Three-Dimensional Planing at High Froude Number

Abstract

The steady motion of a planing surface of moderate aspect ratio at small angles of attack is considered. Linearized theory is used with a square-root type of pressure singularity representing the flow near the leading edge. An asymptotic solution for the pressure distribution on the planing surface at large Froude number (or small β, the inverse of the Froude number) is sought. The lowest-order term of the pressure distribution, obtained by setting β equal to zero, is found to be the same as the pressure distribution on the lower side of the corresponding thin wing. Higher-order terms in β are obtained by an iteration process. Explicit solutions are obtained to order β2 for rectangular planforms. Numerical results are calculated for rectangular flat plate planing surfaces of aspect ratios from 0.5 to 2.0. It is found that for large aspect ratios the lift coefficient is reduced by the gravity effect and for small aspect ratios it is increased, the dividing aspect ratio being about 1.5. The results compare reasonably well with experimental data.