- p {itog 1 



(x)+Ug^(x)} {-B(x)+VS(x)} dx 



(154) 



Because of Green's reciprocal relation, which can apply to x and ip , such 

 as 



f X z 3^ dc = I 

 J C(x) J C(x) 



i 2 



' a - i 



z dn 



dc 



the second and third terms are cancelled. Therefore, we obtain 



F_ = - p 



dx {to (z^-xiJO+iwUip} | X "T~r dc 



-- 2 J 



dx (z -xlji) 



C(x) 



\p -r-r dc 

 z dn 



C(x) 



+ P 



-iO){B(x)-.VS(x)} +U 2- (B(x)-vS(x)} 

 dx 



g-^x) dx 



(155) 



1/2, 

 The last term is derived by integration by parts. If we assume U = 0(e ) 



2 

 and omit the term of 0(6e ), the second term drops out. A similar ex- 

 pression is obtained for the hydrodynamic moment about the y axis. The 

 first term indicates the result obtained by the strip theory, and the other 

 terms give the effect of the forward speed and the three-dimensional motion. 



Numerical Results of Radiation Problem 

 at Zero Forward Speed 



Although numerical analysis works when the forward speed and the 



effect of three-dimensionality are present, no published result of this 



kind is known so far. There is a rather comprehensive result, on the other 



hand, for the case of zero forward speed by means of a similar formu- 



31 

 lation. It is obtained simply by letting U = in the original formula 



for finite speed with no substantial difference in the method of numerical 



58 



