TABLE OF CONTENTS As stated above, radiation forces are defined as the hydrodynamic forces (exclusive of hydrostatic) that arise as a result of forced oscillations of the body on otherwise calm water. The added mass and damping forces are the components of the total radiation force which are in phase with the acceleration and velocity of the body, respectively, in the frequency domain. Unfortunately, even with the assumptions of no viscosity and small amplitudes, there are no analytical solutions available for these forces for any cases of practical interest except for the limiting values of some simple forms at zero and infinite frequency (e.g., the sphere discussed above).
Fortunately there are a variety of numerical methods available to determine these forces. All are computationally intensive, but well within the capabilities of a modern personal computer. Probably the easiest method to understand is the "source distribution method". You should recall that a solid body of revolution moving in an unbounded fluid can be hydrodynamically modeled using an axial distribution of singularities. Distributing singularities on the body surface can accurately represent more general shapes. The function of the singularity is to produce a fictitious flow which will cancel the normal component of the fluid velocity (relative to the body) on the surface, thus satisfying the "no penetration" boundary condition. The strength of the singularity is thus determined by the normal component of the body velocity relative to the fluid.
For a floating...
