On the effect of size - As related to capsize resistance

St4fM E

_{(Aned SLL's}

_Urtc

ON THE EFFECT OF SIZE - AS RELATED

0 CAPSIZE RESISTANCE

INTRODUCTION

This note is intended to clarify the

effects of various yacht parameters, insofar as

we Understand the effects presently, in

determining the relative resistance to a single-wave-impact capsize.

Race organizers have frequently invoked a limit for offshore races which establishes a

minimum size of yacht which is allowed to enter and participate in t-)e race, and one of the

motivations for such a minimum has been safety.

Traditionally this has involved leñgth, and

in response at least one case exists where an entrant added a false nose piece to qualif' for

the race: Cohoe in the 1950 Bermuda Race, and

then discarded it for- the ensuing Transatlantic

Race.

By-and-large the limit has represented the best judgement of the organizers and has been selected without specific numerical basis; not to be arbitrary, but because little exists to

guide-race committees in defining such a limit.

Recall that any such limit is, however,

moré-or-less arbitràry since it is unlikely that

two identical yachts, save one-inch in stern overhang, will respond differently in bad

weather. However, given that some hard limit is desired (or desireable) it remains to develop the best possible measure.

Although length has enjoyed great

popularity, it is rather indefensible. Just as handicap performance "ratings" take into account

many characteristics of a yacht in deerr.ining

its equivalent size, so should a size limit aimed at safety consider more than one dimension. Note that many rating systems have

characterized the rating of a yacht in feet which is equivalent to stating that the yacht will sail as fast as one of some standard

proportions and that length.

In a like manner, it should be possible to

state the equivalent size of a yacht for safety

considerations, and length alone cannot be any

more appropriate for this than for rating.

Until now, we have been denied sufficient information to construct a safety "rating', but recent advances in our knowledge of bad weather

capsize mechanics make possible a try, at least-,

to begin to define size in some multi-variable way.

by

Karl L Kirkman

i Phillips-Birt, Douglas, "British Ocean Racing', Adlard Coles, Ltd., 1960.

39

Faculty WbMT

Dept. of Marine Technology

Mekelweg 2,-. 2628 CD Deift

The Netherlands

This note will develop the basis for making the determination, present the data used in

determining the effects of the selected

variables, and suggest a formulation for

characterizing size from the standpoint of

capsize resistance.

Why -Size?

-The recurring success of voyagers in quite small yachts seems irreconcilable with the

notion that larger is safer; is it possible that

the small yacht will bob like a cork, resisting

the ability of the elements to "get- ahold" of it whereas they destroy its larger counterpart? Could it be that the sthall yacht rolls with thé punches while its resistful large counterpart i-s torn by Targe forces?

The laws of physics say no, àt léast for

the simplified case of

a prismtic yacht form

struck by an incident wave: modeling of the ratio of gravity to dynamic- forces (which is known as Froude Scaling after William Fraude) dooms the outcome to a sithple linear scalar

relationship: the yacht twice as large will survive twice as large a wave.

TECHNICAL APPROACH

In short, what is required parallel.s the

rating situ-ation which -traditionally utilizes a

rating rule to measure t-he equivalent length of

the iÏportant design variations, and a time

allowance table to account for the-

performrice-effects of lehth variations.

Rolling these together- in a situation

analogous to the MHS "VPP" vs. traditiOnal rating schemes seems beyond the reach -of our

present knowledge; but on the other hand this would spare the organizer of a race the task of

specifying storm weather conditions.

-A most difficult philosophical problem also

presents itself. Careful study of this note

will réveal that the practical means of

modifying a yàcht to "optimize" its capsize

rating are bounded to the extent that a twenty

footer cannot be made to start a particular _race where bad weather is expected with the same

One consequence of this may well be that

the small yacht have more strict provisions for

recovering from and surviving a capsize than its

large counterpart for equal safety; an approach which is much more difficult to quantify than

some of the physical capsize phenomenon.

Another might be to try to achieve an

equally small probability of remaining stable

inverted regardless of size; that is, the smaller yacht might be required to possess a

larger range of positive stability than its

large counterpart. Such a standard is

hypothesized herein.

DEVELOPMENT OF A SIZE DEPENDENT CAPSIZE RATING

Hydrodynarnic Considerations

From consideration of the hydrodynamics,

from analysis of incidents involving capsizes,

and from model tests, we have developed and

refined an intuition regarding the parametei-s

which affect capsize resistance (and which do

not significantly affect it).

a) YEL001TA MAPS

Ef

FIGURE 1 JET VELOCITY IN BREAKING WAVE

b) VELOCITY PROFILES

At this time, the significant factors

appear to include the following, each of _which

will be discussed in a subsection:

Mass moment of inertia/gyradius

Displ acement Be am

Vertical center of gravity

In considering the single wave impact

as a single degree of freedom (roll)

spring/mass response, some insight into the

important dimensions can be gained by

mixing test observations with first principles.

First, recall the data on breaking wave velocity maps and velocity profiles

from Reference 2 which is reproduced as

part (a) and (b) of Figure 1 _{respectively.} Piecing that data together schematically as

in Figure 1, part Cc) the wave jet can be simplified by considering the flow to be a

2 Stephens, 0.J., II, Kirkrnan, Karl L., and Pete-son, R.S., 'Sailing Yacht Capsizing' CSYS 1981.

14

r !JUaV.us. I

. ..

I-'

FIGURE 2 YACHT HULL POSITION WHEN STRUCK BY WAVE

a) TIP.E SE0505CE SEETCH DF MODEL CAPSIZE EXPERIMENT

high

veioity,

fairly

localized

uniform

stream

havin

a

velocity,

Vj,

in

the

horizontal plane.

Note that the graphical

data

On

velocity

profiles

_{does not}

correspond ectly to the velocity maps but

is used for illustrative purposes.

A review of capsize model

tests

such

as characterized by the data

in

Figure

2

(part

(a)

and

(b) taken from references 3

and 4 respectively) also show that the hull

at

a

conceptualized "moment of impact" has

already

rolled

at

a

fairly

significant

angle to the vertical, even in the absence

of

wind

This

position

is

shown

schematically in part (c) of Fïgue 2.

Combining

this

physical

notion

of

a

high velocity jet area from Figure

1 and

the sigñificänt roll

angle at the instant

of

impact fom Figure

2,

the geometry at

the

instant

of impact,

and

thè fesulting

forces

and moments can be

hypothesizd

based upon the sketch shown in Figure 3.

FIGURE 3 - DEFINITION SKETCH FOR. ROLL PHYSICS

When

these

are

combined,

it

is

possible.

to

hypothesize

a framework

of

forces and moments which fit the equation

of motion:.

F Ma,

for

the

system

in

roll.

With

sithplificatï'ôn,

the

equation

can

reformulated at the instant of impact:

1/2 pVj2SR

lxx Q

where 1/2 pV'j2 =q of jet

S = drag area

r = moment ,m of jt forcé

lxx -= roll moment of inerti.a

Cr

roll acceleration

Clearly this rèpresentation Includes a

number of gross simplifications including:.

The transfer of ñiomentum from the

jet to the hull

is. neglected

Added mass in roll is neglected

'41

(3)

Roll

moments

from

other

fTow

patterns are neglected.

It

should

be

appreciated

that

this

representation

is

suggested

primarily

tò

give

an

insight

into

the

relative

importance

of

the

various

parameters

and

not to estimate actual values.

Equation

[2)

can be

further

manipulated

to

iepresent

a

level

of

critical acceleration which fOr a specific

design, exceedance will result in "capsize

i.e.

roll

motion

beyond some

arbita-y

thréshold:

&Crjt

e

1/2 2Vj2Sr

lxx

If the jet velocity

is then taken

as

propotioñed to the square root of the wave

height,

and some constants

are d1àrded,

the equation becomes:

O'crit

lxx

where h = wave height

s = struck. area

r = ïadiu

of action of striking

fOfè about VCG

Let

us now

simplify further

by

holding

freeboad as

a fixed proportion of length.

(This

i

done because a

freeboard

change

implies a change in range of stability añd

hence in threshold of capsize, o cnt.)..

As an

side, earlier test results (Ref

3, Figures 21, 2? ãñd 26) show a pronounced

lack

of

sensitivity

tO

_Tikélihood

of

capsize

fOr

fairly

large

variations

in

freeboard.

A

final

simplification

_involves

decomposing

the

capsize

arm

r

into

components related to hull georitetry. 'For a

fixed

VCC, and

freeboard,

this

is

as

follows:

3

Kirkman, K.L., Nagle, T.J., and Salsich, J.O.,'

Sailing Yacht Capsizing',

CSYS 1983.

more particularly: r

b'

+ C

where

b = Beam, and

c

Height,

center

of

pressure

above VCG.

Substituting into (4),

' cnt is

directly proportional

to

B

and (VCG-CP) and Thversely p,oportional to

lxx.

J.(j2

'lxx

(6)

Let us consider now this

is

born out

by model test results.

(1)

C5)

r

s orne be

t

) I

MODEL TESTS

Model tests involving a variation in

wave height have been condîjcted by Salsich

and _{Zseleczky at the U.S. Naval Academy}

Hydrodynamics Laboratory (Ref. 4) to

explore the sensitivïty of a simple

prismatic nodel to capsizing with variation

in a number of parameters: displacement,

gyradius, beam, appendage area, and

freeboard.

Shortcomings of wave family

In pHnciple, the data should allow

for the deriviation of variations in susceptabi-lity, and a simple measure would be as an equivalent change in wave height. Because of the means by which the diffeent

waves were generated as detailed below,

such a direct measure was not possible, and at first glance, these data did not support

the rather severe sensitivities

hypothesized by fundamental considerations described above. This was the cause for

concern which has only tentatively been

assuaged by the following consideration.

The method of generating breaking waves in the laboratory was dïscùssed ih detail in Reference 3; in

sumary

the

dispersion relationship for water Waves was utilized to generate a train which converged

and boke

in the test section

area of the tank,. Although rigoroús

procedure would have involved developing a

new wave train for each wave height and demonstrating that this family was similar to the others, expendency dictatêdthat the height variations be achieved by tampering with the amplitude of all waves generated

but with the phasing relationship

unchanged.

As a result, there is no assurance

that

the

breakers

are

correctly

scaled

versions

of one another, in fact that would be unexpected. Thus, while the data show

the effect of wave size, the nominal height

measured and plotted cannot be used as the scalar of the wave size variation in terms

of energy available to capsize because this is such a sensitive phenomenon.

In the context of the original

experiments, nOne of this presénted any

problem since the data were intended to

répresent more or less severe waves, but it does limit the utility of the data for this

new purpose of estimating numerical values

of

sensitivity.

L

However, as the waves of various sizes were repeatable, the notion

Of uing the

data to check ratios of _{ensitivity One to} another in hypothesis and then in the experiments was introduced. For example,

the ratio of effect of dislacement to

gyradius as postulated iti (4), was checked

using the test data and cnfirrñed approximately, and such checks will have to suffice until _{new tests can be conducted.}

As with many puzzles, unlocking one

relationship allows for clearer understanding of others not previously

possible and this is particularly true in

the case of unlocking the relationship of

beam to capsizing.

The data in Figure 4 (from Reference

4) were presented to show the effect of

beam, but due to the scaling of the models

'N:;

FIGURE 4 - ThE EFFECT OF BEAM VARIATIONS ON CAPSI RESISTANCE

included an unintended displacement-length ratio variation. The result of this seems to have been to disguise a rather marked sensitivity to beam whih can be shown by

manipulating the data as follows:

The beam variation testéd was generated by taking the baseline model and

changing the half-breadth coordinates while

holding the depths to yield variants with

25-percent less and 25-percent more beam. As a result the displacement per unit

length changes proportionately.

Using the relationship that the effect of displacement is linear, and that of gyradius squared, the square root of the ratio of displacements was used to correct the plotted gyradius values, thus creating data for models of equal displacement and

gyradius. The results are shown in Figure

5 and the supremacy of the narrow-beam

model is far more clear than as previously presented.

4 Salsi.ch, J.O. and Zselec-zky, J.J., 'Experimental Studies of Capsizing in Breaking Waves, AIAA/SNAME AI-XIII, October 1983.

o

o

11 12

WAVE HEIGHT IN INCHES

FIGURE 5 - THE EFFECT OF BEAM VARIATION WITH CAPSIZE RESISTANCE WHEN CORRECTED FOR DISPLACEMENT

Recall that one of the sharp design

t-rends shown in Reference 2 and reproduced

herein as Figure 6 was an increase in the

beam of recent racing yachts, and that one of the most definitive relations between

fastnet capsizes and design parameters was shown in the same reference to be with

beam, Figure 7.

At the same time, freeboard has been shown by limited tests to be a relatively unimportant variable and this was

attributed to the bilance bétween the

disadvantage of high freeboard in impact

area balanced by the advantage, of freeboard

on the lee side in avoiding tripping over

the lee rail.

LEGEND ONE TON CHAMPI.ONS

REPRESENTATIVE DESIGNS

FIGURE 6 - TRENDS IN IOR YACHT BE.AM

43

FIGURE 7 - RELATIONSHIP BETWEEN FASTNET CAPSIZES

A1i ¿ÈÁM

Size Rating Rule

Accepting that the' physical model

matchés (6), and the desire to determine an equivalency on a length basis of equal

capsize resistance, one way of expressing the length (using the concept of a base boat of normal proportions) is the fol lowing:

L' =

(.JB)2

+()2.I

(7) where: L = capsize length, feet

L measured length (MH '1). feet base beam given by + 2, feet B = measured beam (MIlS 4"MB), feet

CB base center of pressure above YCS given as 2, feet

C = estimated center of- pressure above VG' giv'en by 2-CGTOT, feet

I = estimated roll omment of inertia, f't' lbs (See Ref S) = base roll moment of inertia given by .135 L4-5, ft2 lbs

This calculation has been performed for the MHS fleet with the results as shown

in Figure 8.

5 'Safety from Capsize Project - 2nd Interim Report of the Directors", USYRU, June 1984. 0.05

o

0. 0'4 -J 0.03 C-0.02 0.01 o '60 '65 '70 '75 '80 7 6 5 4 :AIUS IN NC H ES

BALLAST

-POSITION:

MEASURED LENGTH

FiGURE 8 - COMPARISON _{OF'CAPSIZE LENGTH TO}

MEASURED LENGTH F(R IWtCAL FLEET

me role of range of stability

The phyicai model postulated in

equation (3) _{and developed thereon to the} size rating rule of equation (6) _{aid the L'}

size equivalent was based upon a critical level of roll accé]erati.on, frcrit, which represented a threshold of capsize. It

would seem, thén that _{in additioh to the} size equivalent, L', noted, range Of positive stability may also bé important in

the caØize.

BILGE

SOURCE: UNPTBLISHED RESULTS BY SALSICY & ZSELECZKY

AGRA. AFORO LAB

100 110 120 130 RANGE 0F POSITIVE STABILITY

TOP OF

KEEL

BOTTOM

OF KEEL

140

FIGURE 9 - VARIATION OF CAPSIZE TEÑDANCY WITH RANGE OF STABrLITY

Further, a small range of negative Stability is most important in avoiding

stable inveted equilibrium. _{Cohsider the}

data irs Figure 9 and 10 in _{support of this} role of range of stability:

\ BOTTOM OF'0

KEEL

iDO 110 120 130 140 RANGE DF STABILITY IN DEGREES

FIGURE 10 _{VARIATION OF TENDANCY TO' REMAIN}

- STABLE INVERTED WITh RANGE OF

STABILITY

Observation of the capsize _components seems to indicate that two phases of the

phenomenon: à "snap-roll' phase where inertia domihates and then à phase where

the yacht is left to its Own devices _{as the}

dyna,Úi -forces dissipate and classical static stability _{considerations achieve} dominance If this is the case, _{a yacht}

with a larger range of static stability (other things being equal, eg: roll moment

of inèrtia, displacement, beam, etc.) wiH

be in a better position to use this

characteristic to return to upright as the static stability takês over. This leaves

the issue, what is the role of stability in

capsize resistance and to answer this both

phases must be considered.

It exceeds the scope of. this note to

develop the statistics of this secOnd phase

in detail and Figure 11 of Reference 10, and accompanying text may be useful for background. Suffice it to say that any

experiments, and indeed real life, may be biased by the reàlity that thé band of

disturbance energy present

is quite nàrow

and probably lies adjacent to thè upper

edge of the range of stability of the

yachts of interest so that specific test

results which measure percentages of yachts trapped inverted stable will probably not

match the 'wheel of fotune'! analoy.

10 Kirkman, K.L. "On the Avoidance of Inverted Stable Equilibrium",

A1AA/SNAfr1E, Anciént Interface XIII, Oct 1983.

: / / / /

/

o o o

oa

/ o o o /

/ 0O

Oc _C. o

I

/

/

I

/

/

/

o I

/

o C_

I

LE G'E N D

-C 10G 80 60 40 20 BALLAST POS ITIOU SOURCE

\

N BELGE

\

N TOP OF UNPUBLISHED KEEL SALSICH B ZSELECZF.Y, U.S.N.A. HYDR0 LAB

\

_\

\

MISCELLANEOUS ULDB'S SOR I 1Q _{20 30 40 50 60} o0

00

/

0

/

/

00

/

: r

30 20 10

/

90 80 lo 60 50

Specifically, Figure 11 shows some test results for yachts with masts and

various ranges of stability and the quality

of fit to the analogy. Because the wave used in the tests was sizes to 'just capsize the models a wide range of

disturbance energies was not present and

the result should not be so expected to fit

the dotted line.

C EN T I'; VED T ED SAD.0 0.5

EiLEAIU!

1.0 L 1 I _{I.Q. .(_j...} 90 100 110 120 130 150 160 170 180 RANGE 0F STABILITY

FIGURE 11 - COMPARISON OF VARIATION OF TENDANCY TO REMAIN STABLE INVERTED WITH "WHEEL OF FORTUNE" ANALOGY

Another reason for introducing the role of range of stability as related to

re-righting into the problem of resisting capsizes in the first place is simply this:

with no constraints from either practical

construction, sail carrying power, or

concern from re-righting, it will appear

that an "optimized" configuration considering only the snap-roll phase

involves a high VCG with a maximum roll

moment of inertia. In particular, for a

boat with a small range of stability (i.e.,

a relatively high total VCG, say at the OWL) it may lower the capsize vulnerability

by raise the ballast further! Consider

Figure 12 which indicates a break-even

range of stability of about 120-125

degrees. If the contours of capsize probability are accepted for the moment, either raising or lowering the ballast

seems helpful; but if one refers back to Figure 11 the ballast raising alternative

carries a high probability of inverted

equilibrium whereas the lowering

alternative reduces the probability of same to an extremely low valve. As a practical

benchmark, the yacht tested with a VCG=0 starting point represents a 46-percent

ballast ratio with the VCG of the lead at the top of the keel - terribly close to

contemporary competitive tOR boats.

WHEEL 0F FORTUNE

45

-

BEAM DISPLACEMENT T'ACE OF PRACTICAL BALLAST SHIFT GYRADIUS IN INCHES

FIGURE 12 - VARIATION IN PERCENTAGE OF CAPSIZES WITH GYRADIUS AND VCG

It must be appreciated that the shape of contours may reflect an inadequacy of

the method of accounting for some effects

other than VCG and lxx, and that the implications discussed below as related to

range of stability are only that.

Two lessons can be inferred from

Figure 12, the certainty of which must be tempered by the speculative nature of the

probability of capsize contours:

1) Depending upon the initial valve,

range of stability has a weak influence on

probability of a capsize after inertia effects have been accounted for separately. Further, loweriig the range of stability by. raising the VCG for a yacht with an

excessively low range (from a practical

standpoint) initially may have a large

pay-back in capsize probability reduction, but the yacht will be unable to carry sail,

cannot withstand knockdowns of an

'aerodynamic sort, and will almost certainly stick inverted once pushed down. However,

(2) Practical VCG shifts, as shown by the trace labelled "ballast shift" not only

increase the range of stability but also

tend to lower the probability of capsize.

o Raising ballast from typical

positions has a very weak tendency to

improve probability, so weak as to be

practically negligible.

o Lowering ballast from typical positions has a vèry weak tendency to improve probability, so weak as to be

practically negligible.

o A neutral zone where ballast shifts have a small effect exists with the total VCG near the DWL.

Of course, all of the above are for a single yacht configuration, displacement, beam, appendages, freeboard, etc.

= 150

r

140 130 120 110 X 1 00

P

Based upon this,

it seems justified to

delete from the capsize 'size" formulation

any measure

of

range

_f

stability

to

account for the shift in & cnt value with

this change.

If we accept the contours in Figure 12

for probability of capsize as a function of

range of stability (for fixed length, beam

and

displacement)

a

probability

of

capsizing and remaining stable inverted

is

calculable as follows:

If

we

take

the

probability

of

a

capsize as a funtion of range of stability

from the data in Figure 9 añd shaped as

in

Figure 12, we get a curve as

in Figue 13,

part (a).

Then,

the.

probability

of

inverted

equilibrium,

if capsized, taken from Figure

10 can be taken as in Figure 13, part (b).

The

product

of

these

or

joint

probability of capsize and inverted stable

equilibrium is as Figuré 13, part (c).

This result,

to wit, that a range of

positive stability of 140-degrees implies a

vanishingly small

_{probability of}

inverted

stable equilibrium corresponds well to the

findings

of

Reference

11: "From

observatioh

of

the

tests

it

is

&pparent

that those (yachts-ed) that have angles of

vanishing

stability

less

than

150-160 degrees can be

left flòating

upside down

after encounter'ing a breaking wave."

PROBABILITY 0F INVERTED EQUILIBRIUM

0INT PROBABILITY 0F CAPSIZE AÑO ISVERTED

STABLE EQUILIBRILJII

FIGURE 13 - PROBABILITY 0F IÑVERTED EQUALIBRIUM WITH RANGE 0F STABILITY

THE NATURE 0F BREAKING SEAS

To

this

point,

the

subject

has been

totally

restricted

to

the

rating

of

relative size; how big a breaking wave can

a specific design withstand.

The time has come to answer a far more

complex

question:

For a

given

set

of

charactéristics

for

a

désign

under

considération

how much

bigger or

smaller

standard yacht has the same prObability of

a

capsize?

This

is

the

time

allowance

table analogy to handicapping.

A-

clear

understanding

requires

an

appreciation

of

the

basis

of

rough sea

generation because breaking waves represent

än instability in nature bth in the

iicro

(a pile of water of

a steepness beyond its

dynamic

equivalent

of

"angle

of

repose")

and

in

the

maceo sense. (A.

transient

oceanographic phenomenon, unlikely to occur

for extended timés.)

HOW ARE BREAKING WAVES. FORMED?

In dealing with -bOdy generated waves,.

the wäke of a power boat in a harbor (or a

duck swiasning

along

a

pier)

is

putting

energy into the water via wave-making drag

in a very steady manner.

Ocean waves

of

interest

in

capsize

phenomenon are not so nicely ordered; they

are generated by unsteady phenomenon, they

interact

with

one

another,

and

the'

dispurse

(that is

they travel

across the

ocean

at various

speeds)

so that

to

the

observer they appear quite complicated..

As

a result of this behavior we tend to deal

with

thehi

ih statitical or probabilistic

way. The

classical

ocean

engineering

treatment of

irregular waves assumes that

the.

systemcan

be

designated

by a

"photograph"

which

fixes

it

in

time yet

this does not apply in the case of breaking

wave phenomenon.

Let us consider some basics to see how

all of this applies to our capsize problem.

So much of what we utilize in working

with

waves

is

expressed

in

terms

of

frequency

that

wé must

have a

feel

for

these unfamiliar measures.

Figure 14 shows

socs general descriptions of wave types and

indicates

bot-h

the frequency,

ci,

and the

physical

length of thesE.

Note

that the

descriptions overlap and the zones are not

well

divided;

that is

not important since

the purpose of this graphical presentation

is only to give a féél for the waves under

discussion.

The

ieason

for

introducing

this term for frequency.,

ai,

will

be clear

shortly.

PROBABILITY 0F CAPSIZE

110

id

1 50 170 180

WM'E

HEIGHT

FIGURE 14 - RELATIONSHIP BETWEEN LENGTH MD

FREQUENCY OF 'WAVES

If we were to go back to our view of a

rather confused ocean surface,

freeze the

waves

in place and make a saw cut section

through

the

surface

a

view

of

this

cut

would appear as Figure 15.

This irregular profile can be shown to

be made up of a

large number of component

waves äll superimposed upon one another in

the

oceah

resultiñg

in

the

confused

appearance.

FIGURE 15 - IRREGULAR WAVE HEIGHT TIME HISTORY

In fact,

a Figure 16 reproduced from

Refèrence

6 shows

just

such a

series

of

regular waves which are these components in

part

(a)

and a meahs

of expressing

this

information

called

'a

'spectrum"

in

part

(b).

The

spectrum

is

a way

of eaily

portraying a confused sea where the energy

t each fequency, w,

is plotted vertically

as

in a histogram and the envelope of these

represents the spectrum.

This curve has a

number of useful properties beyond that of

compressing

the many

items

regarding

the

regular

wave components

into

a

single

display;

the

area

beneath

the

spectÑl

curve is a direct measure of the enègy in

the spectrum and the shape tells us how the

energy is distributed.

7

Van Dorn, William,

York 1974.

TIME

6

Principles 'of Nãval Architecture, Snarne, 197O.

i) TYPICAL ENtP.GY SPECTRUM, SHOWING

APPR0Y.iMATI0 B.Y A FINITE SUM 0F

coM:pouEN IS

b) SCALE 0F FREQUENCY SPEC'T'RUM

FIGURE 16 - ,KE-UP OF IRREGULM SEA

The grOwth of a spectrum is 'also key

to

understanding

b'eaking

wave

behavior.

Waves fori as a by-prbdùc.t of the shéàr set

up when wind blows across the sea surface.

This

begins

with

a complex

pattern

of

ripples

which

eventually

grow

to

_sirtall.

waves, etc.

The presence of the ridges of

water causes

a pressure distribútion which

leads to energy being transféred into the

ridge frOm the wind.

However, many practical

sea states do

not grow 'slowly enough, nor does thè wind

blow steadily enough

to reach an orderly

spectrum.

'A means

of

estimating

the

effécts of non-u'niforn conditions

is

iven

by thecumulative sea, state (CSS)

diagram proposed by Van

Dorn7.

'Such a

diagram

allow's. one

to

estiifte

the

relàtive

severity of

a

sea state with an unsteady

wind time history.

An example

of

the

use

of

the

CSS

follows' 'as related 'to Fastnet 79.

A tifflé' histOry of the wind experienced

by thé Fasthet fleet and

as charàcteHzéd

by a number of sumftiary analysis is given in

Figure 17.

What is then required is to go

fròrn

such a

continuous

estimate

of

wind

speed to a wave characteration.

Oceanography and Seamanship", Dodd, Mead & Co., New

47

FIGURE 17 - OBSERVATIONS OF FASTNET WIND

STRENGTH TIMEHISTORY

The method suggested by Van Dorn

entails breaking the wind speed record into discrete time steps with an equivalent wind

speed throughout, and entering the CSS with

the energy from the last segment as a

starting point to build upon. For example,

if the first step is taken as twenty knots for four hours the CSS diagram, Figure 18,

is entered along the "Wind Speed, V

(KNOTS)' contour labeled "20" for a

duration of four hours. This energy level is then maintained while shifting laterally

to the next wind speed (in this case .28

knots-, (2) and along that contour for its

duration. When completing the entire process, (3) the significant wave height

can then be determined using the right-hand auxiliary scale; ih this case the Fastnet

conditions probably were equivalent to a

fully-developed sea (FDS) with a

significant wave height of about 37-feet.

148

RESPONSES

RESPONSES

ESTIMATED SIGNIFICAIJT WAVE HEIGHT IN FEET

a) SIGNIFICNAT WAVE HEIGHT

OCEAN SCIENCE CSS ESTIMATE ESTIMATE / /

/

O 10 20 30 40

o/°

/

.7.

ç

O 10 20 30 40 50 60

It is interesting to correlate this

50

/

o

/

/

O\

\

055 diagram estimate with observations, and

the Inquiry8 gives a great deal of data from participants questionnaires to allow

40 O

/

X

/

\

this.

The participants were queried

regarding the significant and the maximum

30 O

/

/

A _{wave height. Not surprisingly,} the estimates by the respondents ranged widely

as shown in Figure 19, but the circular 20 data points define a frequency polygon in

each case which is near the CSS estimate; in fact the tendency to overestimate wave

10 _height

is belied by this comparison. Perhaps the most surprising factor is that

a measurable portion of the respondents

cited a significant height so far from the likely value that one must wonder whether

the question was widely minunderstood. NO0 13 JUNE MIDNIGHT 1 14 JUNE NODO TIME IN HCU

FEET _{ESTIMATED MAXIMUM WAVE HEIGHT IN FEET}

WIND DURATION IN HOURS b) MAXIMUM WAVE HEIGHT

FIGURE 18 - CSS DIAGRAM OF FASTNET WEAThER _{FIGURE 19}

- OBSERVATIONS OF FASTNET WAVE _HEIGHTS

8 Forbes, Sir Hugh, Laing, Sir Maurice, and Myatt, Lt.-Col. James, '1979 Fastnet Race Inquiry", RYA RORC, 1979.

SEARCH RESCUE ESTIMATE

\

0

o o

/

/

This same CSS method will be employed

later in consolidating our capsize data from a number of catastrophies.

Another feature of the behavior irregular waves which causes great

difficulty in the practical realm is the

rapid appearance of large waves through the dispersive property of components. Since a particularly large wave forms from the

instantaneous combination of a number of

components each traveling at a different speed prior to their combination at a

location in the ocean, they appear seemingly without warning, and this feature

has been a striking one mentioned by a

number of observers. No better example of

this property can be given than to show the test tank surface where the capsizing tests

PHOTOS COURTESY U.S. NAVAL ACADEMY RYDROMECHANICS LABORATORY

FIGURE 20 - PHOTOGRAPHS OF DISPERSIVE PROPERTY 0F WAVES

If 9

for this work were conducted; the scheme involves generating a series of waves which combine at a predetermined location in the tank to give a brEaking wave front. The

photogPaphs in Figure 20 show clearly how

quikly

this large breaker appears; the

time values given are for a full-scale

breaker related to a 40-foot yacht and a

foot breaker.

As mentioned earlier in this paper,

the transfer of energy from wind into waves

is complex and many (most?) actal sea states are not "fully developed' in the terms of the oceanographer; i.e., the

product of a steady wind of unvarying

direction for sufficient duration to

transfer the energy into the waves in

equilibrium. The CSS diagram gives a hint

of how long this might take if the leveling

TIME AT FULL SCALE

6 SEC BEFORE BREAKER

START OF BREAKER

of the contours is used as a measure of '-maturity.

During the non-stationary parts of

irregular wave (i.e. when equi1ibriu between wind and waves does not exist) behavior, a number of phenomenon with

importance to capsizing take place.

The first of these is the rapid appearance of large and steep waves upon increase of the wind speed in an already rough sea. The Dec 81 capsize of a 40-foot

sloop in the Gulf-stream reported in

Reference 9 happened within a short time

after an increase in the wind strength.

Data taken from an offshore tower 2 in

the path of hurricane Camile show the

largest waves appearing before the spectrum had matured as shown in Figure 21 below; and that there waves were of short period

and an accompanying great steepness.

20 22 20 1! 16 12 10 0000 1000 1200 1600 TIME (AUGUST 17. 1969)

FIGURE 21 - TIME VARIATION OF WAVE HEIGHT PARAIIETERS DURING HURRICANE CAMILLE

Van Dorn has shown a relationship

between wind strength and wave breaking behavior which is in concert with this kind of interpretation. Based upon his reported study of a large number of aerial

photographs, he postulates an equation for

the proportion of the largest waves that will be breaking according to the fol lowing:

LB = 2V-20, o<V< 60 (8)

His sample photographs are reproduced n Figure 22, and part (b) is truly awesome

to a sailor. 70 60 50 60 30 20 IO

a) SEA SURFACE UNDER 10-KNOT WINDS. LESS TUA i PERCZNT OF HIGHER

WAVES ARE BREAKING

b) SEA SURFACE UNDER 60 KNOT WINDS 100 PERCENT OF HIGHER WAVES ARE

BREAKI NG

9 Kirkman, K.L., Nagle, T.J.,and Salsich, J.0. "Sailing Yacht Capsizing', CSYS, 1983.

FIGURE 22 - PHOTOGRAPHS OF SEA SURFACE IN VARIOUS WIND STRENGTHS

The Variation of Danger with Sea State.

All of the foregoing data has tended

to _{argue that the prediction of dangerous}

breaking waves is a complex problem; it now falls to us- to make some application of this data in a form which is to sufficient

simplicity to be attractive to the yachtsman.

This task is paradoxical - we know

that the phenomenon cannot be extricated from their time dependence (that is: a

scientific prediction of dangerous breaking

waves depends upon the time history of the

wind and sea conditions, bottom shape, and

currents, yet the user cries for an insight

based on little more than a marine weather forecast.

the most basic diffiulty lies in the fact that large and breaking waves depend upon two independent conditions: large

waves in a mature sea state are not the

threat that is represented by more moderate waves with a sudden increase in wind

strength.

With this qualification to what follows out of the way, let Us prodeed to

make the best of a difficult situation.

Again Van Dorn provides a crucial key in a proposal for estimäting catastrophic

probabilities. The rilethod Should atuà1ly

be studied in detail in the context òf

Reference 7 and will only be summarized

here.

Van Dorn uséd an estilnaté of the most probable value. for a maximum expected wave height passing a stationary observer:

Hm = 2 _J E logs N, (g)

and combined that with the formula which

relates the average wave period to the time

between waves to arrive at the following expression:

0.54 Hm2

y (V/lO)

t = O.0O08(-) (10)

and further presented the results as

contours of encounter expectancy as shown

in Figure 18.

Note that thé only tie to breakiñq wave probability is the subjective oiithàt

is storm conditions the larest waves will

oe breaking. (See equation 8)).

60 , 50 40 30

t

A 3

i 20

t. ENCOUNTER EXPECTANCY IN HOURS 20 40 60 80 100

WAVE HEIGHT IN FEET

FIGURE 23 r- CATASTROPHIC PROBABILITY DIAGRM FOR LARGE BREAKING WAVES Y METHOD OF

VAN bORN

51

Figuré 23 thén gives contours of

equi-catastrophy, that is lines which are estimates of the time befor ea catastrophy

is expected. In the case of Van Dorn,

Figuré 23, the measure of catastrophy was wave height but he points out the rather direct tie of this to a vessel characteristi.c length as a predictor of capsize.

Another way of integrating the Van

Dorn catastrophic probability diagram is to

rilaké a slice at fixed FDS aììd examine the

variation of catastrophic frequency with

vessel size.

PART III - DANGER AND SIZE

The Variation of Danger with Size

Let us now attempt to apply this general data to the case whee data exists from a wide range of yacht sizes caught in

more-or-less the same conditions.

First, à view of the homogeneity of

the. Fastnet storm requires expansion; much

has been said about how the larger yachts escaped the worst conditions in Fastnet by virtué of their location on the course relative to the smaller yachts, but lit-tie

in the analysis of the race supports this

unequivocally. The data within the body of the Fastnet Inqu-iry related to the °worst" weather shows a widespread occurrence of

Beaufort 10 and 11 winds, and the

reanalysis projected the strongest winds to

have occurred through the arCa so that, while the phasing was indeed not

simultaneous, pretty much of the course was

swept by winds of sufficient strength to

cause widespread breakers. On the other

hand those around the rock and reaching for

home might arguably have been on a favored cOurse.

In view of these conflicting data, and

the difficulty of so-doing, no attempt has

been made to correct the raw percentages

_of

knockdown by size bands for lòcation on the

course.

If the Fastnet data on 81 and B2

knockdowns are plotted against a background

of contours of encounter expectancy from

Figure 23, some degree of correlation

exists if the following specific

rnanipulaiton are accepted:

The actual value of encounter time from the Fastnet data is

divided by à factor oF

The encounter time from Fastnet. is taken class by class and is

defined as:

t=

1 .3 0.1 LE SE T

32 tÜDO

G 51 iOC2C

/

G

0.0) 10 20 30 40 50

BOAT LENGTH IN FEET

FIGURE 24 FASTNET Bi AND B2 KNOCKDOWN ENtOUNTERS AS A FUÑCTIOÑ OF BOAT

LENGTH

when t = encounter time in

hours

% capsizes = % of yachts experiencing at least one capsize by class

Duratiôn = length ôf storm, taken as 10 hours

The corélation ïn this case specifically shows that except for Class O the Bi knockdowns fit the slope reasònably

well of a curve for wave height i.25.L in terms of variation of encounter tirne with

size and the data for 82 knockdowns fit the slope reasonably well for a curve of

wave height = 1.5L.

Since certain aspects of this analysis

are totally arbitrary (ex: duration of

storm 10 hous) the values of wavé height

ara considered to represent only a relative difference; i.e. a 20% increase tn. wave size seeriis to möve many resùlts frdm 90

degree wave input knockdowns to full capsi zes.

Twb cbmmnts. should be mäde about the

exclusion of Class O data:

Class O was small enough (about one-forth, the. size) comparèd to the others to give significantly

less weight to the results; in fact the B2 knockdown in O

represented a single incident.

Class O was argued by some (as discussed above) to have been in

different weather/on a diffèrent point of sail.

In the context of all of these

mnipulations and qualifications, the

Fastnet data seems to Support the

equi-catastrophic proposal of Van Dorn in terms of effect of physical size.

Reanalysis of Incidents

-l.5L

In light of this

limted/ualified

success,, is it _{possible to move to}

a more

general _{characte°ation of the}

vàriation of with size? 60 NAME Doubloon Puffin Aba Tilly Twin Wok 000ilmç. Aen pu s Morning Cloud Ear le Sting Soutn er, Riidef Mirebel Halcyon

In order to answer this broader question, the author re-analyzed all

available published accents of accidents at sea related to overwhelming, knockdowns and

capsizes within his possession. These

included:

'TYPE

19-foot day_saik.r' 40-foot yawl - foot yawl 40-foot ketch LOCATION Florida Coastal Gulf stream Medi terranean Biscay Channel Ou 1f s tream DATE 1977 1964 1966 1960 1956

30-foot boop Gulf stream 1964

40-foot schowner Du 1f s tre am 1981

In each case, the FDS value was

estimated using. the method introduced with Figure 18 previously, and the type of event was tabulated. These data, when plotted by

vessel watèrline length make-up Figure 25

which shows, in _addition the following

i t ems.

(i) A band of values

representing Fastnet 79.

Çontours of equi-catastrophy

as suggested by Vàn Dorñ; a first through

the knockdowns and overwhelrinings and a second greater by the factor deduced in

Figure 24 which seems to fit the capsizes.

A "zone of _potential

capsizes" wherein, for the cohditions of

existing ea state plus high winds capsizes have occurrèd in thepast.

This single graph, then, seers to

provide a practical _{guideline för}

characterizing the variation of danger with yacht size.

It must be emphasized that this graph,

while appealingly simple must be carefully

interpreted with the f011owing specific qualifications in mind:

60-foot ShOar Du 1f stre an

29-foot sloop Flri60 Coastal 1h53

(i)

The

'Zone of Potential Capsizes"

is

not

to

be confused with

a

prediction

that

they

will

occur.

As

explained

in

great detail with the text,

rather

short-lived

mixes

of

strong

winds

on

top

of

existing niòderatewaves seem to be a most

dangerous combination,

but others possibly

are important.

(2)

The

length

scale

for

specific

boats should probably be a weighted length

as

given

is

the

section:

"Size Rating

Rulé", (7).

The

variation

of

danger

with

range

of

stability

A _danger

_associated

_with

_range

_of

stability

conies

from

the

need

fòr

an

extraordinarily

large

wave

to

re-right

a

yacht with

great stability

inverted which

conies

with

a

small

range

of

positive

stability.

'èAPS

IZES-\

\

B2 _{IMPACT CAPSIZE} I J 50 BOAT LENGTH IÑ EET

FIGURE 25 - RELATIONSHIp OF REPORTED

CÀÏASTROPHIES TO FDS WIND SPEED AND BOAT SIZE

53

This danger coÌTIes from:

o

loss

of

confidence

in

the,

yacht

resulting

in

subsequent

i nappropriate

seamanship,

o

trapping

of

crew members

hooked-òn on deck,

o problems

associated

with

watertight integrity, and

o

damage/destruction

of

mechanical

systems

intended

for

upright

operation,

ex:

loss

of

engine,

crankcase

oil.

Using

data

from

'Reference

10, and,

combining this with the results in Figure

23, a

feel

for the time trapped inverted

The -esults

of uing these data

are shown i Figure 26 and the ftllowing can be

concluded from that figure:

o In conditions where capsize of a yacht become likely, great danger of relatively

long period of inverted

stable equilibrium is

associated with a low range of positive stability.

o The behaviôr i.s highly

non-linear, so that as a

practical mattér all yachts

with a range of stàbility exceeding 140-degrees will

reright almost instantly.

o Yachts with a range typical

of the lower edge for IOR

yachts may be trapped for period aprbaching 5 minutes

with 2 minutes likely.

TIME TPADPED 1'VCP.TEE ii

'i

JTES 20 18 16 i 12 10 8 RANGE 0F STABILITY 40-FOOT YACHT AD KNOT SOS WIND

S PE E D

O FASINET

EXPEP.-IENCE

FIGURE 26 - VARIAtION OF TIME STABLE INVERTED WITH RANGE OF STABILITY

To those who find the derivation of

this estimate too torturous to accept at face value, consider the data from the Fastnet fliquiy which was discussed in

detail ïn Reference 11. The times dan only

be guesses under such conditiön, but, to

quote the inquiry:

!'These five reports (of inverted

stable equilibrium-Ed) give grounds for concern abqut the ultimate

self-righting ability of certath: boats and

a full stability analysis of two boats, one of a type which reported

remaining inverted för five minutes

and another which reported very rapid

self-righting was commissioned.'

The results of that stability study aré shown on Figure 26 labelled 'Fastnet Experience.

514

An Èqui-Safety Standard

Let us now investigate the

implications of some sort of size-varient

standard of capsize safety; the form chosen

for illustrative purposes is that of a

constait time for probable stàble equilibrium regardless of size.

Simply stated, the lârge vessel i.s

allowed to remain stable inverted for an amount of time porportioned to its

advantage in expected encounter of a

capize -

if it i teh timés more resistant

to capsize in a givèn sea condition as

measured by the expected ençounter time

it-may therefOre stay upside down ten times as long when the capsize cOmes.

this notion may seem illogidal, but

perhaps it is no less so than allowing boats with a two order of magnitude greater

proclivity to capsize over other to race

Side-by-side as in the case if a 30-fOoter

sets out with a fifty footer.

Be that as it may, the results of udh a standard give sothe rètïonàl basis to

support the notion that somehow a l&rge yacht be given some credit for its greater

capsize resistance.

Using the data for cpntructihg the

curve of inverted equilibrium time, a

relationship of ranöe of positive stabilty with size can be defined as in Figure 27. Note that the 30-footer is allowed an

equilibrium time of a few tenths of a

minute while the 40-footer gets a minute,

the 50-footer about nine minutes, and the

60-footer an hour-and-a-half. Note also that it is the slope of the line which is

of importance, and the locàtion is arbitrary. RANGE DF POSITIVE STAB I LI TV

N

4. 30 FOOTER

N

40 FOOTER

N

N

4- 50 FOOTER

N

N

6Ò FOOTER 'I-¿ z:: I - I "+ 20 FOOTER N

MINUTES STABLE INVERTED

FIGURE 27 - RELATÏONSHIP OF SIZE WITH RANGE OF STABILITY FOR EQUAL TIME INVÉRÏEb

11 Claughton, A., and Handley, P., 'An Investigation into the Stability of Sailing Yachts in Large Breaking Waves", University of SöuthamPton,

Jan 84.

If

we now

desire

to

consider

a

specific value of range of stability with

size,

a

replot of the. data cah be rnade

as

in Figure 28.

_{In this case, the values for}

equal

_{probability-time,}

_inverted

_is

repesented by the curved contour bounding

the zone labeled

_{capsize zone'.}

LENGTH IN FEET

FIGURE 28 - PROPOSED CRITERIA FOR RANGE OF STABILITY OF OFFSHORE _YACHTS

17

_-,

it

Frdm other wörk on knockdown capsizes

_{appears from energy consideratiàns}

that if

yachts

are

to resist

knockdowns,

especially when carrying light

sails,

the

righting

moment

characteristics

need

attention in a manner which make a minimum

value for range of positive stability fall

out in the area of 115 to 120 degrees.

För

those who

cannot

appreciate

the

need for this

in

big boats, a withdrwal

eport by a 60-föoter in the St. Pete-Fort

Lauderdale Race of 1984 is instructive:

"At

approximately

1340 EST

while

i-urining under spinnaker ad full main, boat

entered violent roll cycle.

On deep roll

to

port

boat

buried

end

of

boom and

mainsail

preventer

held

boii

in

water.

Boom apparently collapsed as boat took deep

roll

t

starboard

(windward)

and

lay

on beam ends

(80-85°

angle

of

heel).

Boat remained

in

this

position

with

a goqd

portion of spinnaker and

10 or so of pole

in

water

until

force

on

pole

caused

spinnaker car control chain to break.

Pole

then thot up vértically with reference to

water pláne relieving pressure on spinnaker

sufficiently

to

allow

boat

to

right

itself.'

"The "death roll" was so violent and

deep thatcrew members on the starboard rail

were

completely

submerged and

'grinders"

were hanging vertically from the pedestals

(and

maintaining

a

death

grip

on

the

handles, one Shoúld add)!!

The

weather

associated

with

this

incident was reported as wind 20 gusting to

30.

If äne postulates a constant range of

stability minimum to prevent knockdowils of

120-degrees this

is shown

in Figure 28 as

the

straight-

upper

bound

df

the

zohe

labeled "kñockdòwn zone".

If

one then

accepts

a

slope midway

between the two as reasonable and selects

an ánchor point for- à 30-foot yacht at

130-degrees, the relatiOnship:

reg'd = 160-L'

when &=

minimuÌ

requi'ed

rahge

of

positive stability

L = equivalent length as pér (7).

This

would seem

Iike

a

rational

minimuol for yachts

whfth will participate

in true offshore events.

Let us check the implication of such a

standard upon

an

existing Grand-PHx

tOR

yacht.

Figure

29 shows a

sketch

of

currently competitive

tOR

One-Tonner,

and

the result of requiring a range of stability

of this

iaçht of 130-degrees.

The designer

has -estimated that the result would be to

reduce internal ballast to an amount usually

associated

tk,

trimming ballast and that

the keel piôfile would be altered as shown

by the dashed line.

12

Kirkrnan, K.L., "Ultirate Stability in Small Cruiser/Racers", July 1983.

REQD = 160-L. MINIMUM, 1200 KN0C00W1 CAPS I ZE ZONE ZONE 10 20 30 40 50 60 ipo 160 140 C = 120 100 80 -C 60 4° 20 C

CONCLUSIONS

Thi.s

report

presents

a means

for

estimating

the

équivalent

size

of

a

specific

yacht

as

related

to

capsize

vulñerab.ility,

gives

data

on

the

environmental

conditions

where

capsizes

might

be

exected,

énd shows

the

particularly troublesome result of

a smàll

range of stability.

It wOuld seem a simple matter to make

these calculations fOr

a paticulér yacht

and decide on this basis to stay home from

any races where a creditable storm having

an FDS

in

the zone of capsizes for that

size

is

likely;

bût

of

course

with

an

uhderstanding

of

the,

complexity

of

this

latter

process

will

probably

come

reluctance to so simplify.

Of what use,

the,

is the infomation

contained herein?

The

note

began as an

effort

to

determiné

whether

historical

pecedents

related to a minimum size of entrant is an

offshore race was based upon solid ground.

.t isi

With this iñ hànd,

an attempt was made

to quantify this 'size

measure on

a more

rational

basis than length and a formulae

has been

presented

to

do

so;

a

formula

which

is

kind

to

roll

moment of inertia,

displacement, and to low center of gravity

and harsh toward wide beam.

Further,

an accompanyiiig range

of

stability is suggested.

Finally,

the

reanalysis

of

storm

incidents has shown that whenever the wind

blows

for

sustained

periods

at

over

40

knots the zone pf potential capsizes is

at

hand

for

many

yachts.

This

condition,

.56

FIGURE 29 - IMPACT OF STABILITY CRITERIA ON ONE-TONNER

while not sufficient to

_{mancate a capsize,}

suggests

that

one might occur

and

is

so

consnon to off,hore races that yacht design

must

_reflect

_what

_is

_known

_règarding

reducing risk through

a change

in

design

parametrs

and

the

_construction

_and

outfitting of yachts must

prepare them for

this ultimate tèst.

The particular problem of iverted s.tà

bility is so debilitating as to cry for

imme-diate rule chanês tO reduce beam and lower

VCG.

ACKNOWLEDGEMENTS

This

paper

is

an

overview of

récent

research

in

capsizing

and summarizes

contributions

from

Joé Sal.sich and John

Zseleczky of the U.S.

Naval. Academy Hydro

Lab and Andrew MacGruder, Kn Weller,

and

John Wright of USYRU.

BIOGRAPHY

The

author

is

é

graduate

of

Webb

Institute of Naval

Architecture and is

an

active offshore .ai1or.

He is a member of

the SNAME Small

Cràft COmmittee,

Chéirman

of T&R Panel SC-i (Sailing Yachts & Ships),

a

Director

of

the

SNAME/USYRU

Joint

Research Project on Safety frOm Capsizing,

a member

of

the USYRU MHS Committee, a member

of

IOR Research Còmrnittee and

Safety-at-Sea

Committee, and

the

CCA

Technical

Corrimittee and Bermuda Race

Committee.

BEFORE MODIFICATION ATER MODIFICATION

RANGE .0E STABILITY 118° 1 300

OUTSIDE BALLAST 4300 ₆₆₀₀ INSIDE BALLAST 28 OO ₅₀₀ LOA

10-O"

LWL 31

-3"

BEAM

13-3'

DRAFT

7'-5"

DISPL

14,400"

BACKGROUND:

Simplified

screening

formulae

have

proven

use-ful

in

race.

management

as

a means of testing the majority of the population

on

a

simple

basis,

requiring only those caught by the sieve to undergo more

rigorous e amination

Such an approach seems appropriate to dealing with

capsize resistance.

This

note

presents the basis -for the development o-f

a

capsize

resistance

screening

formula suitable -for application

to

Category

races

n accordaflce, with the ORC Special RegulatIons.

F'PROACH:

The published capsize research data has shown two characteristics

o-F

danger

related

to

capsizing

_{the risi}

u-f

being

unduly

easily

capsized.

and

the

risi

of sticling in the inverted position

for

an

extended

time

period.

The

measures of these have been

shown

to

be

"capsize

size".

(referred

t

herein as L).

which is a

function

of

length,

beam,

roll moment of inertia,

and VCG location, and range of

stability, a function of beam arid VCG location.

fri

a study of yacht Gharacteristic

(See Appendix A),as

rElated

to these measures, the following conclusions seem supportable:

1. Historical precedent., and a detailed

analysis

of

capsize iricident, support the not:ion that a yacht o-f

normal proportions, having a waterline length of

approximately 30 feet. seems. to be a good minimum

"size". This seems to

bè

true

because

it

gives

reasonably low probability o-f capsize in true offshore

passages.

Note.:

In visualizing thé concept o-f

"capsize size" for

boats

o-f

other than normal proportions,

it will be

helpful to review the -following general results from

calculating the "capsize size" for a number of

diff-erent boats:

o

a modern yacht o-f moderate displacement and beam

has à capsize.

size

near

her physical

size

(length LWL.).

(example: F3 -- 32 vs. 30.)

o

an old-fashioned heavy yacht will have a capsize

size approximating twice her physical size.

(example: Navy Yawl -

9 vs. 30)

APPENDIX B.

o

an extreme yacht in beam/displacement will have

a capsize size approximately half her physical

si ze.

(example: OLS 30 -- 10.5 vs. 27.5)

For reasonable capsize resistance

a

range

of

stability of:

160 degrees - L'

(L' in feet)

would result in a standard o-f equal time inverted.

For work on knockdowns, a range of stability of

approximately 120 degrees seems to be a minimum

to preclude sail--force induced capsize.

A minimum range o-F stability necessary to limit

the

time stable-inverted to around two minutes, in seas at

the

threshold of capsizing seems to be

approximately

120 degrees.

A difficulty in applying these criteria at the present time

is

that

the available data - particularly under present IOR

measurement

practices

- does

not

include

sufficient hull

form

de-finition

to

characterize either range o-f stability or actual displacement.

3. DEVELOPMENT OF SCREENING FORMULA:

In considering the criteria described in the section above. the

available measurement data, and the yacht characteristics that show

LL

in

both

capsize size and range o-f stability,

the

availability

and

recurrence

of beam data (reinforced by the findings at the University

of

Southampton) drew attention to the possible merit in

a

criterion

that would select against disproportionate beam and light displacement

in the form:

Maximum beam / Cube root o-F displaced volume

where some maximum allowable value would serve as the screen.

Such a formula would deal with beam,

moment o-F inertia in roll

(which is closely tied to displacement),

and size - in the sense that

SIL values tend to decrease with yacht size..

It

remained to select a suitable screen value,

and to

verify

that

surrogate

data

(i.e.

IOR

measurement

values)

would

be

The

use

o-F

surrogate data

in particular the

_IOR

data

_for

dispiacement

was

invest-igated

by

calculating

the

following

'uantities for the entire

R/MHS common fleet:

B MAX (MHS)

Screen (MHS)

(Displacement volume, meas. trim)

B MAX (IOR)

Screen (IOR)

(DSPL 1(0.9 x 64))

(Note:

DSPL/0..9

gives appròx. displacement of lOP

boats).

A

graph of the, correspondance,

for randomly-selected

yachts,

ppears as Fig.

B 1,

_{and the correspOndance is excellent}

_throughout

:he range of screen values.

Perhaps

of equal importance is the fact that the error in

the

OR

"DSL"

correlates

with

range

o-f

positive

stability

in

the

ollowing

sense:

o-F

the entire USYRU lOP fleet on which hull

_line5

Jata exist to calculate range of stabili:ty:

No

case

exists for a yacht having a

range

of

positive

tability

e'-ceeding

120

degrees where the

substitution

of

actual

isplacement

-for

lOP "DSPL" fails to lower the screen

_VaiLle

tO

an

cceptable level

(as defined below); and

No case exists -For a yacht having a range o-f stability

ess than 12Ö degrees where that 'yacht can meet a criterion of

160 degrees -

L

(lOP)

or range of stability.

The

rational selectiOn of a maximum allowable screen value was

'er-Formed

h the following basis:

A

plot o-F capsize length and margin above 160

- L'

was

repared

for

representatiVé yachts,

Fig.

B 2.

On such a plot

the

iagonal shown represents increasing risl

of both capsize and inverted

table equilibrium.

A section cut of Figure B 2

.

representing risk vs. screen

1/4

1/3