wetted surface of the hydrofoil it is assumed that both the camber and the angle of attack are small quantities of the first order squares and higher powers of these quantities can be neglected under this condition since u03b4 0 the cavity which starts from an arbitrary chordwise location on the upper surface and the trailing edge of the bottom surface of the foil extends to infinity with a slender configuration it is reasonable to assume that except for gravitational effects which are neglected the cavity is aligned in the undisturbed flow direction on the cavity boundary it is assumed that the flow velocity is equal to the free stream velocity and hence u 0 on the wetted surface of the hydrofoil the flow must be tangent to the solid surface hence equ7 where y is the hydrofoil coordinate on the free surface y h the linearized bernoulli 39 s equation becomes u g u03bb v 2 u2243 0 when the froude number based on the wave height u03bb is very large on the wetted surface using bernoulli 39 s equation and linearizing it follows that equ8 the above boundary conditions are shown in fig5 by the use of a schwarz christoffel transformation the line y h and the semi infinite line y 0 x gt 0 is transformed onto the real axis of the v plane where v v 1 iv 2 while the whole z plane is mapped onto the lower half of the v plane as shown.