Hydrodynamic Lift on Boats

Abstract: Boats float supported only by buoyancy at rest and at very low speeds. As the speed increases, a hull capable of planing makes a sharp transition to a lifting surface while plowing up the bow wave. As the speed increases further the boat planes, and at a high enough speed buoyancy becomes negligible; hydrodynamic lift carries the weight. More generally, any flow past a lifting surface generates a force perpendicular to the flow once the flow separates from the trailing edge without backflow (without vortex formation). Wings, hydrofoils, sails, and propellers are examples of lifting surfaces. The idea of a planing hull as lifting surface has been discussed inconclusively in the literature. We provide evidence for the onset of lift before planing and also produce an empirically correct lift coefficient for the planing of a v-bottom (prismatic shape) hull at high enough speeds that the wet surface area is confined roughly to a triangular shape near the transom. Our model follows our calculation of the lift on a fully submerged delta wing hydrofoil. The lift is reduced once the hydrofoil pierces the air-water interface.