1. INTRODUCTION 



Motions of a ship advancing with constant average speed in regular waves are 

 predicted theoretically by using approximate theories based on the slenderness of 

 ship forms. These theories are the strip theory,, most useful in the short-wavelength 

 regime, and the complementary low-frequency slender-body theory; these complementary 

 slender-ship approximations have recently been united and extended in a unified 

 slender-ship theory valid for all frequencies. A detailed mathematical presentation 

 and historical account, including extensive references to the relevant literature, 

 of these slender-ship theories may be found in Newman. 



Agreement between strip-theory predictions and experimental measurements has 

 been found, in a large number of cases, to be sufficient for many practical purposes. 

 This, and the relative mathematical and computational simplicity of the strip theory, 

 have made that theory the most widely used method for predicting ship motions. 

 Indeed, the theory, with the improvements of the recently proposed unified slender- 

 ship theory, seems likely to continue to provide a very useful and practical tool 

 in the future, even if significant improvements in computer performance are made and 

 calculations based on a three-dimensional theory become more practical. 



Notwithstanding its many merits, the strip theory evidently has limitation, and 

 in some cases there is a need for potentially more accurate calculations based on a 

 fully three-dimensional theory. For instance, three-dimensional calculations would 

 be useful for predicting the pressure distribution on a complex bow shape, such as 

 one equipped with a bulb or a sonar dome. 



At present, fully three-dimensional calculations represent a difficult task, 



and indeed only a very limited number of numerical results have been obtained by 



2 3 4-7 



only a few authors: Chang, Guevel and Bougis, and Inglis and Price. Further- 

 more, these sets of numerical results are not entirely consistent: while agree- 

 ment is good for some hydrodynamic coefficients, discrepancies are very large for 

 other coefficients. This lack of consistency suggests that the accuracy of three- 

 dimensional calculations may be difficult to control, as is the case for the problem 



8 

 of wave resistance. 



Three-dimensional calculation methods are based either on numerical solution of 



an integral equation for the velocity potential or on related assumed distributions 



of singularities (sources or/and dipoles) on the ship surface. Different integral 



*A complete listing of references is given on page 27, 



