Mach number
The Mach number is the ratio of an object's speed relative to a fluid, or the fluid's flow speed, to the local speed of sound in that fluid. It is a dimensionless measure used to characterize compressible flow and distinguish regimes such as subsonic, transonic and supersonic. Because sound speed changes with the fluid and its temperature, a Mach number is not a fixed speed in kilometres or miles per hour.
Definition and interpretation
The Mach number, conventionally written M, is defined as M = V/a, where V is the speed of an object relative to the surrounding fluid (or the flow speed) and a is the local speed of sound in that fluid. It has no units. Mach 1 means the object or flow is moving at the local speed of sound; Mach 2 means twice that speed. The value of a depends on properties of the medium, including its temperature and composition, so the same Mach number can correspond to different absolute speeds at different altitudes or in different gases.
Flow regimes
Mach number helps describe how compressibility affects a flow. Subsonic flow is below Mach 1, while supersonic flow is above Mach 1. The region around Mach 1 is commonly called transonic; different parts of a body and surrounding flow can be subsonic and supersonic at the same time. As flow approaches and exceeds sonic conditions, density changes and shock waves can become important to aerodynamic forces. Boundaries between regime labels are practical conventions rather than a claim that every point in a complex flow has precisely the same speed.
Why it matters in aerodynamics
At relatively low Mach numbers, changes in air density may be small enough to neglect in some calculations. At higher speeds, compressibility alters pressure, density, lift and drag; supersonic flow can contain shock waves. Mach number therefore helps engineers compare flows and design experiments: wind-tunnel tests intended to represent flight should reproduce relevant flow conditions, including Mach number. It is not sufficient to compare aircraft speeds alone when the local sound speed differs.
Name and history
The parameter is named for Austrian physicist Ernst Mach (1838–1916), whose studies included the behavior and visualization of supersonic flow. NASA's historical account describes his work on the relation between flow speed and sound speed and his experiments photographing bullet-generated shock waves. Aerospaceweb.org reports that Swiss engineer Jakob Ackeret publicized the term Mach number in 1929 in Mach's honour; the label was not coined by Mach himself.
Key facts
- Definition
- Mach number is the ratio of speed relative to a fluid to the local speed of sound in that fluid: M = V/a.
- Units
- It is dimensionless; Mach number expresses a speed ratio rather than an absolute speed.
- Regimes
- Mach numbers below one are subsonic and those above one are supersonic; flow near one is described as transonic.
- Namesake
- The quantity is named after physicist Ernst Mach; historical accounts attribute the naming of the term to Jakob Ackeret, not Mach himself.
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References
- 1.Role of the Mach Number
NASA Glenn Research Center · other · reliability: unverified · retrieved 25 October 2026
Supports: Mach number as speed ratio; effects of subsonic, transonic and supersonic flow on density and compressibility.
- 2.Mach Number
NASA Glenn Research Center · other · reliability: unverified · retrieved 25 October 2026
Supports: Flow regime distinctions, shock waves, dependence on local sound speed and the historical relationship to Ernst Mach.
- 3.Mach number
Encyclopaedia Britannica · other · reliability: unverified · retrieved 25 October 2026
Supports: Definition of Mach number and its use in classifying subsonic/supersonic flow and compressibility.
- 4.Ernst Mach and Mach Number
Aerospaceweb.org · other · reliability: unverified · retrieved 25 October 2026
Supports: Ernst Mach's supersonic-flow studies and the later naming of the ratio by Jakob Ackeret.
References are suggested by the research engine and may be incomplete. Unverified URLs are omitted rather than guessed.
Article history
- Version 125 October 2026 · EditorCreated by Zapia