St4fM E (Aned SLL's Urtc 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.