Oblique Shock Calculator

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The Mach number of the supersonic flow upstream of the shock. Must be greater than 1.
The flow-deflection angle (wedge half-angle) in degrees. If this exceeds the maximum for the given Mach number, the shock detaches.
deg
Ratio of specific heats Cp/Cv. Use 1.4 for diatomic air at standard conditions, 1.667 for monatomic noble gases, 1.3 for hot combustion products.
Wave angle (β)Moderate shock loss
36.94deg

Angle of the oblique shock wave relative to the upstream flow direction.

Downstream Mach (M₂)1.874
Normal upstream Mach (Mₙ₁)1.503
Normal downstream Mach (Mₙ₂)0.7
Pressure ratio (p₂/p₁)2.4675
Density ratio (ρ₂/ρ₁)1.8665
Temperature ratio (T₂/T₁)1.322
Stagnation pressure ratio (p₀₂/p₀₁)0.929
Maximum deflection angle29.8deg
Mach angle (μ)23.58deg
0.929 p₀₂/p₀₁
Strong loss<0.7Significant loss0.7-0.85Moderate loss0.85-0.95Low loss0.95+

Oblique shock at β = 36.94 deg, downstream M = 1.874.

  • The shock wave stands at 36.94 deg from the flow direction, 21.94 deg above the wedge surface.
  • Downstream Mach is 1.874 (supersonic). Oblique shocks almost always leave supersonic flow behind for weak shocks.
  • Static pressure rises by a factor of 2.468 across the shock (146.8% increase).
  • Stagnation pressure ratio is 0.9290: 7.10% of total pressure is lost irreversibly to entropy generation.

Next stepFor inlet design, cascade multiple oblique shocks (each weaker) to minimize total stagnation pressure loss compared to a single normal shock.

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