Aerodynamic shape optimization of hypersonic missiles

For bodies at zero incidence in hypersonic flow, the minimization of pressure drag was investigated. Using Modified Newtonian Theory (MNT), a general analytical model and a numerical optimization algorithm were developed for bodies comprised of cross-sections determined by the super-elliptic Lame function. This function enables the modeling of circular and elliptical cross-section bodies along with bodies whose cross-sections vary from a “star” to a “square”. MNT accounts for pressure drag on body surfaces directly exposed to the free stream so that the coefficient of pressure drag is strictly a function of body geometry and the stagnation pressure coefficient. Using MNT, a computer code was written to minimize the normalized pressure drag by changing the body shape. The body volume and length were fixed in accordance with an initial input shape. The computer code then varied the super-elliptic Lame function parameters along the length of the body in a search for a minimum value of the normalized pressure drag. This was performed for three different classes of bodies. The results of the test cases compared well with linearized known analytic solutions for the optimum ogive shapes.