Mach Number from Airspeed & Altitude
True airspeed plus ISA altitude → Mach number and the local speed of sound.
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The engineering
Sound speed in air depends on temperature alone — not pressure, not density — so Mach number is really a statement about how cold it is outside. The same 250 m/s that is Mach 0.73 at sea level becomes Mach 0.83 at 10,000 m because the tropopause air is 65 °C colder.
This is why jets quote cruise as a Mach number, not an airspeed: the structural and aerodynamic limits (shock formation on the wing) follow M, while the fuel bill follows TAS. Above the tropopause the ISA is isothermal, so the speed of sound flatlines at 295 m/s and the conversion stops moving.
Where this math comes from
Ernst Mach photographed supersonic bullet shocks in 1887 and understood that the speed *ratio* was what mattered, but he never named the number — the Swiss aerodynamicist Jakob Ackeret proposed calling it the Mach number in 1929, in Mach's honor. By the 1940s pilots were meeting the ratio personally as 'compressibility' in dives.
The Machmeter became a cockpit instrument because indicated airspeed lies about shock onset: a P-38 pilot at altitude could be at a dangerous Mach while the airspeed needle looked tame. Once the ISA (standardized 1924) fixed a temperature at every altitude, Mach from TAS became the deterministic arithmetic this card performs.
- 1887Ernst MachPhotographs supersonic shock waves; identifies the speed ratio.
- 1924ICANStandard atmosphere fixes T(h) — Mach from altitude becomes arithmetic.
- 1929Jakob AckeretNames the Mach number.
- 1947Chuck Yeager / Bell X-1Mach 1.06 flown — the ratio becomes a milestone.
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