sue this method to fruition; namely, the predic- 

 tion of service conditions of ships. 



I think there is however a very definite place 

 for the fine work presented in this paper. It 

 seems reasonable that the ultimate solution to the 

 ship-behavior prediction problem lies in a com- 

 bination of theory and experiment. Theory must 

 define the broad general aspects of the problem 

 while experiment verifies and modifies the sim- 

 plified mathematical model. As an illustration 

 of the value of the material here presented, there 

 has just been reported by Cartwright and Rydill^^ 

 the results of an investigation which clearly 

 demonstrate the importance of full-scale experi- 

 ments. The roll and pitch of a vessel (RRS Dis- 

 covery II) were measured in long-crested seas for 

 12 headings and at 63^ knots and also head-on 

 to short-crested storm seas. Waves were re- 

 corded by a ship-borne wave recorder. The rec- 

 ords were spectrum analyzed and the amplitude 

 distributions predicted. At the same time the 

 motions were computed by the simplified equa- 

 tions of motion and again by the "advanced" 

 equations which include coupling terms. Their 

 findings are worth repeating: "The practical re- 

 sults are compared with theoretical relations 

 derived by methods which ignore certain effects 

 but are simple to apply, and advanced methods 

 which estimate some terms with greater precision 

 but at the cost of greater computational labor. 

 The theoretical results are in general quite close 

 to and never very different from, the practical 

 results, the differences largely being due to statis- 

 tical variations." 



To be sure, the results of Cartwright and Rydill 

 are encouraging, but nevertheless their experi- 

 ments were not comprehensive and certainly not 

 conclusive. This paper, however, comprises a 

 cross section of material that covers almost every 

 aspect of the ship-behavior problem that has been 

 investigated theoretically. In addition, the data 

 have been reduced to their probability distribution 

 functions. If now theoretical predictions were 

 made for each pertinent case analyzed in this 

 paper and compared with the author's results, 

 the work of Cartwright and Rydill will have been 

 carried a good deal further in the direction of veri- 

 fication of theory. This appears to be the most 

 profitable approach, at this time. 



Prof. B. V. Korvin-Kroukovsky, Member: 

 The author has presented an excellent paper which 

 invokes admiration, but also a certain amount of 

 criticism. 



The positive side is evident: A tremendous 

 amount of careful observations were made on 

 several ships under many different conditions and 

 the results were analyzed skillfully and presented 

 in a compact and clear set of graphs. The very 

 complex and varying conditions of sea and ship 

 motions are shown to follow a simple statistical 

 law on the basis of which certain conclusions and 

 predictions can be made. 



On the negative side is the over-concentration 

 on pure statistics, and the lack of any reference 

 to the physical nature of the situation (except in 

 the excellent section on endurance strength). 

 This aspect of the problem is taken up in the pre- 

 vious literature on this subject which should not 

 be ignored. Two papers will. be cited here as in- 

 structive examples. 



The first is by A. J. Williams''' who has shown 

 a comparison of the Rayleigh distribution with 

 experimental observations on the rolling of a 

 ship at sea. The importance of this reference lies 

 in that, although the term "Rayleigh distribution" 

 was not used, the expression was derived for use 

 in this particular case on the assumption of sea 

 waves being composed of a number of waves of 

 different amplitudes A and phases <i> traveling in 

 one direction. The waves were of a somewhat 

 peculiar type in that the amplitude A was as- 

 sumed to be a function of time, while the angtdar 

 frequency o was taken as constant. Thus the ex- 

 pression was shown to result physically from an 

 event which has two degrees of freedom in A 

 and <6. 



It is clear from the derivation that it applies 

 directly to sea waves. In apphcation to a rolling 

 ship an additional physical factor enters in, that 

 of the ship response to waves. Thus it can be 

 seen that in using the Rayleigh distribution 

 several factors are neglected, most obvious of 

 which are the spectral composition of waves in re- 

 gard to the frequency, the weU-known variability 

 of wave directions at sea and the ship-resjxinse 

 factor for a specified type of motion (i.e., pitching 

 or rolling) and the direction of ship travel with 

 respect to the mean direction of wave propagation. 

 In view of these physical conditions, it is a pleas- 

 ant surprise that Figs. 2, 4, 6, 8, and 10, show 

 such a good agreement between the Rayleigh dis- 

 tribution and the observed data. Such discrep- 

 ancies as are found to exist should not, however, 

 be attributed to chance errors, but rather to the 

 failiu-e to use a distribution function corresponding 

 to the appropriate number of degrees of freedom 

 of the wave-ship system under consideration. 



As the second reference on sea waves the paper 



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