Speed relative to sound
The Mach number compares a speed with the local speed of sound: M = v ÷ a. It matters because air behaves very differently as an object approaches the speed of sound: pressure waves can no longer move ahead of it, they pile up into shock waves, and drag rises steeply. The number is named after Ernst Mach, who photographed supersonic bullets in the 1880s.
The speed of sound
In air, the speed of sound depends only on temperature: a = √(γ × R × T), with γ = 1.4, R = 287.05 J/(kg·K) and T the temperature in kelvins. At 59°F (15°C) it is about 761 mph (340 m/s).
In the International Standard Atmosphere, used by aviation:
- The temperature falls by 6.5°C per kilometer (about 2°C per 1,000 ft) from 15°C at sea level
- From 11 km (36,089 ft) to 20 km it stays at −56.5°C (−69.7°F)
- Above 20 km it rises slowly again
Example: an airliner at cruise
An aircraft flies at a true airspeed of 560 mph at 35,000 ft:
- Air temperature: −65.8°F (−54.3°C)
- Speed of sound: 296.5 m/s, about 663 mph
- Mach number: 560 ÷ 663 = 0.844, transonic
At sea level the same speed would be only Mach 0.74, because sound travels faster in warm air.
Flow regimes
- Subsonic, below about Mach 0.8: air flows smoothly everywhere.
- Transonic, about Mach 0.8 to 1.2: parts of the flow are supersonic and shock waves form on the wings. Airliners cruise just below this zone.
- Supersonic, Mach 1.2 to 5: a sonic boom follows the aircraft. Concorde cruised at Mach 2.02.
- Hypersonic, above Mach 5: heating of the air and the vehicle dominates, as for re-entering spacecraft.
Limits
Use the true airspeed, not the indicated airspeed shown on the cockpit gauge, which reads lower at altitude. The standard atmosphere is an average: on a real day the temperature at altitude can differ by 10 to 20°C, changing the speed of sound by a few percent. For that case, choose the air temperature option and enter the actual outside air temperature.