Optimum Slenderness Ratio of a Stable Low-Drag Body

Abstract

This paper presents a theoretical and experimental method of selecting the optimum slenderness ratio of a body with cylindrical midsection. Whether such a body is a large submarine or its arch enemy, the depth charge, the problem rem a ins to find a slenderness ratio which will permit the fastest possible velocity consistent with the power or sinking weight available. Considerable research has been done to determine the hydrodynamic characteristics of nose shapes both alone and combined with various afterbodies. In one of our reports we have pointed out that any one of several different nose shapes could be used on a particular body with little change in the total drag coefficient, and tests for certain afterbody shapes would probably bring similar results. Due to practical considerations, most bodies have a cylindrical midsection. Therefore, a typical underwater body of axial symmetry consists of arbitrarily selected nose and afterbody shapes separated by a cylindrical midsection. For dynamic stability, any underwater body must have fins which increase the surface area and, to some degree, the residual drag. We must necessarily consider the effect of such fins on slenderness ratio. In the following discussion of a particular concrete example, the emphasis has been placed on a body with a nose and afterbody with fins, of the same geometrical shape as the MK 13-1 torpedo (less shroud ring). The MK 13-1 torpedo is dynamically stable, has a cylindrical midsection, and has been tested with other nose shapes. After examination of the factors affecting the optimum slenderness ratio, it is found that a reasonably large variation from the theoretical optimum value will have little practical effect on the velocity of the body. Because of practical factors involved in the design of an undersea body, it may be desirable from the designer's point of view to have a relatively large slenderness ratio. This investigation shows that as far as drag per unit volume is concerned, the designer will will pay very little, if any, penalty if he disregards the drag factor and bases his selection of slenderness ratio entirely on such items as tactical requirements of maneuverability, structural design and utilization of internal space.

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