Oblique Shock Calculator

About the Oblique Shock Calculator

An oblique shock wave forms when supersonic flow encounters a wedge, ramp, or deflection. Unlike a normal shock (perpendicular to flow), an oblique shock is inclined at angle β to the freestream, deflecting the flow by angle θ while compressing, heating, and decelerating the gas.

This calculator solves the oblique shock relations. Given the upstream Mach number and deflection angle, it determines the shock angle β using an iterative solver, then computes all downstream properties: Mach number, static pressure ratio, density ratio, temperature ratio, stagnation pressure ratio, and entropy rise.

The tool handles the full range of supersonic Mach numbers from 1+ to hypersonic. It correctly identifies when the deflection angle exceeds the maximum for attached shocks (indicating a detached bow shock). A maximum deflection angle reference table helps engineers design inlet ramps and compressor cascades.

Oblique shock analysis is essential for supersonic inlet design, aircraft nose/wing shaping, ballistic reentry, and wind tunnel nozzle design.

When This Page Helps

Oblique shock calculations are essential for aerospace engineering but involve transcendental equations that cannot be solved in closed form. This calculator handles the iterative solution automatically.

It is invaluable for students, aerospace engineers, and researchers working with supersonic and hypersonic flows. It helps when you need to see how a wedge angle, Mach number, or gas model changes the downstream state without hand-solving the theta-beta-Mach relation.

How to Use the Inputs

1. Enter the upstream Mach number (must be > 1).
2. Enter the specific heat ratio γ (1.4 for air).
3. Enter the flow deflection angle θ in degrees.
4. Alternatively, enter the shock angle β directly to compute from that.
5. Read the downstream Mach number, pressure/density/temperature ratios.
6. Check the stagnation pressure loss — lower is better for efficiency.

Example Calculation

Tips & Best Practices

• For maximum inlet efficiency, design for oblique shocks with β as close to the Mach angle as possible.
• The Mach angle (minimum β) is sin⁻¹(1/M) — it represents an infinitely weak shock (sound wave).
• At M → ∞, the maximum deflection approaches 45.58° for γ = 1.4.
• In hypersonic flow, γ decreases due to vibrational excitation and dissociation — use real-gas corrections.
• Shock-expansion theory combines oblique shocks with Prandtl-Meyer expansions for complete 2D supersonic flow analysis.

Attached vs Detached Shocks

The main design question is whether the shock stays attached to the surface or detaches into a bow shock. Small deflections at a given Mach number usually give an attached weak shock, while too much turning forces detachment and a much larger pressure loss.

Why the Downstream State Matters

Downstream Mach number, pressure ratio, and stagnation pressure loss determine whether the flow can continue through an inlet, diffuser, or nozzle without unacceptable losses. That is why oblique shock results are usually interpreted together instead of one number at a time.

Practical Use

This calculator is useful for preliminary inlet design, compressible-flow homework, and quick sanity checks before CFD or wind-tunnel work. It gives the key shock parameters in one place so you can compare geometry choices quickly.

Frequently Asked Questions

• What is the difference between weak and strong oblique shocks?

  For a given M₁ and θ, two β solutions exist. The weak shock (smaller β) keeps the flow supersonic downstream. The strong shock (larger β, close to 90°) makes it subsonic. In practice, the weak shock almost always occurs.

• When does a detached shock form?

  When the deflection angle θ exceeds the maximum for the given Mach number. The shock detaches from the surface and becomes a curved bow shock standing upstream of the body.

• What is a normal shock?

  A special case of an oblique shock with β = 90°. It produces the maximum pressure jump and always makes the downstream flow subsonic.

• Why does stagnation pressure decrease across a shock?

  Shocks are irreversible — they generate entropy. The entropy rise is proportional to the stagnation pressure loss: Δs/R = −ln(p₀₂/p₀₁). Stronger shocks lose more stagnation pressure.

• How is this used in supersonic inlet design?

  Supersonic inlets use a series of weak oblique shocks to gradually decelerate the flow, followed by a weak normal shock. This reduces total stagnation pressure loss compared to a single normal shock.

• What is γ for different gases?

  Air at moderate temperatures: γ = 1.4. Monatomic gases (He, Ar): γ = 1.667. Diatomic at high temperature (vibration excited): γ ≈ 1.3. CO₂: γ ≈ 1.3.