### 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'

+ Cwhere

### 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

) IMODEL 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

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

### and boke

in the test sectionarea 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 showthe 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 ESBALLAST

-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 50Specifically, 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 INCHESFIGURE 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 180WM'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 60It 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; thetime 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 100WAVE 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 50BOAT 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 beconcluded 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 WINDS 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 resistantto 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 NMINUTES 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 CCONCLUSIONS

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