1. What is the Oblique Shock Equation?

The oblique shock equation calculates the turn angle (θ) produced when a supersonic flow encounters a wedge or corner with a given wave angle (β). This is fundamental in aerodynamics and compressible flow analysis.

2. How Does the Calculator Work?

The calculator uses the oblique shock equation:

Where:

• \( \theta \) — Turn angle (degrees)
• \( \beta \) — Wave angle (degrees)
• \( M \) — Mach number (dimensionless)
• \( \gamma \) — Specific heat ratio (dimensionless)

Explanation: The equation relates the flow deflection angle to the shock wave angle for a given Mach number and specific heat ratio.

3. Importance of Oblique Shock Calculation

Details: Calculating oblique shock angles is crucial for designing supersonic aircraft, missiles, and turbine blades, as well as analyzing shock wave interactions.

4. Using the Calculator

Tips: Enter Mach number (must be >1), wave angle in degrees (between 0 and 90), and specific heat ratio (typically 1.4 for air). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for γ (gamma)?
A: For air at standard conditions, γ = 1.4. For other gases: monatomic = 1.67, diatomic = 1.4, triatomic ≈ 1.3.

Q2: What is the maximum turn angle?
A: The maximum turn angle depends on Mach number. For a given Mach, there's a maximum θ beyond which the shock detaches.

Q3: What happens if β is less than the Mach angle?
A: If β < μ (where μ = arcsin(1/M)), the solution is invalid as weak oblique shocks cannot form.

Q4: How does this relate to the θ-β-M relation?
A: This is the θ-β-M relation, providing θ for given β and M. The inverse problem (finding β for given θ) requires numerical solution.

Q5: What are the assumptions in this equation?
A: Assumes steady, inviscid, adiabatic flow of a perfect gas with constant γ across the shock.