1/2 

 if terms of order 6 £ are retained. The terms involving the effect of 



steady forward potential prevents the straightforward solution, so that 



this case should not be used for the practical purpose of prediction. 



1/2 

 If the forward speed is low, namely U = 0(e ), the ratio of wave 



length to ship's length is of the order of e. Since each term in the 



three-dimensional Laplace equation has the same order of magnitude, its 



two-dimensional version is no longer valid. Therefore, the strip theory is 



not applicable to the diffraction problem in the longitudinal waves. An 



alternative method for the diffraction problem in short waves will be 



discussed later. 



Wave Pressure and Hydrodynamic Forces 



As was mentioned before, the diffraction problem requires not only the 

 integrated total force, but some local quantities such as wave pressure at 

 each point on the hull surface and the distribution of forces along the x- 

 axis. If we write 



<b = A + d> (202) 



T y D T w 



the periodical pressure on the hull surface is given by 



-i(p-P )-i.* + u|i + U3/|4 + U^|f (203, 



up to the order of 6 £, if U and a) are both of the order of unity. Al- 

 though the third and fourth terms are omitted in the usual theory, they 

 appear in the same order as the first and second terms, so they have to be 

 taken into account if the effect of forward speed is considered. The 

 vertical force is given in the same way as in the radiation problem, so 

 Tuck's theorem can be applied again. The vertical force is given by 



F = P 



= P 



jj (^M^fi^if)!^ 



3x 3* 



iux|> -~ -U<|> -^ ) dS 0: 



73 



