What This Calculator Does
The Prandtl-Meyer expansion relation describes how a supersonic flow accelerates and turns as it passes around a convex corner. This calculator finds the Prandtl-Meyer function value at two Mach numbers and the flow turning (deflection) angle between them, along with the Mach angles.
The Formula
The Prandtl-Meyer function is ν(M) = √((γ+1)/(γ−1)) × atan(√((γ−1)/(γ+1) × (M²−1))) − atan(√(M²−1)), valid for M ≥ 1, where γ is the gas’s specific heat ratio (1.4 for air). The turning angle produced by expanding from M1 to M2 is simply θ = ν(M2) − ν(M1). The Mach angle is μ = asin(1/M).
- This relation applies to isentropic (loss-free), steady, two-dimensional supersonic flow expanding around a corner.
- Both Mach numbers must be at least 1, since the Prandtl-Meyer function is only defined for supersonic flow.
This uses the standard compressible-flow Prandtl-Meyer relation for general aerospace engineering education and reference purposes.
Last reviewed August 2026