Three-Dimensional Mathematical Investigation of Dynamic and Hydrostatic Pressure Distributions on Planing Hulls

A mathematical model is utilized in order to calculate three-dimensional pressure distributions on planing hulls. This type of modeling is able to determine the hydrodynamic and hydrostatic pressures acting on the bottom of these hulls. As a result, the total 3-dimensional pressure exerted on the planing hull as a sum of hydrostatic and hydrodynamic pressures can be evaluated. Empirical equations introduced in previous works have been used as the fundamentals for the present mathematical modeling method. The obtained results are compared against available experimental results and results of empirical equations in order to validate the proposed method. The outcome of the -squared tests conducted on these comparisons shows favorable accuracy of the results. After evaluation of hydrodynamic pressure, the effects of trim and deadrise angles and wetted length on the 3-dimensional pressure distribution are analyzed. Finally, the total pressure on planing hull and the effect of velocity coefficients are studied. 1. Introduction Determining the exerted pressure on the planing hulls is essential to the study of their dynamics. By computing this pressure, it becomes possible to calculate the lift force, center of pressure, vessel’s dynamic, and water spray. Complexities concerned with 3-dimensional pressure distributions have made their direct calculation improbable, if not impossible. Therefore, a common approach is to first measure the pressure distribution using 2-dimensional longitudinal and transverse solutions which can be later used for calculation of 3-dimensional pressure distribution acting on the planing hull. Additionally, experimental methods can be used for calculation of pressure distribution in this type of vessel. Among these experimental works, results of Kapryan and Boyd [1] and Smiley [2, 3] are of high importance. On the other hand, Wagner [4] used analytical methods to evaluate pressure distribution over a wedge in a water-entry problem which is identical to the pressure distribution acting on an infinite planing plane. It was proved in Smiley’s experiments [3] that the longitudinal pressure distribution on the side sections of the center line is less than that on the other sections. Based on these results, empirical equations for evaluation of longitudinal pressure distribution were proposed. Later, Kapryan and Boyd [1] showed in their experimental studies that pressure on planing hulls will be reduced with an increase in the deadrise angle. With the advances in computational and computer resources, mathematical modeling methods for the