Oblique Shock Calculator
Solve the theta–beta–M relation for the weak shock and compute key post-shock properties.
How to Use This Calculator
Enter upstream Mach number
M₁ must be greater than 1.
Enter flow deflection angle
θ is the turning angle imposed by a wedge or compression corner.
Select γ
Use 1.4 for air at standard conditions, 1.67 for monatomic gases, etc.
Calculate
The tool returns weak-shock solution for β, M₂, and property ratios.
Formula
tan θ = 2 cot β · (M₁² sin² β − 1) / (M₁² (γ + cos 2β) + 2)
After solving β, use normal-shock relations with Mn1 = M₁ sin β to compute post-shock properties and then M₂ = Mn2 / sin(β − θ).
Example: M₁ = 2.0, θ = 10°, γ = 1.4 ⇒ β ≈ 26.6°, M₂ ≈ 1.65, p₂/p₁ ≈ 2.21.
About Oblique Shock Calculator
Oblique shocks arise when supersonic flow is turned into itself by a compression corner. The theta–beta–M relation gives the shock angle β for a given deflection θ and upstream Mach M₁.
When to Use This Calculator
- Aerodynamics: Wedges, cones, and supersonic inlets.
- Nozzles and diffusers: Shock interactions with boundaries.
- Education: Visualize compressible flow relations.
Why Use Our Calculator?
- ✅ Robust: Numerically solves the weak-shock branch.
- ✅ Informative: Outputs key property ratios.
- ✅ Practical: Works for typical γ and Mach ranges.
Frequently Asked Questions
What if there is no solution?
For large θ at a given M₁, attached shocks are impossible and the shock detaches. Reduce θ or increase M₁.
Weak vs strong shock?
The weak solution (smaller β) is commonly observed for aerodynamic applications. The strong solution has larger pressure rise and typically is not realized.
Units?
Angles in degrees for input/output. Mach number is unitless. γ is the ratio of specific heats.