Murthy 



and an explicit solution is possible. 



The velocity potential due to the air cushion now derived can 

 be shown to be of the same general form as that previously obtained 

 for the acceleration potential of an amphibious ACV in Reference 1. 

 There is, however, an additional term now in the form of a surface 

 integral over the longitudinal planes of the hulls which provide a ver- 

 tical barrier along the lateral sides of the cushion. 



The Green's function to be used for steady motion is 



G(x f y f z;* f »!,*•) = [(x - I f + (y -V f + (z -f ) 2 ] - 



- (x-0 2 + (y -v) 2 + ( z +n 2 + 4^ Re 



tt/2 L 

 r r - p(z+ T) + ip (x- £ ) cos 



/ / -2 cos My y,) sin ^ d0 ' (6-22) 



Z A e - p V cos 



M B ** 



where M is the contour along the real axis of the complex p-plane 

 passing above the point 



a 2 



p = p = ° sec 6 



° v 2 



The integrand in (6-22) is complex, but as we are interested 

 only in the real part of the integral, we must seek the contribution 

 from the real part along the real p-axis and that of the imaginary 

 part along the semi -circle above the simple pole 



2 



p = k sec 6 

 o 



where k = g/V . We thus obtain after evaluating the residue 

 o 



G(x,y,z;£,»,n = [(x - { ) 2 + (y - n ) 2 + (z - f ) 2 ] 



P 



t? t ? i ,. 2 ' 1/2 



(x - | ) + (y - i? ) + (z + f ) 



.7^ 



rfi 2 



/ -k (z+ T ) sec ^ -| 



/e sin k (x- % ) sec 



o J o L ° J 



148 



