| The two dimensional unsteady problem of a flat planing surface is analyzed based on Bessho's theory. The present analysis treats the effect of the time varying wetted length on the added mass and damping coefficient. When the reduced frequency becomes very small, the wetted length change approaches the displacement of the intersection of the planing surface and undisturbed water surface. In the limiting case of zero frequency, the wetted length change reduces to zero. It is noted that the damping coefficient by the present analysis indicates the negative value in the very small reduced frequency, as Bessho predicted before in his theory derived from the different point of view.;In appendix, the analysis by the perturbation theory in a mapping plane is carried out based on Woods' theory. The result turns out to be identical with the calculation by airfoil theory in which the wetted length change is not taken into account. |
