Prandtl–Meyer Calculator
Supersonic flow turning around a convex corner. Give it the corner angle and it returns the expansion — or work back from either Mach number. At any γ.
| Quantity | Upstream before the corner | Downstream after the fan |
|---|
ν against Mach number
ν(M)
the turn, θ
ν_max, as M → ∞
What this is computing
NOT WRITTEN YET — Iliya writes this, 300–500 words.
Deliberately loud so it cannot ship by accident. Worth covering:
- That ν is not a physical angle but a bookkeeping device: only differences in ν mean anything, and the whole method is ν₂ = ν₁ + θ.
- Why the expansion is isentropic while the compression through an oblique shock is not — the fan spreads the turning over infinitely many Mach waves, so no single wave is strong enough to raise entropy.
- The maximum turn, and what happens past it. ν is bounded, so from any M₁ there is a finite angle beyond which the flow cannot follow the wall and separates with vacuum behind it. This is the expansion's counterpart to shock detachment.
- Why the fan opens forward: μ narrows as the flow accelerates, so the trailing Mach line is shallower than the leading one and the rays never cross.
- Where this actually gets used — nozzle contours, over-expanded plumes, the suction side of a supersonic aerofoil — and the fact that a compression corner is the oblique shock page instead.