MAE 3293 · Fundamentals of Aerodynamics · High-speed flow

Compressible Aerodynamics Calculator

KARA Lab website

Ratio of Specific Heats (γ)

Calculate from:

Input Value:

Results

Mach Number (M)

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p₀/p

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ρ₀/ρ

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T₀/T

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A/A*

–

Calculate from:

Input Value:

Results

M₁

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M₂

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p₂/p₁

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ρ₂/ρ₁

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T₂/T₁

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p₀₂/p₀₁

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p₀₂/p₁

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Flow Across the Shock

Arrow length is proportional to flow speed. Mass conservation across the shock gives u₂/u₁ = ρ₁/ρ₂, so the flow slows sharply while pressure, temperature and density jump.

Enter any two values to calculate the third.

Mach number M₁

Deflection angle θ (deg)

Shock angle β (deg)

Results

M₁ₙ

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M₂ₙ

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M₂

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p₂/p₁

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ρ₂/ρ₁

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T₂/T₁

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p₀₂/p₀₁

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Wave Geometry

Drawn to scale. Streamlines turn through θ at the shock; β is measured from the upstream flow. Only the normal component M₁ₙ = M₁ sin β is processed by the shock, which is why M₂ stays supersonic for the weak solution.

Upstream Mach number M₁

Expansion angle θ (deg)

Results

ν(M₁) (deg)

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μ₁ (deg)

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ν(M₂) (deg)

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μ₂ (deg)

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M₂

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p₂/p₁

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ρ₂/ρ₁

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T₂/T₁

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Freestream Mach (M₁)

Wedge Half-Angle (δ deg)

Angle of Attack (α deg)

Final Pressures

P_lower / P₁

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P_upper / P₁

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Wave Geometry

Drawn to scale with the freestream horizontal and the wedge pitched nose-up by α. Arrows show the pressure pushing on each face, length ∝ p/p₁ (red p > p₁, blue p < p₁).

Intermediate Steps (Lower Surface)

Type

Shock

Deflection θ_lower (δ + α)

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Shock Angle β_lower

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M₁ₙ

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M₂

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Intermediate Steps (Upper Surface)

Type

Shock

Deflection θ_upper (δ - α)

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Shock Angle β_upper

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M₁ₙ

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M₂

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Type

Expansion

Expansion Angle θ_upper (α - δ)

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ν(M₁)

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ν(M₂)

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M₂

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Type

Aligned Flow

Deflection Angle (δ - α)

0.00

M₂

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