the prospective shipowner might frown at the 

 rationality of the refinements especially when the 

 weight of the hull is increased over and above what 

 is safe past practice. The writer wishes to em- 

 phasize that improvements in the hull structural 

 design are made not so much by acknowledging 

 the existence of many complex parameters and 

 pleading for their acceptance for design purpose, 

 but in determining how important and really sig- 

 nificant they might be. Only research can separate 

 the wheat from the chaff, and it is here that inves- 

 tigations such as represented by the subject paper 

 can play their most important role. 



Mr. Wilbur Marks, ^^ Visitor: In recent years 

 there has been a flurry of activity in the field of 

 ship motions, hull stresses, and the like. Theoret- 

 ical developments, though not fully verified, 

 have reached the point where, given a particular 

 ship and seaway, certain ship-behavior statistics 

 may be predicted. One of the most prominent of 

 these theories is mentioned in this paper (15). 

 Although simplifying assumptions are used, the 

 mathematics take on such a formidable appearance 

 as the development progresses that the end result 

 of statistically reducing the motion spectra, in- 

 stead of providing a handy tool for ship-motions 

 prediction, has created rather an atmosphere of 

 uncertainty in many places. 



Following this work by St. Denis and Pierson, 

 a hue and cry arose, the substance of which was 

 the demand for a simplification of the treatment 

 and a set of rules (or graphs) from which a ship's 

 captain, for example, could tell immediately his 

 vessel's response for a given set of conditions. At 

 this writing no such simplicity has evolved. The 

 reason for this will be discussed. The fact re- 

 mains that, although the answers are obtainable in 

 principle, electronic analyzing equipment or ex- 

 pensive calculating machines are required. There 

 is little doubt that a prediction system, albeit sta- 

 tistical, that is simple to apply is needed. The 

 present paper attempts to solve the ship-perform- 

 ance problem by utilizing the experimental ap- 

 proach. The difficult task undertaken by the 

 author can be appreciated readily. If any aspect 

 of ship behavior under any particular set of condi- 

 tions is considered to be an "event," then the in- 

 finite population of events being investigated is 

 comprised of the different behaviors of all ships, 

 in all sea states, traveling at all speeds and head- 

 ings. The object of the experimental approach is 

 to describe the population by a law (or laws) 

 derived from a sample (or samples) whose proper- 

 ties are believed to be the same as those of the 



''■ David Taylor Model Basin, Washington, D. C. 



population. This then is the method used by the 

 author in his attempt at solving the problem. 



To be sure, the data collected are voluminous 

 and a determined assault on such a veritable moun- 

 tain of information is in itself praiseworthy. Yet 

 it is implied in the summary that, to answer the 

 question for a particular ship under particular 

 conditions, more data, either full scale or in the 

 model tank must still be collected. The fact is 

 that the sample analyzed here is not in itself 

 sufficiently adequate to answer all questions, but 

 is intended rather to point the way to the solution. 



There is little doubt that the analysis demon- 

 strates the applicability of the Rayleigh and log- 

 normal laws to the data sampled, even if the possi- 

 bility that other laws may fit the data as well, or 

 better, is not precluded. The difficulty lies rather 

 with the number E. It is this factor which deter- 

 mines the slopes of the straight lines which pass 

 through the origin and this must be known in 

 order to find the distribution of x for any par- 

 ticular case. For every possible combination of 

 conditions there is an E, and in order to solve the 

 seaworthiness problem a representative sample of 

 E must be obtained. Just how many are needed? 



Consider for a moment, the number of tests re- 

 quired to make up an adequate sample of the 

 population. The experimental variables might 

 be : (a) 7 ship parameters (hull oscillations, heave 

 acceleration, bow submergence, etc.) (b) 7 basic 

 ship hull designs, (c) 3 loading conditions, (d) 5 

 seaways, (e) 5 ship speeds and, (/) 5 headings. The 

 result is that 18,375 separate tests, either full scale 

 or in the model tank, must be made, in order to 

 characterize the population. Can data collection 

 on such a scale be practical ? 



Suppose for the sake of discussion such data 

 have been collected; what then? It will then be 

 required, as it was of St. Denis and Pierson, to 

 present these data in a simple form. If graphs of 

 ship performance, as a function of ship speed and 

 heading, are assembled, there will be 735 curves 

 through which a ship's captain might have to pore 

 and even then be faced with the problem of inter- 

 polation between different designs, loading condi- 

 tions and seaways. It is quite possible that the 

 presentation can be simplified and indeed the es- 

 tablishment of a central forecast agency, equipped 

 with high-speed computers or a punch-card sys- 

 tem, may solve the prediction problem but, as 

 long as prediction rests with ship personnel, the 

 data will necessarily be in a clumsy form, simi- 

 lar to those just described. This perhaps is the 

 reason why the theoretical solution has not yet 

 been reduced to a simple set of rules. By these 

 arguments, I feel that the author has assigned 

 himself a difficult task indeed, if |ie seeks to pur- 



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