Davis and Oates 

 For a varying forward velocity 



a = a^[l + 2(G-Gj] + a^(l + G-Gj (45) 



this expression is derived as follows. Consider the instantaneous velocity 



where 



u^ = reference or steady-state velocity, 

 u = the perturbation of craft velocity, and 

 u^ = the horizontal component of wave orbital velocity. 



Now 



Vi . . 



o 



where 



(the normalised velocity perturbation). 

 Thus 



o Y . 



(w - x(9 + y(^ - w^) 

 a + 7 



1 + u - u. 



(1 + u - uj 



(46) 



Now steady lift L = 1/2 pU^' S„ x f(a,h) and unsteady lift = 1/2 p({]^+u)^Sx f(a,h). 



Normalising is based on u^ the steady-state reference velocity thus Cl„ is 

 normalised with respect to l/2°pU„2s and a = w/(U„ + u) . Therefore we have to 

 consider the variation in the product V^^ a; 



622 



