Hydrofoil Motions in a Random Seaway 



Z(t,x) = j cos I ojt - — X - A v/2<l)^(f) df . (31) 



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Equation (31) can be differentiated to give what can be assumed to represent the 

 vertical component of the water particle orbital velocity. Thus, 



w(t,x) = Z(t,x) = - [ sin fojt - — x-0jV2<l>^(f) df (32) 



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where the spectral density for the vertical velocity is given by 



(D^Cf) = (27rf)2 (t.^(f) . 



The hydrofoil ship in the random seaway 



The random seaway can be considered as a disturbance input to the hydro- 

 foil craft. These inputs induce motions, which are not present in calm water, 

 and which result from a combination of wave elevation, orbital velocities and 

 the forward velocity of the craft. If the reference coordinate system is chosen 

 fixed to the hydrofoil ship, then the effects of the seaway and craft velocities 

 can be combined together to produce wave elevation and orbital velocity forcing 

 functions which are functions of craft speed. This is accomplished by trans- 

 forming the original seaway spectra by a change of variable to produce new 

 spectra which are functions of frequency of encounter. 



To illustrate briefly, consider the coordinate systems as illustrated in Fig. 

 10. The moving coordinate system is designated by primes. The coordinate 

 transformation is then given by 



X = x' +Vt and Z = Z' (33) 



where v, the ship speed, is defined to be negative in head seas. 

 Substituting Eq. (33) in Eq. (31) gives 



Z(t,x') = j cos (co't - -^x' -0)v'2$^(f ') df ' (34) 



where the frequency of encounter co' is given by 



a,' = a.-X^2 , 2rrf' (35) 



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and the "transformed" wave elevation spectrum by 



•^z(f ) = 2V ■ (36) 



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 635 



