Numerical solutions are presented for solving the free-surface flow generated by a three-dimensional body moving beneath the free surface with a constant velocity at an angle of attack. The solution is obtained using a panel method based on the perturbation potential, which employs Havelock sources and normal dipoles distributed on the body surface and Havelock normal dipoles in the wake downstream of the trailing edge. A pressure Kutta condition is implemented to satisfy the equal pressure on the left and on the right side at the trailing edge. Numerical computations are done for an ellipsoid at zero angle of attack, a rectangular platform wing at a small angle of attack in the limit of zero Froude number. Free-surface flows and hydrodynamic forces acting on the submerged spheroid and parabolic strut are also calculated. Discussions are made about the validity of the present method.


Theoretical and experimental predictions of ship wave resistance have been important topics to naval architects since William Froude (1810–1879) suggested a prediction method of residual resistance. Michell (1898) derived an analytical expression for the wave resistance of a thin ship and alternative methods have been derived by many other researchers. Free-surface lifting problem occurs in the yawed motion of a ship. and the straight motion of SWATH due to the interaction between the two hulls and the steady motion of hydrofoil with a camber. However, it is somewhat difficult to include free surface effects in the analysis of the lifting problem, so in general the problem is solved either by simplifying the body geometry or limiting the body speed. Hess (1972) calculated the steady flow about a three-dimensional lifting configuration in an unbounded fluid using a surface panel method and applied it to analyze marine propellers later.

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