Oblique Shock Calculator

Oblique shock in a calorically perfect gas. The θ–β–M relation ties the upstream Mach number, the flow deflection angle θ and the wave angle β: give any two and the third follows, together with the property ratios across the shock, which depend only on the normal Mach number M_n,1 = M₁ sin β. The γ in the top bar applies to every value on the page.

Section 9.2 · Oblique shock relations

Calculator

Enter any two of the three inputs

weak branchstrong branchθ_max

Reference

Relations used

The θ–β–M relation

For a given M₁, θ rises from 0 at the Mach angle μ = sin⁻¹(1/M₁) to a maximum θ_max and falls back to 0 at β = 90°, the normal shock. Every θ < θ_max therefore has two solutions: the weak one (smaller β, usually observed on wedges and corners) and the strong one. For θ > θ_max no attached shock exists and the shock detaches. The calculator finds β, or M₁, by bisection on (9.23).

Across the shock

These are the normal-shock relations (9.15)–(9.17) applied to M_n,1; the tangential velocity is unchanged across the shock.

Background

Calculator

Relations used

The θ–β–M relation

Across the shock

Where these relations come from