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How It Works
The Mach number is the ratio of an object's speed to the local speed of sound. Below Mach 1 the flow is subsonic, at Mach 1 it is transonic, above Mach 1 supersonic, and above Mach 5 hypersonic. Each regime produces fundamentally different aerodynamic behavior, including shock waves and dramatic changes in drag.
The speed of sound depends on the fluid and its temperature. In air at 20 °C it is about 343 m/s (767 mph). The same aircraft speed corresponds to different Mach numbers at different altitudes because temperature changes with altitude.
Example Problem
A fighter jet flies at 680 m/s at an altitude where the speed of sound is 310 m/s. What is its Mach number?
- M = v / a = 680 / 310
- M = 2.19
At Mach 2.19 the jet is well into the supersonic regime. Oblique shock waves form on its leading edges, and the drag coefficient is significantly higher than at subsonic speeds.
Frequently Asked Questions
How fast is Mach 1 in mph?
At sea level and 20 °C, Mach 1 is about 767 mph (1,235 km/h). At cruising altitude (roughly −57 °C) the speed of sound drops to about 660 mph, so the same aircraft speed corresponds to a higher Mach number.
Why does the Mach number change with altitude?
The speed of sound in an ideal gas depends on temperature, not pressure. Since temperature generally decreases with altitude in the troposphere, the speed of sound falls and the Mach number for a given airspeed increases. In the stratosphere, temperature stabilizes and so does the local speed of sound.
What happens at the sound barrier (Mach 1)?
As an aircraft approaches Mach 1, shock waves form on its surfaces and drag increases sharply (the transonic drag rise). With enough thrust the aircraft passes through the barrier. A sonic boom is produced because the pressure disturbances can no longer propagate ahead of the aircraft.
What is hypersonic speed?
Flows above Mach 5 are classified as hypersonic. At these speeds, aerodynamic heating becomes extreme (surface temperatures can exceed 1,500 °C) and the air itself may dissociate into its atomic components. Spacecraft re-entry occurs at Mach 25 or higher.
Related Calculators
- Cauchy Number Calculator — compressibility ratio equal to Mach² for an ideal gas.
- Eckert Number Calculator — assess viscous dissipation heating in high-speed flows.
- Knudsen Number Calculator — determine rarefied-gas flow regime at high altitudes.
- Reynolds Number Calculator — characterize whether flow is laminar or turbulent.
- Sound Wave Calculator — compute the speed of sound used in the Mach number formula.
- Speed Unit Converter — convert between m/s, mph, km/h, and knots.