Newtonian Flow Theory for Slender Bodies

TLDR

Newtonian flow theory is examined as a first‑order approximation in gas dynamics for hypersonic small‑disturbance problems, providing an aid to aerodynamicists designing airframes above Mach 5. The theory introduces a similarity parameter \(N=(7+l)/(7-l)\,ikfo0\,5\) and requires that the surface pressure coefficient never reach zero, limiting its applicability. A general first‑order solution for slender bodies at zero angle of attack is derived, and the theory is applied to cones and bodies with shape \(r=x\).

Abstract

As an aid to the aerodynamicist in the design of air frames for hypersonic speeds (speeds faster than about Mach 5), Newtonian flow theory is examined from the point of view of gas dynamics and hypersonic small-disturbance theory. The usual theory is shown to result as the first approximation of an expansion valid for small X = (7 — 1 ) / ( Y + 1). A basic similarity parameter N = (7 + l ) / ( 7 — l)ikfo0 5 is introduced. A general solution of the first approximation for the flow past slender bodies (bodies which cause only a small disturbance to the stream) a t zero angle of attack is given. An important condition which limits the application of the theory is noted—namely, that the pressure coefficient on the surface not fall to zero. The theory is then applied to cones and to bodies whose shape is r = x.