A nonlinear hydrodynamic theory for three-dimensional planing surfaces at infinitely high Froude number is developed and applied to predict the wetted length, pressure distribution, lift coefficient and center of pressure.;Once the pressure distribution is obtained, the wetted area is predicted corresponding to the calculated pressure distribution. For the calculated wetted area the procedure is repeated and the pressure distribution is determined. The lift and center of pressure are obtained for the calculated pressure distribution.;Results of calculation using nonlinear theory are in good agreement with experimental data. The nonlinear effect is more significant at high trim angles and the theory is verified to be useful to predict the hydrodynamic characteristics of planing surfaces.;An integral equation is developed relating the shape of the planing surface to the pressure distribution on the wetted surface moving at high speed on the calm surface of deep water. The problem is formulated according to linear and nonlinear theory, resulting in surface integral equations of the first kind. The solution of the integral equations is obtained by mode approach, in which the form of the pressure distribution function is assumed with unknown coefficients. We solve for these coefficients of the pressure distribution function. The linear solution to the problem is the building-block for the nonlinear solution.
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