Three-Dimensional Bodies of Minimum Total Drag in Hypersonic Flow

The problem of constructing three-dimensional bodies of minimum total drag is studied within the framework of a local interaction model. Under certain assumptions, this model can be adopted to describe the distributions of both pressure and skin friction on the body during its high-speed motion through gases and dense media. Without any constraints on the possible drag law within the scope of the accepted model, the optimum shapes providing the minimum drag are found without any simplifying assumptions regarding their geometry. It is shown that, for a given base area and specified limitations on the body size, one can construct an infinite number of optimum forebody shapes. It is proved that the desired shapes are formed by combinations of surface parts whose normal makes a certain constant angle with the direction of motion. The optimum angle is determined by the velocity and medium characteristics in terms of the constants of the drag law. A method of optimum shape design is proposed; in particular, it allows one to construct optimum bodies like missiles with aft feather and optimum bodies with a circular base. All the bodies constructed have the same minimal total drag for the given base area. Even for asymmetrical bodies, the acting force has no component in a plane perpendicular to the direction of motion. Special attention is paid to the particular case of the minimum drag body design in hypersonic flow, when the pressure on the body is specified by the Newton formula. A comparative study of the results obtained for Newtonian flow shows that the proposed shapes are more effective in providing a drag reduction than bodies found to be optimum in earlier studies under special simplifying assumptions.