Mach number

FA-18 Hornet breaking sound barrier (7 July 1999)

Comparison US standard atmosphere 1962

Transsonic flow over airfoil 1

Transsonic flow over airfoil 2

Mach number (Mach number) is a dimensionless quantity in fluid dynamics and aerodynamics that represents the ratio of the speed of an object moving through a fluid to the local speed of sound within that fluid. Named after the Austrian physicist and philosopher Ernst Mach, the Mach number is a critical parameter in the study of high-speed aerodynamic phenomena, including sonic booms, shock waves, and the transition between subsonic and supersonic flight.

Definition

The Mach number (M) is defined as: \[M = \frac{v}{a}\] where:

• \(v\) is the velocity of the object relative to the fluid,
• \(a\) is the speed of sound in the fluid at the given conditions.

The speed of sound, and thus the Mach number, varies depending on the temperature, composition, and phase of the fluid. In air at sea level and at 15°C, the speed of sound is approximately 340.3 m/s (1,225 km/h; 761 mph).

Categories of Mach Numbers

Mach numbers categorize the speed regime of flight or flow:

• Subsonic: M < 1, where the flow velocity is less than the speed of sound.
• Transonic: M ≈ 1, where the flow velocity is close to the speed of sound, and both subsonic and supersonic flows are present around the object.
• Supersonic: 1 < M < 5, where the flow velocity is greater than the speed of sound.
• Hypersonic: M ≥ 5, where the flow velocity is much greater than the speed of sound, and the chemistry of the air can change.

Significance

The Mach number is significant in the design and analysis of aircraft, missiles, and spacecraft. At different Mach numbers, air behaves in fundamentally different ways, affecting lift, drag, and overall aerodynamic performance. For example, as an aircraft transitions from subsonic to supersonic speeds, it experiences a sharp increase in drag near Mach 1, known as the sound barrier. Modern aircraft and engines are designed with specific Mach number regimes in mind, optimizing performance for their intended operational speeds.

Applications

In addition to its importance in aeronautics and astronautics, Mach number is also relevant in the study of natural phenomena and engineering problems involving the flow of gases and liquids. Examples include the analysis of explosions, the design of wind tunnels, and the study of meteorological phenomena.

See Also

• Ernst Mach
• Speed of sound
• Sonic boom
• Shock wave
• Subsonic and supersonic flight
• Hypersonic flight