Breaking the Sound Barrier
The Mach number ($Ma$) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after Austrian physicist and philosopher Ernst Mach.
Because the speed of sound is not a constant (it changes depending on the temperature and density of the surrounding gas), an aircraft traveling at exactly $1000 , \text{km/h}$ might be flying at Mach 0.8 at sea level, but could be flying at a supersonic Mach 1.1 at $40,000$ feet where the air is extremely cold and the speed of sound is lower.
Flight Regimes
Aerospace engineers classify aircraft speeds into highly distinct regimes based entirely on the Mach number, because the fundamental physics of the air changes drastically at each boundary:
- Subsonic ($Ma < 0.8$): Commercial airliners fly here. The air behaves like an incompressible fluid flowing smoothly around the plane.
- Transonic ($0.8 < Ma < 1.2$): A highly volatile regime where air flowing over the curved wings can reach supersonic speeds while the rest of the plane is subsonic, creating localized shockwaves and extreme vibration.
- Supersonic ($1.2 < Ma < 5.0$): Fighter jets and the Concorde fly here. The aircraft moves faster than the pressure waves it creates, generating a massive sonic boom.
- Hypersonic ($Ma > 5.0$): The Space Shuttle and ICBMs re-enter the atmosphere here. At these extreme speeds, atmospheric friction generates so much heat that the air chemically dissociates into plasma.
The Formula
Example Calculation
A fighter jet is flying at $500 , \text{m/s}$ through high-altitude air where the local speed of sound is only $300 , \text{m/s}$.
- Divide Velocity by Speed of Sound: $500 / 300 \approx 1.67$.
The jet is flying at Mach 1.67, which is well into the supersonic regime, meaning it is trailing a massive conical sonic boom behind it.