Linearized Three‐Dimensional Planing in Deep and Shallow Water

ABSTRACT The traditional analysis of three‐dimensional planing is studied in detail using potential‐flow theory together with linearized free‐surface conditions. The work is extended here to the case of water of finite depth. The planing surface is modeled as a traveling pressure distribution. Thus, the analysis solves the inverse problem of finding the pressure that generates the hull shape. Specifically, the pressure is discretized as a two‐dimensional array of overlapping tent‐function pressure elements. The current study includes a careful study of the convergence properties of the method with respect to the numerical integrations needed to compute the response functions from the pressure elements, and also the number of elements needed to represent the pressure accurately. The predictions are compared with the available towing‐tank model experimental data for both flat and prismatic planing surfaces. There are encouraging predictions for various trim angles, deadrise angles, length‐to‐beam ratios, and Froude numbers. Additionally, the theory correctly predicts the dependence of the lift, drag, and the location of the center of pressure as the water depth is decreased.