Uncover the critical relationship between Mach number, shock wave angle, and wedge angle in supersonic flow regimes. This Mach Wedge Angle Calculator accurately determines the deflection angle for oblique shock waves, a vital calculation for aerospace design, compressible fluid dynamics, and high-speed aerodynamics analysis.
Formula:
The Mach Wedge Angle (θ), also known as the deflection angle, is derived from the oblique shock relations, connecting the upstream Mach Number (M1) and the Shock Wave Angle (β). The formula is given by:
tan(θ) = [2 ⋅ cot(β) ⋅ (M12 ⋅ sin2(β) - 1)] / [M12 ⋅ (γ + cos(2β)) + 2]
Where:
- M1: Upstream Mach Number (dimensionless, must be > 1 for supersonic flow)
- β: Shock Wave Angle (degrees, angle of the shock wave relative to the upstream flow direction)
- γ: Ratio of Specific Heats (dimensionless, typically 1.4 for air)
- θ: Mach Wedge Angle or Deflection Angle (degrees, the angle the flow turns through the shock)