Mach number
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Mach number
also mach number (mäk) 
n. (Abbr. M)
The ratio of the speed of an object to the speed of sound in the surrounding medium. For example, an aircraft moving twice as fast as the speed of sound is said to be traveling at Mach 2.
n. (Abbr. M)
The ratio of the speed of an object to the speed of sound in the surrounding medium. For example, an aircraft moving twice as fast as the speed of sound is said to be traveling at Mach 2.
[After Ernst MACH.]
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Mach number
In the flow of a fluid, the ratio of the flow velocity, V, at a given point in the flow to the local speed of sound, a, at that same point. That is, the Mach number, M, is defined as V/a. In a flowfield where the properties vary in time and/or space, the local value of M will also vary in time and/or space. In aeronautics, Mach number is frequently used to denote the ratio of the airspeed of an aircraft to the speed of sound in the freestream far ahead of the aircraft; this is called the freestream Mach number. The Mach number is a convenient index used to define the following flow regimes: (1) subsonic, where M is less than 1 everywhere throughout the flow; (2) supersonic, where M is greater than 1 everywhere throughout the flow; (3) transonic, where the flow is composed of mixed regions of locally subsonic and supersonic flows, all with local Mach numbers near 1, typically between 0.8 and 1.2; and (4) hypersonic, where (by arbitrary definition) M is 5 or greater.
Perhaps the most important physical aspect of Mach number is in the completely different ways that disturbances propagate in subsonic flow compared to that in a supersonic flow. Shock waves are a ubiquitous aspect of supersonic flows. See also Compressible flow; Shock wave; Sonic boom; Supersonic flight.
Oxford Dictionary of the US Military:
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mach number
[ܒmäk ܒnǝmbǝr]
See the Introduction, Abbreviations and Pronunciation for further details.
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Breaking the Sound Barrier |
Mach is not the speed of sound; it's the ratio of the speed of an object to the speed of sound. An object moving at the speed of sound is moving at Mach 1. An object moving twice as fast as the speed of sound is said to be traveling at Mach 2, and so on. The Mach number was named for physicist Ernst Mach, born on February 18, 1838. Mach noted that air flow changes dramatically when it exceeds the speed of sound. A believer in logical positivism — the philosophy that knowledge should be based on logical inference from tangible and observable facts — Mach influenced Albert Einstein and his theory of relativity.
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From our Archives: Today's Highlights, February 18, 2011
Mach number (mäk) [for E. Mach], ratio between the speed of an object and the speed of sound in the medium in which the object is traveling. An airplane that has the velocity of Mach 3.0 is traveling at three times the speed of sound as measured in the prevailing atmospheric conditions.
Science Q&A:
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What is a Mach number?
A Mach number is the equivalent of the speed of sound; therefore Mach 2 is twice the speed of sound, Mach 0.5 is half the speed of sound, etc.
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Dictionary of Cultural Literacy: Science:
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Mach number
(mahk)
The unit is named after Ernst Mach, an Austrian physicist of the nineteenth century.
The speed of an object, measured in multiples of the speed of sound. Thus, an airplane traveling at the speed of sound is said to be at Mach 1; at twice the speed of sound, it is said to be at Mach 2.
McGraw-Hill Dictionary of Aviation:
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Mach number
The ratio of the velocity of a body to that of sound in a surrounding medium. A Mach number of 0.8 or 1.2 means that the aircraft is flying at 0.8 or 1.2 times, respectively, the local speed of sound at that ambient temperature. Also known as a relative Mach number.
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categories related to 'mach number'
- Aviation and Aerodynamics - mach number: ratio of airspeed of an object to the speed of sound at given altitude and atmosphere, being 762 mph at sea level
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Mach number
"Mach 2" redirects here. For the film, see Mach 2 (film).
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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (August 2011) |
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In fluid mechanics, Mach number (
or 
) (generally 
/ˈmɑːk/, sometimes /ˈmɑːx/ or /ˈmæk/) is a dimensionless number representing the speed of an object moving through air or other fluid divided by the local speed of sound.[1][2] It is commonly used to represent the speed of an object when it is traveling close to or above the speed of sound.
where
is the Mach number,
is the velocity of the source relative to the medium and
is the speed of sound in the medium.
Mach number varies by the composition of the surrounding medium and also by local conditions, especially temperature and pressure. The Mach number can be used to determine if a flow can be treated as an incompressible flow. If M < 0.2–0.3 and the flow is (quasi) steady and isothermal, compressibility effects will be small and a simplified incompressible flow model can be used.[1][2]
The Mach number is named after Austrian physicist and philosopher Ernst Mach, a designation proposed by aeronautical engineer Jakob Ackeret. Because the Mach number is often viewed as a dimensionless quantity rather than a unit of measure, with Mach, the number comes after the unit; the second Mach number is "Mach 2" instead of "2 Mach" (or Machs). This is somewhat reminiscent of the early modern ocean sounding unit "mark" (a synonym for fathom), which was also unit-first, and may have influenced the use of the term Mach. In the decade preceding faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1."[3]
In French, the Mach number is sometimes called the "nombre de Sarrau" ("Sarrau number") after Émile Sarrau who researched into explosions in the 1870s and 1880s.[4]
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Contents
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Overview
The Mach number is commonly used both with objects traveling 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 (corresponding to a temperature of 15 degrees Celsius), the speed of sound is 340.3 m/s[5] (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature and atmospheric composition and largely independent of pressure. Since the speed of sound increases as the temperature increases, the actual speed of an object traveling at Mach 1 will depend on the fluid temperature around it. Mach number is useful because the fluid behaves in a similar way at the same Mach number. So, an aircraft traveling at Mach 1 at 20°C or 68°F, at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft) at -50°C or -58F, even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F.[6]
High-speed flow around objects
Flight can be roughly classified in six categories:
| Regime | Subsonic | Transonic | Sonic | Supersonic | Hypersonic | High-hypersonic |
|---|---|---|---|---|---|---|
| Mach | <1.0 | 0.8–1.2 | 1.0 | 1.2–5.0 | 5.0–10.0 | >10.0 |
For comparison: the required speed for low Earth orbit is approximately 7.5 km/s = Mach 25.4 in air at high altitudes. The speed of light in a vacuum corresponds to a Mach number of approximately 881,000 (relative to air at sea level).
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. 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)
As the speed increases, the zone of M>1 flow increases towards both leading and trailing edges. As M=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)
 |
 |
| (a) | (b) |
Fig. 1. Mach number in transonic airflow around an airfoil; M<1 (a) and M>1 (b).
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 a 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 M=1 it is hardly a cone at all, but closer to a slightly concave plane.
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. (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.)
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.
It is clear that any object traveling 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.
High-speed flow in a channel
As a flow in a channel becomes supersonic, one significant change takes place. The conservation of mass flow rate leads one to expect that contracting the flow channel would increase the flow speed (i.e. making the channel narrower results in faster air flow) and at subsonic speeds this holds true. However, once the flow becomes supersonic, the relationship of flow area and speed is reversed: expanding the channel actually increases the speed.
The obvious result is that in order to accelerate a flow to supersonic, one needs a convergent-divergent nozzle, where the converging section accelerates the flow to sonic speeds, and the diverging section continues the acceleration. Such nozzles are called de Laval nozzles and in extreme cases they are able to reach hypersonic speeds (Mach 13 (9,896 mph; 15,926 km/h) at 20°C).
An aircraft Machmeter or electronic flight information system (EFIS) can display Mach number derived from stagnation pressure (pitot tube) and static pressure.
Calculation
Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from Bernoulli's equation for M<1:[7]
![{M}=\sqrt{\frac{2}{\gamma-1}\left[\left(\frac{q_c}{p}+1\right)^\frac{\gamma-1}{\gamma}-1\right]}\,](http://wpcontent.answcdn.com/wikipedia/en/math/3/2/3/3235fb9ddd80dcd95b85c6fa7b4c2bb0.png)
where:
is Mach number
is impact pressure and
is static pressure
is the ratio of specific heat of a gas at a constant pressure to heat at a constant volume (1.4 for air).
The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:
![\frac{q_c}{p} = \left[\left(\frac{\gamma+1}{2}\right)M^2\right]^\left(\frac{\gamma}{\gamma-1}\right)\cdot \left[ \frac{\gamma+1}{\left(1-\gamma+2 \gamma \cdot M^2\right)^\left(\frac{1}{ \gamma-1 }\right)} \right]^\left(\frac{1}{ \gamma-1 }\right)-1](http://wpcontent.answcdn.com/wikipedia/en/math/a/8/7/a87cdc9345b6c152b969185e1840c49d.png)
or for air, a simplified formula:
![{M}=0.88128485\sqrt{\left[\left(\frac{q_c}{p}+1\right)\left(1-\frac{1}{[7M^2]}\right)^{2.5}\right]}](http://wpcontent.answcdn.com/wikipedia/en/math/c/3/f/c3f79fe489ea7efa1a846f3a62fb6123.png)
where:
is now impact pressure measured behind a normal shock.
The Mach number at which an aircraft is flying at can be calculated by
where:
- is Mach number
is velocity of the moving aircraft and- is the speed of sound at the given altitude
Note that the dynamic pressure can be found as:
See also
Notes
- ^ a b Young, Donald F.; Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch (2010). A Brief Introduction to Fluid Mechanics (5 ed.). John Wiley & Sons. p. 95. ISBN 978-0-470-59679-1.
- ^ a b Graebel, W.P. (2001). Engineering Fluid Mechanics. Taylor & Francis. p. 16. ISBN 978-1-56032-733-2.
- ^ Bodie, Warren M., The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5
- ^ Blackmore, John T. (1972). Ernst Mach: His Life, Work, and Influence. University of California Press. p. 112. ISBN 978-0-520-01849-5.
- ^ Clancy, L.J. (1975), Aerodynamics, Table 1, Pitman Publishing London, ISBN 0-273-01120-0
- ^ ([1]). National Aeronautics and Space Administration website page "Mach Number", NASA.
- ^ Olson, Wayne M. (2002). "AFFTC-TIH-99-02, Aircraft Performance Flight Testing." (PDF). Air Force Flight Test Center, Edwards AFB, CA, United States Air Force.
External links
- Gas Dynamics Toolbox Calculate Mach number and normal shock wave parameters for mixtures of perfect and imperfect gases.
- NASA's page on Mach Number Interactive calculator for Mach number.
- NewByte standard atmosphere calculator and speed converter
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