Breslin, Savitsky, and Tsakonas 



and where A(aj) is the amplitude function relating the wave amplitude to ampli- 

 tude of ship motion for regular waves of a given frequency w. 0(a;) is the phase 

 angle between the crest of a regular surface wave and the peak of the corre- 

 sponding sinusoidal motion of the ship. Dalzell found that the transfer functions 

 obtained in the cross-spectral analysis agreed very well with those obtained 

 from tests of the DD692 in regular waves over a range of speed- length ratios 

 from to 1.25. The experimental values of the transfer function (A(w) and ^(aj)) 

 for pitch and heave are summarized in Figs. 1 and 2 of Dalz ell's paper. 



Fancev used the transfer function obtained by Dalzell to develop the impul- 

 sive response function K(t) relating the motion of the destroyer at the LCG to 

 the instantaneous wave profile recorded by the wave wire located ahead of the 

 test model. As developed in a preceding section of this paper (Eq. (42), ex- 

 panded): 



00 



K(t) - —\ [P(^) cos cot - Q(co) sin cot] dco . 



Fancev performed this integration by a graphic numerical method and his re- 

 sults are plotted in Figs. 3 and 4 of this paper showing the heave and pitch im- 

 pulsive response functions of the destroyer at a Froude number of 0.187. It is 



Fig. 3 - Pitch innpulsive response function for destroyer in head seas 



478 



