Contributions to the virtual mass theory of hydrodynamic planing

Virtual mass solutions (Payne, 1974, 1980a) for the normal force on a flat planing plate gave good agreement with experiments for wetted length to beam ratios (l = l/b) in excess of unity. In an article by Payne (1981a), the region below l = 1 was faired into the known two-dimensional solution (infinite aspect ratio) by means of a bridging function. A subsequent study (Payne, 1980c) of the virtual mass of a rectangular plate led to another bridging function which seemed to be more funamental, and might give better agreement between theory and experiment below l = 1 than was the case in the work by Payne (1981a). In the present note this is shown to be so. And although the lift curve slope of a wing and a planing plate (when the cavity lift contribution is neglected) are identical for slender planforms (l > 1) and in the two dimensional flow (l = 0) the plate is found to have a higher lift curve slope in between. There is no relationship between the pitching moment of a planing plate and an aerofoil.