THREE-DIMENSIONAL VORTEX-LINE THEORY OF A HYDROFOIL OPERATING IN WATER OF LARGE DEPTH. PART 1. THE WAVE DRAG OF A SINGLE HYDROFOIL WITH PRESCRIBED LIFT-DISTRIBUTION

The bound-vortex drag was computed for different lift distributions of a single, straight bound-vortex line which, in conformance with Prandtls airplane wing theory, replaced the hydrofoil. The bound-vortex line was parallel to the undisturbed interface and approximately at the centers of lift of the wing sections of the hydrofoil. The analysis neglected viscous forces and assumed irrotational fluid motion everywhere outside the bound vortex and trailing vortex sheet. Equations give the drag for cases of very short, very long, and arbitrary span. A curve shows the drag calculated for Froude number NFr of 10.85 and a rectangular lift distribution. The arbitrary span equations include the cases of very large and very small NFrs. The problem of the optimum lift distribution of a hydrofoil is qualitatively discussed.