The two examples taken from the previous liter- 

 ature have shown that ship motions in a seaway 

 follow certain weU-known statistical laws. The 

 present author collected much more data and pre- 

 sented the case so forcibly that no possible doubt 

 about this can exist. On the other hand, it ap- 

 pears to be clear that it is not advisable to con- 

 centrate completely on one method of statistical 

 presentation, as in doing so certain valuable fea- 

 tures of wave and ship motions or ship stresses 

 can be overlooked. In particular, a distribution 

 of a Rayleigh type should not be taken as an arbi- 

 trary statistical law of a fixed form, but the ap- 

 plicability of a given form to the problem must 

 be considered on a physical basis. The distribu- 

 tion will take somewhat different forms (i.e., more 

 peaked or flatter) depending on the number of 

 variables affecting the variate which is under 

 study. 



Dr. V. G. SzEBEHELY, Member: The writer wiU 

 begin his comments by quoting Dr. von Karman : 

 "The layman is amazed and the expert is left 

 wondering." We are amazed by the fact that 

 such a great amount of data could be organized 

 according to relatively simple basic laws. The 

 profession is grateful to the author for collecting 

 this useful information and we wish to congratu- 

 late him for the clear and orderly presentation of 

 the data. The amazement and wonderings of 

 the reader might justify the following questions 

 in order to evaluate the merits of the paper under 

 discussion. 



1 Why log-normal and why Rayleigh distribu- 

 tions? Haveother laws been tried also? Is there 

 a more basic physical law which governs the 

 phenomena and from which the foregoing named 

 statistical distribution laws can be derived? Does 

 the long-term distribution follow from the short- 

 term distribution, or to state the question another 

 way — should there exist in principle a definite 

 relation between the two distributions which, 

 after all, represent basically the same phenomenon ? 



It is suspected that the answer — to at least 

 some of these questions — ^is affirmative. 



2 How are the results of the paper to be used 

 to answer the ever recurring questions : What will 

 be the performance of a ship in a given sea? If 

 two sets of ship lines are given, which vessel should 

 be built for a certain operation? Will a ship with 

 a U-bow lose more speed in a state 5 sea than a 

 ship with a V-bow? What is the speed at which 

 slamming starts for a given design in a given sea? 

 What is the threshold for operation; i.e., what is 

 for instance the maximum speed and maximum 



sea state in which the pitch angle will stay below 

 5 deg? (It is possible that these questions cannot 

 be answered from the impressive amount of data 

 in this paper.) 



3 What is the real significance of the line giv- 

 ing the hull-girder stress distribution for a destroyer 

 in Fig. 9? Would this line be entirely different 

 for another destroyer? Do we have to measure 

 stresses for long periods of time on several de- 

 stroyers in order to find out the relative merits of 

 the various designs? Wouldn't it be simpler to 

 run several destroyers parallel in the same sea for, 

 say, 30 min and compare the results? 



4 An elaboration on the claim of the paper — 

 "to predict service conditions for ships" — would 

 be appreciated. What is the relative merit of the 

 following approach ? Determine the transfer func- 

 tions of a given vessel in regular waves on model 

 scale and then, using the energy spectrum of a 

 certain sea, find the expected behavior of the 

 vessel ? 



Answers to these questions wiU not destroy 

 thft appreciative amazement and might help to 

 guide the wonderings. 



Mrs. Margaret D. Bledsoe,^* Visitor: This 

 writer recently had the opportunity to perform 

 statistical analyses of motion records obtained 

 during full-scale trials of Dutch destroyers. It is 

 believed that these results might serve to cor- 

 roborate the work of the paper under discussion. 

 The analyses were performed both by using the 

 author's approach of assuming the motions to be 

 described by the Rayleigh distribution and by us- 

 ing the autocorrelation technique to find the asso- 

 ciated power spectrum. The two methods should 

 yield the same results for the total energy provided 

 most of the energy is concentrated in a narrow fre- 

 quency band, i.e., the assumption of the Rayleigh 

 distribution is valid. From a knowledge of the 

 total energy one can, of course, determine such 

 quantities as significant amplitude of motion, 

 average height of the upper tenth highest waves, 

 and so on. 



The analyses were performed for several samples 

 of pitch data where a continuous recording was 

 obtained for 10-min intervals. Of the samples 

 analyzed, some were obtained in head seas, both 

 moderate and heavy, and some were obtained 

 in moderate quartering head seas. Ship speeds 

 varied from 12 to 22 knots. The theoretical 

 Rayleigh distribution was computed and com- 

 pared with the experimental histogram and in all 

 cases the Rayleigh distribution was found to de- 



M David Taylor Model Basin. Washington, D. C. 



48 



