Development of Empirical Equations for Planing Craft Motions in Irregular Waves through Genetic Algorithms

An approximate and quick prediction of planing boat performance in irregular waves is useful for verifying concept designs and for seeing the effects of speed, wave height and various geometric parameters on motions. Simple, but fairly accurate for initial design, empirical equations currently only exist for estimating vertical accelerations and added resistance, but not for heave and pitch motions. The present paper studies the effect of planing boat geometry parameters, speed and wave height on the resulting motions and accelerations. A genetic algorithm, a regression method that mimics natural evolution to optimize a solution, was used to develop the empirical equations. Data sets were taken from prismatic model tests by Fridsma(1971) and Brown (1980); and a free software tool, Eureqa, was used to generate several equations for heave, pitch, accelerations at the center of gravity and bow. The equations were narrowed down by hand picking and looking at trend graphs, and the final equations were selected on the basis of simplicity, accuracy and physical correctness. The accuracy of the newly generated equation was then compared against the existing methods, Fridsma's charts for heave and pitch and Savitsky's empirical equations for accelerations. Additional validation was performed using model results from Coast Guard 47 ft. MLB standard series and a few other newer hull forms tested in the Davidson Laboratory.