070 0.0459, -0.0540' -0.5800 -1.0064 -0.7489 -0.4818. u5 -0.O07 -0.0004 -0.0268 0.1133. -O.2026 -0.1648 -0.1174

z Q c'1 o-o 25 29 50 calc: 25 29

Figure 9 Delta Resistance due to 200 Heel of Bare Hull

10000 8000 6000 z o 4000 2000 o

Resld:Reslst.Bare Hull 20 degheel

meas and caic (Rrh+ dRrh2O) 10m Lwl D

meas: 43

Figure IO Residuary Resistance of Bare Hull at 200 Heel

3-2 APPENDAGE RESISTANCE

The resistance of the bare hull and the appendages are dealt with separately. The viscous

resistance of the appendages has been found to be independent of the heel angle and

therefore only one expressions is formulated for the calculation of this viscous part. Based on the DSYHS experiments with systematic keel variations underneath various hulls it was concluded that the residuary resistance of the appendages is significantly influenced by the (immediate) presence of the free surface and therefore definitely has a heeling dependency. So the residuary resistance of the appendages is determined in the upright condition first and a delta resistance dUe to heel is formulated thereafter.

15' Internationäl HIS WA Symposium 1998 ₂₀

DeIta'Resjst..BareHuIl due 20 heel

Measured & Calculated 10m Lwl D meas: 0.2 0.25. 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Fn 50 0.2 0:25 0.3 0.35 0.4 Fn 0.45 0.5 0.55 0.6

-46

3-2-1 UPRIGHT APPENDAGE RESISTANCE

3-2-1-1 VISCOUS RESISTANCE

The viscous resistance 'Rv' of the appendages is considered to be a summation of the

frictional resistance and "other" viscous effects accounted for by the introduction of a

"form" factor.

Rv= Rf(1+k)

For the calculation of the frictional resistance 'Rf' use is made of the follöwing expression:

Rf.p.V2.S.Cf

in which

0.075

(log(Rn) 2)2

originates from the ITTC '57 extrapolation line and is valid for a fully turbulent flow. For the determination of the Reynolds number 'Rn' the average chord length of the appendage may be used or, if the appendage is span wise divided in several segments, the local chord length of such a section.

No attempt is being made here to take into account more complex dependency on the cross section profiles of the appendage and so possibly for mixed flow, i.e. a combination of

laminar and turbulent flow over the chord of the appendage. There are no principal

procedural problems however for taking these mixed flow possibilities in account except maybe the correct formulation of the frictional and form effeçts.

The viscous and formdrag is taken into the calculation by makmg use of the well known

formulation for 'k' as given by Hoerner's "Fluid Dynamic Drag" Ref. 7 and generally

accepted in the aeronautical sciences, which determines the formfactor a sole function of the relative thickness of the sections, according to:

(1+ k) = [1

±2

+ 60

Each of the appendages, i.e. keel and rudder(s),, is treated in a similar manner using the same formulations.

For the "straight course" upright resistance a possible wake effect from the keel on the

rudder may be introduced. From experiments, in which the wake behind the keel on

sufficient distance aft of the keel has been measured on a 3.5 meter Lwl model, an

C

15th International HISWA Symposium 1998

acceptable mean reduction valúe of 0.80 times the free stream velocity has been found for the water velocity over the ruddèr, see Ref. 8 and Ref. 9. The general applicability of this value may be disputed however and because the rudder will only be in the wake completely if the yachts sails with absolutely no heel and no leeway, the necessity öf such an approach is also questionable.

3-2-1-2 APPENDAGE RESIDUARY RESISTANCE

The very existence of a significant residuary resistance of the appendages beneath the hull in the upright condition has long been disputed. A report in 1975 by Beukelman and Keuning Ref 10 however already showed an influence of the keel sWeepback (i.e. lcngitudinal

distribution of the displaced keel volume over the length) on the upright resistance of a yacht. From analysis of the results of the experiments with bare hull and the appended model within the DSYHS, in which series one and the same keel has been tested underneath

a wide variety of

hulls, it became obvious that a residuary resistance of the appendages should be taken into account.

Straight forward comparison of the appended and unappended results withiù the DSYHS

however necessitated the subtraction of two big, quantities to produce the residuary

resistance of the keels. This yielded too much scatter in the relatively small keel residuary

resistance component to justify a reliable assessment. Therefore an additional Dei ft

Systematic Keel Series (DSKS) has been set up, in which so far a family of 6 different keels has been tested underneath two IACC type hulls with different Beam to Draft ratio's. These

experiments are extensively described in Ref. 9 and Ref. 4. Also the results of recent

investigations on the DSKS by R W M Meulemans, Ref. 14, are included. Therefore this research will only be summarised briefly here. During these experiments with the DSKS the resistance- and liftforces on the appendages were measured directly and separately as well as the forces on the model as a whole. The tests program contained experiments both with

the bare hulls as with the hulls equipped with the various appendages. The standard

measurements and test program of the Delft Shiphydromechanics Laboratory have been used during these experiments. The profiles and main dimensiOns of the keels used in the experiments are presented in Figure 14 and Table 7 and for the two model hulls in Figure li, Figure 12 and Table 8.

L SAI

II

.-n.

411IIII

O II IO 13 4 I B

II 12

Model 3 29

Figure 11 Drawing of 1ACC Model 329 Hull

Model 366

11 15 II lO IB 19 20 21 22

Figure 12 Drawing of IACC Model 366 Hull

The parameters tested for their influence on this residuary resistance of the keel in the upright position were: the span of the 'keel, the displaced volUme and the vertical height of the centre of buoyancy of the keel, the beam to draft ratio of the hull and the taper ratio of the keel. In the analysis the keel resistance was determined as the difference between the resistance of the appended and the unappended condition, so possible interference effects between hull and appendage are contained in the keel resistance component. These results are used to develop the pólynornial expression for the keel resistance.

It should be noted that this DSKS is still under development and future extensions are

foreseen, which are intended to lead to an increased reliability of the keel residuary

resistance assessment.

Another systematic keel series has been tested, which consisted of a series of 13 widely different keels underneath one and the same hull, described in Ref. 11. This series is refered to as the Deift Various Keel Series (D\TKS).

In this series the hull of a IOR type maxi has been used to compare the usual IOR type keel with a number of alternatives both for racing and cruising, like an Elliptical keel, keels with Winglets, Centre boards, Shallow Draft keels , Upside-down keels etc. etc.

In the present assessment of the keel residuary resistance only the IOR-, the Upside-down-and the Shallow Draft keel are being used because the others are not sufficiently consistent with the rest of the keels used. A side view and the main particulars of these keels are presented in Figure 15 and Table 7. The particulars of the IOR type hull, Model 232, are presented in Table 8.

Table 7 Main Form Parameters of Keels

Table 8 Main Hull Form Parameters of Different Yacht Test Series

This selection was supplemented with the measurements carried out with the standard DSYHS keel underneath the three parent models and the half span standard keel as tested underneath Model 1.

So the expression for the residuary resistance of the keel is derived from the following data: The IOR-, the Shallow- and the Upside-down keel in the Deift Various Keel Series (DVKS),

5 of the 6 keels tested in the Delft Systematic Keel Series with the IACC type hulls (DSKS) and the parent models of the DSYHS of which Model 1 with half span keel also.

The plan views of these keels are presented in Figure 13 through Figure 15, in which

figures all the keels are shown in correct relative size.

Yacht Keel' AR TR A tic

DSYHS Model i

DSYHS Model 23. .28 DSYHS Model 43

Standard DSYHS keel 0.65 0.63 45.0 15.0

Model 117 20° sweep back version 0.94 1.00 20.0 15.0

Model 232 'IOR' keel 0.92 0.51 28.0 12.5

'Shoal Draft' keel 0.28 0.79 33M 11.0

ftJp Side Down' keel 0.92 1.98 28.0 12.5

Model 329 'IACC 1' and Model 366 'IACC 2' (10 configurations) 1 1.62 0.75 4.0 10.0 3 p.70 0.84 1.2 6.6 4 0.70 0.84 7.2 15.0 5 1.62 2.50 4.0 10.0 6 i.62 0.40 4.0 10M Yacht

jy

LCB % LCF % Cb Cp BWI Tc Vc"3 DSYHS Model 1 3.1:5 3.99 4.78 -2.3 -3.3 0.36 0.56 DSYHS Model 28 4.50 6.75 6.99 -2.1 -6.0 0.40 0.54 DSYHS Model 43 2.78 6.29 4.98 -3.3 -6.5 0.39 0.55 Model 117 3.19 5.27 5.05 -4.2 -4.6 0A2 0.58 Model 232 3.55 5.22 5.46 -42 -4.5 0.40

55

Model 329 'IACC P 4.52 4.82 6.63 -5.0 -6.4 0.34 0.53 Model 366 'IACC 2' 5.73 3.00 H 6.63 -5.0 -6.4' 0.34 0.53

Figure 13 DSYHS keel (model Lw! = 2.0 m), DSYHS half span (model Lw! = 1.6 m) and Model 117 keel

Sideylew Keel Model: i29.5

Figure 14 Keels of the Delft Systematic Keel Series Sldeolew Keel Model: 129.6

Figure 15 Keels of the Deift Various Keel Series

15th International HIS WA Symposium 1998 ₂₅

Sideelew Keel Model: i SideiewKeel Model: i.U4 Sldevlew Keel Model: 1iI:

Sideview Keel Model: jU.i Sldeeew Keel Model: 3el.3 Sldewlew Keel Model: 39.4

The following expression yielded a quite satisfactory fit through all the data and is based on

the relation between keel and hull volume, the taper ratió of the keel, the Beam to Draft ratio of the hull, the vertical distance of the centre of buoyancy of the keel volume to the free surface Zcb and the ratio of canoe body volume to keel volume.

(16)

Rrk T Tc+Zcbk

=A0+A1

Vkp.g

Bwl 2 Vk' Vk in which;:

Rrk residuary resistance of keel N

Vk volume of displacement of keel m3

T total draft of hull with keel m

Bwl beam of waterline m

Tc draft of canoe body rn,

Zcbk vertical position of centre of buoyancy of keel m

Vc volume of displacement of canoe body

For the lower Froude numbers the contribution of the residuary keel resistance in the total resistance is not very large, but it increases for the high speeds. The data set however is still rather limited for such a delicate resistance component and further resçarch will certainly contribute to increasing the reliability of these expressions.

With the data set described above the following coefficients were found for the coefficients of the polynomial expression:

Table 9 Coefficients for Polynomial: Residuary Resistance of Keel

Fn 0.20 0.25 030 035 0.40 0.45 0.50 0.55 0.60

A0 -0.00104 -0.00550. -0.01110 -0.00713 -0.03581 -0.00470 000553. 0.04822 0.01021

A1. 0.00172 0.00597 _{0.01421 0.02632} 0.08649 _{0.11592 0.07371} 000660 _0J41173

A2 0.00117 0.00390 0.00069 -0MO232

0.00999 -00064

0.05991 0.07048 0.06409

A3 -0.00008 -0.00009 0.00021: 0.00039 0.00017 0.00035 -0.00114. -0.00035 -0.00192

Calculated- compared with Total Measured Upright Resistance for two models: 10000 8000 6000 z 4000 2000 o

e -

_Rfh Rt (up)

e-íRvk

o-.Rvr

o-Rrh

o--dRrhphi -H-dRrtrim

Figure 16 Total Upright Resistance, Measured and Calculated for Model 43 10000 8000 6000 z 4000 2000 o

e

-Rfh Rt (up)

e-Rvk

o-Rvr

o-Rrh

Figure 17 Total Upright Resistance, Measured and Calculated for Model 366.1

15ih International HIS WA Symposium 1998 ₂₇

Total Ydcht RublatiuIt.0

Caic vs. Meas, optional:phiand beta _{calculated: I measured:}

0.10 0.20 0.30 0.40

Fn

0.50

calculated: I measured:

Caic vs. Meas, optional phi and beta

0.10 0.20 0.30 0.40

Fn

3-2-2 CHANGE IN APPEN' AGE RESISTANCE DUE TO REEL

The viscous resistance of the appendages is considered not to be influenced by the heeliñg of the yacht. This is a quite justifiable assumption. Things are different however when considering the residuary resistance of the appendages. This residuary - or wavemaking resistance of the appendages, in particular the keel, is strongly influenced by the fact that the volume of the appendage is brought closer to the free surface due to the heel angle of the yacht. All experimental data strongly confirm

this change. This was already clearly

demonstrated by Beukelman and Keuning in their paper of 1975 ReL 10 in which amongst others photos of the heeled hull with resulting the free surface waves with and without sideforce production of the keels were shown.

The approach used for the assessment of this resistance in the present study is along two lines of thought.

Firstly the amount of wavemaking resistance of the keel due to heel (no sideforce!!) is considered to be dependent on how close the volume is brought to the free surface, i.e. to be dependènt on the beam to draft ratio of the hull and the relative submergence of the keel volume, i.e. the ratio between keel spari and hull depth and secondly to the amount of wavemaking of the hull itself, i.e. related to the length displacement ratio. These influences of course will be dependent on the heeling angle but in addition to this also on the speed of the yacht and hence to its primary wave generation, i.e. the Froude number.

The following figure presents how the measurement data from the 'heel and leeway'

experiments have been split in the components for pure Heeled' Residuary Resistance 'Rrp' and the Induced Resistance 'Ri':

1000

800

600

400

200

Residualy Resistance and Heeled Force

20 degheeI, for.one velocfty

RCi

Heeled Residuaiy Resistance at no Sideforce

Induced Resistance

due to Sideforce

z measured - flt through measurements

o

0.OE+00 510E+06 1.OE+07 1.5E+07 20E+07 2.5E+07 3LOE+07 3.5E+07

Fh'2 [N"2]

Figure 18 Offset for Heeled Residuary Resistance and Slope for Resistance due to

Sideforcè

Consequently to further separate the effects contributed by the keel alone, the resistance components associated with the upright condition and the delta through heel of the hull itself should be subtracted from this heeled residuary resistance:

ARrkq(p,0.) = Rrço Rr ARrhço

Where 'Rrp' and 'Rr' represent the Values for the hull with keel and rudder. Hence the following expression has been used to approximate these data:

(17)

ARrkço

=Ch.Fn2.ço

Vk.p.g

where the following expression has been found for the assessment of Ch:

( 18)

Tc 11w! Tc Bwl Lw!

Ch = H1 - +

+ H3 -

+ H4

T Tc T Tc Vc'

of which the coefficients H through H4 have been determined using a least square fit regression analysis. These coefficients are presented in Table 10. The heeling angle 'qf in

radians.

Table 10 Coefficients for Polynomial: Delta Resistance of the Keel due to Heel

The data set to determine the coefficients with included tests with the following models: 24 models of the DSYHS IJO configurations of the DVKS and 3 configUrations of the DVKS. Some results of calculations executed with this polynomial are presented in the following chapter in together with the Induced Resistance component in Figure 20 and up.

H1 -3.5837

H2 -0.0518

H3 0.5958

H4 0.2055

I5' International HISWA Symposium 1998 ₃₀

4 - INDUCED RESISTANCE

The results from previous studies on the induced resistance as presented amongst others by Gerritsma et al. in Ref. i and Ref. 2, have been completely revised in the present study. This is primarily dUe to a change in the definition of the iflduced reSistance itself and partly due to taking the effect of other parameters in assessing it into account.

In the initial approach the induced resistance was simply defmed as the difference in the 'total resistance of the sailing yacht in its upright conditiön and sailing at the same speed under heel and leeway (with sideforce). By doing so a number of changes in the total resistance were considered to be part of the induced resistance, which were however not directly related to the sideforce production itself.

In the present approach most of the components of the resistance difference between these

two conditions (i.e. the upright and the heeled and yawed conditidn) are dealt with

separately, i.e. the changes in both the residuary- and viscous resistance due to heel alone and no sideforce involved are considered,, as it is extensively described in the previous chapters. The induced resistance is now solely related to the actual sideforce generation of the hull and the appendages.

The present approximation method however is still based on the same fundamental physical principles as they are originating from the aeronautical sciences, i.e. the "effective span" approach as presented in Ref. 1. The basic idea behind this approach is as follows:

As known from the aeronautical sciences the induced resistance,

i.e the additional resistance component due to the sideforce production of a wing with finite span, is related to the circulation around the foil and its geometry by the following set of expressions

Ri=CD .pV2 Aiat

Fh=C1 .+PV2 .Alat in which:

Alat=ckT

and: Ri induced resistance N

CDI induced resistance coefficient

Alat lateral surface of hull with keel m2

Fh heeling force N

C1 lift coefficient

ck mean chord of keel m

The induced drag coefficient CDI is related to the loading of the foil by:

(21)

Di

Ri=

Te2

AR=

e Alat

In the formulation the "effective" aspect ratio 'ARe' is used rather than the aspect ratio 'AR' itself. This "effective" dèsignation is meant to take account of the free surfàce effects. The effective span is in agreement with the effectIve aspect ratio and is the equivalent total effective draft of the hull plus keel combination 'Te'. The addition "effective" originates from the fact that a reduction (or sometimes increment) of the geometrical aspect ratio Is found which is dèpendent on the free surface-, hü11keel interaction- and endplate effects associated with the keel - hull combination moving with forward speed in and in the close proximity of the free surface (such as waves, pressure relief and "talk-over" effects etc.). With the expressions for ARO, CL and CDI combined the. induced resistance may now be written as: Eh2 2TARe

pV2 4lat

Eh2

Ri=

ir.Te2 .f pV2

The induced resistance is proportional to the

slope 'RCi' of the line fitted through the

measurement data as illustrated in Figure 18. Now the effective span 'Te' of the hull with

appendages is determined from the

measurement data with:

I Eh2

Te= j

r.Ri.4 pV2

Te=i

1

V rRCi.-pV2

From the measurements it became obvioüs that the effective draft Te and its change with heeling angle 'p', was strongly dependent on the Beam to Draft ratio of the hull above it as

(22)

11eeIingForce'Fh'

Sideforce 'SF'

Eh SE

cos(q)

Figure 19 Heeling Force and Sideforce

(23)

well as with the relation between the canoe body depth and the keel span. In addition to this a speed dependency was found. For each of the heeling angles tested, i.e. Ø0 10°, 20° and 30°, this relationship could be satisfactory established with the following expression:

(24)

ck.

Where 'TR' is the Taper Ratio of the keel: TR , with 'ck' being the keel chord. Ck,00,

The coefficients of this expression have been determined using a least square fit regression analysis through the measured data. The data set included tests with the following models: 20 models of the DSYHS, 10 configurations of the DVKS and 3 configurations of the DVKS. The coefficients are presented in Table 11.

Table 11 Coefficients for the Polynomial: Effective Span

Residuary Resistance ar1dHeeiingiorce

20 deg heel oath line a Oelocity

- fit for each velocity

A typical illustration of the obtained accuracy of the fit to the measured data of the

resistance due. to heel of bóth the hull and the appendages and the induced resistance is presented in Figure 20 and following. In these figures a graphical representation is given of

the resistance as a function of the generated sideforce squared for 3 different models

belonging to the DSYHS, i.e. Model 1, 24 and 25 and two different angles of heel, i.e. 20° and 30°.

Figure 20 Measured and Calculated Resistance at 20° Heel and Leeway for Model i at Fn = 0.30, 0.35, 0.35 and 0.45 (p 0 10 20 30 A 3.7455 4.4892 3.9592 3.4891 A2 -36246 -48454 -3.9804 -2.9577 A3 00589 0.0294 0.0283. 0.0250 A4 -0.i296 -0.0176 -0.0075 -0.0272 B0 1.2306 1.4231 1.5450 1.4744 B1 -0.7256 -1.2971 -1.5622 -1.3499

15th_{International HIS WA Symposium 1998}

32

O.OE+OO i .OE+07 2.OE+07 3.OE+07

Fh2 INA2I

Figure 21 Measured and Calculated Resistance at 30° Heel and Leeway for Model 25 at Fn

=

0.32, 0.36 and 45

Figure 22 Measured and Calculated Resistance at 30° Heel and Leeway for Model 33 at Fn

= 0.32, 0.36, 0.41 and 0.45

Figure 23 Measured and Calculated Resistance at 20° Heel and Leeway for IACC Model 329 With Keel 5 (Up Side Down) at Fn = 0.27, 0.35 and 0.39

3500 3000 2500 z 2000 + , 1500 1000 500 O 00E+0O

Residuary Resistance sndHeeiedForce

30 deg heel, each line a velocity

1 OE+07

> measured fit for each velocity

2.OE+07 3.OE+07 FhA2 1NA2I 4:OE+07 5ME+07 2500 2000 1500 + 1000

ReslduaryReslstance and Heeling Force

30 deg heel, each line a velocity

15th_{International HISWA Symposium 1998}

33

x measured - fit for each velócity

o

O.OE+00 5OE+06 1.OE+07 1.5E+07 2.OE+07 25E07

Fh2 [N2J

Resiclualy Kesistance ana Heerea lorce 20 dog heel,' eech line e veloddy

1000 X 600 600 _>< n:: + 'C P- 400 200

>< measured fit for each velocity

O

O.OE+O0 5.OE+06 i .OE+07 i .5E+07 2.OE+07

5 - SIDEFORCE PRODUCTION

The sideforce production of the models of the DSYHS under heel has been measured in a series of yawed and heeled tests carried out at various forward speeds. All these tests have been carried out with the models equipped with the standard keel and rudder of the DSYHS. The main particulars of this standard keel and rudder are presented in Figure 13 and Table 3. The following models of the series have been tested during the yawed and heeled tests:

Series 1, all models Series 2, all models

Series 3, models 31 and 33

Finally, model i has been tested also with the standard keel reduced to half span and the results of these measurements are also included in the analysis.

The results of the analysis did not yield significant different results from those previously presented in Ref. 2. A satisfactory fit for the total lift force delivered by the hull, keel and rudder combination and the leeway angle through the experimental: data was obtained by the following expressión

ßFh.cos(cO)

(Bo+B2.ço2)+B3.ço2.Fn

XPV 'Sc

in which expression the first term accounts for the lift slope of the hull, keel and rudder combination and the second term takes care of the, free surface effect clearly evident from the experimental data with the higher beam to draft ratio models.

The slope depends on the effective aspect ratio of the underwater part of the hull, keel and rudder. It was found that this "lift curve slope" could be expressed with sufficient accuracy by the following expression:

Fh.cos(ço)

=b1L+b2.Ii+b3.T+b

ß'XpV2'Sc

Sc

Sc)

T "

T Sc

in which: heeling angle 13 leeway angle

T total draft of hull with keel rn

Sc wetted surface of canoe body rn2

Tc draft of canoe body rn

The coefficients b1 through b4 have been determined for the four heeling angles tested and 30 degrees and are presented in the following Table 12.

Table 12 Coefficients for the Po1ynomia1: Lift Curve Slope

The coefficient B3 has been determined from the experimental results as:

(27)

B3 = 0092

Bwl Tc

Tc T

This term only contributes significantly to the sjde force production when the models have a relatively high beam to draft ratio.

6 - ADDED RESISTANCE DUE TO WAVES

The added resistance of sailing yachts moving through wind generated surface waves has been a research topic since a long tirne Noticeable in this respect is the paper of Gerritsma ea.. in 1'973 Ref. 6 on the dependency of this added resistance n waves on the length-displacement ratio and the pitch radius of gyratión., based on measurements and calculations carried out on the Standfast 43, i.e. the first parent model of the DSYHS.

The calculation of the added resistance in waves generally requires an extensive and

elaborated numerical tool, usually based on either 2-D or 3-D potential theory. The rather

complicated and detailed input needed for such types of calculations as Well as the

computatiönal! time required for the calculations, usually makes their use impractical in a

"designers" VPP. In such VPP's a larger number of designs, most likely also in the

preliminary design stage, must be compared on their performance in a short time when detailed linesplans are not yet available.

So an approximation method has been sought which is suitable for the use in a VPP

environment and yet still accurate enough to distinguish on the influence of the most

important parameters influencing this performance in waves. The approximation method presented in this report is based on numerous calculations of the added resistance in waves

with a selection of the models belonging to the DSYHS.

However first a validation of the computational method used has been established. It Was known already that the computations using the so-called "ordinary strip theory" approach, as extensively described' in Ref , in which the added resistance is calcUlated using the

Gerritsma - Beukelman method.

(p _{0 10 20 .30}

b1 2.025 1.989; 1.98O '1.762

b2 9.551 6.729 0.633 - 4.957

b3 0.631 0.494 0.194 -O.O87

b4 -6.575 -4.745 -0.792 2.766

in which: Ç Raw s wave amplitude added resistance spectral density

encounter frequency of the waves

The method yielded quite satisfactory results for the "average" type of hulls like the parent hulls of Series i and 2. These yachts in particular have no extreme values, either up or down, for the beam to draft- and the length to displacement ratio's.

For the development of the aforementioned approximation method however a more wider use Within the DSYHS was needed, so the results of the computations using this approach have been checked with two additional and rather more extreme models. These results were presented in Ref. . Using a series of towing tank experiments with the two DSYHS Series

2 models 26 and 27 in head waves the accuracy of the calculations as well as the influence of the heeling angle, the leeway and the sideforce (lift-) production of the appendages on the added resistance, normally not accounted for in these computations, was investigated. A typical result of this study is presented in Figure 24 In this figure the transfer ftinctions in head regular waves of the heave- and the pitch motion as well as of the added resistance in waves are presented for a forward speed of the model corresponding to Fn = 0.35 in both the upright and the heeled and yawed conditions.

15th International HISWA Symposium 1998 ₃₆

In this method the added resistance of the ship in regular waves is approximated by the

calculation of the radiated energy of the damping waves of the sections of the ship,

according to: Lwl Te RAW

-. J Jb.V2 _dx,dt in which X Wave length m t Time _s

b' Cross sectional damping coefficient, corrected for

forward speed

Relative vertical velocity of the considered cross sectiOn with respect to the water surface

Te Perkd of wave encounter s

Xb Length ordinate of the hull m

The relative vertical velocity V of each cross section depends on the heave- and the pitch-motions and the vertical component of the incident wave velocity. In this approach V is calëulated using the well known and relatively simple 2-D strip theory method without three dimensional effects.

In irregular waves for a known wave spectrum the mean value of the added resistance may be calculated using the linear superposition principle yielding

From these results it was concluded that the calculation method was sufficiently accuúate for the assessment of the added resistance for high beam to draft ratio model (BIT = 12) but lacked sufficient accuracy for the extremely low beam to draft ratiO (B/T = 2) model. The influence of the heeling angle on the added resistance was generally small except for the low beam to draft ratio model and well within the accuracy range obtained with these type of calculations anyway and therefore the heeling angle was omitted from the further investigations. All tests and calculations have been carried out with the models in the upright condition.

The influence of the leeway angle and the sideforce produced by the appendages underneath the hull on the motions and the added resistance of the yacht was also very small. So all tests and calculations to derive the approximatiön method are based on the results obtained for the unappended hulls only.

0.4 0.5 0.2 01 - I 1' I -0 0.5 1.0 0 0.0 0.0

LA-.

PITCO L/).-+ . 20° 0.5 1.0 0 0.0 [.0

LA-00010 00500TAXCI

Figure 24 Motions and Added Resistance in Waves of Models 26 and 27

15th International HIS WA Symposium 1998

-

Calcal.t100 0.5 1.0

LI).-2.0} -Za' 1.0 1.0 la 0.0 - Ca1c1t1 4 - 0° 0.5 1.0 0 0.5 1.0

LI). -

uoVe

LI).

-4- 0° 4. + - 20° 0.5 0.0 0 0.5 1.0 LI). -

LI).

-+ - 0° + - 200 0.5 1.0 0 0.0 0.0 00010 01010TM4CO 37 iI%l iinrniii

.m.ii

111l

1

lulL I1IMJII

'uaI_{aI1 O.. -4.5}

0./ql - 5

u..

ijrai'a

i FN -0.20 _{PN 010} 10 - 0 - 0° A p - 5°

w1

20° 2.0 Za I 4 - -4 - 20° 1.0 Oa IIZAVI 0 -1.0 0

LI).

-To investigate the applicability of the 2-D strip theory based calculation method usedeven

further a new and extensive series of towing tank experiments in waves with 5 models of

DSYHS Series 4 have been carried out in head waves by M. Levadou at the Deift

Shiphydromechanics Laboratory in 1994, see Ref. 12 and Ref. 5. These models were: model 42, 43, 44, 45 and 46 which series contains basically a systematic variation in length-beam ratio and length displacement ratio. In these new tests the influence of the length-beam to draft ratio has been investigated implicitly once again, but now within a much more usual range as compared with those tested with the models 26 and 27 of DSYHS Series 2. In addition also the influence of the longitudinal radius of gyration has been investigated on

model 44 (jarent model DSYHS Series 4) and checked against the results of the

computations.

Some typical results of this investigation are presented in Figure 25 through Figure 27. In this figures the transfer functions for the added resistance in head waves are presented

obtained by both the experiments and the calculations as a function of the

length-displacement ratio, the length beam ratio and the longitudinal radius of gyration 'kr,'.

ei 0.4 oi 0.% AddedTesietNnCc. P, - 0.325. s. Ie---42LJTII42 - 121 104

f \%i

IJL measured calculated

Figure 25 Dependency of Added Resistance on Length Displacement Ratio

ej e., Added reoI,to,,ce, P 0.325, - 0f 1.139 1.304 Q--.L. 0.773

4" p\\

Il.' /

''ses

//' I

¿hic . J. --- '0l1 ilL Seoway. _N = 000° -L10. 4.379 -1.l3'. 0.497 V-.VL3 0304 ø-81..42. 0.421 o-el.10. Z.fl, measured calculated

Figure 26 Dependency of Added Resistance on Length to Beam Ratio

-Addod oeIc0. F2 -O,125 ô- 0

86.

2

Table 14 Main Dimensions of Models for Added Resistance

SeawNy. F 0.325,

From these results it was concludéd that the prediction based on the 2-D strip theory

apprOach yielded good results for range of the length-displacement ratio (and beam-draft ratio) and the range in the radius of gyration as tested, but for the length beam ratio the calculations showed hardly any dependency while the measurements showed a considerable

lower added resistance for the high length beam ratio model.

In general the trends in added resistance with changing parameters are predicted correctly however. Therefore the general correlation between the measured and calculated values was considered good enough for an assessment of the added: resistance based on these results for

incorporation in a VPP.

In 1993 a first approach to the introdUction of an added resistance assessment in the VPP was launched by Gerritsma et;al.. The added resistance was calculated using the described method for forwards speeds of the yachts corresponding to 0.15 < Fn < 0.60 in waves with incident angles rangmg from t = 135° (corresponding to close hauled condition) to ji

Variation Model Nr. Lwl/Bwl Lwl3/Vc kILwl

Base Hull IMS-40-3 3.31 123 0.25

LIB ratio IMS-40-2 2.77

IMS-40-4 4.16

L3/V ratio IMS-40-1 104

IMS40-5 156

kIL ratiO IMS-40-3 0.30

IMS-40-1 IMS-40-2 IMS40-3 IMS-40-3 IMS-40-4 IMS-40-5

Lwl ml 1.71 1.71 1.71 1.71 1.71 i 1.71 Loa rn 2.09 2.16 2.11 2.11 2.08 2.16 Bwl m 0.52 062 0.52 0.52 0.41 0.52 Tc m 0.14 0.10 0.12 C.12 0.15 0.09

k/L

0.25 0.25 0.25 0.30 0.25 0.25 Ac kg 48.13 40.53 40.53 4053 40.53 32.07 -04 03 02 02 02 0.L 0I

15th International HIS WA Symposium 1998 ₃₉

measured calculated

Figure 27 Dependèncy of Added' Resistance on Pitch Gyradius of Parent Model Table 13 Model Hull Variations for Added Resistance