Sohmitke and Jones 



Consider now the case where a hydrofoil ship is travelling at 

 speed U into a head sea. The wave elevation spectrum, expressed 

 in terms of frequency of encounter, is 



*. ( y;) = »("> (19) 



1 | 2U o" 



with a similar expression holding for the transformed orbital velocity 

 spectrum, <J>^ ( w '). 



2 



«' ! = « + " U " (20) 



g 



is the angular frequency of encounter. <£' and 4>^. are plotted in 

 Figures 14 and 15 for U = 50 knots and V = 24 knots (Sea State 

 5). 



The white noise technique for simulating a random head sea 

 will now be described. The basis of this method is that a signal with 

 a prescribed spectrum can be generated by passing white noise of 

 spectral density 4> through a linear filter so designed that the 

 square of its frequency response, H (a>), has the desired shape. 

 Filter output is, then, 



$ (u) = H ( w) <J> (21) 



I I o 



In particular, the generation of waves with spectrum <£>' can be ac- 

 complished using a filter network consisting of three high pass filters 

 and two integrators ; the approximation to <i>' which is thus obtained 

 is shown in Figure 14. Taking the vertical orbital velocity to be the 

 input to the last integrator multiplied by a suitable constant results 

 in the approximation to <£' shown in Figure 15. Proper phasing bet- 

 ween wave elevation and orbital velocity has been achieved, while 

 also obtaining good approximations to the spectra. 



In head seas the waves seen by the main foil lag those at the 



304 



