🚀 Oblique Shock Calculator
Calculate the flow deflection angle and downstream conditions produced by an oblique shock wave, given the upstream Mach number and shock (wave) angle.
What an oblique shock is
An oblique shock wave forms when supersonic flow is turned by a wedge, ramp, or corner, deflecting the flow direction while abruptly increasing pressure, density, and temperature and decreasing Mach number. Unlike a normal shock, the wave forms at an angle to the oncoming flow rather than straight across it.
The formula
Given the upstream Mach number M₁ and the shock (wave) angle β, the component of Mach number normal to the shock is M₁ₙ = M₁ sin β. The flow deflection angle follows the θ-β-M relation: tan θ = 2 cot β (M₁² sin²β − 1) / (M₁²(γ + cos 2β) + 2). Downstream conditions are then found by applying the normal-shock relations to M₁ₙ, and the downstream Mach number is M₂ = M₂ₙ / sin(β − θ).
If M₁ sin β is less than 1, no shock can form at that angle for that Mach number. This calculator uses air’s default specific heat ratio (γ = 1.4) and is intended for general aerodynamics education and reference.