On the Existence of Zero Form-Drag and Hydrodynamically Stable Supercavitating Hydrofoils

The linearized complex acceleration potential is obtained for a hydrofoil of arbitrary shape in steady motion beneath a free surface with cavity of infinite length in simple and compact form. Under appropriate limiting conditions, it is shown that the solutions obtained from this potential reduce to the known solutions of Green for a planing foil, and of Auslaender and Hsu for a flat plate foil with or without flat flap near the free surface. Using some numerical results obtained from the complex potential, it is shown that there exists theoretically a supercavitating hydrofoil with finite lift coefficient and zero form drag. It is also shown that there exists theoretically a supercavitating hydrofoil with stable characteristics when shallowly submerged; that is, the lift coefficient increases as the submergence increases. Possible shapes for these hydrofoils are suggested so that the free streamlines from the leading edges do not. intersect the foil surface (the hydrofoils are physically real) and so that the pressure on the pressure surface is everywhere greater than cavity pressure and less than stagnation pressure (except near the leading and trailing edges).