Mach Number⚠ unverified
Aerospace / Aerodynamics · Compute the Mach number
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| V | V | m/s | 1.0 | Flow velocity |
| a | a | m/s | 1.0 | Local speed of sound |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | M | — | Mach number (dimensionless). Returns 0.0 when ``a <= 0`` |
The science & history
Understanding the Parameters
- $v$ — true airspeed (or flow speed) in the same frame as $a$.
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$a$ — depends on temperature (and composition): for ideal gas $a = \sqrt{\gamma R T}$ (Speed Of Sound). Do not use a fixed 340 m/s if $T$ differs from standard day.
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$M$ — compressibility effects grow as $M$ approaches 1; shock waves appear for $M > 1$.
Derivation (Approaching a Proof)
Acoustic waves propagate at speed $a$. The ratio of convective speed to wave speed is the natural nondimensional compressibility parameter $M = v/a$ arising in the dimensionless Euler/Navier–Stokes equations. It is a definition, once $v$ and $a$ are known.
History
Ernst Mach’s studies of shock waves led to naming $M$; it is fundamental in gas dynamics and flight test (indicated vs true vs Mach).
Related Concepts: Speed Of Sound, Dynamic Pressure, Reynolds Number, Drag, Lift
Notes: Registry calculator fluids-mach-number (unverified). Local $a$ required for meaningful $M$.