Bessho 



For a simple example, the pressure distribution deduced from 



m(x,y) = (b2-y2) (l-x2) 



(17) 



is shown in Fig. 1. 



VERTICAL SCALE IS ARBITRARY 

 » " 5 . b 0-2 



X^./.ob 



Fig. 1 - Pressure distribution 

 of a wave -free potential 



By the way, there are wave-free distributions with finite displacement 

 (payload) in the two-dimensional problem, but their displacement is very small 

 compared with their static buoyancy for high speed. This means that there is a 

 large negative lift at high speed with wave -free distributions (11). 



In another way, the potential f(x,y,z) of Eq. (14) is always wave-free for an 

 arbitrary function m(x,y) without the conditions of Eqs (12) and (15), because it 

 satisfies the surface condition of Eq. (4), but higher order singularities than the 

 doublet must be introduced. 



Thus, an arbitrary large number of pressure distributions exist with the 

 same displacement and wave resistance as the following simple cases: 



1. The longitudinal line distribution along the two segments ly| = b, |x| < 1 , 

 which may be called the twin hull ship type. 



2. The slender ship as the limiting case b = of the above. 



3. The transversal line distribution along one or two segments |y| ^ b, 

 which may be called the planing surface type. 



778 



