High speed theory for the planing of a flat plate at high Froude number

A harmonic function K is introduced. The harmonic function is the Green function only in the limiting case when Froude number goes to infinity. The Green's theorem together with K yields the solution of the first order potential. Then we obtain the angle of attack asα∼WρLWB1U,where LW,B,W are the wetted length, breadth and weight of the plate. The hydrodynamic pressure is zero at the leading edge and increases toward the trailing edge where the pressure is infinitely large due to a logarithmic singularity. The lift L is a monotone function of Froude number and approaches W as Froude number goes to infinity whereas the drag D decreases paradoxically to zero in the limiting case.