Compressible Aerodynamics Calculator

Isentropic flow and shocks.

A simple tool to calculate typical compressible aerodynamic properties for isentropic flow, normal shocks, and oblique shocks.

Disclaimer: This calculator is for educational and curiosity purposes only. No guarantee on accuracy is inferred by a result.

Isentropic Flow Relations (for a calorically perfect gas)

=
\[M\]
\[\mu \: (^\circ)\]
\[\nu \: (^\circ)\]
\[p_o/p\]
\[T_o/T\]
\[\rho_o/\rho\]
\[p/p^*\]
\[T/T^*\]
\[\rho/\rho^*\]
\[A/A^*\]

Normal Shock Relations (for a calorically perfect gas)

=
\[M_1\]
\[M_2\]
\[\rho_2/\rho_1\]
\[T_2/T_1\]
\[p_2/p_1\]
\[p_{0,2}/p_{0,1}\]
\[p_{0,2}/p_1\]

Oblique Shock Relations (for a calorically perfect gas)

M1  =
=
\[\theta \: (^\circ)\]
\[\beta \: (^\circ)\]
\[M_{n,1}\]
\[M_{n,2}\]
\[M_2\]
\[p_2/p_1\]
\[p_{0,2}/p_{0,1}\]
\[\rho_2/\rho_1\]
\[T_2/T_1\]

Nomenclature

\(A\) Throat area
\(A^*\) Throat area at sonic conditions
\(M\) Mach number
\(M_1\) Mach number upstream of shock wave
\(M_2\) Mach number downstream of shock wave
\(M_{n,1}\) Normal component of the Mach number upstream of shock wave
\(M_{n,2}\) Normal component of the Mach number downstream of shock wave
\(p\) Static pressure
\(p^*\) Static pressure at sonic conditions
\(p_1\) Static pressure upstream of shock wave
\(p_2\) Static pressure downstream of shock wave
\(p_0\) Total pressure
\(p_{0,1}\) Total pressure upstream of shock wave
\(p_{0,2}\) Total pressure downstream of shock wave
\(T\) Temperature
\(T_0\) Total temperature
\(T^*\) Temperature at sonic conditions
\(T_1\) Temperature upstream of shock wave
\(T_2\) Temperature downstream of shock wave
\(\beta\) Wave angle
\(\theta\) Deflection angle
\(\mu\) Mach angle
\(\nu\) Prandtl-Meyer function