Machnummer

Machnummer, or Mach number, is a dimensionless quantity used in fluid dynamics and aerodynamics to express the ratio of an object's speed to the local speed of sound in the surrounding medium. It is defined by M = v / a, where v is the flow velocity relative to the gas and a is the local speed of sound. For an ideal gas, a = sqrt(γ R T), with γ the heat capacity ratio, R the specific gas constant, and T the absolute temperature. The Mach number therefore depends on temperature and composition of the gas in addition to velocity.

The Mach number indicates the level of compressibility effects in the flow. For M much less than 1, the flow is essentially incompressible and many aerodynamic analyses assume constant density. As M approaches and exceeds 1, density changes become significant and shock waves may form, profoundly affecting lift, drag, and stability.

Local versus free-stream: M can vary along a flow field. The free-stream Mach number M∞ is used to categorize the overall flight condition, while local Mach numbers describe conditions at specific points on surfaces or within the flow.

Typical regimes: subsonic roughly M < 0.8, transonic about 0.8–1.2, supersonic greater than 1, and hypersonic often defined as M ≥ 5. In the transonic range, both subsonic and supersonic regions can coexist, with shock waves forming on surfaces and influencing performance.

Applications: the concept is fundamental for aircraft design, propulsion, and aerodynamics, governing wave drag, lift, and the behavior of nozzles and turbines. It is also central to wind tunnel testing and computational fluid dynamics to ensure similarity between model tests and real-world conditions.

In German usage, Machzahl or Machnummer denotes the same quantity as the English Mach number.