velocity of the forward motion, and the oscillatory displacement are considered. 



Ref, [29] call this as "displacement effect" and calculated the effect on the 



motions. 



Figs. Hand 12 show the three-dimensional effect, non-linear effect 



and displacement effect for the motion of series 60, C = 0.70. The respec- 



B 



tive effects are significant, but the agreement with the experimental value 

 in the totally corrected calculation is still unsatisfactory. 

 3) Small amplit u de ship motions 



Here it is assumed that the unsteady body displacements are small so 

 that the hull boundary condition can be satisfied at the mean position of the 

 ship. 



Large-Amplitude Ship Motion 



In linear ship-motion theories, it is assumed not only that the free- 

 surface conditions can be linearized, but also that the ship displacements are 

 small relative to the ship dimensions . The exact body boundary condition then 

 can be approximated by satisfying it at the mean position of the hull. However, 

 ship motions are not always small. In fact, they can be on the order of magni- 

 tude of the ship dimensions even in typically moderate sea conditions. 



So a method should be developed for predicting large amplitude ship 

 motions. This is a difficult non-linear problem both for the boundary con- 

 ditions at the hull or at the free-surface. Non-linearities resulting from 

 the large amplitude rolling motion influence both the hydrodynamic problem and 

 the equations of motion. 



In the hydrodynamic problem, the use of average wetted surface is no 

 longer justified as the geometry of the wetted surface changes significantly 

 during one cycle of motion. This means that the added inertia is a function 

 of the angular position and systematic experiments conducted by [37 ] indicate 

 that the added inertia of rolling mota n varies with the amplitude of motion. 



75 



