Empirical Equations for Planing Hull Bottom Pressures

Abstract

Recently there has been increasing interest in the fluid-structure interaction problem of planing hull bottom structure during slamming events. Significant work has been done in estimating the bottom pressures that occur during a slam and incorporating this into structural models of planing craft. In this article, empirical equations for the pressure distribution on prismatic planing hulls are developed, including both hydrostatic and hydrodynamic effects, deadrise variation, trim, and wetted length. The empirical method is based on relevant experimental measurements of planing hull bottom pressures that have been made over an 80-year period. This analysis may readily be extended to the impact problem by substitution of an equivalent planing velocity, which is discussed in the article. The end result is a closed form solution for bottom pressures on prismatic planing craft that can be rapidly calculated using a simple spreadsheet. The method is applicable for deadrise angles from 0 to 40 , trim angles up to 30 , and wetted lengths up to five beams. This wide range of parameters is significantly larger than most current models. The empirical method is modular, allowing for substitution of more accurate formulae as more data become available in the future.

Experimental and Numerical Research on the Influence of Stern Flap Mounting Angle on Double-Stepped Planing Hull Hydrodynamic Performance

“…A series of non-dimensional evaluation coefficients were applied during our data process. The nondimensional pressure coefficient Cp and torque coefficient CMΔ are specified in Equations (14) and 15: As mentioned previously, the stern flaps have an obvious influence on the pressure and movement distribution. Clarifying the characteristics of stern flaps is important in the analysis of the flap action mechanism, in order to evaluate the hydrodynamic characteristics of the stern flap.…”

“…A series of non-dimensional evaluation coefficients were applied during our data process. The non-dimensional pressure coefficient C p and torque coefficient C M∆ are specified in Equations (14) and 15:…”

“…A series of model tests on a double-stepped planing hull were carried out to research the resistance performance influencing factors of the hull. Besides the numerical method, other research has also been conducted focusing on the stepped planing hull [13][14][15].…”

Introducing a particular mathematical model for predicting the resistance and performance of prismatic planing hulls in calm water by means of total pressure distribution

“…Finally, P YSTAG / P N represent pressure distribution on the stagnation line. All these parameters are explained in detail by Morabito (2014). Regarding the range of applicability of these equations, the following range has been previously used by Morabito (2010) in his studies which may be considered as a suitable range of applicability.…”

Water Entry Hydroelasticity Analysis of Lattice Sandwich Panel With Imperfection: Simulation and Engineering Model

“…Early in 1929, Von Karman [1] firstly introduced a significant contribution on this subject. Following Karman's classic works on hull-water impact, a series of studies on the theoretical analysis of water entry problem have been reported (Wagner [2], Kapsenberg [3], Faltinsen [4][5] Morabito [6], Korobkin [7][8] and Abrate [9] et al). Due to the complexities of this problem (such as multi-physics interaction phenomenon, free surface tracking et al), only a few special cases of wedges entry water vertically at a constant velocity can be solved analytically.…”