Three-Dimensional Bodies of Minimum Total Drag in Hypersonic Flow

The three-dimensional motion of optimalpyramidal bodies

“…This property is common to all the local models, and it was used to solve the problem of optimizing the shape of a body with respect to its resistance [1,2,4] and depth of penetration [3], when the resistance and depth of penetration can be represented in the form of functions which depend explicitly on the shape of the body. For rectilinear motion of the body, which has a specified base area Sb, within the framework of the model (1.2)-(1.5) for the resistance of the body Fd, Fd = -(F • s2), where s2 is the unit vector of the longitudinal axis of the body in the direction of motion (see Fig.…”

“…Shape optimization was carried out for rectilinear motion of the body in [1][2][3][4]. The motion of the body in the medium may be perturbed, and then, as the results of experimental and theoretical investigations show [5][6][7][8][9], the features of the body shape turn out to have an important influence on the development of the perturbations and nature of motion of the body.…”

“…It is well known [1][2][3][4] that if the cone has an optimum aperture angle, such configurations belong to the class of optimal configurations. For non-separating flow around bodies and small perturbations, imposed at the initial instant of time on the parameters of the rectilinear motion, an analytical solution of the problem of the plane motion of thin bodies, the contour of the base of which is a rhombus or a star, consisting of four symmetrical cycles, was constructed in [9].…”

“…Exact solutions of problems of optimizing the shape of a body (with respect to the resistance and depth of penetration) within the framework of the model of local interaction were obtained in [1][2][3][4] for a specified length and a specified area of the base of the body without simplifying assumptions regarding its geometry. A method of constructing optimal shapes was proposed in [1][2][3][4], which enables an infinite set of optimal configurations to be constructed, all of which, for the same conditions of penetration into the medium, have the same resistance and ensure the same depth of penetration.…”

“…A method of constructing optimal shapes was proposed in [1][2][3][4], which enables an infinite set of optimal configurations to be constructed, all of which, for the same conditions of penetration into the medium, have the same resistance and ensure the same depth of penetration.…”