Yim 



T" 



CO 



V 



O + k O = 



m = SOURCE STRENGTH 

 HI = DOUBLET STRENGTH 



Fig. 1 - Image system of 

 a simple zero-wave ship 



proportional to the perturbation pressure on the mean free surface caused by a 

 double model of the same ship. It is found that the image system of the simple 

 zero-wave ship is very simple (Fig. 1). This image system can be applied to 

 build ships by tracing streamlines from the optimum singularity distributions 

 for bulbous ships. 



Through Lagally's theorem, it is found that the force equivalent to the stern 

 wave resistance of the symmetric ship is exerted on the doublet distribution 

 which is distributed along the stem line forming the bow bulb and which cancels 

 the regular bow waves. Thus the regular wave along the surface waterline of 

 the hull of an optimum bulbous ship may be very small. Yet, with the expense 

 of the force exerted on the bow bulb the stern wave energy can be propagated 

 far away. 



ASSUMPTIONS AND BASIC EQUATIONS 



We consider a Michell thin ship in a steady, incompressible, inviscid flow 

 with a free surface and with an infinitely deep bottom. We locate the origin of 

 the coordinate at the bow and on the mean free surface which forms the xy plane. 

 The flow at infinity is in the positive x direction. The z axis is positive upward. 



We use the solution (see Ref. 3) for the Laplace equation 



v'0 = , (1) 



where is a perturbation potential, with the conventional linearized boundary 

 condition 



(2) 



on the mean free surface z = 0, where k^ = g/v^, g is the acceleration of gravity, 

 and V is the flow velocity at co. The wave height i is 



682 



