NASA Oblique Shock Calculator

Oblique Shock Relations:

\[ \tan(\theta) = 2 \cot(\beta) \frac{M_1^2 \sin^2(\beta) - 1}{M_1^2 (\gamma + \cos(2\beta)) + 2} \]

Deflection Angle (θ):

Downstream Mach Number (M₂):

Pressure Ratio (P₂/P₁):

Density Ratio (ρ₂/ρ₁):

Temperature Ratio (T₂/T₁):

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1. What is Oblique Shock?

An oblique shock wave is a shock wave that forms at an angle to the flow direction, typically occurring when a supersonic flow encounters a corner or wedge. It's fundamental in aerodynamics for analyzing supersonic flow around wings, nozzles, and other aerospace components.

2. How Does the Calculator Work?

The calculator uses NASA's oblique shock relations:

\[ \tan(\theta) = 2 \cot(\beta) \frac{M_1^2 \sin^2(\beta) - 1}{M_1^2 (\gamma + \cos(2\beta)) + 2} \]

Where:

\( M_1 \) — Upstream Mach number
\( \beta \) — Shock wave angle
\( \theta \) — Flow deflection angle
\( \gamma \) — Specific heat ratio (1.4 for air)

Explanation: The equation relates the shock angle to the flow deflection angle and Mach number for a perfect gas.

3. Importance of Oblique Shock Calculations

Details: These calculations are essential for designing supersonic aircraft, rockets, and spacecraft, helping engineers predict shock waves and their effects on pressure, temperature, and flow direction.

4. Using the Calculator

Tips: Enter upstream Mach number (must be ≥1), shock angle in degrees (between 0-90), and specific heat ratio (1.4 for air). The calculator will determine the flow deflection angle and other shock properties.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between oblique and normal shocks?
A: Normal shocks are perpendicular to flow, while oblique shocks are at an angle. Oblique shocks cause flow deflection.

Q2: What is the maximum deflection angle?
A: There's a maximum deflection angle for each Mach number above which a detached shock forms.

Q3: When does a weak vs. strong solution occur?
A: For a given Mach and deflection angle, there are typically two possible shock angles - the weak shock (smaller angle) is more common.

Q4: How does γ affect the results?
A: Higher γ (more diatomic/polyatomic gases) generally results in stronger shocks for the same conditions.

Q5: What if I get NaN results?
A: This means the combination of inputs doesn't satisfy the oblique shock relations - try different values.