The spray volume shed by an uncambered planing hull in steady planing

Abstract

Earlier papers (Payne, 1981 a,b,c) have developed what might be called a virtual mass theory which in principle permits the forces on any planing hull form to be calculated. In the present paper, this methodology is extended to calculate the thickness and momentum of the jet or spray sheet thrown off by the planing surface. For a two-dimensional flat planing plate—the only case where comparison is possible—the theory gives essentially the same result as that of Pierson and Leshnover (1948). For a three-dimensional flat plate and prismatic hulls, the results seem physically reasonable. For the small trim angles associated with efficient planing, on a weightless inviscid fluid the total pressure drag of any hull can be reduced to close to zero by deflecting the jet rearwards and parallel to the undisturbed surface, the residual resistance being due to the cross-flow force which varies as (trim angle) 2.