The seakeeping and steering performance of sailing yachts. Part I: Seakeeping performance Part II: Steering performance

I

Report No. 311

may 1913

r-LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

THE SEAKEEPING AND STEERING PERFORMANCE OF SAILING YACHTS

part I : Seakeeping performance part II Steering performance

by

J .Gerritsma G .Moeyes

SAIL

The seakeeping performance and steering properties of sailing

yachtsx)

by

xx)

xx)

J. Gerritsma

and G. Moeyes

Part II: Steering properties

Modern yachtsmen and yacht designers are fully aware of the

importance of steering properties for the performance of

sailing yachts. If a

cht is oscillating along an average

course, not only the path of the ship is unnecessarily

lengthened, but also every rudder action or yaw motion causes

additional resistance. It is clear that yawing oscillations

can result from bad steering abilities, either of the ship or of

the helmsman.

In extreme weather conditions a well controllable ship can

keep the cruising skipper further off from total exhaustion

of his (often síail) crew or even from wet feet. It can also

permit the racing skipper to keep his sails up longer than

his opponent, when conditions get worse.

Unfortunately experimental teting of the steering properties

of a yacht model takes a lot of time and mostly specialized

and expensive devices like a so-called planar motion

mechanism [4] or rotating arm. It will be realised that this

kind of testing is impossible for the individual yacht

designer from a financial point of view. Thus, for progress

in this field, fundamental co-operative research should be

carried out and unrestrictedly published, from which the

general conclusions can be used for particular designs.

Figure 1 shows a schematic representation of a yacht. When

the yacht is not steered, which can be obtained by mechanically

fixing the helm at a certain angle, the yachts course (the

output) is the reaction, to forces and moments due to the fixed

rudder angle and to disturbances caused by wind and waves{input).

x)

Abstract of paper to be presented at the Third HISWA Synposium on

yachts,, Amsterdam 21/22 March 1973

-2-Because there is no mutual influence between input and output the yacht with fixed controls (unsteered yacht) is called an open loop system.

When a helmsman is steering, he continuously compares the

ac-tual course with the desired course. and sets the helm accordingly.

Additional information is provided by the rate of turn, the

force on the helm, visual observation of sails and waves, etc. Because there is a feed-back of the output to the helmsman

the steered yacht is called a closed ioop system.

Just as in research in merchant ship manoeuvring, also in the yacht field attention has been paid at first to the open loop system: the ship with fixed controls.

If all external conditions are constant the yacht with fixed controls sails in the equilibrium condition on a straight

course. The stability of this equilibrium condition is related to the behaviour of the yacht after an initial, short

dis-turbance. If the yacht then settles at any new straight path, it is called controls fixed stable. If it does not and it is ultimately going to sail around a circle the yacht is called controls fixed unstable.

The controls fixed stability can be quahtitatively denoted by the value of the so-called stability roots or indices. These

roots, which can be determined by solving the linearized equations of motion, should ha\e negative real parts to get a controls

fixed stable ship. Positive roots indicate unstability. Neutral equilibrium, which has often been reported in practice for ships sailing off the wind in a breeze, results from a stability

root which nearly equals zero.

However, these zero stability roots could not be found by

Spens et al [i] , nor by Gerritsma {2] if the ship with zero

rudder angle, was mathematically described by a coupled swaying and yawing system, following common practice in merchant shi research. In this case all roots indicated a high controls

fixed stability. However, owing to the relatively large vertical distance between centre of gravity and effective lateral centre of a sailing yacht, its motions should be described with a coupled set of equations in sway, roll and yaw.

The coefficients of these equations have been determined experimentally in the Deift Shipbuilding Laboratory for

half ton yacht (figure 3), "Columbia" and "Valiant".

Besides, from a physical point of view the aerodynamic

sail forces should be included in the equations of motion.

Every extension mentioned above of the basic sway-yaw-system causes an increase in the number of stability roots, which

is two in the basic case.

Calculation of the extra stability roots shows that the coupIing

with roll has a destabilizing effeöt, which indeed could explain

the features of nearly neutral stability, observed in practice on a ship sailing downwind.

Including aerodynamid forces in the equations of. motion causes

the appearance of a fifth root, which Ìs in many cases even

positive. Thus, a mathematical description of the system in this extended way, which is without doubt physically the most realistic one, indicates that the running yacht is nearly neutral or éven

slightly controls fixed unstable. This is illustrated by figure 4 where t'he path of the half-ton yacht after an initial

dis-turbance has been calculated by computer, using the three different sets of linear equations of motion mentioned above. If in reality

no physical "non-linear" restrictions should exist the yacht with

fixed controls should finally rotate around its axis with an

ever increasing rate of turn.

Fortunately in most cases a helmsman or wind vane is present to

correct a ships natural tendency to broach..

It has been felt that a beginning broach could better be resisted

if the turning moment due to a cexain rudder angle should be

increased.

So the influence of rudder size and location upon the turning

moment has become of interest.

Spens et al

{iJ

measured the turning moment on models with different keel-rudder-configurations (figure 2) Locating the rudder more aft (from model 2811-i tb2811-2) showed to be an

-4-Gerrit.sma [2j investigated _{the model of a half-ton yacht}

with fin keel and well separated _{spade rudder (figure 3). An}

analysis of the dimensionless results obtained by Spens and Gerritsma showed the well located, high aspect spade rudder to be far superior to the rudder just behind a keel or a long skeg.

The importance of rudder size and location are clearly illus-trated by the turning moments exerted by the rudders of the

12-meter yachts "Columbia" and "Valiant" _{(figure 5). "Columbia"}

has an old style rudder faired into the aft part of the keel

with a rather large area. "Valiant"'s _{rudder is situated further}

aft but has a smaller area. It produces a smaller turning

moment. Its action is reduced because _{it operates in the wake}

of the hull,. possibly in a zone where flow separation _occurs.

Experimentally zero or even negative turning moments have been observed at rudder angles up to about ten degrees. It should be realized that "Valiant"'s rudder configuration is not very peculiar because many modern ocean racing yachts show in

prin-ciple the same features: _{a relatively small rudder connected}

with an afterbody which ii _{ather blunt with steep buttock}

lines in order to increase _{the prismatic coefficient and to shift}

the centre of buoyancy further aft.

It is the authors' opinion that a well separated, high aspect,

large area rudder! in combination with a non-separated flow in the afterbody area should be preferred

In merchant ship research the closed loop system representing the

ship steered by a helmsman or autopilot, has only in recent years

become the subject of _{investigation. The helmsman's behav±our}

has been studied with the aid of simulators, which consist of a

well copied navigation bridge _{with instruments and controls.}

An analog computer, which has been programmed with the dynamic properties of the ship, computes the response of the ship to any

steering action by the. helmsman. _{This response will be visulized}

on a screen by changing the relative position of the projected

-5-The study of the sailing yacht as a closed loop system is still in an initial stage. Some attempts have been made to investigate

the course stability of a yacht steered by a wind vane 3

The Delft Shipbuilding Laboratory started in co-operation with the Institute for Perception, Netherlands, a basic study on the steering behaviour of the helmsman of a yacht by means of a schematic yacht simulator. The purpose, is to investigate the influence of the steering gear (helm or wheel, length of helm,

balance of the rudder, etc.) upon the behaviour of the helmsman

and thé performance of the total system. To this end, the

dynamic properties of the yacht had to be determined. Because

the downwind condition offers most of the control difficulties

this situation has been taken up first. If no waves are assumed

the yacht is a system performing coupled sway, roll and yaw motions. The coeff.icients in the linearized équations of motion

can experimentally be determined with a planar motion mechanism [4]. From the equations of motion the response function of yaw to rudder angle can be determined, which th.n comprises terms due to sway, roll and yaw amplitudes, velocities and accelerations.

A thorough analysis of the response functions of the half-ton

yacht and "Columbia" showed that, if the rudder is continuously used, the influence of roll is negligible with regard to the yaw response to rudder angle. In other words: the small

contributions of forces and moments owing to roll, which have a remarkable destabilizing effect in the controls fixed case, are overruled by the rudder forces and moments. This can also be concluded for the aerodynamic forces which do not contribute significantly to the yaw response to rudder angle.

If a sinusoidal rudder angle with circular frequencyC) and

amplitude 3a is exerted the resulting sinusoidal yaw response

is given by its amplitude ¶j). and phase angle E,between yaw

and rudder motion. For different circular frequencies these data can be compiled in a so-called Bode-plot. The Bode-plot

of the half-ton yacht running at 8 knots, (f igure 6) constructed

with the three different sets of equations of motion mentioned

earlier, confirms the possibility to neglect the influence of rolling and sail forces and moments in the response function of yaw to

rudder angle (the frequency range of interest is about in between

-6-This conclusion reduces the mathematical description of the

sys.tem to a lower order, which also decreases the demand

for experimental data (and money involved) in future

investigations.

With the analog computer programmed with the lower order system

some pilot experiments have been carried out at the yacht

simu-lator. An example of one of the runs is given

The distïrbance is equivalent to a yw moment

waves, the helm angle has been exerted by the

recorded co.urse deviation results

from both.

Definite results and conclusions have not yet

but shall be published in t'he future.

in figure 7.

due to wind and

helmsman, the

become available,

REFERENCES

[i._J

P.G. Spens, P. de Saix and P.W. Brawn,

Soms further experiitental studies of the sailing yacht

The Society cf Naval Architects arid Marine Eigineers, 1967

J. Gerritna

Course keeping qualities and notions in waves of a sailing yacht

Proceedings of the third AIM. Symposium on the Aero/hydrodynamics

of sailing, California, 1971

A.L. Buchan and J.R. Flewitt

The behaviour and stability of wind operated steering systems

for sailing yachts

Transactions of the ibyal Institution of Naval Architects,

Vol. 110, 1968

H.J. Zunderdorp and M. Buitenhek

Oscillating techniques at the Shipbuilding Laboratory

Des i red.

course

Course

deviation

Helmsman

Feed back

Helm

angLe.

Fìg.1: BLock diagram of the steered yacht.

n

L

Disturbances.

Yacht

Closed Lop system

Qp.1en Loop system

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coupled sway

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coupled sway -roll-yaw description with sails.

o o o

5000

..

O CoLumbia

4000.

kgrn

1'

3000E turning

moment

u

_Valiant

Fig. 5:. Turning moment versus., rudder angle..

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2000

1000

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rudder. angle

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Research

Seakeeping.

Performance

This is part I of a 2-part article

abstracted from papers presented at

the Third HIS WA Symposium on

Yachts, Amsterdam, in March 1973.

The authors are researchers at the

prestigious De lit Shipbuilding Labo-ratory and their work represents some of the most detailed yet done on the subject of hull shapes. Part 2 covers Steering Properties, or

direc-tional stability of yachts.

Although for manyyears there has been extensive use of model tests

to evaluate the performance of

sail-ing yachts in still water, compara-tively little has been done with

re-gard to determining performance in

waves.

Here at Delft Shipbuilding

Labora-tory, in the Netherlands, we have recently applied our experience in evaluating merchant ship hull per-formance in wave conditions to a

program for sailing yachts, with very interesting results.

One of the few publications in this field was produced in 1967 by P. G. Spens et al for the Society of Naval Architects and Marine Engineers (1).

They reported the results of tests in waves with a model of the 12-meter Sovereign In the Davidson Labora-tory and one of the important

conclu-sions was the favorable effect of a

low gyradius*. (weight concentrated in center of a vessel - long

gyra-dius. weight distributed into ends)

with regard to motion and added resistance of a yacht in a seaway.

This was already known by many experienced yachtsmen, but the ad-vantage of such model tests is In the estimation of the quantitative effect of the longitudinal . distribution of

weight in a sailing yacht.

Model tests in waves are

expen-sive because of the many

combina-tions of yacht speed and wave dl-.

mensions that have to be considered.

Compared with the conventional still water model test many more runs In waves are necessary.

Because of the cost, a large part of

the analysis of seakeeping

perform-ance for merchant ship design is now

carried out with the aid of computer programs; thus reliable estimates of

pitching and heaving motions, as well

as of the added resistance In regular

and irregular waves, can be made.

Initially, of course, the theoretical re-sults had to be confirmed by careful

model experiments and also by full scale trials in measured sea

condi-tions.

Yachts have a rather extreme form when compared with the majority of

merchant ships. They have a very low length-beam ratio, a rather low prismatic coefficient, a high

speed-length ratio and a very shallow draft

hull.

Some of these differences are the

cause of difficulties when the exist-ing theories for calculatexist-ing motions

and resistance in waves are used for the non-linear form of the sailing yacht. However, despite this fact, the calculated pitching and heaving

mo-tions of an actual half ton yacht in

waves bore good, although not

per-fect, correlation to the results

ob-tained. by a model of the same boat in. the test tank.

For the half ton yacht, a very

im-pressive increase of resistance was

found in resonant regular waves.

Resonant conditions occur when the

natural period of pitch (or heave) is equal to the period of encounter of

the waves. Resonant pitching results in a large resistance increase and a substantial decrease of the forward speed of the yacht.

However, the waves at seaare

al-most never as regular as they usually

are in the towing tank and the aver-aging effect of the irregular seaway makes things more reasonable. But

also, the effect on speed of two or three almost "resonant" waves Is

known to those who sail at sea.

Recently a practical method to

compute the added resistance in a

by J. Gerrltsma and G. Moeyes

and with the aid of this theory the

in-fluence of displacement and

gyra-dius was investigated for a small

systematic series of yacht designs.

The theory was tested with the use

of model experiment results of two

12-meters Valiant and Columbia. The

necessary design data has kindly been put at our disposal by Spark-man and Stephens and the model

seakeeping experiments have been

carried out in Deift.

An example of the comparison be-tween calculation and experiment is given In Figure 1 for Valiant, which

shows a satisfactory agreement.

As the computer costs are only a small fraction of a comparable

sea-keeping test program, the analysis of

three designs of the Admiral's Cup racers (from the drawing board of

Frans Maas) could be carried out to

cover a range of gyradii as well as

irregular sea conditions.

Additional tests were carried out

in the Delft Tank to compare the still water performance Of the three de-signs with regard to the speed made good and the running condition.

To have a realistic average

gyra-dius for the analysis, the yacht

Standfast published as Admiral (4),

which resulted from the design

series, was oscillated manually to

determine the natural pitching

pe-riod.

With the obtained period, the

known geometry of the yacht and a

calculation of the hydrodynamic

mass moment of inertia, the-yacht's gyradius could be determined as

ap-proximatély 25% of the overall

length. Therefore, a gyradius of 23%, 25% and 27% was used in the pres

-ent analysis.

The lines of the three designs are

given in Figure 2. They all have the

same waterline length, breadth, beam

and IOR rating. However, the

dis-placements are8207 kg, 9759 kg, and 11443kg.

The still water performance tests

showed that design I with the lightest

Fig. 1: Pitch, heave and added resistance in waves of 'Valiant."

F::

t

VI 2f rS o 1000 500

.

speed = 7knots wave height = i rrt catcutatiort -experiment. . s O miDO 50 30 20 15 Wave length -w m.

Fig. 2: Lines of systematic series.

i

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Model I

Model III

w,

Fig. 3: Wave spectra and added wavé resistance operators

for design i. _£000

3

o

o

displacement is the best of the

three, although design Ill has the

lowest, resistance per ton'

displace-ment.

lt was concluded that, at least for

the- windward performance, this is

due to the more favorable

aspect-ratio of keel i-.

The heavy displacement hull is

deeper, but at eqtial total- draft, less depth is available for the fin keel This in turn has an adverse effect on the windward, performance,

For the three yacht designs the

motions and the added resistance. in a range of wave conditions were

cal-culated for the three gyradii already

mentioned.

The irregular-waves, as used in the analysis correspond. to. the spectral

* "gyradius _{or radius of gyration Is}

the square root of the ratio of. the

longi-tudinal mass moment of Inertia of the yacht and its mass. Gyradius has the

dimension of length and in our analysis

k,, is related to L,, the-overall length of'

Fig. 4Wâve spectra

density multiplied by added wave -resistance operatori 3 ¿ I I 'I t 20 15 10

wave Length - in.

density formulation (S) as' given by

Pierson-Mòskovitch- (a mathematica!

method of determining the

composi-tion of waves: power, direction,

height, frequency and so on.) The seaway is characterized by the sig-.

nificant wave height. In most sea

spectra, higher energy content, and

thus higher waves correspond to.

larger wave lengths- when- the high frequency (small wave length) range of the -sea spectrum is. considered.

This applies to ocean wave

spec-tra. as well as to coastal wave

spectra and -this property' seems to be important. for the-analysis of sail-ing' yachts in a seaway, -because-of. the- modest length of yachts1 com-pared with the lengths of sea waves. Figure 3** shows, thét in-the main,

the yacht; Thus'in Figure 5 k,,/L is

used-as abscissa of the- diagram.'.'

** In Figure 3 the ordinate RAW/c.1 is the added resistance- over the- squared wave -amplitude .. The added resistance RAW-is-the difference between the'total

resist-RadIus of gyrotlon

a yacht's resistance will not be af-fected by the -frequency range

of-maximum wave energy.

Multiplication of the wave spectral

densities (S) with the

correspond-ing added wave resistance -operators

(RAW/2) results in the. three sets of

curves in figure 4*** Here only one

wave spectrum is considered -as an

example. The area under these

curves is proportional to the added -resistance in the. considered wave

condition.

-Figure 4 shows the influence' of the

gyradius: the yachts with the largest

gyradlus experience - the largest

added resistance fri waves. Concen-

-tration ,of weight 'in -the mid portion.

of- the. yacht's hull -is advantageous:

in- all cases, the added resistance is

ance in waves and the- still water resist-ance at the same forward speed:'of -the

yacht.

-"° In -Figure 4 thié' expression is

múlti-plied by the wave spectral density Sçç.

st 7 g 6 100 I t I I 50 £0 30 25

Dnç. Z v.17e noti Wino ho.9t.202nn tJ3 Lo-rado,. o! rition 027 Lo o 11

Fig. 5: Added resistance in waves

,:t2 ?ÓL'Ò 2 S

b''''IY'''

h

Doo. 32 V.IX knoti

W.o h.çht.200nn

Cfrcular trequoncy o! eo-counte - rad½.

125 5000 30 OS 20 lO 9 9 7

025

023

V1.v In9th

-Row

Fig. 6: Speed-made-good In waves.

Dno,. X

V.970 knot, Way. hOh1 2.00no

8

lower for small radii of gyration. Figure 3 reveals that this ¡s due to

the shift.of the response curve

to-wards.larger wave lengths when the gyradlus is increased. A condensed

plot of all the computed added

re-sistances in a range of wave

condi-tions is shown in Figure 5 for one

forward speed: V = 6.74 .knots. In Table i the added resistance Is-given as a percentage of the

corre-sponding still water resistance at a

speed of 6.74 knots and, a gyradius of 25%.

Table i

Added resistance ¡n waves

V 6.74 knots significant

wave height

mm. .deslgn:l design Il designill

The Table shows that the lightest design (i) has the largest percentage

increase, when referred to the still water upright condition, although it

has the -smallest absolute resistance

increase.

-When sailing to windward the still water upright resistance is Increased due to leeway and heeling angle by

approximately 59%, 66% and 74%

for design I', Il and Ill respectively.

These figures show the influence of

the aspect ratio of the fin keel: the

light displacement yacht is better

because-of the better keel.

An overall picture of the windward

performance in waves is given In

-Figure 6- for three windspeeds and a

range of wave conditions. This

re-sult. shows thàt the influence of dis-placement becomes less significant

for -higher values- of the trUe wind

speed.

In addition to the quantitative

in

-- formation obtained by this analysis

of the seakeeping performance of a series: of sailing, yacht- designs, it may be concluded that still water model tests also remain a meaning-FUI tool for the yacht designer.

-References

(1) P. 0. Spens, P. de Saix-and P. W

Brown. Some further experimental-studies of the -sailing yacht The:Society of -Naval

-Architects and. Marine Engineers, 1967.

- -(2) J -Gerritsma: Course. keeping

quali-ties and motions 'in waves of a sailing-yacht. Proceedings of the third AIAA:

--- Symposium on the Aero/hydrodynamics

of saiiIng California igii. - - -

-(3) J; Gerrltsma and -W. Beukelman -- - Analysis of the resistance Increase

in

- waves of a fast cargo ship. international Shipbuilding Progress 1972. --- - - -

-- - - (4) Yachting World Annual 1971.

Lon-r

-- don hufe books. - r

290 82% 79% 76% 2.15 66% 64% 61% 1.70 52% 51% 48% 1.10 20% 25% 24% 3 i 2

null Design

o, o, o >, 'ja

l

-o,

» i

Steering Performance

by J. Gerritsma and G. Moeyes

»'q

Model of the 12-Meter Valiant undergoes tests in the test tank at Deift.

Figure 1

Block diagram of the stéered yacht. desired course

P

+_o course deviation helmsman disturbances

I open loop sysi]

r-Iclosed loop system

-ç-1--i helm

R

actual course yacht -angle I

L___J

This Is the second part of an article abstracted from papers presented at

the third HIS WA Symposium on

Yachts, Amsterdam. ¡n March 1973.

The first part, dealing with the

sea-keeping performance of hull shapes, appeared in SAIL, April 1973. In this part the authors, researchers at the Dell t Shipbuilding Laboratory, reach significant conc!usions about the di-rectional stability of yachts.

Ii1

odem sailors and yacht design-ers are well aware of the importance of steering properties in the

perform-ance of sailing yachts. A boat that

oscillates even slightly to either side of a straight-line course sails a

long-er distance and each ruddlong-er action

or yaw motion creates added

re-sistance.

This yawing is caused by either

the bad steering qualities of the boat

or of the helmsman.

In extreme weather conditions, a boat with steering control is less

ex-hausting on the crew (often small) than a boat that is hard to control.

Likewise, a racing boat that has di-rectional stability permits the crew to

drive it longer and harder than one

that must reduce sail to maintain

con-trol.

Unfortunately, experiments with the

steering properties of yachts take a

lot of time and must be undertaken

with expensive special devices. Such

testing is financially impossible for

individual designers with a particular

design.

For progress in this field,

funda-mental cooperative research and un-restricted publication of the conclu-sions such as we have done at Delft

is the answer. These conclusions are

thus available for all to apply to

particular designs.

In system analysis a yacht (Fig. 1)

is either an open loop system or a

closed loop system. When a boat is not steered (i.e., the rudder angle is

mechanically fixed), the yacht's

course (output) is the reaction to forces and moments caused by the

fixed rudder angle input and to

dis-turbances caused by winds and

waves. Such a boat with fixed con-trols is considered as an open loop

system.

However, when a helmsman is

con-tinually adjusting the helm to

maIn-tain a course in response to the effects of disturbances, the system

is considered as a closed loop

sys-tem.

feed back

Figure 2a

Fixed control behavior of ship with real stability roots.

Most research in yacht

maneuver-ability has been done with models without regard for the effect of ad-justments to the rudder angle. Our research, though, examines the ef-fects of both the steering properties of sailboat designs and the actions

of the helmsman.

The Effect of Design

A yacht with fixed controls will maintain a straight course as long as external conditions remain constant.

it meets a brief disturbance (i.e.,

wave, a gust or shift of wind), it will respond in one of two ways. The

yacht may settle on a new straight path after the disturbance. The

de-sign may then be said to be fixed control stable. If it does not settle on

a new course, it will ultimately sail around in a circle and is fixed

con-trol unstable (Fig. 2A).

Whether a boat will be stable or

unstable can be determined mathe-matically by solving linear equations of motion. If all the so-called stability roots or indices are negative, the design is stable. However, if one root

is positive, the design is unstable..

With complex roots, the behavior of

a yacht with fixed controls is

oscilla-tory: either stable or unstable (Fig.

2B).

Neutral equilibrium, often reported

in practice for yachts sailing off the

nd in a breeze, results from a stability root which equals nearly zero. However, in experiments (1 and

i

r.

- y

Model 2811-1 Model 2811-2 Model 2988 FIgure 4

Plans of 12-meter models tested in the Delit Shipbuilding Laboratory.

2) these zero roots could not be

found if the boat with zero rudder

angle was mathematically described

by a coupled swaying and yawing system of the type commonly used

in merchant ship research. All roots

indicated a high controls fixed

sta-bility.

Owing to the large vertical

dis-tance between the center of gravity

and effective lateral center of a sail-Ing yacht, its motions should be

de-scribed with a coupled set of equa-tions in sway roll, and yaw. Also, the aerodynamic sail forces should

be included in the equations of

mo-tion. All of these extensions to the

basic sway-yaw system increase the

number of stability roots over the

original two.

Calculation of the extra stability roots shows that the coupling with

roll has a destabilizing effect, whIch indeed could explain the nearly neu-tral. stability observed in actual

yachts sailing downwind.

Including aerodynamic forces in

the equations of motion causes the appearance of a fifth root, which In

many cases is positive. As a result,

a mathematical description of the

system in this extended way

indi-cates that the running yacht is nearly

neutral or even slightly controls

Figure 2b Figure 3

Fixed control behavior of ship Linea of models tested by Spens et. al. Eli with complex stability roots.

fixed unstable.

In the last case, the yacht will

rotate around its axis with an

in-creasing rate of turn.

Fortunately, on actual yachts, a

helmsman or wind vane can correct this natural tendency to broach.

Rudder Location and Size

A very important factor in deter-mining steering ability is the turning

moment as influenced by rudder size and location. The models considered

y Spens (Fig. 3) (1) all have poor udder action, although the design with the rudder separated from the

keel (model 2811-2) was an

improve-ment over the original configuration

(model 2811-1).

The 12-meter Columbia (Fig. 4) is considerably more effective than any

of the three models In Figure 3. Its

combined long keel and rudder

gen-erates a large side force owing to

the influence of the rudder angle upon the flow pattern around the

whole keel. However, also because of this influence, the center of effort

of the side force is not on the rudder, but more forward on the keel.

The smaller arm results in

Colum-bia's having a turning effectiveness

about half of that of the Half Ton model (Fig. 5) we tested. The rudder

of the Half Tonner, separated from the keel and located well aft, is by ar the most effective steering

de-vice of any of the designs we

ex-amined.

-Our conclusion is: a well-located,

high aspect spade rudder is far su-perior to a rudder behind a keel or

long skeg. This finding may surprise

those sailors who believe that long

keel yachts have better fixed control stability.

The characteristics of Valiant (Fig.

4) are worth noting. The turning

moment versus rudder angle of

Columbia shows a normal linear plot

(Fig. 6), whereas the turning momenti

rudder angle of Valiant is not only

very small but strongly non-linear. Because of the flow separation at

the blunt afterbody of Valiant, the small rudder acts fully in the wake. At small rudder angles almost no

turning moment is produced and

even a turning moment in the wrong direction has been observed both in

the towing tank and at the helm of

Valiant under sail. In fact, If the

helmsman of Valiant gives a rudder

angle smaller than 10° she could turn In the opposite direction from

that intended.

During our performance tests at

Delft, we have noticed the same flow

separation phenomena on several

modern ocean racers with very- full afterbodies. Both the windward per---formance and the turning properties could be improved in those designs by fairing the buttock lines.

Yacht designers, when increasing the prismatic coefficient and shifting

the center of buoyancy aft, should be aware of the adverse effect of

30 20 10

1000 2000 3000 4000 5000 5000 4000 3000 2000 O Columbia D Valiant kgm

t

turning moment N8.8 1000

rudder angle 8-degrees

10 20 30

-C

J C

making buttock lines too steep and

strongly curved.

The Behavior of the Helmsman Small boats, because of their much smaller mass, react much more quickly than large ships. The time

delay between the rudder action and its effect is short. Unlike the

helms-man of a ship, the helmshelms-man of a

yacht performs nearly continuous

rudder action to neutralize the effects

of disturbance and of his own prior

rudder actions.

Thus any analysis of steering

abili-ties should be extended to include

the helmsman's performance.

Wheth-er the design has fixed control stabil-ity or not, it can be steered, although a very unstable system will probably be much more difficult to steer than a stable, neutral, or only slightly

un-stable one.

The Delft Shipbuilding Laboratory,

in cooperation with the Institute for

Perception, Netherlands, has begun a basic study of the steering behavior

of the helmsman of a yacht by means

of a schematic yacht simulator. We

are investigating the Influence of the steering gear (tiller or wheel, length

of tiller, balance of the rudder, etc.)

upon the behavior of the helmsman and the performance of the total

system.

First we determined the dynamic

properties of the yacht using the

downwind condition since this Is

where most control difficulties

be-Figure 5 Figure 6

j.

come apparent.

If we assume an absence of waves,

a boat sailing before the Wind is a system performing coupled sway

roil and yaw motions. The cbeffl-cients in the linearized eqùations. of: motion can experirnentallybe

deter-mined with a planarmotion

mecha-nism (3).

From the equations of màtion, the

response function of yaw-to-rudder

angie can be determined. This

.fimnc-tion can then.be computed in terms of sway, roll, and yaw amplitudes,

velocities and accelerations.

A thorough analysis of the

re-sponse functions of the Half Ton yacht and Columbia showed that, if

the rudder is continuously.used, the

influence of roll is negligible on the

yaw response to rudder angle. In

short, the forces and moments of

roll, which have a remarkable

de-stabilizing effect in the controls fixed situation, are overruled by the rudder forces and moments. The same can be concluded about the aerodynamic

forces which do not contribute

'sig-nificantly to the yaw response to

rudder angle.

If 'a sinusoidal rudder angle with

circular frequency. w and amplitude

is exerted, the resulting sinusoidai yaw response'is given by its

ampli-tude and phase angle p between

yaw and rudder motion.

For different circular. frequenóies,

thisdata can be. complled.'În a so-calléd Bode-plot. The Bodeplot. of

the Half Tonner running at eight

knots (Fig.. 7) constructed with three

'different sets of equations of motion

mentioned above, confirms the pos-sibility_ofignoringtheinfluenceof roll. and sail, forces. and momènts in

Figure 8 Record'oí simu!atlofl run.

10 5 0.5 '005 0.01 description coupledswayrolIyaw

-description without sails

- -- coupled sway-roll-yaw

description with sails

i i il .iiii i i i i I 111111 i

ii

0.1

w w

ti

'

i u uI iiii.l i i litii 10 100

the respónse functión of yaw-to-.

rudder'angle.

As a result the mathematical de-.

script!on' of. the system can be

reduced to a.'lower order that

de-creases the need . for expensive

experimental data in future.

investi-gatlons

Wlththe--analogcomputerprö-.

grammed with the lower order

syè-tern, some pilot experiments .have been carried out at the yacht simu-ator. An example of. one of these

runs is given in Figure 8:

The disturbance is equivalent to.a

yaw moment becausé of wind and

waves; the helm angle has been ex-erted by the helmsman, and the re-corded course deviation results from

both.

Definite results and conclusions

are not yet.avaiiable from this analy-sis of the helmsman's behavior, but

the findings, will. be published at a

later date.

REFERENCES

P. G Spens, P. de Saix and P. W.

Brown

Some further experimental 'studies of

the sailing yacht. . The Society of

Naval Architects and Mar!ne

Engi-neers, 1967 J. Gerritsma

Course keeping qualities änd motions in waves of. a sailing yacht.

Proceedings of the third AIAA

Sym-posium on the Aero/ hydrodynamics of sailing, California, 1971

ft J. Zunderdórp and M. Bùitenhek. Oscillating techhiques at the

Ship-building Laboratory.

Deift' Shipbuilding' Laboratory, report

1 11' (3): 0.0v i t

i liitl

i i i i i i 111111 i 'i i + 1800. +90° 0°' _900 180° -i I i l!iiI I i i i l'iiiil FIgure 7 Bode-diagram

of half-ton yacht 100 I I I III I I I₁₁₁₁₁₁ I I I,.IIII. I I jI

SAIL.

The Seakeeping Performánce and Steering Properties of Sailing YachtsC

by

J. GerritsmaXC and G. MoeyesX

Part 1. Seakeeping Performance.

1.

In comparison with the rather extensive use of model tests to evaluate the performance of sailing yachts in still water, there is very little information with regard to the performance in

waves. One of the very few publications in this field was given

in 1967 by P.G. Spens et al for the Society of Naval Architects

and Marine Engineers [i] . They reported the results of tests

in waves with a model of the 12 meter "Sovereign" in the Davidson Laboratory and one of the important conclusions was the favourable

effectaa small gyradius with regard to motions and added

resistance of a yacht in a seaway. This was already known by many experienced yachtsmen, but the advantage of such modeltests is

in the OEtimation of the quantitative effect of the longitudinal distribution of weights in a sailing yacht.

Model tests in waves are expensive, because many combinations of

yacht speed and wave dimensions have to be considered. Compared

with the conventional still water model test a multitude of runs in waves is necessary with a corresponding increase of cost. For this reason a large part of seakeeping performance analysis for merchant ship design is carried out with the aid of computer programs. For this type of vessels the theory of ship motions in waves has been developed to such a degree, that reliable estimates

of pitching and heaving motions, as well as the added resistance in regular and irregular waves, can be made. Of course the

theoreti-cal results had to be confiimdby careful model experiments and

also . full scale trials in measured sea conditions have been

carried out to this end.

'Abstract of paper to be presented at the Third HISW Symposium on yachts, Amsterdam, 2 1/22 March Ï973

2.

Yachts have a rather extreme form when compared with the majority of merchant ships. They have a very low length-beam ratio, a

rather low prismatic coefficient, a high speed-length ratio and a very shaithw draft hull.

Some of these differences are the cause of difficulties when the existing theories for caldu.lating motions and resistance in

waves are used for yachts: the "non-linear" form of the sailing yacht does not match too well with the simplifying assumptions in the

theory, which are' not harmful for the average merchant ship.

Despite this fact a rather encouraging result was found for a half-ton sailing yacht; the calculated pitching and heaving motions

in waves showed a rather good, although not perfect, correlation with corresponding model test results [2]

For the half. ton yacht, a very impressïve increase of resistance was found in resonant regular waves. Resonant conditions occur

when the natural period of pitch (or heave) is equal to the period

of encounter of the waves. Resonant pitching results in a large resistance increase and a substantial decrease of the forward speed of the yacht. However the waves at sea are almost never as regular as towing tank waves usually are and the averaging effect of the irregular seaway makes things more reasonable. But also,

the fect on speed of two or three almost "resonant" waves is

known to those who sail at sea.

Recently a practical method to compute the added resistance in a

given seaway became available [3] and with the aid of this theory

the influence of displacement and gyradius was investigated for a small systematic series of yacht designs. The theory was tested with the use of model experiment results of two i2 meters: "Valiant" and "Columbia". The necessary data of these designs have kindly

been put at our disposal by Sparkman and Stephens and the

model seakeeping experiments havé been carried out in Deift.

An example of the comparison between calculation and experiment

is given in Figure 1 for "Valiant", which shows a satisfactory agreement.

A _{thè cputer costs are oily a staii fraction f a cmparable}

seakeeping test program, the analysis of three designs of Admiral Ctp racers (from the drawing board of. Frans Maas) could be carried

3.

Additional tests were carried out in the Deift Tank to compare the still water performance of the three designs with regard to the speed made good and the running conditiön. To have a

realistic average gyradius for the analysis, the yacht "Standfast", published as "Admiral" in [4], which resulted from the design

series, was oscillated manually to determine the natural pitching period. With the obtained period, the known geometry of the yacht and a calculation of the hydrodynamic mass moment of inertia, the

yacht's gyradius could be determined as approximately 25% of the

overall length. Therefore a gyradius of 23%, 25% and 27% wa:s used in the present analysis.

The lines of the three designs are given in Figure 2. They all have the same waterline length1 breadth and IOR rating. However the displacements range from 8207 kg to 11443 kg.

The still water performance tests showed that design I with the

lightest displacement, is the best of the three, although design III

has the lowest resistance per ton displacement. It was conclu.ed

that, at least for the windWard performance, this is due to the

more favourable aspect-ratio of keel I. The heavy displacement

hull is deeper and at equal total draft less depth is available for the fin keel.This in turn has an adverse effect on the

windward performance.

For the three yacht designs the motions and the added resistance

in a range of wave conditions were calculated for the three gyradii already mentioned.

The irregular waves, as used in the analysis, correspond to

a formulation given by Pierson-Moskovitch. The seaway is charac-terized by the significant wave height. In most sea spectra

highèí: energy content, and thus higher waves, correspond to larger wave lengths when the high frequency (small wave length)

range of the sea spectrum is considered. This applies to ocean wave spectra as well as to coastal wave spectra and this property

seems to be important for the analysis of sailing yachts in a seaway, becauseof the modest length of yachts, compared with

the lengths of sea waves. Figure 3 shows clearly that the main

part of the response characteristic of the sailing yacht with regard to resistance lies outside the frequency range of

4.

Multiplication of the wave spectral densities with the corres-ponding added wave resistance operators results in the three

sets of curves in figure 4, where only one wave spectrum is

considered as an example. The area under these curves i's propor-tional to the added resistance in the considered wave condition.

Figure 4 shows the influénce of the gyradius: the yachts with

the largest gyradius experience the largest added resistance in waves.

Figure 3 reveils that this is due to the shift of the response

curve towards larger wave lengths when the gyradius is increased.

A condensed plot of all the computed added resistances in a range

of wave conditions is shown in Figure 5 for one forward speedi V = 6.74 knots.

In Table i the added resistance is given as a percentage of the

corresponding still water resistance at a speed of 6.74 knots and

a gyradius of 25%.

Table i

Added resistance in waves V = 6.74 knots significant

wave height in m,. design I design II ' design III

The Table shows that the lightest design (I) has the largest increase percentage, when referred to the still water upright condition, although it has the smallest absolute resistance increase. When sailing to windward the still water upright

rsstance is increased due to leeway and heeling angle by

approxi-mately 59%, 66% and 74% fbr design I, II and III respectiveiy. These figures show the influence of the aspect ratio of the fin,

keel: the light displacement yacht is better because of the

better keel.

2.90 82% 79% 76%

2.1,5 66% 64% 61%

1.70 52% 51% 4'8%

5.

An overall picture of the wndward performance in waves is gïven

in Figure 6 for three wind.speeds and a range of wave conditions.

This result shows that the influence of displacement becomes less significant for higher values of the true windspeed.

In addition to the quantitative information obtained by this analysis of the seakeeping performance of a series of sailing yacht designs, it may be concluded th'at still water model tests remain a meaningful tool for the yacht designer.

References

[i] P.G.. Spens, P. de Saix and P.W. Brown

Some further experimental studies of the sailing yacht

ThêSöcièty of Naval Architects and Marine Engineers, 197

J. Gerritsma

Course keeping qualities and motions in waves of a sailing yacht

'Proceedings of the third AIAA Symposium on the Aero/ hydrodynamics of sailing, California 1971

J. Gerritsma en W. Beukelman

Analysis of the resistance increase in waves of a fast cargo ship

International Shipbuilding Prog,ess 1972 Yachting World Annual 1971

e

w D) w

o

i::o

speed = 7knots

wave height = i in

calculation.

experiment. .

.

.

100 50

30

20

15

10

7.5

Wave length

m.

D

_:jjjj

FIGURE.2

LINES OF SYSTEMATIC SERIES.

MODEL I

radius of gyration 0.27 LOA

wave height

,-220nt

circular frequency of encounter

-w- radis.

-3000 2000 N 1000 O O 1 2 3 4 5 6 I

J;J

I.

111111

11

1 1 1

I

I 100

500

3O

25 2015

10 9 8 7 6

wavelength

'- m.

Fig 3

Wave spectra and added wave resistance operators for design I

ti

w

IA N

0.7E

:

0.2 O

Design i Va 674 knots Wave height a 290m. 3 L L. i 51010

3)2'5 2b''iY ''

_{' ib} 3

w-radius of gyration 027L O o

i

DesignI Va6.74 knots

Wave height a290m.,

I î 1 2 3 I

II

I I

Lililli

5040 3025 20 15 I I

-

I radius of gyration 027 L L

Ii

Wave Length - rn F1g4: Wavé spectr density ireLtiplied by added wons resistance

ib 1. 1. Deslgnm Va 676 knots Wave height a 290m

I.

i 2 3

CircuLar frequency o? encounter - rad.

i i 1111111 I i I I I I - I

8 7

Fig.5: Added resistance in wäves.

150 loo 50 I t i I t Design V=6.71. knots.

Stia water resistance 154 kg. wave:heighj 19m. k

Radius of gyration

'OA

023 0.25 0.27 150 loo 50 I- - I Design W 74 knots.

Stia water resistance 180 kg.

0.23 0.25 0.27

o

o

r

11

Sighificant wave height

rn

Fig 6: Speed

-

made - good. in. waves.