In case of longitudinal motions there are two cases which can be 

 considered as dynamic lift, namely, 



a) One is that proportional to the pitching angle 



b) The other is that proportional to the ratio of the velocity of 

 heaving to the advance speed. 



The latter may contribute considerably to the damping force. 

 2 ) Linearization of free-surface conditions 



It is assumed that the wave slopes of the incoming as well as ship 

 generated waves are sufficiently small so that the non-linear free-surface 

 boundary conditions can be replaced by the linearized condition. 



Ref [4 5] dealt with hull-shape non-linearity and showed that the 

 calculated amplitude of motion differs considerably from that of the linear 

 calculation. Ref [44], by calculating the second-order approximation of the 

 diffraction problem regarding the two-dimensional body, showed that when the 

 period of motion is short there are considerable differences from the first- 

 order approximation. Also Ref. [30] discussed about the hydrodynamic force 

 which is proportional to the product of the perturbed velocity due to the 

 forward velocity of the vessel and that due to ship motions and calculated 

 its effect on the motions as shown in Fig. 11 and IZ 



Ref. [29] concludes that the ship motion calculations must take into 

 account the non-linearity effect which is extremely important for slamming and 

 deck wetness. 



In the strip method, all the perturbed potential which are more 

 than the square are neglected. 



In the slender body theory, aside from the effect already stated in 

 the non-linear effect as discussed above, the existence of the effect of 

 the hydrodynamic force which is proportional to the product of the perturbed 



73 



