Understanding and Prediction of Ship Motions 



the measured wave height and the wave slope at the C.G. of ship is 77/2 - (w^/g)D, 

 and this gives 





and therefore, 



sAt = 



dcr(co) 

 dco 



KW g 



When the character of the frequency response, H(w), is known before we start 

 the computation, the above-mentioned value can be estimated. This is, however, 

 not the case usually. At that time, as is shown in Fig. 5, Tp can be taken as a 

 good estimate of sAt. This value can be decided after computing the cross 

 covariance function. Namely, in the case where the input is considered to be 

 fairly white in the range of our concern, we can obtain a fairly good overall 

 estimate of H(aj) by shifting the center of the lag window or the origin of the 

 time axis of the cross covariance function to that time point T where the maxi- 

 mum of the absolute value of the sample cross covariance function occurs. 

 Pierson and Dalzell [6] showed very interesting analyses for two cases, one for 

 wave measurements where the apparent low coherency between two wave meas- 

 urements was improved and another in which the coherency between the waves 

 and the ship response was improved. I have also described [7] the intuitive and 

 practical method to find the amount of shift. The above-mentioned theory shows 

 more generally the way to find the proper amount of shift. A large bias because 

 of the large phase shift which usually occurs at the peak of the amplitude gain, 

 induced by the use of windows, is prevented in this way. 



R«v(t) 



Figure 5 



103 



