Breslin, Savitsky, and Tsakonas 



Surface Piercing Hydrofoil Craft in Head Seas 



The impulsive response technique was also applied by Bernicker to compute 

 the heave and pitch time histories of a fully wetted surface-piercing dihedral 

 hydrofoil craft in irregular waves. The test model was a simulated hydrofoil 

 craft with twin surface-piercing dihedral foils placed symmetrically fore and 

 aft of the center of gravity. The surface wave profile was measured by a probe 

 located at 82 percent of the foil spacing ahead of the center of gravity. Pitch 

 and heave motions were measured about the center of gravity. 



The transfer functions for both heave and pitch were determined by Bernicker 

 from cross- spectrum analysis of tests in irregular seas. The complex transfer 

 function for heave and pitch, for a particular test speed, are reproduced in Figs. 

 9 and 10 respectively. The P(co) and Q(co) functions plotted thereon are used to 

 calculate the impulsive response function [Eq. (42)]. Since both P(aj) and Q(co) 

 are given in graphical form, an IBM 1620 program was used to evaluate this in- 

 tegral numerically. The results of these integrations are given in Figs. 11 and 

 12 which plot the impulsive response function in heave and pitch, respectively. 

 It will be noted from these plots that K( t ) does not vanish for negative values of 

 time and hence some future time of the surface wave input is required to evalu- 

 ate the convolution integral. Bernicker attributes the requirement of input for 

 negative or future time to the particular longitudinal location of the surface 

 wave probe used in these tests. Since the longitudinal position of the wave probe 

 affects only the phase component of the transfer function of the hydrofoil craft, 

 it is clear that the "system" impulsive response function is dependent upon the 

 position of the wave probe and, hence, is not unique to the craft characteristics. 

 As can be ascertained from Eq. (52) of this report, there is some optimum 

 spacing between the wave probe and test model which will result in an impulsive 

 response function that exists only for positive values of time. This optimum 

 spacing was not determined in Bernicker's paper. 



Figure 13 shows the results of evaluating the time history of hydrofoil 

 heave and pitch motion using the impulsive response functions of Figs. 11 and 12 

 in the convolution integral together with the surface wave time history i?^(t). 

 The solid lines are the original time history as taken in experiment, and the 

 discrete points are from the computer calculation. It is seen that the compari- 

 son, for the most part, is quite good. 



Bending Moment Time Histories 



In addition to computing motion time histories by the method of the impul- 

 sive response function, Dalzell also computed time histories of midship bending 

 moments on a destroyer in irregular, long-crested head seas. The analytical 

 procedure was identical to that previously discussed and the results are given 

 in Fig. 14. Once again the agreement between computed and experimental re- 

 sults is excellent. 



488 



