Breslin, Savitsky, and Tsakonas 





(64) 



+ 2r 



where 



= maximum roll amplitude, 

 co^ = natural roll frequency of submerged body, 

 CO = wave frequency, 

 Vo = surface wave amplitude, 



h = depth to center of vertical fin on submerged body, and 

 i' = damping ratio in roll. 

 Since the wave orbital motion at depth h has an amplitude equal to 



then the response amplitude, A(c^)^, defined as the ratio of maximum roll am- 

 plitude to wave amplitude at depth is equal to: 



A(-)h = ^ 



(65) 



The phase angle, cp, between passage of the wave crest over the submerged body 

 and maximum roll amplitude of the submerged body can be derived from Ref. 5 

 to be: 



2^' — 



cp(w) = arc tan ^ " ~k ■ (66) 



The transfer function for the submerged body in roll is thus known (Fig. 7). 



0(0;)^ = A(co)^^ e^^^") = P(a;) + iQ( oj) 



where A(co) and (p(&j) are given by Eqs. (65) and (66) above. 



Evaluating the real and imaginary parts of the transfer function results in 

 the following: 



484 



