THE CONSTRUCTION OF THE OPTIMAL CONTOUR OF THE LEADING-EDGE OF A BODYIN A SUPERSONIC-FLOW

The problem of the profiling of the contour of the leading edge of a p lane body which, on joining the initial and final fixed points, gives minimum drag in a uniform supersonic flow of an ideal (inviscid and no n-heat-conducting) gas is considered. According to previous investigat ions, it is close to a segment of a straight line in that part of the space D of the governing parameters of the problem (the Mach number M( infinity), or the dimensionless velocity of the free stream V-infinity , the relative thickness tau, and so on) for which there is an attache d shock wave in a flow past the required contour. By making use of thi s fact one can find the ''main correction'' to the rectilinear generat rix in an explicit form and represent the characteristics of practical ly optimal leading edges in the form of isolines in the V(infinity)tau -plane. The approach naturally leads to an exact result in the case of a rectilinear optimal generatrix (a wedge). It is well known that a w edge in the body of minimum drag for zero reflection coefficient lambd a of pressure perturbations from the oblique shock wave which occurs i n a flow past a wedge. It is shown that the above-mentioned possibilit y is not unique. In addition to the case when lambda(V-infinity, tau) = 0 the rectilinear generatrix is also optimal for lambda not equal 0 when the flow beyond the oblique shock wave is sonic.