THE MINIMUM PROBLEM OF THE 



WAVE RESISTANCE OF THE SURFACE 



PRESSURE DISTRIBUTION 



Masatoshi Bessho 



Defense Academy 



Yokosuka, Japan 



INTRODUCTION 



The minimum problem of the wave resistance has no solution in thin ship 

 theory, and this means that singularity distributions exist which have no wave 

 resistance. On the other hand, the wave-free distribution belonging to the usual 

 functional class has no displacement, but wave -free distributions with a finite 

 displacement exist in the theory of the slender ship, although the wave-resistance 

 integral has no finite value in such case (1,2). This apparent contradiction is 

 caused by the confusion of the functional class of the distribution, but the intro- 

 duction of the function of the wider class or the higher order singularity makes 

 the theory more fruitful (3), 



This paper explains such a situation of the problem with respect to the sur- 

 face pressure distribution (1,4,5). The theory is very similar to the thin and 

 slender ship theory. 



By the way, this theory is the case in which the ship surface and the pres- 

 sure are given in the framework of linearized theory, so that it may be interest- 

 ing to compare it with the so-called second-order theory. 



PRESSURE DISTRIBUTION 



Consider a uniform stream with unit velocity, and Cartesian coordinates, 

 taking the origin at the water surface, the x axis as positive toward the upstream 

 side, and the z axis as positive upward. If a pressure p(x,y) acts over the 

 surface s at the water surface, some wave motion occurs. Let <P(x,y,z) be the 

 velocity potential of this motion; then it must satisfy the conditions (6) 



-p(x,y) % - — 0(x,y,O) - gZ(x,y) , (1) 



'■^ ax 



p(x,y) = outside of S, (2) 



775 



