singular Perturbation Problems in Ship Hydrodynamios 



2.3. Slender Body 



In the previous section, we considered the flow around a 

 slender body which was oriented with its long dimension perpendicu- 

 lar to the incident flow. Now we consider the flow around a slender 

 body which is oriented with its long dimension approximately parallel 

 to the incident flow. The same geometrical restrictions will be 

 applied to the body in this problem, nanmely, that its transverse 

 dimensions should be small compared with its long dinnension and 

 that cross-section shape, size, and orientation should vary gradually 

 along the length. 



Although both this section and the previous section concern 

 slender bodies in an incident flow, convention says that only this 

 section really presents "slender-body theory, " 



In ship hydrodynamics problems, slender-body theory has 

 been applied mostly to nonlifting bodies, i.e. , bodies not generating 

 trailing vortex systems. I shall limit myself here to such prob- 

 lems too. Specifically, I assume that there is no separation of the 

 flow from the body; furthermore, there are no sharp edges at which 

 a Kutta condition might be applied. The potential function should be 

 continuous and single-valued throughout the fluid domain. 



This restriction is not generally desirable. Certainly an 

 important aspect of aerodynamics is the calculation of lift on a 

 slender body which does generate a vortex wake; modern high-speed 

 delta- wing aircraft and many slender missiles are genuine slender 

 lifting bodies. There are several important ship-hydrodynamics 

 problems which may ultimately be best analyzed by a slender- wing ' 

 approach. Most important, perhaps, is the problem of a maneuvering 

 ship. An attempt is made in this direction by Fedyayevskiy and 

 Sobolev [ 1963] , but it is not very successful because they use the 

 conventional methods of slender- wing theory, and these break down 

 in application to wings which are not more-or-less delta shaped,* 

 A modern approach to slender-wing theory is given by Wang [ 1968] , 



Obviously, a ship is a "lifting body," but I think it is commonly 

 understood that the term implies a dynamic lift process, and that 

 is the way I use it. 



"Slender wing," "wing of very low aspect ratio," and "slender 

 lifting surface" are all equivalent terms in my usage. 



Conventional slender-wing theory can be used for wings in which the 

 span increases monotonically downstream, ending in a squared- off 

 trailing edge. If the incident stream is uniform and steady, the 

 wing does not have to end at the location of the maximum span, but 

 the part of the wing aft of this location must be uncambered. Not 

 all of these conditions are satisfied in the interesting ship maneuver- 

 ing problems. 



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