Dfag measurements on star-shaped body at m ? 6 and 8

Abstract

Results have been obtained in recent years which make it possible to get an idea of the optimal shape of a three-dimensional body at high supersonic speeds. It has been shown [1–6] that bodies with a cross section in the form of a star with certain limitations have the least wave drag and remain optimal with respect to total drag with approximate account for the friction forces. The transition from the optimal body of revolution to the star-shaped body of equivalent volume and length makes a several-fold drag reduction. These theoretical results, initially obtained on the basis of the Newton drag law, were then confirmed by the exact solution [7] for bodies which were close in form to the optimal. Subsequent experimental studies investigated the flow pattern between two lobes representing an element of the star over a wide range of included angles. The experiments showed that there actually exists a flow between the rays corresponding to the solution [7], that this flow is stable, and that the wave drag calculated from the pressure distribution over the body surface is several fold less than for the equivalent cone. Although these results are encouraging, they do not prove the advantages of the star-shaped form for practical use. The point is that the “star” has considerably more wetted area; therefore the effect of the marked reduction of the wave drag may be compensated by an increase of the friction drag. The references above to the theory which considers friction are not convincing, since the friction estimates are approximate, while real friction is complicated by the presence of shock waves within the flow, the possibility of a turbulent boundary layer, separation, etc. Not all these factors are amenable to calculation, and it is clear that conclusions can be drawn on “star” drag only after making direct measurements of the total force acting on a model in a flow.