Curiosities of two-dimensional planing

The traditional deep-water analysis of two-dimensional planing is studied in detail and applied to efficient splash-free and optimal profiles, as well as to flat plates. The methodology is used to analyze both free-to-rise and free-to-rise-plus-trim profiles. In some cases, the predictions exhibit unexpected discontinuous behavior for the lift, wetted length and other results, with respect to the parameters describing the curvature of the planing surface. These discontinuities are due to the nonlinearities inherent in the practical planing problem, as opposed to previous simplified analyses in which the wetted length was specified.