Doctors 



even more dramatic than in deep water. More striking, however, is 

 that for this and for all other two-dimensional cases studied, the 

 wave resistance becomes negative beyond a certain velocity in finite 

 depth. The resistance then asymptotically approaches zero. (The 

 ordinate in this figure is plotted on an arsinh scale. ) The depth 

 Froude number at which the negative peak resistance occurs in shal- 

 low water has been found to be 



F = 1+2 Vac/gd (36) 



The resistance of an accelerating three-dimensional pressu- 

 re distribution is shown in Fig. 7a (deep water) and Fig. 7b (finite 

 depth). In deep water, the wave resistance shows similar, but less 

 marked, effects due to acceleration as does the corresponding two- 

 dimensional case (Fig. 6a). In finite depth, there is again a strong 

 reduction in the main peak as well as an elimination of nearly all the 

 low-speed oscillations. However, there is no region of negative wave 

 resistance -thus indicating the influence of the diverging wave pattern. 



IV. RECTILINEAR MOTION IN A TANK 



IV. 1. The Potential 



We now consider the problem of an ACV moving along the 

 centerline of a rectangular tank of length L and width B . The 

 initial distance at t = between the starting end of the tank and the 

 coordinate axes xyz fixed to the model is taken as a . This pro- 

 blem is crucial to the testing of models, as one must know the effect 

 of tank walls. For instance, during steady motion in an infinitely long 

 tank, Newman and Poole showed that the effect of tank width in the 

 neighborhood of unit depth Froude number to be importance (see Eq- 

 (4)). 



We utilize Eq (22) for the potential in a horizontally unbound- 

 ed region, and satisfy the additional condition of no flux through the 

 four tank walls, by employing a system of image ACVs as shown in 

 Fig. 8. We consider first only the array of distributions on the tank 

 centerline, and later on apply the boundary condition on the tank 

 sidewalls. The potentials for the individual distributions, <p , are 



related to the primary potential, 4> , as follows : 



4> ( £ > y» z, t) - (f>( £ - nL, y, z, t) for n even, 



48 



