Concept

Mach independence — where it appears

The property that above about Mach eight the pressure coefficient, density ratio and shock shape round a blunt body stop changing with speed. What they depend on instead is the ratio of specific heats, so the question becomes one about the gas rather than about the flight condition.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Also named here as shock standoff — the same set of essays touches all of them, so they are one junction rather than several.

The density ratio and the nose pressure coefficient, against Mach number. Two quantities across a normal shock, on a logarithmic Mach axis. Both approach limits that depend on γ and on nothing else: six for the density ratio and 1.8394 for the pressure coefficient at the stagnation point. By Mach five the second is within three per cent of its limit and by Mach twenty within a tenth of a per cent. Above that the flow round a blunt body has stopped depending on how fast it is going and started depending on what the gas is.

A shock that lies on the body

Above about Mach eight the flow round a blunt body stops depending on how fast it is going. The density ratio, the nose pressure coefficient and the shock standoff all reach limits set by γ alone — and going from a perfect gas to a dissociating one halves the standoff.

compressible · Shock layer

γ for air, against temperature. The ratio of specific heats for air as a mixture of nitrogen and oxygen, with the vibrational mode filling according to the Einstein function. It is 1.400 at room temperature, where only translation and rotation are available; 1.337 at a thousand kelvin; and 1.288 at six thousand. The usual compressible-flow tables use 1.4, and that is the value for a gas that is not hot — which, behind any shock worth drawing, it is not.

When gamma stops being a number

Every perfect-gas result uses γ = 1.4, which counts the ways a nitrogen molecule can hold energy at room temperature. Behind a Mach 10 shock the gas is at 3,800 kelvin and the count is different — and the pressure barely moves while the temperature falls by fifteen per cent.

compressible · Real gas

Behind a strong shock the layer is an exact rotational flow, squeezed into a tenth of the shock's radius. Streamlines of the constant-density shock layer between a spherical shock (radius 1) and a sphere at density ratio ε = 0.167, from the solution ψ = sin²χ(ar⁴ + br² + c/r): the body sits at 0.8944 of the shock's radius, a standoff of 0.118 body radii. The gas enters along the shock, turns, and runs round the body in a layer whose vorticity over r sin χ is the same everywhere.

The shock layer is Hill's vortex, and it heats the nose a tenth harder than Newton says

Behind a strong bow shock the gas is squeezed six-fold or more and turned round the nose in a thin layer, and if its density is taken as constant there the layer has an exact solution: the same family of rotational flows as Hill's spherical vortex, fitted to the shock's three conditions. It stands off further than a mass balance says, and its gas accelerates away from the stagnation point a fifth faster than Newton's pressure law implies. Since a nose's heating goes as the square root of that acceleration, the layer heats the nose about ten per cent harder than the estimate every first calculation of re-entry uses.

compressible · Shock layer

Named alongside it

The objects these essays reach for when they reach for this one.

Shock standoff Crocco theorem Density Measurement Model limit Normal shock Vibrational excitation Aerodynamic heating Energy equation Entropy Entropy layer Exact solution

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