Mach number

Mach number (Ma) (pronounced as "mack" in International English or "mock" in the American English) is defined as a ratio of speed to the speed of sound in the medium in case. The Mach number is commonly used both with objects travelling at high speed in a fluid, and with high-speed fluid flows inside channels such as nozzles, diffusers or wind tunnels. As it is defined as a ratio of two speeds, it is a dimensionless number. At standard sea level conditions, Mach 1 is 1,225 km/h (765.6 MPH) in the atmosphere.

High-speed flow around objects

High speed flight can be classified in five categories:

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• Subsonic: Ma < 1
• Sonic: Ma = 1
• Supersonic: 1.2
• Transsonic: 0.8 < Ma < 1.2
• Hypersonic: Ma > 5

(For comparison: the required speed for low Earth orbit is ca. 7.5 km/s = Ma 22.06 in air at sea level)

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At transsonic speeds, the flow field around the object includes both sub- and supersonic parts. The transsonic regime begins when first zones of Ma>1 flow appear around the object. In case of an airfoil (such as an aircraft's wing), this typically happens above the wing. Supersonic flow can decelerate back to subsonic only in a normal shock; this typically happens before the trailing edge. (Fig.1a)

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As the velocity increases, the zone of Ma>1 flow increases towards both leading and trailing edges. As Ma=1 is reached and passed, the normal shock reaches the trailing edge and becomes a weak oblique shock: the flow decelerates over the shock, but remains supersonic. A normal shock is created ahead of the object, and the only subsonic zone in the flow field is a small area around the object's leading edge. (Fig.1b)

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Fig. 1. Mach number in transsonic airflow around an airfoil; Ma1 (b).

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When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the sonic boom heard as fast moving aircraft travels overhead. A person inside the aircraft will not hear this. The higher the speed, the more narrow the cone; at just over Ma=1 it is hardly a cone at all, but closer to a wall only slight bending backwards.

Related Topics:
Sound barrier - Aircraft - Shock wave - Sonic boom

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At fully supersonic velocity the shock wave starts to take its cone shape, and flow is either completely supersonic, or (in case of a blunt object), only a very small subsonic flow area remains between the object's nose and the shock wave it creates ahead of itself. (In the case of a sharp object, there is no air between the nose and the shock wave: the shock wave starts from the nose.)

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As the Mach number increases, so does the strength of the shock wave and the Mach cone becomes increasingly narrow. As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase. The stronger the shock, the greater the changes. At high enough Mach numbers the temperature increases so much over the shock that ionization and dissociation of gas molecules behind the shock wave begin. Such flows are called hypersonic.

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It is clear that any object travelling at hypersonic velocities will likewise be exposed to the same extreme temperatures as the gas behind the nose shock wave, and hence choice of heat-resistant materials becomes important.

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