Mach number
The Mach number (M or Ma), often only Mach, (/mɑːk/; German: [max]) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
where: By definition, at Mach 1, the local flow velocity u is equal to the speed of sound.
The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas.
As the Mach number is defined as the ratio of two speeds, it is a dimensionless quantity.
It was also known as Mach's number by Lockheed when reporting the effects of compressibility on the P-38 aircraft in 1942.
[5] Mach number is a measure of the compressibility characteristics of fluid flow: the fluid (air) behaves under the influence of compressibility in a similar manner at a given Mach number, regardless of other variables.
[6] As modeled in the International Standard Atmosphere, dry air at mean sea level, standard temperature of 15 °C (59 °F), the speed of sound is 340.3 meters per second (1,116.5 ft/s; 761.23 mph; 1,225.1 km/h; 661.49 kn).
[7] The speed of sound is not a constant; in a gas, it increases proportionally to the square root of the absolute temperature, and since atmospheric temperature generally decreases with increasing altitude between sea level and 11,000 meters (36,089 ft), the speed of sound also decreases.
For example, the standard atmosphere model lapses temperature to −56.5 °C (−69.7 °F) at 11,000 meters (36,089 ft) altitude, with a corresponding speed of sound (Mach 1) of 295.0 meters per second (967.8 ft/s; 659.9 mph; 1,062 km/h; 573.4 kn), 86.7% of the sea level value.
This occurs because of the presence of a transonic regime around flight (free stream) M = 1 where approximations of the Navier-Stokes equations used for subsonic design no longer apply; the simplest explanation is that the flow around an airframe locally begins to exceed M = 1 even though the free stream Mach number is below this value.
Meanwhile, the supersonic regime is usually used to talk about the set of Mach numbers for which linearised theory may be used, where for example the (air) flow is not chemically reacting, and where heat-transfer between air and vehicle may be reasonably neglected in calculations.
So the regime of flight from Mcrit up to Mach 1.3 is called the transonic range.
Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1.
Sharp edges, thin aerofoil sections, and all-moving tailplane/canards are common.
Modern combat aircraft must compromise in order to maintain low-speed handling.
Flight can be roughly classified in six categories: At transonic speeds, the flow field around the object includes both sub- and supersonic parts.
The transonic period begins when first zones of M > 1 flow appear around the object.
Supersonic flow can decelerate back to subsonic only in a normal shock; this typically happens before the trailing edge.
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 a fast moving aircraft travels overhead.
At fully supersonic speed, 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.
As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase.
It is clear that any object travelling at hypersonic speeds 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.
As a flow in a channel becomes supersonic, one significant change takes place.
When the speed of sound is known, the Mach number at which an aircraft is flying can be calculated by
where: If the speed of sound is not known, Mach number may be determined by measuring the various air pressures (static and dynamic) and using the following formula that is derived from Bernoulli's equation for Mach numbers less than 1.0.
Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is:[8]
Aircraft flight instruments, however, operate using pressure differential to compute Mach number, not temperature.
Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is found from Bernoulli's equation for M < 1 (above):[8]
