then valid but without any effect of the forward speed. It should be noted 

 that the diffraction problem cannot be treated in the same way, because the 

 assumption of the slow variation along the x-axis is no longer valid. The 

 diffraction in short waves will be discussed in another section. 



Hydrodynamic Forces in Heaving and 

 Pitching 



It is widely known that the hydrodynamic forces and moments acting on 

 oscillating ships are predicted by strip theory with fairly good accuracy. 

 However, the reliability of the strip theory is still open to doubt as 

 discrepancies between computed and measured results are observed occa- 

 sionally. These discrepancies may be attributed to the effect of the 

 forward speed and fluid motion in three dimensions. In the preceding 

 section, we have observed that both the forward speed and the three- 

 dimensionality can be taken into account within a plausible approximation 



1/2 

 of the perturbation scheme, if the forward speed is of the order of £ 



where £ is the beam-to-length ratio. 



The hydrodynamic forces are obtained by the integration of pressure 



over the hull surface. The fluid pressure in the near field is given by 



a . sa(2D) a ^(2D) a .(2D) a *(2D) 



3cj> 3<j) 3<j>. 3c() 3<j>- 



- - (p-p n ) ^mMd^ + d^ • t^ + u ir^ *ir- ( 141 ) 



p r r 1 dx 9y dy dz dz 



up to the order of 8e. The hydrostatic pressure is omitted because it is 

 simply determined by the geometrical relations. Although the third and 

 fourth terms are omitted in the usual linearized theory for oscillating 

 ships, they appear in the same order of magnitude as the second term, so 

 that they have to be retained if one wishes to take account of the effect 

 of the forward speed. The vertical force is given by the integral 



■If. 



F 9 = (P- Pn ) |f dS (142) 



2 ^ r 0' 3n 



54 



