Mach number: the local meaning of sonic speed
Mach number compares flow velocity with the local speed of sound. At Mach 1, those speeds are equal, so the value identifies a relationship rather than a single fixed speed in miles per hour. The quantity belongs to fluid dynamics and is dimensionless because it divides one speed by another. Its symbols are M and Ma, and it takes its name from Austrian physicist and philosopher Ernst Mach. Local conditions matter to the comparison: in air, the speed of sound varies with the square root of thermodynamic temperature, changing the reference speed used in the ratio.
The flow boundary can take several forms. It may be an object immersed in a moving fluid or the wall of a channel, such as a nozzle, diffuser, or wind tunnel. The medium can be a gas or a liquid. An object may move through the medium, the medium may move along a stationary boundary, or both may move at different velocities. The relevant quantity is their relative velocity. In the formula M equals u divided by c, u denotes that local flow velocity relative to the boundary and c denotes the speed of sound in the medium.
The name Mach number followed a proposal by aeronautical engineer Jakob Ackeret in 1929 to honor Ernst Mach's achievements. Mach remains capitalized because it derives from a proper name and identifies a dimensionless quantity. The number follows the word, as in Mach 1. Lockheed also used the term Mach's number when reporting compressibility effects on the P-38 aircraft in 1942. Fractional values express the same comparison: Mach 0.65 corresponds to 65% of the local speed of sound, while Mach 1.35 corresponds to a speed 35% faster than that local reference. These examples distinguish subsonic and supersonic motion.
The International Standard Atmosphere gives a concrete setting for Mach number. In dry air at mean sea level and a standard temperature of 15 degrees Celsius, sound travels at 340.3 meters per second, or 761.23 miles per hour. The model reduces temperature to minus 56.5 degrees Celsius at an altitude of 11,000 meters. There, the corresponding speed is 295.0 meters per second, or 659.9 miles per hour, only 86.7% of the sea-level value. Temperature generally decreases with altitude across that interval. In parts of the stratosphere and thermosphere, heating instead causes the speed of sound to increase with height.
Mach number helps determine when simplified flow calculations are appropriate. If the value is below roughly 0.2 to 0.3 and the flow is quasi-steady and isothermal, compressibility effects are small enough for simplified incompressible-flow equations. Its role also appears when the continuity equation for compressible flow is made dimensionless. Relating density changes to pressure through an isentropic relation introduces a factor equal to the square of the velocity-to-sound-speed ratio. In the limit as that ratio approaches zero, the equation reduces to the incompressibility condition. The quantity therefore connects the speed comparison with the importance of density variation in fluid behavior.
Airflow near an aircraft can occupy different speed regimes at the same time. In the transonic range, some regions are subsonic while others are supersonic. The critical Mach number is the lowest free-stream value at which airflow over any part of the aircraft first reaches the local sonic speed. Supersonic zones can develop above a wing even while the free stream remains below that threshold of Mach 1. A normal shock can decelerate supersonic flow back to subsonic flow, typically before the trailing edge. As speed increases, the supersonic region grows toward both leading and trailing edges.
Those flow differences influence aircraft shape. Subsonic aircraft commonly have slender wings and rounded noses and leading edges. Transonic aircraft usually have swept wings, delaying drag divergence, and often follow the Whitcomb area rule. Supersonic aircraft commonly use sharp edges, thin airfoil sections, and all-moving tailplanes or canards. Combat aircraft must also accommodate low-speed handling. At very high speeds, thermal control becomes a dominant consideration: structures may need to operate hot or receive protection from special tiles. Chemically reacting airflow can corrode the skin, while aerodynamic heating can favor blunt configurations as the radius of curvature decreases.
Flight instruments provide another way to determine Mach number. Although the quantity is a function of temperature and true airspeed, aircraft instruments use pressure differences in their calculations. For subsonic compressible flow, a formula follows from Bernoulli's equation with air treated as an ideal gas. Supersonic calculations use the Rayleigh pitot equation, with pressure measured behind a normal shock. The unknown appears on both sides, requiring a numerical solution in practical use. A subsonic calculation first checks whether the value exceeds 1.0; its result can then initialize fixed-point iteration for the supersonic formula. Newton's method is another available numerical approach.