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Information about Mach Number

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An F/A-18 Hornet at transonic speed and displaying the Prandtl-Glauert singularity just before breaking the sound barrier.
Mach number (Ma) (pronounced: [mɑːk], [mɑx], [mæk], see IPA) is a dimensionless measure of relative speed. It is defined as the speed of an object relative to a fluid medium, divided by the speed of sound in that medium:

where
is the Mach number


is the velocity of the object relative to the medium and


is the velocity of sound in the medium


Mach number is the number of times the speed of sound an object or a duct, or the fluid medium itself, move relative to each other. It is named after Austrian physicist and philosopher Ernst Mach. Unlike most units of measure, with Mach the number comes after the unit, so one says "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 man flying faster than sound, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1".[1]

Overview

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 a temperature of 15 degrees Celsius and at sea level, Mach 1 is 340.3 m/s (1,225 km/h, 761.2 mph, or 661.7 kn) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; For example, it is dependent on temperature and atmospheric composition. In the stratosphere it remains constant irrespective of altitude even though the air pressure varies with altitude.

Since the speed of sound increases as the temperature increases, the actual speed of an object travelling 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 travelling at Mach 1 at sea level (340.3 m/s, 1,225.08 km/h) will experience shock waves in much the same manner as when it is travelling at Mach 1 at 11,000 m (36,000 ft), even though it is travelling at 295 m/s (654.632 mph, 1,062 km/h, 86% of its speed at sea level).

It can be shown that the Mach number is also the ratio of inertial forces (also referred to aerodynamic forces) to elastic forces.

High-speed flow around objects

High speed flight can be roughly classified in five categories: (For comparison: the required speed for low Earth orbit is ca. 7.5 km·s-1 = Ma 25.4 in air at high altitudes)

At transonic speeds, the flow field around the object includes both sub- and supersonic parts. The transonic period 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)

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)

(a)(b)
Fig. 1. Mach number in transonic airflow around an airfoil; Ma<1 (a) and Ma>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 Ma=1 it is hardly a cone at all, but closer to a slightly concave plane.

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.)

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 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.

High-speed flow in a channel

As a flow in a channel crosses M=1 becomes supersonic, one significant change takes place. Common sense would lead 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 M=1, 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 incredible, hypersonic velocities (Mach 13 at sea level).

An aircraft Machmeter or electronic flight information system (EFIS) can display Mach number derived from stagnation pressure (pitot tube) and static pressure.

Calculating Mach Number

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:[2]



where:
is Mach number


is impact pressure and


is static pressure.


is the ratio of specific heats.


The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:



where:
is now impact pressure measured behind a normal shock


As can be seen, M appears on both sides of the equation. The easiest method to solve the supersonic M calculation is to enter both the subsonic and supersonic equations into a computer spreadsheet. First determine if M is indeed greater than 1.0 by calculating M from the subsonic equation. If M is greater than 1.0 at that point, then use the value of M from the subsonic equation as the initial condition in the supersonic equation. Then perform a simple iteration of the supersonic equation, each time using the last computed value of M, until M converges to a value--usually in just a few iterations.[2]

See also

 •  • [ e]
Dimensionless numbers in fluid dynamics
Archimedes • Bagnold • Bond • Brinkman • Capillary • Damkhler • Dean • Deborah • Eckert • Ekman • Etvs • Euler • Froude • Galilei • Grashof • Hagen • Knudsen • Laplace • Lewis • Mach • Magnetic Reynolds • Marangoni • Nusselt • Ohnesorge • Pclet • Prandtl • Rayleigh • Reynolds • Richardson • Rossby • Rouark • Schmidt • Sherwood • Stanton • Stokes • Strouhal • Taylor • Weber • Weissenberg • Womersley

References

1. ^ Bodie, Warren M., The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5
2. ^ 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.

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Speed is the rate of motion, or equivalently the rate of change in position, many times expressed as distance d traveled per unit of time t.

Speed is a scalar quantity with dimensions distance/time; the equivalent vector quantity to speed is known as
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speed of sound describes how much distance such a wave travels in a given amount of time. In dry air, at a temperature of 21 °C (70 °F) the speed of sound is 344 m/s (1238 km/h, or 769 mph, or 1128 ft/s).
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Ernst Mach (pronounced [max], see IPA) (February 18, 1838 – February 19, 1916) was a Bohemian-Austrian physicist and philosopher and is the namesake for the "Mach number" (also known as Mach speed) and the optical illusion known as Mach bands.
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1 fathom =
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Mach may refer to:
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A nozzle is a mechanical device designed to control the characteristics of a fluid flow as it exits (or enters) an enclosed chamber or pipe.

A nozzle is often a pipe or tube of varying cross sectional area, and it can be used to direct or modify the flow of a fluid (liquid
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wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects.

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In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
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trillion fold).]]

Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
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knot is a unit of speed. The abbreviation preferred by maritime authorities in the USA[1], and Canada [2], as well as the Institute of Electrical and Electronics Engineers and the International Bureau of Weights and Measures is kn.
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Earth's atmosphere is a layer of gases surrounding the planet Earth and retained by the Earth's gravity. It contains roughly (by molar content/volume) 78% nitrogen, 20.95% oxygen, 0.93% argon, 0.
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to scale: from Earth's surface to the top of the stratosphere (50km) is just under 1% of Earth's radius. (click to enlarge)]]

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Sonic could refer to:
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Transonic is an aeronautics term referring to a range of velocities just below and above the speed of sound (about mach 0.8–1.2). It is defined as the range of speeds between the critical mach number, when some parts of the airflow over an aircraft become supersonic, and a
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supersonic. Speeds greater than 5 times the speed of sound are sometimes referred to as hypersonic. Speeds where only some parts of the air around an object (such as the ends of rotor blades) reach supersonic speeds are labelled transonic (typically somewhere between Mach 0.
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hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime is a subset of the supersonic regime.
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Low Earth Orbit (LEO) is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km. Given the rapid orbital decay of objects below approximately 200 km, the commonly accepted definition for LEO is between 200 - 2000 km
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Sound Barrier was a heavy metal band from Los Angeles from 1980 to 1987.

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Sound Barrier was most notable for the fact that all four members were African American, which garnered them significant publicity, but which didn't result in commercial success.
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aircraft is a vehicle which is able to fly through the air (or through any other atmosphere). All the human activity which surrounds aircraft is called aviation. (Most rocket vehicles are not aircraft because they are not supported by the surrounding air).
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shock wave (or simply "shock") is a type of propagating disturbance. Like an ordinary wave, a shock wave carries energy and can propagate through a medium (solid, liquid or gas), or, in special cases, through a field such as the electromagnetic field in the absence of a
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sonic boom is commonly used to refer to the shocks caused by the supersonic flight of a military aircraft or passenger transports such as Concorde (Mach 2.03, no longer in service) and the Space Shuttle (up to Mach 27).
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shock wave (or simply "shock") is a type of propagating disturbance. Like an ordinary wave, a shock wave carries energy and can propagate through a medium (solid, liquid or gas), or, in special cases, through a field such as the electromagnetic field in the absence of a
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