CURRENT PROGRESS IN THE SLENDER 

 BODY THEORY FOR SHIP MOTIONS 



J. N. Newman and E. O. Tuck 



David Taylor Model Basin 



Washington, D.C. 



ABSTRACT 



This paper describes current work towards a complete systematic the- 

 ory for the motions of a slender ship in a seaway. Part I contains an 

 introduction and a general discussion of the results which are obtained, 

 and presents calculations of pitch and heave response at zero speed. 

 Part II contains a complete derivation of the zero speed theory for har- 

 monic oscillations in the presence of oblique incident waves. Part III 

 contains a derivation of a more general theory with forward speed, for 

 arbitrary forced oscillations in calm water. A significant feature of 

 this paper is the splitting of the velocity potential and forces into parts 

 which are dependent on free surface effects, plus parts which corre- 

 spond to the motion of the double body in infinite fluid or specifically to 

 the case of a rigid free surface. 



1. INTRODUCTION 



A fundamental motivation of the theoretical physicist is his desire to bring 

 a sense of order to the physical world, by means of mathematical models which 

 are derived from the basic physical principles governing the problem at hand. 

 Practical problems in ship hydrodynamics have resisted this ordering process, 

 however, not because the basic physical principles were unknoAvn, but because 

 their mathematical representation has been comparatively intractable, at least 

 by comparison with most other problems in classical mechanics. The predic- 

 tion of ship motions in waves is typical of this situation, and in spite of con- 

 certed efforts we are still short of our desired goal of giving engineering pre- 

 dictions of ship motions from a rational theory. 



It is generally accepted that, for most purposes at least, the desired theory 

 can be attained by considering that the water around the ship to be an ideal (in- 

 compressible, inviscid) fluid, and by linearizing the unsteady motions (wave 

 heights and ship motions). Within this framework there have been several dif- 

 ferent approaches, which can be distinguished according to the assumptions 

 made concerning the hull shape and forward velocity (Table 1). At zero speed it 

 is possible to proceed without any assumptions as to hull geometry, and we 



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