This paper describes an attempt to design by analytic means a class of axisymmetric bodies having low drag in incompressible flow for the case where the boundary layer is fully turbulent over the entire body. The drag is to be made small solely by proper shaping of the body, and the drag coefficient to be minimized is that based on a reference area equal to the two-thirds power of the body's volume. Clearly the flow should be unseparated for low drag. A comparison of various drag-calculation methods shows that the Truckenbrodt formula, which expresses drag as an integral of a power of the potential-flow surface velocity, is sufficiently accurate, and this formula is adopted as the chief analytic tool. Among the consequences of this choice is that bodies with low drag at one Reynolds number have low drag at all. Drag performances of various types of bodies are compared, including those of " cavitation shapes" derived from a new inverse potential-flow program, it appears that there is a preferred range of fineness ratio from three to about seven. Two-dimensional optimization studies are carried out using an integral formula for drag analogous to that of Truckenbrodt. The principal conclusion is that for bodies having fineness ratios in the preferred range and having unseparated fully turbulent boundary layers the drag coefficient based on the two-thirds power of volume is not very sensitive to body shape, and thus that within these constraints no significant additional drag reduction can be obtained from shaping alone.

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