Maneuvering Hydrodynamics of Ellipsoidal Forms

The hydrodynamical forces and moments acting on a triaxial ellipsoid moving in an incompressible and inviscid fluid are analyzed. The rigid ellipsoid is allowed to move in the most general manner with time-dependent velocity and six degrees of freedom. The force and moment expressions are obtained by applying the Lagally theorem to the image singularities system representing the body in the presence of exterior disturbances. First, expressions for the Lagally force and moment acting on a maneuvering ellipsoid in an unbounded medium are derived and then these expressions are generalized to include the effect of an exterior source moving in an arbitrary manner. It is also shown how the Lagally expressions for an exterior source can be used to obtain closed-form expressions for the hydrodynamical forces and moments acting on a maneuvering ellipsoid in the presence of an arbitrary exterior disturbance. The analysis, which is based on the application of ellipsoidal harmonics, is demonstrated in a simple case of propeller-hull interaction. Here the motion of the ellipsoid is restricted to the major axis, and the propeller at the stern is represented by an isolated sink in accordance with Dickmann's model. 'Practical expressions for the thrust-deduction coefficient, wake fraction, and propeller-induced vibration are then derived for ellipsoidal, spheroidal and spherical hulls..