Two-dimensional planing at high Froude number

Abstract

This paper examines the flow characteristics of a body of small slope planing at high Froude number over a water surface. An equation is obtained relating the slope of the planing surface to an integral containing the pressure distribution on the planing surface. The equation is expanded for large Froude number and a solution is obtained by an iteration process. At each stage of the iteration process the integral equation of ordinary thin aerofoil theory is solved. The pressure distribution on the planing surface is derived as a series in inverse powers of the Froude number F, as far as the F−4 term. Computations are performed for the planing of a flat plate, a parabolic surface, and a suitable linear combination of these shapes which results in a flow without a splash at the leading edge.