The motion of a simple wedge along the water surface

Abstract

The two-dimensional flow of a stream past a simple wedge partly immersed in water is investigated by linearized theory. The results are expressed in terms of a non-dimensional speed V = U(ρα/gL) ¼ , where U is the velocity of the stream, ρ is the water density, α is the incidence of the sloping face and L is the lift on the wedge per unit beam. As the speed increases from zero, the immersion of the wedge increases to a maximum and becomes small at high speeds; the frictional drag increases to a maximum at the hump speed and falls to a constant value at high speeds. Notation X, Y co-ordinates (figure 1) U stream velocity x = X/l = – cos θ U H hump speed y = Y/l V non-dimensional speed U(ρα/gL ) ¼ 2l loaded length p pressure on surface h immersion of rear edge L lift per unit beam 2l 0 loaded length in floatingcondition D resistance or drag condition D p pressure drag h 0 immersion of rear edge in floating condition D f friction drag D w wave resistance ρ density of liquid D j jet resistance g gravitational acceleration C p pressure coefficient 2p/ρV 2 α incidence of sloping face C f skin friction coefficient k = gl/U 2 CL lift coefficient L/ρU 2 l a semi-amplitude of waves