We seek the solution of the planing of a flat plate at high Froude numbers by a perturbation procedure. The angle of attack of the plate is assumed to vary with the speed of the plate in the present study. A harmonic function K is introduced for the solution of the first-order disturbance potential which becomes the Green function in the limiting case when the Froude number tends to infinity. We get the solution of the first-order potential from Green's theorem applied to K and the first-order potential. Then we obtain the asymptotic solutions of the angle of attack ??, lift L and drag D as follows: ?? ??? sqrt(frac(W, ?? LW)) frac(1, U), frac(L, W) ??? 1 - frac(2, ??) [1 - ln (2 sin ??)] ??, frac(D, W) ??? ??, where ?????1. Here W, LW, and U are the weight of the plate per unit width, wetted length, and speed of the plate, respectively. ?? 2008 Elsevier Ltd. All rights reserved.
Chung, Y. K., & Chun, H. H. (2008). On the planing of a flat plate at high Froude numbers in a two-dimensional case. Ocean Engineering, 35(7), 646–652. https://doi.org/10.1016/j.oceaneng.2008.01.004