Mach Number
The Mach number is a dimensionless quantity defined as the ratio of the speed of a body (or flow) to the local speed of sound in the surrounding medium. Named after Austrian physicist Ernst Mach, it is the primary parameter characterising compressibility effects in aerodynamics; below Mach 1 (subsonic) flow behaves nearly incompressibly, while above it (supersonic) shock waves form. The Mach number determines the applicable aerodynamic model, the nature of pressure disturbances, and the onset of critical phenomena such as wave drag and sonic booms.
Key Formula
M = v / a
LaTeX: M = \dfrac{v}{a}
| Symbol | Meaning | Unit |
|---|---|---|
| M | Mach number (dimensionless) | — |
| v | Speed of the object or flow | m/s |
| a | Speed of sound in the local medium | m/s |
Worked Example
Problem
An aircraft flies at 850 km/h at an altitude where the speed of sound is 295 m/s. Calculate the Mach number.
Solution
Step 1: Convert aircraft speed to m/s: 850 km/h ÷ 3.6 = 236.1 m/s. Step 2: Apply the Mach number formula: M = v / a = 236.1 / 295. Step 3: M = 0.80.
Answer
M ≈ 0.80 (high subsonic / approaching transonic regime)
Speed of Sound and Mach Equivalents at Various Altitudes (ISA)
| Altitude (km) | Temperature (°C) | Speed of Sound (m/s) | Mach 1 (km/h) | Mach 2 (km/h) |
|---|---|---|---|---|
| 0 (sea level) | 15 | 340 | 1225 | 2450 |
| 5 | −17.5 | 320 | 1152 | 2304 |
| 10 | −50 | 299 | 1078 | 2155 |
| 20 | −56.5 | 295 | 1062 | 2124 |
| 30 | −46.6 | 301 | 1084 | 2168 |
Interactive Tools
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Related Terms
Aerodynamics
Aerodynamics is the branch of fluid mechanics that studies the motion of air and other gases, and the forces they exert on solid bodies moving through them. It forms the scientific foundation for the design of aircraft, rockets, automobiles, and buildings, governing phenomena such as lift, drag, and pressure distribution. Understanding aerodynamic principles is essential for optimising vehicle performance, fuel efficiency, and structural stability at various speeds and altitudes.
Aerodynamic Drag
Aerodynamic drag is the resistive force exerted on a body moving through a fluid (such as air), acting parallel and opposite to the direction of motion. It consists of pressure drag (form drag), skin friction drag, and induced drag, all of which dissipate kinetic energy and reduce vehicle efficiency. Minimising drag is a primary goal in the aerodynamic design of aircraft, rockets, and high-speed ground vehicles.
Aerodynamic Stall
An aerodynamic stall occurs when the angle of attack of a wing exceeds the critical angle, causing boundary layer separation over most of the upper surface and a sudden, dramatic reduction in lift accompanied by a large increase in drag. It is not related to engine failure but is a purely aerodynamic phenomenon that can occur at any airspeed and any attitude. Recovery requires reducing angle of attack by lowering the nose, applying full power, and levelling wings — making stall recognition and recovery a core pilot training requirement.
Named after Austrian physicist and philosopher Ernst Mach (1838–1916), who made pioneering studies of supersonic projectiles and shock waves. The term "Mach number" was coined by aerodynamicist Jakob Ackeret in 1929.