Lewis 



The basic theoretical tool available to us is the principle of superposition 

 first applied by St. Denis and Pierson [2] to the study of ship responses to ir- 

 regular seas. The essential empirical data that make it workable are system- 

 atic model tests, such as those of Vossers [3,4], and observational data on ocean 

 wave spectra, such as those of Pierson and Moskowitz [5]. However, for prac- 

 tical application of even the best theory it is necessary to have a suitable calcu- 

 lation procedure. This may or may not be programed for electronic computer 

 computation. Furthermore, for practical people to accept the results of such 

 calculations it is necessary that they be able to visualize the factors involved 

 and understand the trends obtained. It is the purpose of this paper to describe a 

 convenient procedure whereby the performance of a ship in realistic irregular 

 seas can be predicted and then to show the sort of trends and conclusions that 

 can be obtained by the method. 



The work discussed here has been carried out largely in connection with 

 research sponsored by the American Bureau of Shipping and Society of Naval 

 Architects and Marine Engineers. The paper itself has been prepared under 

 ONR Grant Nonr(G)00063-64. 



NON-DIMENSIONAL REPRESENTATION 



It has been previously pointed out [6] that the dimensional characteristics 

 of the conventional form of presenting sea spectra and ship response curves 

 make it difficult to understand and interpret the results of the calculations, par- 

 ticularly when comparing geometrically similar ships of different size. Accord- 

 ingly, a quasi-non-dimensional method of presentation was developed at Webb 

 Institute based on a sea spectrum showing component wave slopes as a function 

 of the logarithm of wave length [6]. Since the original proposal was made, it 

 has been found that a suggestion of Dr. Y. Yamanouchi to use loggOj instead of 

 logg X. results in a truly non-dimensional representation which appears more 

 suitable for general adoption. Here w is circular frequency, 2tt/T, t is wave 

 period, and ^ is wave length. In this log-slope scheme not only is the sea 

 spectrum independent of the units used, but geometrically similar ships will 

 have similar response operators. Hence, it will be shown that the effect of ship 

 size and form, sea spectrum shape, etc., can be clearly visualized. It is unnec- 

 essary to convert to frequency of encounter as originally proposed [2]. 



In order to explain the new form of presentation, reference is made first to 

 Fig. 1 showir^ the transformation of a typical wave amplitude spectrum (a), 

 [t(co)] 2 vs CO, to log-slope form (c). The first step is the transformation from 

 o) to log^co base. This is accomplished by finding the increment on log^o) scale, 

 S(log oj) that corresponds to 8co, thus: 



S (log„a;) 



d (logg w) 

 do) 



So) 



Hence, for an incremental area to be the same in both systems, 



188 



