Vassilopoulos and Mandel 



0.5 



2g 



Fig. 70 - A versus S 



oscillating ship in a stationary fluid, the excitation forces and moments can be 

 determined by exactly the same arguments used in the calculation of the coeffi- 

 cients of the equations. There are, however, two distinct points of difference 

 which must be allowed for in the computation of the exciting loads: 



a. Whereas in the calculation of the coefficients of the equations of motion 

 the total force and moment are obtained by summing up strip contributions for 

 sections in identical flow, in the case of wave excitation loads consideration 

 must be given to the distinct flow which each section sees when the wave pattern 

 encounters it. In other words, differential exciting forces depend on the ship 

 section properties as well as the local static and dynamic state of the wave. 



b. At every section and hence on the whole ship, an extra force and moment 

 is brought about on account of the fact that the relative water flow at a given 

 section involves a pressure gradient which is typical of gravity waves. This so- 

 called "Smith effect" is due to the orbital motion of the water particles and must 

 be allowed for since the differential exciting forces at a given section depend on 

 whether the section is instantaneously on a wave crest or trough. The best ap- 

 proximate way of allowing for this effect is to consider in the calculations the 

 static and dynamic state of an "effective subsurface" rather than the actual wave 

 surface. Havelock has suggested [46] that the effective subsurface is located at 

 a mean draught equal to V/A^ or (Cg/Cyj,) H, a result which is accurate for wall- 

 sided ships. Since we shall compute the loads on the basis of two-dimensional 



340 



