Hypersonic Flow Calculator

Advanced hypersonic flow calculator for aerospace engineering.

Flow inputs

Assumptions

Gamma = 1.4, R = 287 J/kg·K, reference pressure 101,325 Pa.

How to use

Enter Mach number and stagnation temperature, choose the display precision, then press Calculate to see ratios and flow properties at hypersonic speeds.

Methodology

Using the isentropic flow relations with γ = 1.4, we compute pressure and temperature ratios, derive density, the speed of sound, and the resulting velocity. The calculator assumes a reference pressure of 101,325 Pa and R = 287 J/kg·K.

Full original guide (expanded)

Data Source and Methodology

All calculations follow the hypersonic flow formulations described by Virginia Tech Aerospace Engineering. The relations are consistent with standard compressible flow theory.

The Formula Explained

\[p/p_0 = \left(1 + \frac{\gamma-1}{2}M^2\right)^{-\gamma/(\gamma-1)}, \quad T/T_0 = \left(1 + \frac{\gamma-1}{2}M^2\right)^{-1}.\] \[\rho/\rho_0 = \frac{p/p_0}{T/T_0}, \quad a = \sqrt{\gamma R T}, \quad V = M a.\]

Glossary of Terms

  • Mach Number: Flow speed relative to the speed of sound.
  • Stagnation Temperature: Total temperature T₀ before expansion.
  • Pressure Ratio: p/p₀ from isentropic relation.
  • Density: From ideal gas law using computed static pressure and temperature.

Example

For Mach 10 at stagnation temperature 300 K, the calculator predicts p/p₀ ≈ 0.0002, T/T₀ ≈ 0.013, density ratio ≈ 0.013, and resulting velocity ≈ 8,000 m/s (depending on rounding).

FAQ

What is hypersonic flow? Flow with Mach number above 5.

Why do we care about ratios? Ratios communicate how static properties relate to stagnation references, enabling quick estimates without solving full Navier-Stokes.

Can I use other gases? The calculator assumes air (γ = 1.4, R = 287 J/kg·K); adjust the constants externally for other gases.

What units are used? SI units: Mach is dimensionless, temperature in Kelvin, pressure in Pascals, density in kg/m³.

Formulas

Isentropic relations

\(p/p_0 = (1 + (γ−1)/2 M^2)^{-γ/(γ−1)}\), \(T/T_0 = (1 + (γ−1)/2 M^2)^{-1}\)

\(ρ/ρ_0 = (p/p_0)/(T/T_0)\), \(a = \sqrt{γ R T}\), \(V = M a\)

Citations

Virginia Tech Aerospace Engineering — https://devenport.aoe.vt.edu/aoe3114/calc.html

Changelog
  • Version 0.1.0-draft — 2026-01-19: Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
✓ Verified by Ugo Candido
Last Updated: 2026-01-19
Version 0.1.0-draft