Current Progress in the Slender Body Theory- 

 problem can be reduced to a sequence of two-dimensional problems.* An addi- 

 tional drawback of the strip theory is that, by hypothesis, it cannot be rationally 

 applied with forward speed. Slender body theory, on the other hand, attempts to 

 account for longitudinal changes in the flow, either from interference effects or 

 from the effects of forward motion, but at the expense of transverse interference 

 phenomena since the beam is assumed small compared to a wavelength. 



Thus it would seem natural to apply the techniques of slender body theory, 

 which have been well established in aerodynamics, to the prediction of ship 

 motions in waves. However, this seemingly obvious ;inion was not consummated 

 vintil recently. Now progress is being made by several workers and we can 

 optimistically hope that a rational and successful theory for predicting ship 

 motions in waves will be forthcoming in the near future. 



This paper contains an outline of some recent developments toward the 

 above goal. Our results are still incomplete, and to some extent disjoint, but 

 they are sufficient to suggest the practical utility of a truly rational approach 

 to ship motion predictions. To support this statement we will show numerical 

 computations for practical ships which, at least in parts of the domain of inter- 

 est, are as accurate as available experimental data. Our paper will be divided 

 into three parts and these will be presented in the inverse order from that which 

 is customary, so that the most important results are exhibited before we become 

 engrossed in the details. 



The Essential Features of Slender Ship Motions 



Our theory assumes the ship to be long compared to its beam and draft, to 

 be floating on the surface of an ideal incompressible fluid, and to be excited in 

 unsteady motion either by external forces or by an incident plane progressive 

 wave system. We assume moreover that the iinsteady motions are of small 

 amplitude compared to all of the other characteristic lengths (i.e., the ship 

 dimensions and wavelength) so that linearization is possible. Finally we as- 

 sume that the wavelength of the incident wave system or the waves radiated 

 from the body is of the same order as or greater than the ship's length. The 

 last assumption ensures that the transverse dimensions of the body are small 

 compared to a wavelength and greatly simplifies the interference effects be- 

 tween points on the ship's surface. 



It is convenient to introduce a small parameter e, which may be defined as 

 the beam-length ratio of the ship. The slender body solution of our problem is 

 then developed by formulating a boundary value problem for the appropriate 

 velocity potential, whose gradient represents the unsteady fluid velocity vector, 

 and then finding an approximate solution of this boundary value problem which 

 is asymptotically valid for small values of e. The first order slender body 



*However, if incident waves are present from any angle other than abeam, the 

 resulting two-dimensional problem is governed by the wave equation rather than 

 Laplace's equation. This complication is frequently overlooked in analysing the 

 exciting forces from strip theory. 



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