Evaluation of Motions of Marine Craft in Irregular Seas 



K(t) from Irregular Wave Tests 



One method of obtaining the impulsive response function from motion rec- 

 ords is to first calculate the frequency response function from the relation 



or 



^(^') = —^ (45) 



and then to proceed to K(t) as indicated above. 



Another procedure is to use spectral analysis techniques which have been 

 applied to the statistical analysis of ship motions. The spectrum of the model 

 motion is given by the calculation 



m^^) 







2^ J 



lim 



T^ CO 



1 r''' 



^ J X(t) X(t-T)dt 



dr 



(46) 



and the wave height spectrum is similarly provided by 



^ J lim ^ J 77(t) T](t-T) dt 



riioi^ 



dr . 



(47) 



The amplitude of the frequency response function is related to the motion 

 and wave spectra by 



|$(a)) 



iX(a;J 



and the phase cp is calculated from 



cp(&Jg) = tan'* 



where is the cross-spectrum defined by 



Im 0(a) ) 



Re 0(a. ) 



(48) 



(49) 



V^(^'e) 



2^ J lim Y J T7(t) X(t - r) dt 



dr 



(50) 



473 



