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Encyclopedia > Mach number
An F/A-18 Hornet at transonic speed and displaying the Prandtl-Glauert singularity just before reaching the speed of sound

Mach number (Ma) (generally pronounced /ˈmɑːk/, sometimes /ˈmɑːx/ or /ˈmæk/) is the speed of an object moving through air, or any fluid substance, divided by the speed of sound through that substance: Image File history File links Download high resolution version (2100x1500, 1416 KB) U.S. Navy F/A-18 at transonic speed. ... Image File history File links Download high resolution version (2100x1500, 1416 KB) U.S. Navy F/A-18 at transonic speed. ... The McDonnell Douglas (now Boeing) F/A-18 Hornet is a modern all-weather carrier-capable strike fighter jet, designed to attack both ground and aerial targets. ... Transonic is an aeronautics term referring to a range of velocities just below and above the speed of sound. ... F/A-18 demonstrating singularity effect The Prandtl-Glauert singularity, at which point a sudden drop in air pressure occurs, is generally accepted as the cause of the visible condensation cloud that often surrounds an airplane traveling at transonic speeds, though there remains some debate. ... This box:      A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of how small the applied stress. ... For other uses, see Speed of sound (disambiguation). ...

$M = frac {{v_o}}{{v_s}}$

where

$M$ is the Mach number
$v_o$ is the velocity of the object relative to the medium and
$v_s$ is the velocity of sound in the medium

The Mach number 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] Ernst Mach Ernst Mach (February 18, 1838 â€“ February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ... A fathom is the name of a unit of length in the Imperial system (and the derived U.S. customary units). ... U.S. Navy F/A-18 breaking the sound barrier. ...

## Contents

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 a temperature of 15 degrees Celsius and at sea level, the speed of sound is 343 m/s (1235 km/h, or 770 mph, or 1129 ft/s) 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. Mach may refer to: Ernst Mach Mach number, as a measure of speed inertial mass GNU Mach The microkernel on which GNU Hurd is based Mach kernel, an operating systems kernel technology used in Mac OS X Mach band, an optical illusion Mach Five, the name of the car in... Rocket Nozzle A nozzle is a mechanical device designed to control the characteristics of a fluid flow as it exits from an enclosed chamber into some medium. ... Diffuser can refer to any device that diffuses in some manner such as: Diffuser (automotive), a shaped section of a cars underbody which improves the cars aerodynamic properties Diffuser (breathing set part), a device fitted over an underwater breathing sets blowoff hole to break up the resulting... NASA wind tunnel with the model of a plane A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... For other uses, see Temperature (disambiguation). ... For other uses, see Celsius (disambiguation). ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... Metre per second (U.S. spelling: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector), defined by distance in metres divided by time in seconds. ... Kilometres per hour (American spelling: kilometers per hour) is a unit of both speed (scalar) and velocity (vector). ... Miles per hour is a unit of speed, expressing the number of international miles covered per hour. ... Feet per second is a unit of speed; it expressses the number of feet traveled in one second. ... Air redirects here. ... Atmosphere diagram showing stratosphere. ...

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 sea level (340.3 m/s, 761.2 mi/h, 1,225 km/h) will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft), even though it is traveling at 295 m/s (654.6 mph, 1,062 km/h, 86% of its speed at sea level). A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, â€² â€“ a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ...

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) Subsonic has two possible meanings: A speed lower than the speed of sound is called subsonic. ... Look up Sonic in Wiktionary, the free dictionary. ... Transonic is an aeronautics term referring to a range of velocities just below and above the speed of sound. ... A United States Navy F/A-18E/F Super Hornet in transonic flight. ... Boeing X-43 at Mach 7 In aerodynamics, hypersonic speeds are speeds that are highly supersonic. ... A low Earth orbit (LEO) is an orbit in which objects such as satellites are below intermediate circular orbit (ICO) and far below geostationary orbit, but typically around 350 - 1400 km above the Earths surface. ...

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). Drawing to show Mach number variation around an airfoil at transsonic speed, 0. ... Drawing to show Mach number variation around airfoil at transsonic speed, 1. ...

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. U.S. Navy F/A-18 breaking the sound barrier. ... Flying machine redirects here. ... Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ... For other uses, see Sonic boom (disambiguation). ...

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. Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ...

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). Diagram of a de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making an hourglass-shape. ... Boeing X-43 at Mach 7 In aerodynamics, hypersonic speeds are speeds that are highly supersonic. ...

An aircraft Machmeter or electronic flight information system (EFIS) can display Mach number derived from stagnation pressure (pitot tube) and static pressure. Diagram illustrating the face of a Machmeter A Machmeter shows the ratio of the speed of sound to the true airspeed an aircraft is flying. ... EFIS is a stucco material usually applied to rigid insulation to provide an exterior protective coating on buildings. ... A Pitot tube is a measuring instrument used to measure fluid flow. ...

## 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] An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces, where the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container and each other and are in constant random motion. ... In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ...

${M}=sqrt{frac{2}{gamma-1}left[left(frac{q_c}{P}+1right)^frac{gamma-1}{gamma}-1right]}$

where:

$M$ is Mach number
$q_c$ is impact pressure and
$P$ is static pressure
$gamma$ 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: Static pressure is a term used in ventilation engineering, airspeed indication, fluid statics, hydraulics and flow measurement. ... In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with the heat transfer within the fluid. ...

${M}=0.88128485sqrt{left[left(frac{q_c}{P}+1right)left(1-frac{1}{[7M^2]}right)^{2.5}right]}$

where:

$q_c$ 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] Screenshot of a spreadsheet under OpenOffice A spreadsheet is a rectangular table (or grid) of information, often financial information. ...

Diagram illustrating the face of a Machmeter A Machmeter shows the ratio of the speed of sound to the true airspeed an aircraft is flying. ... For other uses, see Speed of sound (disambiguation). ... True airspeed (TAS) is the speed of an aircraft relative to the airmass in which it flies, i. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... --68. ... An Archimedes number, named after the ancient Greek scientist Archimedes, to determine the motion of fluids due to density differences, is a dimensionless number in the form where: g = gravitational acceleration (9. ... The Bagnold number, named after Ralph Alger Bagnold, used in granular flow calculations, is defined by where is the mass, is the grain diameter, is the surface tension and is the interstitial fluid viscosity. ... The Biot number (Bi) is a dimensionless number used in unsteady-state (or transient) heat transfer calculations. ... In fluid mechanics, the Bond number, notated Bo, is a dimensionless number expressing the ratio of body forces (often gravitational) to surface tension forces: where is the density, the acceleration associated with the body force, e. ... The Brinkman Number is a dimensionless group related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing. ... The capillary number represents the relative effect of viscous forces and surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids. ... The DamkÃ¶hler numbers (Da) are dimensionless numbers used in chemical engineering to relate chemical reaction timescale to other phenomena occurring in a system. ... The Dean number is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. ... The Deborah number is a dimensionless number, used in rheology to characterize how fluid a material is. ... The Eckert number is a dimensionless number used in flow calculations. ... The Ekman number, named for V. Walfrid Ekman, is a dimensionless number used in describing geophysical phenomena in the oceans and atmosphere. ... In fluid dynamics the EÃ¶tvÃ¶s number (Eo) is a dimensionless number named after Hungarian physicist LorÃ¡nd EÃ¶tvÃ¶s (1848-1919). ... The Euler number or cavitation number is a dimensionless number used in flow calculations. ... The Froude number is a dimensionless number used to quantify the resistance of an object moving through water, and compare objects of different sizes. ... In fluid dynamics, the Galilei number (Ga), sometimes also referred to as Galileo number (see discussion), is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642). ... The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy force to the viscous force acting on a fluid. ... The Hagen number is a dimensionless number used in forced flow calculations. ... The Knudsen number (Kn) is the ratio of the molecular mean free path length to a representative physical length scale. ... The Laplace number (La) is a dimensionless number used in the characterisation of free surface fluid dynamics. ... The Lewis number is a dimensionless number approximating the ratio of mass diffusivity and thermal diffusivity, and is used to characterize fluid flows in where there are simultaneous heat and mass transfer by convection. ... The Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and is used for determining whether a flow will be laminar or turbulent. ... The Marangoni number (Mg) is a dimensionless number named after Italian scientist Carlo Marangoni. ... In fluid dynamics, the Morton number () is a dimensionless number used together with the EÃ¶tvÃ¶s number to characterize the shape of bubbles or drops. ... The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface compared to the heat transferred if just conduction occurred. ... The Ohnesorge number, Z , is a dimensionless number that relates the viscous and surface tension force. ... In physics, the PÃ©clet number is a dimensionless number relating the forced convection of a system to its heat conduction. ... The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. ... In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with the heat transfer within the fluid. ... In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ... The Richardson number is named after Lewis Fry Richardson (1881 - 1953). ... In fluid mechanics, the Roshko number is a dimensionless number describing oscillating flow mechanisms. ... The Rossby number, named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow, usually in geophysical phenomena in the oceans and atmosphere. ... The Ruark number (RU) is a dimensionless number see in fluid mechanics. ... The Schmidt number is a dimensionless number approximating the ratio of momentum diffusivity (viscosity) and mass diffusivity, and is used to characterize fluid flows in where there are simultaneous momentum and mass diffusion convection processes. ... The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. ... The Stanton number is a dimensionless number which measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. ... The Stokes number is a dimensionless number corresponding to the behavior of particles suspended in a fluid flow. ... In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. ... The Laplace number (La), also known as the Suratman number (Su), is a dimensionless number used in the characterization of free surface fluid dynamics. ... In physics, the Taylor number is a dimensionless quantity that characterizes the importance of rotation of a fluid about a vertical axis. ... The Weber number is a dimensionless quantity in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. ... The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. ... A Womersley number is a dimensionless number in biofluid mechanics. ...

## References

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

Results from FactBites:

 Mach number - Wikipedia, the free encyclopedia (892 words) 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. At a temperature of 15 degrees Celsius, Mach 1 is 1,225 km·h The mach number is not a constant; it is temperature dependent.
 Ernst Mach - Wikipedia, the free encyclopedia (768 words) Ernst Mach (February 18, 1838 – February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the "Mach number" (aka Mach speed) and the optical illusion known as Mach bands. Mach returned to the University of Vienna as professor of inductive philosophy in 1895, but he suffered a stroke two years later and retired from active research in 1901, when he was appointed to the Austrian parliament. Mach's paper on this subject was published in 1877 and correctly describes the sound effects observed during the supersonic motion of a projectile.
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