ABSTRACT 
A nonlinear mathematical model has been formulated of a 
craft having a constant deadrise angle, planing in regular waves, 
using a modified low-aspect-ratio or strip theory. It was 
assumed that the wavelengths would be large in comparison to 
the craft length and that the wave slopes would be small. The 
coefficients in the equations of motion were determined by a 
combination of theoretical and empirical relationships. A 
simplified version for the case of a craft or model being towed 
at constant speed was programed for computations on a digital 
computer, and the results were compared with existing experi- 
mental data. Comparison of computed pitch and heave 
motions and phase angles with corresponding experimental data 
was remarkably good. Comparison of bow and center of 
gravity vertical accelerations was fair to good. 
ADMINISTRATIVE INFORMATION 
This investigation was authorized by the Naval Sea Systems Command with initial 
funding under Task Area SR-023-0101 and completion under Task Area ZF-43-421001. 
INTRODUCTION 
Computer programs for estimating the motions of displacement ships in waves for all 
headings and speeds have been in existence for some time. Comparable computational 
schemes for planing craft do not exist except in limited and restricted cases. A program for 
planing craft would be quite useful to the small craft designer, providing a means for 
systematically exploring the effects of numerous design variations on performance of the 
craft in waves. With minor modification, the program could also be used to examine the 
merits of a hybrid craft design, e.g., a combination of planing craft and hydrofoil. 
Predicting the motions of a planing craft in wave’s is by no means a simple problem. 
The analytical description of a high-speed craft, planing in waves, involves several different 
types of flow phenomena, including planing; hydrodynamic impact, and, to a lesser extent, 
surface wave generation and hydrostatics. Also, the mathematics tend to become nonlinear 
rapidly as the motion increases or, like the real craft, can in some instances exhibit large 
instabilities such as porpoising. 
Development of a computer program that would take into account all of the previously 
described factors and would be applicable for a wide range of speed and wave conditions 
requires a careful and systematic study in several stages with appropriate verification at each 
stage. To lay the foundation for such a general program, a simpler problem has been 
