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ON THE EFFECT OF SIZE - AS RELATED0 CAPSIZE RESISTANCE

Faculty WbMT by Karl L Kirkman Dept. of Marine Technology Mekelweg 2,-. 2628 CD Deift The Netherlands INTRODUCTION

This note is intended to clarify the effects of various yacht parameters,insofar as This note will develop the basis for making we Understand the effects presently, in thedetermination, present the data used in determining the relative resistance to a single- determining the effects of the selected wave-impact capsize. variables, and suggest a formulation for characterizing size from the standpoint of Race organizers have frequently invoked a capsize resistance. limitfor offshore raceswhich establishes a minimum size of yacht which is allowed to enter Why -Size? - andparticipate in t-)e race, and one ofthe motivations for such a minimum has been safety. The recurring success of voyagers in quite small yachts seems irreconcilable with the Traditionally this has involved leñgth, and notion that larger is safer; is it possible that in response atleast one case exists where an the small yacht will bob like a cork, resisting entrant added a false nose piece to qualif' for the ability of the elements to "get- ahold" of it the race: Cohoe in the 1950 Bermuda Race, and whereas they destroy its larger counterpart? then discarded it for- the ensuing Transatlantic Could it be that the sthall yacht rolls with thé Race. punches while its resistful large counterpart i-s torn by Targe forces? By-and-large the limit has represented the best judgement of the organizersandhas been The laws of physics say no, àtléast for selected without specific numerical basis; not the simplified caseofa prismtic yacht form to be arbitrary,but because little exists to struckby an incident wave: modeling of the guide-race committees in defining such a limit. ratio of gravity todynamic- forces (which is known as Froude Scalingafter William Fraude) Recall that any suchlimit is, however, doomstheoutcome to a sithple linear scalar moré-or-less arbitràry since it is unlikely that relationship: the yacht twice aslarge will two identical yachts, saveone-inch in stern survive twice as large a wave. overhang, will respond differently in bad weather. However, given that some hard limit is TECHNICAL APPROACH desired (or desireable) it remains todevelop the best possible measure. In short, what is required parallel.sthe rating situ-ation which -traditionally utilizesa Although length has enjoyed great rating rule to measure t-he equivalent length of popularity, it is rather indefensible. Just as the iÏportantdesign variations, and a time handicap performance "ratings" take into account allowance table to account forthe- performrice- many characteristics ofa yachtin deerr.ining effects of lehth variations. its equivalent size, so should a size limit aimed at safety consider more than one Rolling these together- in a situation dimension. Note that many rating systems have analogous to the MHS "VPP" vs. traditiOnal characterizedthe rating of a yacht in feet ratingschemesseems beyond the reach -ofour whichis equivalent tostating that the yacht present knowledge; buton the other hand this will sail as fast as one of some standard would spare the organizer of a race the task of

proportions and that length. specifying storm weather conditions. -

In a like manner,it should be possible to A most difficult philosophical problem also state the equivalent size of a yacht for safety presents itself. Carefulstudy of this note considerations,and length alone cannot beany will réveal that the practical means of more appropriate for this than for rating. modifying a yàcht to "optimize" its capsize rating are bounded to the extent that a twenty Until now, we have been denied sufficient footer cannot be made to start a particular information to construct a safety "rating', but race wherebadweather is expectedwith recent advances in our knowledge of bad weather the same probability of capsize as a sixty footer. capsize mechanics make possible a try, at least-, to beginto define size in some multi-variable way.

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

39 One consequence ofthis may wellbe that the small yacht have more strict provisions for At this recovering from and surviving a capsize than its time, the significant factors large counterpart for equal safety;an approach appear to include the following, each ofwhich whichis much more difficult to quantify than will be discussed in a subsection: some of the physical capsize phenomenon. Mass moment of inertia/gyradius Displ acement Another might be to try to achieve an Be am equally smallprobability of remainingstable Vertical center of gravity inverted regardless of size; that is, the smaller yacht mightbe requiredto possess a In considering the single wave impact larger range of positivestability than its as a single degree of freedom large counterpart. Such a standard is (roll) spring/mass response, some insight into hypothesized herein. the important dimensions can be gained by mixing test observations DEVELOPMENT OF A SIZE DEPENDENT CAPSIZE RATING with first principles. Hydrodynarnic Considerations First, recall the data on breaking wave velocity maps and velocity From consideration of the hydrodynamics, profiles fromReference 2 which from analysis ofincidents involving capsizes, is reproduced as part (a)and (b) of Figure 1 andfrom model tests, wehavedeveloped and respectively. Piecing that data together schematically refined an intuition regardingthe parametei-s as in Figure 1, part whichaffect capsizeresistance(and which do Cc)the wave jet can be simplified by considering the flow to be not significantly affect it). a

Ef 14 r !JUaV.us. I . ..

I-'

a) TIP.E SE0505CE SEETCH DF MODEL CAPSIZE EXPERIMENT

a) YEL001TA MAPS b) VELOCITY PROFILES

\ b) PHOTO SEQUENCE OF CAPSIZE

FIGURE 2 YACHT HULL POSITION WHEN STRUCK BY FIGURE 1 JET VELOCITY IN BREAKING WAVE WAVE

2 Stephens, 0.J., II, Kirkrnan, Karl L., and Pete-son, R.S., 'Sailing Yacht Capsizing' CSYS 1981. highveioity,fairlylocalizeduniform (3)Roll moments from other fTow stream havin a velocity,Vj, in the patterns are neglected. horizontal plane. Note that the graphical data On velocityprofiles does not Itshould be appreciatedthatthis correspond ectly to the velocity maps but representationissuggestedprimarilytò is used for illustrative purposes. give an insight into the relative importanceofthevariousparameters and A review of capsize modeltestssuch not to estimate actual values. as characterized by the datainFigure 2 (a)and (part (b) taken from references 3 Equation [2) can be further and 4 respectively) also show that the hull manipulated to iepresent a level of at a conceptualized "moment of impact" has critical acceleration which fOr a specific alreadyrolledat a fairlysignificant design, exceedance will result in "capsize angle to the vertical, even in the absence i.e. rollmotionbeyond some arbita-y of wind This position is shown thréshold: schematically in part (c) of Fïgue 2. &Crjte 1/2 2Vj2Sr t) Combiningthisphysicalnotionof a lxx high velocity jet area from Figure 1 and the sigñificänt rollangle at the instant If the jet velocityis then takenas ofimpact fom Figure2,the geometry at propotioñed to the square root of the wave theinstantofimpact, andthè fesulting height,and some constantsare d1àrded, forces and moments can be hypothesizd the equation becomes: based upon the sketch shown in Figure 3. O'crit I lxx where h = wave height s = struck. area r= ïadiuof action of striking fOfè about VCG

Let us now simplifyfurther byholding freeboad asa fixed proportion of length. (Thisi donebecause a freeboardchange 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 Tikélihoodof FIGURE 3 - DEFINITION SKETCH FOR. ROLL PHYSICS capsizefOrfairlylargevariationsin freeboard.

A final When these are combined, it is simplification involves decomposing the capsize arm possible.tohypothesize a framework of r into forces and moments which fit the equation components related to hull georitetry.'For a fixed VCC, and freeboard, thisis as of motion:. follows: F Ma, (1) r C5) for the system in roll. With s orne sithplificatï'ôn, the equation can be reformulated at the instant of impact: more particularly: r b'+ C 1/2 pVj2SR lxx Q where 1/2 pV'j2 =q of jet where S = drag area b = Beam, and r = moment ,m of jt forcé c Height,centerofpressure above VCG. lxx -= roll moment of inerti.a Substituting into (4), Crroll acceleration ' cnt isdirectly proportionalto B and (VCG-CP) and Thversely p,oportional to Clearly this rèpresentation Includes a lxx. number of gross simplifications including:. J.(j2 The transfer of ñiomentum from the 'lxx (6) is. neglected jet to the hull Let us consider now thisisborn out Added mass in roll is neglected by model test results.

3 Kirkman, K.L., Nagle, T.J., and Salsich, J.O.,'Sailing Yacht Capsizing', CSYS 1983. '41 MODEL TESTS However, as the waves of various sizes were repeatable, thenotion Model tests involving a variation in Of uing the wave height have been condîjcted by Salsich data to check ratios of ensitivity One to another in hypothesis and Zseleczky at theU.S. Naval Academy and then in the experiments wasintroduced. Hydrodynamics Laboratory (Ref. 4) to For example, the ratio of effect of explore the sensitivïty of a simple dislacement to prismatic nodel to capsizing with variation gyradius as postulated iti (4), was checked using the in a number of parameters: displacement, test data and cnfirrñed gyradius, beam, appendage area, and approximately, and such checks will have to freeboard. suffice untilnew tests can be conducted. As with many puzzles, unlocking one Shortcomings of wave family relationship allows for clearer understanding of others not previously possible and this is In pHnciple, thedata should allow particularly true in the case of unlocking the relationship of for the deriviation of variations in beam to capsizing. susceptabi-lity,anda simple measure would be as an equivalent change in wave height. Because of the means by which the diffeent The datain Figure 4 (from Reference 4) were presentedto waves were generated as detailed below, showthe effect of such a direct measure was not possible, and beam, but due to the scaling of the models at first glance, these data did not support the rather severe sensitivities hypothesized by fundamentalconsiderations described above. This wasthe cause for concern which has only tentatively been assuaged by the following consideration.

The method of generating breaking waves in thelaboratorywasdïscùssed ih detail in Reference 3; in sumary the 'N:; dispersion relationship for water Waves was utilized to generate a train which converged and boke in the test section area of the tank,. Although rigoroús procedure would have involved developing a newwave train for each wave heightand demonstrating that this family was similar FIGURE4 - ThE EFFECT OF BEAM VARIATIONS ON to the others, expendency dictatêdthat the CAPSI RESISTANCE height variations be achieved by tampering with the amplitude ofallwaves generated but with the phasing relationship included an unintended displacement-length unchanged. ratio variation. The result of this seems tohave been to disguisea rather marked As a result, there is no assurance sensitivity to beam whih can be shown by thatthebreakers arecorrectly scaled manipulating the data as follows: versionsof one another, in fact that would be unexpected. Thus, while the data show The beam variation testéd was the effect of wave size, the nominal height generated by taking the baseline model and measured and plotted cannot be used as the changing the half-breadth coordinates while scalar of the wave size variation in terms holding the depths to yield variants with of energy available to capsize because this 25-percent less and 25-percent more beam. is such a sensitive phenomenon. As a result the displacement per unit length changes proportionately. In the context of the original experiments, nOne of this presénted any Using the relationship that the effect problem sincethedata were intendedto of displacement is linear, and that of répresent more or less severe waves, but it gyradiussquared, thesquare root of the does limit the utility of the data for this ratio of displacements was used to correct new purpose of estimating numerical values the plotted gyradius values, thus creating ofsensitivity. data for models of equal displacement and gyradius. The results are shown in Figure 5 and the supremacy of the narrow-beam modelis 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.

L 7

6 :AIUS IN NC H ES 5

11 12

WAVE HEIGHT IN INCHES

FIGURE 5 - THE EFFECT OF BEAM VARIATION WITH FIGURE 7 - RELATIONSHIP BETWEEN FASTNET CAPSIZES CAPSIZE RESISTANCE WHEN CORRECTED A1i ¿ÈÁM FOR DISPLACEMENT

Recall thatone ofthe sharpdesign t-rends shown in Reference 2 and reproduced Size Rating Rule hereinas Figure 6 was an increase in the beam of recent racing yachts, and that one Accepting that the' physical model ofthemostdefinitive relationsbetween matchés (6), and the desire to determine an fastnet capsizes and design parameters was equivalency on a length basis of equal shown in the same referenceto be with capsize resistance,one way of expressing beam, Figure 7. thelength (using the concept of a base boat of normal proportions) is the At the same time,freeboard hasbeen fol lowing: shown by limited tests to be a relatively unimportant variable and this was

attributed to the bilance bétween the (.JB)2 L'= +()2.I disadvantage of highfreeboard in impact (7) area balanced by the advantage, of freeboard on thelee side in avoiding tripping over where: L = capsize length, feet the lee rail. 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

LEGEND

o ONE TON CHAMPI.ONS o REPRESENTATIVE DESIGNS 0.05 o

0. 0'4

-J 0.03 C- 0.02 This calculation has been performed for the MHS fleet with the results as shown 0.01 in Figure 8.

o '80 '60 '65 '70 '75

FIGURE 6 - TRENDS IN IOR YACHT BE.AM

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

43 Further, a small range of negative Stability is most important in avoiding stable inveted equilibrium. Cohsider the data irs Figure 9 and 10 in o0 support of this 00 / role of range of stability: 0 // 00 / : r / o // o / o / oa/ 10G / o 30 o o I o / -80 / 0O \ 20 / I 60 Oc C. N / BELGE BALLAST / o LE G'E N D C POS ITIOU / \ 10 I o MISCELLANEOUS N / ULDB'S 40 C_SOR / TOP OF SOURCE UNPUBLISHED KEEL I I SALSICH B \ 20 ZSELECZF.Y, U.S.N.A. 1Q 20 30 40 50 60 \ HYDR0 LAB \ MEASURED LENGTH \ BOTTOM OF'0 KEEL iDO FiGURE 8 - COMPARISONOF'CAPSIZELENGTH TO 110 120 130 140 MEASURED LENGTH F(R IWtCAL FLEET RANGE DF STABILITY IN DEGREES

me role of range of stability FIGURE 10 VARIATION OF TENDANCY TO' REMAIN

- STABLE INVERTED WITh RANGE OF The phyicai model postulated in STABILITY equation (3)and developed thereon to the size rating rule of equation (6)aid the L' size equivalent was based upona critical levelof roll accé]erati.on, frcrit,which represented a threshold of capsize. It would seem,thén thatin additioh to the Observation of the capsizecomponents seems size equivalent, L', noted, range Of to indicate that twophasesof the phenomenon: positive stability may also bé important in à "snap-roll' phase where the caØize. inertia domihates and thenà phase where the yacht is left to its Own devicesas the dyna,Úi -forces dissipate and classical static stability considerations achieve dominance If this is the case,a yacht with a largerrangeof staticstability (other things being equal,eg: roll moment 90 BALLAST - POSITION: of inèrtia, displacement, beam, etc.) wiH BILGE be in a better position to use this

80 TOP OF characteristic to return to upright as the KEEL static stability takês over. Thisleaves

BOTTOM the issue, what is the role of stability in lo OF KEEL capsize resistance and to answer this both phases must be considered.

60 It exceeds the scope of. this note to develop the statistics of this secOnd phase in detail and Figure11 of Reference 10,

50 SOURCE: UNPTBLISHED RESULTS BY SALSICY & ZSELECZKY and accompanying text may be useful for AGRA. AFORO LAB background. Suffice it to say thatany experiments,and indeed reallife, may be biasedby the reàlity thatthé band of disturbance energy presentis quite nàrow andprobablylies adjacentto thè upper edge of the range of stability of the yachtsof interestso that specific test 100 110 120 130 140 results which measure percentages of yachts RANGE 0F POSITIVE STABILITY trapped inverted stable willprobably not match the 'wheel of fotune'! analoy. FIGURE 9 - VARIATION OF CAPSIZE TEÑDANCY WITH RANGE OF STABrLITY

10 Kirkman, K.L. "On the Avoidance of Inverted Stable Equilibrium", A1AA/SNAfr1E, Anciént Interface XIII, Oct 1983.

: Specifically, Figure 11 shows some T'ACE OF PRACTICAL test results for yachts withmasts and - BEAM BALLAST SHIFT various ranges of stability and the quality DISPLACEMENT of fit to the analogy. Because the wave used in the tests was sizes to 'just capsize the models a wide range of = 150 disturbanceenergieswas notpresent and r the result should not be so expected to fit 140 the dotted line. 130

120

1.0 110 X 1 00

GYRADIUS IN INCHES

C EN T I'; VED T ED FIGURE 12 - VARIATION IN PERCENTAGE OF CAPSIZES SAD.0 0.5 EiLEAIU! WITH GYRADIUS AND VCG

It must be appreciated that the shape WHEEL 0F FORTUNE of contours may reflect an inadequacy of the method of accounting for some effects other than VCG and lxx, and that the L 1 implications discussed below as related to range of stability are only that. I I.Q. .(_j... 90 100110 120 130 150160 170180 Two lessons can be inferred from RANGE 0F STABILITY Figure 12, the certainty of which must be tempered by the speculative nature ofthe probability of capsize contours:

FIGURE 11 - COMPARISON OF VARIATION OF TENDANCY 1) Depending upon the initial valve, TO REMAIN STABLE INVERTED WITH range of stability has a weak influence on "WHEEL OF FORTUNE" ANALOGY probability of a capsize after inertia effects have been accounted for separately. Further, loweriig the range of stability by. Another reason for introducing the raising the VCG for a yacht with an role ofrange ofstability as related to excessively low range (from a practical re-rightinginto the problem ofresisting standpoint) initially may have a large pay- capsizes in the first place is simply this: backin capsize probability reduction, but withno constraints from either practical the yacht will be unable tocarry sail, construction, sail carrying power, or cannot withstand knockdowns of an concernfromre-righting, it will appear 'aerodynamic sort, and will almost certainly that an "optimized" configuration stick inverted once pushed down. However, considering only the snap-roll phase involves a highVCG with a maximum roll (2) Practical VCG shifts, as shown by moment of inertia. In particular,fora the trace labelled "ballast shift" not only boat with a small range of stability (i.e., increasethe range ofstability but also a relatively high totalVCG, say at the tend to lower the probability of capsize. OWL)it may lower the capsize vulnerability byraise theballast further! Consider o Raising ballast from typical Figure 12 which indicates a break-even positions has a very weak tendency to range of stability of about 120-125 improve probability,so weak as to be degrees. If the contours of capsize practically negligible.

probabilityare accepted forthemoment, o Lowering ballast from typical either raising or lowering the ballast positions has a vèry weak tendency to seems helpful; but if one refers back to Figure 11the ballast raising alternative improve probability, so weak as to be practically negligible. carries a high probability of inverted equilibrium whereas the lowering alternative reduces the probability of same o A neutral zone where ballast shifts have a small effect exists with to an extremely low valve. As a practical the total VCG near the DWL. benchmark, the yachttested with a VCG=0 starting point represents a 46-percent of the above are for a ballast ratio with the VCG of the lead at Of course, all single yacht configuration, displacement, thetopof thekeel - terribly closeto contemporary competitive tOR boats. beam, appendages, freeboard, etc.

45 P

Based upon this,it seems justified to delete from the capsize'size" formulation any measure of range fstabilityto THE NATURE 0F BREAKING SEAS account for the shift in & cnt value with this change. Tothispoint,thesubjecthas been totallyrestricted to the rating of If we accept the contours in Figure 12 relative size; how big a breaking wave can for probability of capsize as a function of a specific design withstand. range of stability (for fixed length, beam and displacement) a probability of The time has come to answer a far more capsizing and remaining stable invertedis complexquestion: For a givensetof calculable as follows: charactéristics for a désign under considérationhow muchbiggerorsmaller If we take the probabilityof a standard yacht has the same prObability of capsize as a funtion of range of stability acapsize? Thisisthetimeallowance from the data in Figure 9 añd shaped asin table analogy to handicapping. Figure 12, we get a curve asin Figue 13, part (a). A- clear understandingrequires an appreciationofthebasisofrough sea Then, the.probabilityof inverted generation because breaking waves represent equilibrium,if capsized, taken from Figure än instability in nature bth in theiicro 10 can be taken as in Figure 13, part (b). (a pile of water ofa steepness beyond its dynamicequivalentof"angleofrepose") The product of these or joint and inthe maceo sense. (A.transient probability of capsize and inverted stable oceanographic phenomenon, unlikely to occur equilibrium is as Figuré 13, part (c). for extended timés.)

This result,to wit, that a range of HOW ARE BREAKING WAVES. FORMED? positive stability of 140-degrees implies a vanishingly smallprobability ofinverted In dealing with -bOdy generated waves,. stable equilibrium corresponds well to the the wäke of a power boat in a harbor (or a findings of Reference 11: "From duckswiasning along a pier)isputting observatiohofthetestsitis&pparent energy into the water via wave-making drag that those (yachts-ed) that have angles of in a very steady manner. vanishing stability less than 150-160 degreescan be left flòatingupside down Ocean waves ofinterestincapsize after encounter'ing a breaking wave." phenomenon are not so nicely ordered; they are generated by unsteady phenomenon, they interact with one another, and the' dispurse(thatisthey travelacross the oceanatvariousspeeds)so thattothe observer they appear quite complicated.. As a result of this behavior we tend to deal withthehiih statitical or probabilistic PROBABILITY 0F CAPSIZE way. The classical ocean engineering treatment ofirregular waves assumes that the. systemcan be designated by a "photograph"whichfixesitintime yet 110 id 1 50 170 180 this does not apply in the case of breaking wave phenomenon. PROBABILITY 0F INVERTED EQUILIBRIUM 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 frequencythatwé musthave a feelfor loo 120 160 180 these unfamiliar measures. Figure 14 shows socs general descriptions of wave types and 0INT PROBABILITY 0F CAPSIZE AÑO ISVERTED indicatesbot-hthe frequency,ci,and the STABLE EQUILIBRILJII physicallength of thesE. Notethat the descriptions overlap and the zones are not welldivided;thatisnot important since the purpose of this graphical presentation is only to give a féél for the waves under discussion. Theieasonforintroducing this term for frequency.,ai,willbe clear shortly. FIGURE 13 - PROBABILITY 0F IÑVERTED EQUALIBRIUM WITH RANGE 0F STABILITY i) TYPICAL ENtP.GY SPECTRUM, SHOWING APPR0Y.iMATI0 B.Y A FINITE SUM 0F coM:pouEN IS i00000 idòo ib 0.1 WAVE LENGTH IÑ FEET

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 wavesin place and make a saw cut section throughthesurface a viewofthiscut would appear as Figure 15. b) SCALE 0F FREQUENCY SPEC'T'RUM This irregular profile can be shown to be made up of alarge number of component waves äll superimposed upon one another in the oceah resultiñg in the confused appearance. FIGURE 16 - ,KE-UP OF IRREGULM SEA

The grOwth ofa spectrum is'also key WM'E tounderstandingb'eakingwave behavior. HEIGHT TIME Waves fori as a by-prbdùc.t of the shéàr set up when wind blows across the sea surface. Thisbeginswith a complex patternof rippleswhich eventually grow tosirtall. waves, etc. The presence of the ridges of water causesa pressure distribútion which leads to energy being transféred into the FIGURE 15 - IRREGULAR WAVE HEIGHT TIME HISTORY ridge frOm the wind. However, many practicalsea states do not grow 'slowly enough, nor does thè wind In fact,a Figure 16 reproduced from blow steadily enoughto reachan orderly spectrum. 'A means ofestimating the shows such a seriesof Refèrence6 just effécts of non-u'niforn conditionsisiven regular waves which are these components in by thecumulative sea, state (CSS)diagram part(a)and ameahs ofexpressingthis proposedby VanDorn7. 'Such a diagram informationcalled 'a 'spectrum"inpart allow's. one to estiifte the relàtive (b). The spectrumisa wayof eaily portraying a confused sea where the energy severity of a sea state with an unsteady t each fequency, w,is plotted vertically wind time history. asin a histogram and the envelope of these An exampleofthe CSS represents the spectrum. This curve has a useofthe number of useful properties beyond that of follows' 'as related 'to Fastnet 79. compressingthe manyitemsregardingthe A tifflé' histOry of the wind experienced regular wave components into a single by thé Fasthet fleet andas charàcteHzéd display;the areabeneaththespectÑl by a number of sumftiary analysis is given in curve isa direct measure of the enègy in Figure 17. the spectrum and the shape tells us how the What is then required is to go fròrnsuch a continuousestimateofwind energy is distributed. speed to a wave characteration.

6 Principles 'of Nãval Architecture, Snarne, 197O.

7 Van Dorn, William, Oceanography and Seamanship", Dodd, Mead & Co., New York 1974. 47 It is interestingto correlatethis o O\ 055 diagram estimate with observations, and 50 / / \ the Inquiry8gives a great deal of data / fromparticipantsquestionnaires to allow this. 40 O X \ / The participants were queried regarding the significant andthe maximum /O A 30 wave height. Not surprisingly, the / estimates by the respondents ranged widely / as shown in Figure 19, butthe circular 20 data points define a frequency polygon in each case which is near the CSS estimate; in fact the tendency to overestimatewave 10 height is belied by this comparison. Perhaps the most surprising factor is that a measurable portion of the respondents

NO0 MIDNIGHT NODO cited a significant height so far from the

13 JUNE 1 14 JUNE likely value that one must wonder whether the question was widely minunderstood. TIME IN HCU

FIGURE 17 - OBSERVATIONS OF FASTNET WIND STRENGTH TIMEHISTORY

The method suggested by Van Dorn entails breaking the wind speed record into OCEAN discrete time steps with an equivalent wind SCIENCE CSS ESTIMATE ESTIMATE speed throughout, and entering the CSS with the energy fromthe 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 RESPONSES (KNOTS)' contour labeled "20" for a / duration of four hours. This energy level // is then maintained while shifting laterally O tothe next wind speed (in this case .28 knots-, (2) and along that contour for its duration. When completing the entire process, (3) the significantwaveheight can then be determined using the right-hand 10 20 30 40 auxiliary scale; ihthis case the Fastnet ESTIMATED SIGNIFICAIJT WAVE HEIGHT IN FEET conditionsprobably were equivalent to a fully-developed sea (FDS) with a significant wave height of about 37-feet. a) SIGNIFICNAT WAVE HEIGHT

SEARCH RESCUE ESTIMATE

RESPONSES / \ / o0 o/° / .7. ç O 10 20 30 40 50 60

FEET ESTIMATED MAXIMUM WAVE HEIGHT IN FEET

WIND DURATION IN HOURS b) MAXIMUM WAVE HEIGHT

FIGURE 18 - CSS DIAGRAM OF FASTNET WEAThER FIGURE 19 -OBSERVATIONSOF FASTNET WAVEHEIGHTS

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

148 This same CSS method will be employed for this work were conducted;the scheme later in consolidating our capsize data involves generating a series of waves which from a number of catastrophies. combine at a predetermined location in the tank togive a brEaking wave front. The Another feature of the behavior photogPaphs inFigure 20 show clearly how irregular waves which causes great quikly this large breaker appears; the difficulty in thepractical realm is the time values given arefor a full-scale rapid appearance of large waves through the breaker related toa 40-foot yacht and a dispersive property of components. Since a foot breaker. particularly large wave forms from the instantaneouscombinationof a number of As mentionedearlier in this paper, componentseach traveling at a different the transfer of energy from wind into waves speed prior to their combination at a is complex and many (most?) actal sea location in the ocean, they appear states arenot "fully developed' in the seemingly without warning, and this feature terms of the oceanographer; i.e., the has been a strikingone mentioned by a product of a steady wind of unvarying number of observers. No better example of direction for sufficient duration to this property can be given than to show the transfer the energy into the waves in test tank surface where the capsizing tests 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

1 SEC AFTER BREAK

PHOTOS COURTESY U.S. NAVAL ACADEMY RYDROMECHANICS LABORATORY FIGURE 20 - PHOTOGRAPHS OF DISPERSIVE PROPERTY 0F WAVES

If 9 '- of thecontours is used as a measureof maturity.

During the non-stationary parts of irregular wave (i.e. when equi1ibriu between wind andwaves does not exist) behavior, a number of phenomenon with importance to capsizing take place.

The first of these is the rapid appearance of largeandsteep wavesupon increase of the windspeedin 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 a) SEA SURFACE UNDER 10-KNOT WINDS. had matured as shown in Figure 21 below; LESS TUA i PERCZNT OF HIGHER and that there waves were of short period WAVES ARE BREAKING and an accompanying great steepness.

22 70 20 1! 60

16 50

60 12

10 30

b) SEA SURFACE UNDER 60 KNOT WINDS 0000 1000 1200 1600 100 PERCENT OF HIGHER WAVES ARE TIME (AUGUST 17. 1969) BREAKI NG

FIGURE 22 - PHOTOGRAPHS OF SEA SURFACE IN FIGURE 21 - TIME VARIATION OF WAVE HEIGHT VARIOUS WIND STRENGTHS PARAIIETERS DURING HURRICANE CAMILLE

The Variation of Danger with Sea State.

All of the foregoing data has tended Van Dorn has shown a relationship toargue that the prediction of dangerous between wind strength andwave breaking breaking waves is a complex problem;it now behavior which is in concert with this kind falls tous- to make some application of of interpretation. Based upon his reported this data in a form which is to sufficient study of a large number of aerial simplicity to be attractive to the photographs, he postulatesan equation for yachtsman. the proportion ofthelargest waves that will be breaking according to the This task is paradoxical - we know fol lowing: thatthe phenomenoncannot beextricated from theirtime dependence (that is: a LB = 2V-20, o

9 Kirkman, K.L., Nagle, T.J.,and Salsich, J.0. "Sailing Yacht Capsizing', CSYS, 1983. the most basic diffiulty lies in the fact that large and breaking waves depend Figuré 23 thén gives contours of equi- catastrophy, that upon two independent conditions: large is lines which are waves in a maturesea state arenotthe estimates of the time befor ea catastrophy threat that is represented by more moderate is expected. In the case of Van Dorn, Figuré 23, waves with a sudden increase in wind the measure of catastrophy was strength. wave height buthepointsout the rather direct tie of this to a vessel With this qualification to what characteristi.c length as a predictor of follows out of the way,let Us prodeed to capsize. make the best of a difficult situation. Another way of integrating the Van Again Van Dorn provides a crucialkey Dorn catastrophic probability diagram is to in a proposal for estimäting catastrophic rilaké a slice at fixed FDSaììd examine the probabilities. The rilethod Should atuà1ly variation of catastrophic frequencywith be studied in detail in thecontext òf vessel size. Reference 7 andwill only be summarized here. PART III - DANGER AND SIZE Van Dorn uséd an estilnaté of the most probable value. for a maximum expected wave height passing a stationary observer: The Variation of Danger with Size

Let us now attempt to apply this general data to the case whee data exists Hm = 2JE logs N, (g) from a wide range of yacht sizes caught in more-or-less the same conditions. and combined that withthe formula which First, à view ofthe homogeneity of relates the average wave period to the time the. Fastnet storm requires expansion; much between waves to arrive at thefollowing has been said about how the larger yachts expression: 2 escaped the worst conditions in Fastnet by 0.54 Hm virtué of their locationon the course y (V/lO) relative to the smaller yachts, but lit-tie t = O.0O08(-) (10) in the analysis of the race supports this unequivocally. The data within the body of the Fastnet Inqu-iry related to the °worst" and the results further presented as weathershows a widespread occurrence of contours of encounter expectancy asshown Beaufort 10 and 11 winds, and the in Figure 18. reanalysis projected the strongest winds to have occurredthroughthe arCa so that, Notethat thé only tieto breakiñq while the phasing was indeed not wave probability is the subjective oiithàt simultaneous, pretty much of the course was is storm conditions the larest waves will sweptby winds of sufficient strengthto oe breaking. (See equation 8)). cause widespread breakers. Onthe other hand those around the rock and reaching for home might arguably have been on a favored cOurse.

60 In view of these conflicting data, and the difficulty of so-doing, no attempt has , 50 been made to correct the raw percentagesof 40 knockdown by size bands for lòcation on the course.

30 t If the Fastnet data on 81 and B2 A knockdowns are plotted against a background 3 i 20 of contours of encounter expectancy from ENCOUNTER EXPECTANCY Figure 23, some degree of correlation IN HOURS t. exists if the following specific rnanipulaiton are accepted:

The actual value of encounter time from the Fastnet datais 20 40 60 80 100 divided by à factor oF

WAVE HEIGHT IN FEET The encounter time from Fastnet. is taken class by class and is defined as: FIGURE 23 r- CATASTROPHIC PROBABILITY DIAGRM FOR LARGE BREAKING WAVES Y METHOD OF t= VAN bORN % caSizê/Dürat.iOn

51 1 .3 LE SE T 32 tÜDO Reanalysis of Incidents G 51 iOC2C -l.5L In light of this limted/ualified success,, is it possible to move toa more general characte°ation of thevàriation of with size?

In order to answer this broader 0.1 / question, the author re-analyzed all available published accents of accidents at sea related to overwhelming, knockdowns and capsizes within his possession. These included: G

0.0) 10 20 30 40 50 60

NAME 'TYPE LOCATION DATE BOAT LENGTH IN FEET 19-foot daysaik.r' Florida Coastal 1977

FIGURE 24 FASTNET Bi AND B2 KNOCKDOWN Doubloon 40-foot yawl Gulf stream 1964 ENtOUNTERS AS AFUÑCTIOÑ OFBOAT Puffin - foot yawl Medi terranean 1966 LENGTH Aba Biscay 1960

Tilly Twin Channel when t = encounter time in 1956 hours Wok000ilmç. 40-foot ketch Ou 1f s tream Aen pu s

% capsizes = % of yachts Morning Cloud

experiencing at least one capsize Ear le 60-foot ShOar Du 1f stre an by class Sting 29-foot sloop Flri60 Coastal 1h53

Duratiôn = length ôf storm, taken Soutn er, 36-foot 1oob Ne Zealand 1603 Riidef as 10 hours Mirebel 30-foot boop Gulf stream 1964

The corélation ïn this case Halcyon 40-foot schowner Du 1f s tre am 1981 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 for82 knockdowns fit the slope reasonably well fora curve of In each case, the FDS value was wave height = 1.5L. estimated using. the method introduced with Figure 18 previously, and the type of event Since certain aspects of this analysis was tabulated. These data, when plotted by are totallyarbitrary (ex: duration of vessel watèrline length make-up Figure 25 storm 10 hous) the values of wavé height which shows, in addition the following ara considered to represent only a relative i t ems. difference; i.e. a 20% increase tn. wave size seeriis to möve many resùltsfrdm 90 (i) A band of values degree wave input knockdowns to full representing Fastnet 79. capsi zes. Çontours of equi-catastrophy Twb cbmmnts. should be mäde about the as suggested by Vàn Dorñ; a first through exclusion of Class O data: the knockdowns and overwhelrinings and a second greaterby the factor deduced in Class O wassmallenough(about Figure 24 which seems to fit the capsizes. one-forth, the. size) comparèdto the others to give significantly A "zone of potential lessweight to theresults; in capsizes"wherein, for thecohditions of fact the B2 knockdown in O represented a single incident. existing ea state plus high winds capsizes have occurrèd in thepast. Class O wasarguedby some (as discussed above) to have been in This single graph, then, seers to different weather/on a diffèrent provide a practical guideline för point of sail. characterizing the variation of danger with yacht size. In the context of all of these mnipulations and qualifications, the It must be emphasized that this graph, Fastnet data seems to Supportthe equi- while appealingly simple must be carefully catastrophic proposalof Van Dornin terms interpreted with the f011owing specific of effect of physical size. qualifications in mind: 'èAPSIZES- \\

B2 IMPACT CAPSIZE I J

BOAT LENGTH IÑ EET

FIGURE 25- RELATIONSHIp OF REPORTED CÀÏASTROPHIES TO FDS WIND SPEEDAND BOAT SIZE

The (i) 'Zone of Potential Capsizes" This danger coÌTIes from: isnottobe confused with a prediction thattheywilloccur. Asexplainedin great detail with the text, o lossofconfidenceinthe, rather short- yacht resulting livedmixes ofstrongwinds on topof in existing niòderatewaves seem to be a most subsequent i nappropriate dangerous combination,but others possibly seamanship, are important. o trapping of crew members hooked-òn on deck, (2) The lengthscaleforspecific boats should probably be a weighted length o problems associated as givenisthesection: "Size Rating with Rulé", (7). watertight integrity, and o damage/destruction The variationof dangerwithrangeof of stability mechanical systems intended foruprightoperation,ex: loss of engine, crankcase A danger associatedwithrange of oil. stability conies from the need fòr an extraordinarilylargewavetore-right a Using datafrom'Reference 10, and, yacht withgreat stabilityinverted which combining this with the resultsin Figure conies with a small range ofpositive 23, a feelfor the time trapped inverted stability. can be reconstructed.

53 The -esults of uing these dataare An Èqui-Safety Standard shown i Figure 26 and the ftllowing can be concluded from that figure: Let us now investigate the implications of somesort of size-varient o In conditions where capsize standard of capsize safety; the form chosen of a yacht become likely, for illustrative purposes is that of a great danger of relatively constait time for probable stàble long period of inverted equilibrium regardless of size. stable equilibrium is associated with alow range Simply stated, the lârge vessel i.s of positive stability. allowed to remainstable invertedfor an amount of time porportioned to its a o The behaviôr i.s highly non- advantage in expected encounter of linear, so that as a capize -if it i teh timés more resistant practical mattér all yachts to capsize in a givèn sea condition as with a range of stàbility measured by the expected ençounter time it- exceeding 140-degrees will may therefOre stay upside down ten times as reright almost instantly. long when the capsize cOmes.

o Yachts with a range typical thisnotion may seemillogidal, but of the lower edge for IOR perhaps it is no less so thanallowing yachts may be trapped for boats with a two order of magnitude greater period aprbaching 5 minutes proclivity to capsize over other to race with 2 minutes likely. Side-by-side asin 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 supportthenotion thatsomehow a l&rge 20 yacht be given some credit for its greater 18 40-FOOT YACHT AD KNOT SOS WIND capsize resistance. 16 S PE E D i Using thedata for cpntructihgthe TIME TPADPED 12 O FASINET EXPEP.- 1'VCP.TEE ii curve of inverted equilibrium time, a 10 IENCE JTES 'i 8 relationship of ranöe of positive stabilty with size can be defined asin Figure 27. Note that the 30-footer is allowed an equilibriumtime of a few tenths of a minute while the 40-footer getsa minute, 90 100 110120 130 140 150 160170 180 the 50-footer about nine minutes,and the RANGE 0F STABILITY 60-footer an hour-and-a-half. Notealso that it is the slope of the line which is of importance, and the locàtion is arbitrary. FIGURE 26 - VARIAtION OF TIME STABLE INVERTED WITH RANGE OF STABILITY

I I -

"+ 20 FOOTER To those whofind the derivationof N this estimate tootorturous to accept at N 4. 30 FOOTER face value, consider thedata from the which was discussed in RANGE DF N Fastnet fliquiy POSITIVE detail ïn Reference 11. The times dan only STAB I LI TV 40 FOOTER be guessesundersuch conditiön,but, to N quote the inquiry: N 50 FOOTER !'These five reports(of inverted 4- stable equilibrium-Ed) give grounds N for concern abqut the ultimate self- N righting ability of certath: boats and 6Ò FOOTER 'I- a full stability analysis of two boats,one of a type whichreported remaining inverted för fiveminutes ¿ z:: and another which reported very rapid MINUTES STABLE INVERTED self-righting was commissioned.'

results of that stabilitystudy The FIGURE 27 - RELATÏONSHIP OF SIZE WITH RANGE OF aré shownonFigure 26 labelled 'Fastnet STABILITY FOR EQUAL TIME INVÉRÏEb Experience.

11 Claughton, A., and Handley, P.,'An Investigation into the Stability of Sailing Yachts in Large Breaking Waves", University of SöuthamPton, Jan 84. 514 If we now desire to consider a rollt starboard(windward) and layon specific value of range of stability with beam ends (80-85°angleofheel). Boat size, a replot of the. data cah be rnadeas remainedinthispositionwith a goqd in Figure 28.In this case, the values for portion of spinnaker and10 or so of pole equal probability-time, inverted is in water until force on pole caused repesented by the curved contour bounding spinnaker car control chain to break. Pole the zone labeledcapsize zone'. 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 completelysubmerged and 'grinders" were hanging vertically from the pedestals ipo (and maintaining a deathgrip on the handles, one Shoúld add)!! 160

140 REQD = 160-L. MINIMUM, 1200 The weather associated with this C = 120 incident was reported as wind 20 gusting to KN0C00W1 30. 100 ZONE CAPS I ZE 80 ZONE -C 60 4°

20 C If äne postulates a constant range of 10 20 30 40 50 60 stability minimum to prevent knockdowils of 120-degrees thisis shownin Figure 28 as LENGTH IN FEET thestraight-upper bound dfthe zohe labeled "kñockdòwn zone". FIGURE 28- PROPOSED CRITERIA FOR RANGE OF STABILITY OF OFFSHORE Ifonethenaccepts a slope midway YACHTS between the two asreasonable 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 Frdm other wörk on knockdown capsizes 17-,itappears from energy consideratiàns L = equivalent length as pér (7). that ifyachtsareto resistknockdowns, especially when carrying lightsails,the This would seem Iike a rational righting moment characteristics need minimuol for yachtswhfth will participate attention in a manner which make a minimum in true offshore events. value for range of positive stability fall out in the area of 115 to 120 degrees. Let us check the implication of such a standard upon an existing Grand-PHx tOR Förthose whocannotappreciatethe yacht. need forthisinbig boats,a withdrwal eport by a 60-föoter in the St. Pete-Fort Figure 29 shows a sketch of Lauderdale Race of 1984 is instructive: currently competitive tOROne-Tonner, and the result of requiring a range of stability "At approximately 1340 EST while of thisiaçht of 130-degrees. The designer i-urining under spinnaker ad full main, boat has -estimated that the result would be to entered violent roll cycle. On deep roll reduce internal ballast to an amount usually to port boat buried end of boom and associated tk,trimming ballastand that mainsailpreventerheld boiiinwater. the keel piôfile would be altered as shown Boom apparently collapsed as boat took deep by the dashed line.

12 Kirkrnan, K.L., "Ultirate Stability in Small Cruiser/Racers", July 1983. LOA 10-O" LWL 31-3" BEAM 13-3' DRAFT 7'-5" DISPL 14,400"

BEFORE MODIFICATION ATER MODIFICATION

RANGE .0E STABILITY 118° 1 300

OUTSIDE BALLAST 4300 6600

INSIDE BALLAST 28 OO 500

FIGURE 29 - IMPACT OF STABILITY CRITERIA ON ONE-TONNER

CONCLUSIONS while not sufficient tomancate a capsize, suggests thatone might occurandisso consnon to off,hore races thatyacht design Thi.s report presents a means for must reflect what is estimating the équivalent known règarding size of a reducing risk through achangeindesign specific yacht as related to capsize parametrs and the construction and vulñerab.ility, gives data on the outfitting of yachts mustprepare them for environmental conditions where capsizes this ultimate tèst. might be exected, énd shows the particularly troublesome result ofa smàll range of stability. The particular problem of iverted s.tà bility is so debilitating as to cry for imme- It wOuld seem a simple matter to make diate rule chanês tO reduce beam and lowerVCG. these calculations fOra paticulér yacht and decide on this basis to stay home from any races where a creditable storm having an FDS inthe zone of capsizes for that sizeislikely;bûtofcoursewith an uhderstanding ofthe,complexityofthis ACKNOWLEDGEMENTS latter process will probably come reluctance to so simplify. Thispaperis an overview ofrécent Of what use,the,is the infomation research in capsizing contained herein? and summarizes contributionsfromJoéSal.sich andJohn Zseleczky of the U.S.Naval. Academy Hydro The note began as an effortto Lab and Andrew MacGruder, Kn Weller,and determiné whether historical pecedents John Wright of USYRU. 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 ona more rationalbasis thanlength anda formulae BIOGRAPHY has beenpresentedto do so; aformula whichiskindtorollmoment of inertia, displacement, and to low center of gravity The authoris é graduateof Webb Institute of NavalArchitecture andisan and harsh toward wide beam. active offshore .ai1or. He isa member of the SNAME SmallCràft COmmittee,Chéirman Further, an accompanyiiig range of stability is suggested. of T&R Panel SC-i (Sailing Yachts & Ships), a Director of the SNAME/USYRU Joint Research Project on Safety frOm Capsizing, Finally, the reanalysis of storm amemberoftheUSYRU MHS Committee, a incidents has shown that whenever the wind member of IOR Research Còmrnittee and blows sustained for periodsatover 40 Safety-at-Sea Committee, and the CCA knots the zone pf potential capsizes isat Technical Corrimittee and Bermuda Race hand for manyyachts. Thiscondition, Committee.

.56 APPENDIX B.

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 resistancescreening 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 afunction of length, beam, roll moment of inertia, and VCG location, and range of stability, a function of beam arid VCG location.

fri a study of yacht Gharacteristic (See Appendix A),as rElated to these measures, the following conclusions seem supportable:

1. Historical precedent., and a detailed analysis of capsize iricident, support the not:ion that a yacht o-f normal proportions, having a waterline length of approximately 30 feet. seems. to be a good minimum "size". This seems to bè true because it gives reasonably low probability o-f capsize in true offshore passages.

Note.:In visualizing thé concept o-f"capsize size" for boats o-f other than normal proportions, it will be helpful to review the -following general results from calculating the "capsize size" for a number of different boats:

o a modern yacht o-f moderate displacement and beam has à capsize. size near her physical size (length LWL.). (example: F3 -- 32 vs. 30.) o an old-fashioned heavy yacht will have a capsize size approximating twice her physical size. (example: Navy Yawl - 9 vs. 30)

57 o an extreme yacht in beam/displacement will have a capsize size approximately half her physical si ze. (example: OLS 30 -- 10.5 vs. 27.5)

For reasonable capsize resistance a range of stability of:

160 degrees - L' (L' in feet)

would result in a standard o-f equal time inverted. For work on knockdowns, a range of stability of approximately 120 degrees seems to be a minimum to preclude sail--force induced capsize.

A minimum range o-F stability necessary to limit the time stable-inverted to around two minutes, in seas at the threshold of capsizing seems to beapproximately 120 degrees.

A difficulty in applying these criteria at the present time is that the available data - particularly under present IOR measurement practices- does not include sufficient hull form de-finition to characterize either range o-f stability or actual displacement.

3. DEVELOPMENT OF SCREENING FORMULA: In considering the criteria described in the section above. the available measurement data, and the yacht characteristics that show LL in both capsize size and range o-f stability, the availability and recurrence of beam data (reinforced by the findings at the University of Southampton) drew attention to the possible merit in a criterion that would select against disproportionate beam and light displacement in the form:

Maximum beam / Cube root o-F displaced volume where some maximum allowable value would serve as the screen.

Such a formula would deal with beam, moment o-F inertia in roll (which is closely tied to displacement), and size - in the sense that SIL values tend to decrease with yacht size..

It remained to select a suitable screen value, and to verify that surrogate data (i.e. IOR measurement values) would be appropriate. The use o-F surrogate data in particular the IOR data for dispiacement was invest-igated by calculating the following 'uantities for the entire R/MHS common fleet:

B MAX (MHS) Screen (MHS) 1/3 (Displacement volume, meas. trim)

B MAX (IOR) Screen (IOR) 1/4 (DSPL 1(0.9 x 64))

(Note:DSPL/0..9gives appròx. displacement of lOP boats).

A graph of the, correspondance, for randomly-selected yachts, ppears as Fig. B 1, and the correspOndance is excellent throughout :he range of screen values.

Perhaps of equal importance is the fact that the error in the OR "DSL" correlates with range o-f positive stability in the ollowing sense: o-F the entire USYRU lOP fleet on which hull line5 Jata exist to calculate range of stabili:ty:

Nocase exists for a yacht having arange of positive tability e'-ceeding 120 degrees where thesubstitution of actual isplacement -for lOP "DSPL" fails to lower the screenVaiLle tO an cceptable level(as defined below); and

No case exists -For a yacht having a range o-f stability ess than 12Ö degrees where that 'yacht can meet a criterion of

160 degrees -L (lOP) or range of stability.

The rational selectiOn of a maximum allowable screen value was 'er-Formed h the following basis:

A plot o-F capsize length and margin above 160 - L' was repared for representatiVé yachts, Fig. B 2. On such a plot the iagonal shown represents increasing rislof both capsize and inverted table equilibrium.

A section cut of Figure B 2 . representing risk vs. screen

59 /0 2.0 /0 ,0 cD°' /Q / gO o / c f4U EcN B-1(soR) e4p54e¿(/VC171, 'rILrM MGI) Zo o -20 value. was prepàréd as shown in Fig. B 3 Where the risk equal tö just meeting 16Ö - L' is plottedthereon., the scréen cutoff of 2.uÖ indi catad is

4.. FROF'OSED FORMULA:

Based upon the development above, the follòwing is proposedas an addition to the ORC SpecialRegulations:

In order tò eligible toparticipate. in a race of Category 1., a yacht must have a capsizescreen value less than or equal tó 200 as given by the following far-mula:

B Max Capsize screen value = 1/3 DSPL /(0.9 x 64.0 n Yachts unable to pass this screen may bé permitted to substitute the displacement value inmeasurement trim in place of the bracleted termin the denominator in the screen f cbrmul a.

Yachts still unable to pass the revised screen may, by presentation of an estimate*of capsize length grèater than 30 0 feet. and arange of stability greater than 160degrees minus capsize length. beaccepted for Catégory 1races.

Performed in accordancewith the methodsoutlined inAp pendi> A of the Final Report ofthe SNAME/USYRIJ Safety From Capsize Committee In the event moment of inertiais not readily calculable,, it may be estimated from the displacement using the relationship shOwn below: Displacement Moment of Inertia =

35.5

where moment of inértia isin pound feet, and displacement is in pounds The formula is derived from FigureA - 4 on page. 24 of the Setònd Ïnterim Reportofthe Directors of the NAME/USyRu Safety From CapsizeCommittee).

62 z. ¿I J.G o ACuRE R I K 3 REFERENCES

The first group of references is a list of earlier publications on casizin by authors associated with th roject:

i. Stephens, Olin J. II, Kirkman, Karl L. and Peterson RobBrt S.: "Sailing Yacht Casizing". CSYS. 1981.

2. .Kirkma.n. Karl L.: "Sailing Yacht CaQsizin SNAME New England Section. March 1982.

3. Kirkman. Karl L. and Salsich. Joseph O., "SNAME/USYRU Safety Erggr Egr.t" Ancient Interface XII, 1982.

4. Kirkman Karl L. Nagle Toby Jean. and Salsich Joeph O.: "Sailing Yacht Cagsizing". CSYS 198! (Note This paper forms the Appendix of Reference 5).

5. SNAME/USYRIJ Joint Committee on Safety From Capsizing: Interim .Reort ôf the birectors April. 1983.

Salsich., Joseph O., and Zseleczky. John J.: "Exerimenta1 Studies of CaQsi:ing in Breal.ang Waves" Ancient Interface XIII. 1983.

Kirkman Karl L., "Ön the;Avc-idance of Inverted Stable Euilibriurn" Ancient Intèface XIII. 1983. SNAME/USYRU Joint Committee on Safety Erom Öapsi2ing: Second Interim ReQort of the DïrectorsJune. 1984.

Kirkman, Karl L.. the Effect of SLze As Related Cagsize Resistance". SNAME Southeast Section. Sept 19ë4 (Ñòte - This paper forms the appendix to this report). Strohmeier, Daniel D. "Fastnet Disaster Cagsizingtud", SNAME Metropòlitan Section. Feb. J, 1985.

Other References:

Forbes, Sir Hugh; Laing. Sir Maurice; Myatt.. Lt. Còl. James; '1979 Fastnet Race Inguiry"RYA. RORC. 1979

Motcea, S.. Shïmamato. :5., and Fujino. M.. "CasizingÈxaer.iment on a Totally Enclosed Lifeboat" Second International tonference on Stability of Ships and Ocean Vehicles. tokyo, October. 1982

6/4 Claughton, A., and Handley., P., "AnInvestigation into the Stability of Sailing Yachts in Large Breaking s"Wo1-f son Unit, University of Southanipton, January,1984.

Lin, W. M., Newman, J. N., yue, D.K. "Non-linear Forced Motions g± Floating Bodies", 15thSynposium on Naval Dynamics, Sept. 1954

Hayes, Bruce "Interim Report n 1aht Qradius Studi", U.S.N.A. Hydromechanics Laboratory ReportFeb. 1985

(Note: The foregoing list gives thereferences that are cited in the main body o-f the report. Appendix A is a complete technical paper.and in it are cited various references, some the sameas those above and some not listed above. Papers re4erred to in Appendix A may not carry the same numbers listed abovefor the sáme. papers when re-f erréd to inthe main body. Thus when looking up a reference from the main report., theforegoing list should be used. When looking up a referenceas cited in Appendix A, the reference- system there should be used).