Normal Shock Relations
Jump conditions across a normal shock: M₂ and the pressure, density, temperature, and total-pressure ratios.
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The engineering
A normal shock is the flow's way of paying an overdue bill in one installment: supersonic in, subsonic out, with static pressure, density, and temperature all jumping while total pressure — the useful, recoverable kind — is destroyed. At M₁ 2 you lose 28% of it; by M₁ 3, 67%.
That last row is why supersonic inlets are shaped the way they are: an engine swallowing a single normal shock at M 3 wastes two-thirds of its ram pressure, so real inlets stage the deceleration through weaker oblique shocks first (next card).
Where this math comes from
The jump conditions came from two people who never met over the problem: William Rankine derived them from thermodynamics in 1870, and Pierre-Henri Hugoniot, a French ballistician, independently in 1887 — hence Rankine-Hugoniot. Ernst Mach had photographed the shock itself off a supersonic bullet in 1887, settling by schlieren image an argument theory alone couldn't.
For decades shocks were a ballistics curiosity; then aircraft started meeting them from the other side. The 'sound barrier' of the 1940s was this card's physics arriving over a wing, and Chuck Yeager's 1947 flight through it in the X-1 was less a barrier broken than a table of these ratios properly respected.
- 1870William J. M. RankineShock jump conditions from thermodynamics.
- 1887Pierre-Henri HugoniotIndependent derivation — the Rankine-Hugoniot relations.
- 1887Ernst MachSchlieren photograph of a bullet's shock wave.
- 1947Chuck Yeager / Bell X-1First piloted supersonic flight — the relations flown.
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