ON THE EFFECT OF SIZE - AS RELATED
0 CAPSIZE RESISTANCE
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
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.
Karl L Kirkman
i Phillips-Birt, Douglas, "British Ocean Racing', Adlard Coles, Ltd., 1960.
Dept. of Marine Technology
Mekelweg 2,-. 2628 CD Deift
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
-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.
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
DEVELOPMENT OF A SIZE DEPENDENT CAPSIZE RATING
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
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.
r !JUaV.us. I
FIGURE 2 YACHT HULL POSITION WHEN STRUCK BY WAVE
a) TIP.E SE0505CE SEETCH DF MODEL CAPSIZE EXPERIMENT
Note that the graphical
correspond ectly to the velocity maps but
is used for illustrative purposes.
A review of capsize model
as characterized by the data
(b) taken from references 3
and 4 respectively) also show that the hull
conceptualized "moment of impact" has
angle to the vertical, even in the absence
schematically in part (c) of Fïgue 2.
high velocity jet area from Figure1 and
the sigñificänt roll
angle at the instant
impact fom Figure2,
the geometry at
forcesand moments can be
based upon the sketch shown in Figure 3.
FIGURE 3 - DEFINITION SKETCH FOR. ROLL PHYSICS
forces and moments which fit the equation
reformulated at the instant of impact:
where 1/2 pV'j2 =q of jet
S = drag area
r = moment ,m of jt forcé
lxx -= roll moment of inerti.a
Clearly this rèpresentation Includes a
number of gross simplifications including:.
The transfer of ñiomentum from the
jet to the hull
Added mass in roll is neglected
patterns are neglected.
not to estimate actual values.
critical acceleration which fOr a specific
design, exceedance will result in "capsize
If the jet velocity
is then takenas
propotioñed to the square root of the wave
and some constants
the equation becomes:
where h = wave height
s = struck. area
r = ïadiu
of action of striking
fOfè about VCG
a fixed proportion of length.
idone because a
implies a change in range of stability añd
hence in threshold of capsize, o cnt.)..
side, earlier test results (Ref
3, Figures 21, 2? ãñd 26) show a pronounced
components related to hull georitetry. 'For a
Kirkman, K.L., Nagle, T.J., and Salsich, J.O.,'
Sailing Yacht Capsizing',
more particularly: r
b = Beam, and
Substituting into (4),
' cnt is
and (VCG-CP) and Thversely p,oportional to
Let us consider now this
by model test results.
rs orne be
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
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
dispersion relationship for water Waves was utilized to generate a train which converged
and bokein 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
As a result, there is no assurance
versionsof 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
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
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.
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
FIGURE 6 - TRENDS IN IOR YACHT BE.AM
FIGURE 7 - RELATIONSHIP BETWEEN FASTNET CAPSIZES
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:
(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
o0. 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
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
SOURCE: UNPTBLISHED RESULTS BY SALSICY & ZSELECZKY
AGRA. AFORO LAB
100 110 120 130 RANGE 0F POSITIVE STABILITY
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
iDO 110 120 130 140 RANGE DF STABILITY IN DEGREES
FIGURE 10 VARIATION OF TENDANCY TO' REMAIN
- STABLE INVERTED WITh RANGE OF
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 /
/ 0OOc C. o
ILE G'E N D -C 10G 80 60 40 20 BALLAST POS ITIOU SOURCE
\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
: r30 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
-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
o Lowering ballast from typical positions has a vèry weak tendency to improve probability, so weak as to be
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.
r140 130 120 110 X 1 00
Based upon this,
it seems justified to
delete from the capsize 'size" formulation
account for the shift in & cnt value with
If we accept the contours in Figure 12
for probability of capsize as a function of
range of stability (for fixed length, beam
capsizing and remaining stable inverted
calculable as follows:
capsize as a funtion of range of stability
from the data in Figure 9 añd shaped as
Figure 12, we get a curve as
in Figue 13,
if capsized, taken from Figure
10 can be taken as in Figure 13, part (b).
probability of capsize and inverted stable
equilibrium is as Figuré 13, part (c).
to wit, that a range of
positive stability of 140-degrees implies a
stable equilibrium corresponds well to the
that those (yachts-ed) that have angles of
than150-160 degrees can be
after encounter'ing a breaking wave."
PROBABILITY 0F INVERTED EQUILIBRIUM
0INT PROBABILITY 0F CAPSIZE AÑO ISVERTED
FIGURE 13 - PROBABILITY 0F IÑVERTED EQUALIBRIUM WITH RANGE 0F STABILITY
THE NATURE 0F BREAKING SEAS
relative size; how big a breaking wave can
a specific design withstand.
The time has come to answer a far more
standard yacht has the same prObability of
table analogy to handicapping.
generation because breaking waves represent
än instability in nature bth in the
(a pile of water of
a steepness beyond its
themaceo sense. (A.
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
energy into the water via wave-making drag
in a very steady manner.
phenomenon are not so nicely ordered; they
are generated by unsteady phenomenon, they
observer they appear quite complicated..As
a result of this behavior we tend to deal
ih statitical or probabilisticway. The
irregular waves assumes that
this does not apply in the case of breaking
Let us consider some basics to see how
all of this applies to our capsize problem.
So much of what we utilize in working
wé musthave a
these unfamiliar measures.
Figure 14 shows
socs general descriptions of wave types and
length of thesE.Note
descriptions overlap and the zones are not
not important since
the purpose of this graphical presentation
is only to give a féél for the waves under
this term for frequency.,ai,
PROBABILITY 0F CAPSIZE
id1 50 170 180
FIGURE 14 - RELATIONSHIP BETWEEN LENGTH MD
FREQUENCY OF 'WAVES
If we were to go back to our view of a
rather confused ocean surface,
in place and make a saw cut section
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
FIGURE 15 - IRREGULAR WAVE HEIGHT TIME HISTORY
a Figure 16 reproduced from
regular waves which are these components in
(a)and a meahs
portraying a confused sea where the energy
t each fequency, w,
is plotted vertically
in a histogram and the envelope of these
represents the spectrum.
This curve has a
number of useful properties beyond that of
curve is a direct measure of the enègy in
the spectrum and the shape tells us how the
energy is distributed.
Van Dorn, William,
Principles 'of Nãval Architecture, Snarne, 197O.
i) TYPICAL ENtP.GY SPECTRUM, SHOWING
APPR0Y.iMATI0 B.Y A FINITE SUM 0F
b) SCALE 0F FREQUENCY SPEC'T'RUM
FIGURE 16 - ,KE-UP OF IRREGULM SEA
The grOwth of a spectrum is 'also key
Waves fori as a by-prbdùc.t of the shéàr set
up when wind blows across the sea surface.
The presence of the ridges of
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
effécts of non-u'niforn conditions
by thecumulative sea, state (CSS)diagram proposed by Van
sea state with an unsteady
wind time history.
follows' 'as related 'to Fastnet 79.
A tifflé' histOry of the wind experienced
by thé Fasthet fleet and
by a number of sumftiary analysis is given in
What is then required is to go
speed to a wave characteration.
Oceanography and Seamanship", Dodd, Mead & Co., New
FIGURE 17 - OBSERVATIONS OF FASTNET WIND
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.
ESTIMATED SIGNIFICAIJT WAVE HEIGHT IN FEET
a) SIGNIFICNAT WAVE HEIGHT
OCEAN SCIENCE CSS ESTIMATE ESTIMATE / /
/O 10 20 30 40
çO 10 20 30 40 50 60
It is interesting to correlate this
055 diagram estimate with observations, and
the Inquiry8 gives a great deal of data from participants questionnaires to allow
The participants were queried
regarding the significant and the maximum
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
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
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
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
quiklythis large breaker appears; the
time values given are for a full-scale
breaker related to a 40-foot yacht and a
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
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
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
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:
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
i 20t. 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
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
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
ofknockdown by size bands for lòcation on the
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
1 .3 0.1 LE SE T
G 51 iOC2C
G0.0) 10 20 30 40 50
BOAT LENGTH IN FEET
FIGURE 24 FASTNET Bi AND B2 KNOCKDOWN ENtOUNTERS AS A FUÑCTIOÑ OF BOAT
when t = encounter time in
% 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
In light of this
success,, is it possible to move to
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
19-foot daysaik.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
'Zone of Potential Capsizes"
be confused witha
great detail with the text,
existing niòderatewaves seem to be a most
but others possibly
boats should probably be a weighted length
\B2 IMPACT CAPSIZE I J 50 BOAT LENGTH IÑ EET
FIGURE 25 - RELATIONSHIp OF REPORTED
CÀÏASTROPHIES TO FDS WIND SPEED AND BOAT SIZE
This danger coÌTIes from:
hooked-òn on deck,
watertight integrity, and
combining this with the results in Figure
for the time trapped inverted
of uing these dataare 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
'iJTES 20 18 16 i 12 10 8 RANGE 0F STABILITY 40-FOOT YACHT AD KNOT SOS WIND
S PE E D
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.
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
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
N4. 30 FOOTER
N4- 50 FOOTER
N6Ò 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,
specific value of range of stability with
replot of the. data cah be rnade
in Figure 28.
In this case, the values for
repesented by the curved contour bounding
the zone labeled
LENGTH IN FEET
FIGURE 28 - PROPOSED CRITERIA FOR RANGE OF STABILITY OF OFFSHORE YACHTS
Frdm other wörk on knockdown capsizes
appears from energy consideratiàns
especially when carrying light
attention in a manner which make a minimum
value for range of positive stability fall
out in the area of 115 to 120 degrees.
need for this
big boats, a withdrwal
eport by a 60-föoter in the St. Pete-Fort
Lauderdale Race of 1984 is instructive:
i-urining under spinnaker ad full main, boat
entered violent roll cycle.
On deep roll
Boom apparently collapsed as boat took deep
layon beam ends
portion of spinnaker and
10 or so of pole
spinnaker car control chain to break.
then thot up vértically with reference to
water pláne relieving pressure on spinnaker
"The "death roll" was so violent and
deep thatcrew members on the starboard rail
were hanging vertically from the pedestals
handles, one Shoúld add)!!
incident was reported as wind 20 gusting to
If äne postulates a constant range of
stability minimum to prevent knockdowils of
in Figure 28 as
labeled "kñockdòwn zone".
between the two as reasonable and selects
an ánchor point for- à 30-foot yacht at
130-degrees, the relatiOnship:
reg'd = 160-L'
L = equivalent length as pér (7).
minimuol for yachts
whfth will participate
in true offshore events.
Let us check the implication of such a
Figure29 shows a
the result of requiring a range of stability
iaçht of 130-degrees.
has -estimated that the result would be to
reduce internal ballast to an amount usually
trimming ballast and that
the keel piôfile would be altered as shown
by the dashed line.
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
particularly troublesome result of
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
the zone of capsizes for that
reluctance to so simplify.
Of what use,
is the infomation
notebegan as an
related to a minimum size of entrant is an
offshore race was based upon solid ground.
With this iñ hànd,
an attempt was made
to quantify this 'size
basis than length and a formulae
moment of inertia,
displacement, and to low center of gravity
and harsh toward wide beam.
Further,an accompanyiiig range
stability is suggested.
incidents has shown that whenever the wind
knots the zone pf potential capsizes is
FIGURE 29 - IMPACT OF STABILITY CRITERIA ON ONE-TONNER
while not sufficient to
mancate a capsize,
one might occurand
consnon to off,hore races that yacht design
reducing risk througha change
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 lowerVCG.
fromJoé Sal.sich and John
Zseleczky of the U.S.
Naval. Academy Hydro
Lab and Andrew MacGruder, Kn Weller,and
John Wright of USYRU.
Institute of Naval
Architecture and isan
active offshore .ai1or.
He is a member of
the SNAME Small
of T&R Panel SC-i (Sailing Yachts & Ships),
Research Project on Safety frOm Capsizing,
ofthe USYRU MHS Committee, a member
ofIOR Research Còmrnittee and
TechnicalCorrimittee and Bermuda Race
BEFORE MODIFICATION ATER MODIFICATION
RANGE .0E STABILITY 118° 1 300
OUTSIDE BALLAST 4300 6600 INSIDE BALLAST 28 OO 500 LOA
a means of testing the majority of the population
requiring only those caught by the sieve to undergo more
rigorous e amination
Such an approach seems appropriate to dealing with
presents the basis -for the development o-f
formula suitable -for application
n accordaflce, with the ORC Special RegulatIons.
The published capsize research data has shown two characteristics
of sticling in the inverted position
measures of these have been
herein as L).
which is a
roll moment of inertia,
and VCG location, and range of
stability, a function of beam arid VCG location.