- IdlT 



Breslin, Savitsky, and Tsakonas 



and again 



CO 



e ^ ^ dr = 2Trh{a> - cS) 



and 



CO i oi ' \ a' I g i &) I w I f 



2tt \ t (co ) e e ^ ^ - Irri {oS) e 



OJ ' = - CO 



Then 



00 CO , \ci>\ ai\ ^ 



^,(t;^,0 = ^j .(r';^,o| '^"^y^ ~^e^(^-')da.d.'. (38) 



- CO - CO 



Now if one wishes to refer this to the wave at the surface 



CO -a.'^C 



^(t';^,0 = ^1 ^(t";^,0) I e ^ e''^'^'^'-^") do^'dr". (39) 



- 05 - 00 



The same integration procedure applies and the previous result is obtained, 

 namely, 



2, 



:,(.;f,0 = 5^1 ,(r;f,0)| ^'"' ^''"^ e'—'^e'-'-'d.. (40) 



Thus it is seen that the response calculated in terms of the subsurface motions 

 as given by (38) is the same as that given by (40) when the subsurface motion is 

 referred to that on the surface by Eq. (39). 



Evaluation of the Impulsive Response Function for Ships 



It is clear from Eq. (35) that the impulsive response function for coupled 

 motion depends upon a knowledge of the response of the system to normalized 

 forces and moments at discrete frequencies, i.e., one must know the frequency 

 response operators, or what is called the transfer function. One may seek to 

 evaluate ^^q^^A and ^0^{oS) from theory alone or from experimental records of 

 model responses in either regular or irregular waves. 



At present one may calculate the transfer functions from theory by using 

 Grim's [10] methods for estimation of the body coefficients, eight of which are 

 frequency dependent. Gerritsma's [11] recently completed work on determina- 

 tion of the body coefficients has given strong support to the procedures used by 

 Korvin-Kroukovsky and Jacobs [12] for ship motion calculations. It is to be 

 noted that, in dealing with a "lumped" heave-pitch and pitch-heave response op- 

 erators, it is also necessary to specify the normalized excitations as functions 



470 



