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 as it is in that substance:

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

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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout Transonic is an Aeronautics term referring to a range of velocities just below and above the Speed of sound (about mach 0 FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Sound is a vibration that travels through an elastic medium as a Wave. Austria (Österreich ( officially the Republic of Austria (Republik Österreich Ernst Mach (max ( February 18, 1838 &ndash February 19, 1916) was an Austrian Physicist and Philosopher and Unlike most units 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. A fathom is a unit of Length in the Imperial system (and the derived U In the decade preceding man flying faster than sound, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1". WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout ^[1]

1 Overview
2 High-speed flow around objects
3 High-speed flow in a channel
4 Calculating Mach Number
5 See also
6 References
7 External links

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. A nozzle is a mechanical device or Orifice designed to control the characteristics of a Fluid flow as it exits (or enters an enclosed chamber or Pipe. A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects As it is defined as a ratio of two speeds, it is a dimensionless number. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units At a temperature of 15 degrees Celsius and at sea level, the speed of sound is 340. 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 The Celsius Temperature scale was previously known as the centigrade scale. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface 3 m/s^[2] (1225 km/h, or 761. (For the South African airport with IATA code "KMH" see Johan Pienaar Airport. 2 mph, or 1116 ft/s) in the Earth's atmosphere. The foot per second (plural feet per second) is a unit of both Speed (scalar and Velocity (vector quantity which includes direction Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five 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. The stratosphere is the second major layer of Earth's atmosphere, just above the Troposphere, and below the Mesosphere.

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. A foot (plural feet or foot; symbol or abbreviation ft or sometimes &prime – the prime symbol) is a non-SI unit 6 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

Flight can be roughly classified in five categories:

Subsonic: Ma < 1
Sonic: Ma=1
Transonic: 0. Transonic is an Aeronautics term referring to a range of velocities just below and above the Speed of sound (about mach 0 8 < Ma < 1. 2
Supersonic: 1. For other uses see Supersonic. The term supersonic is used to define a speed that is over the Speed of sound ( Mach 1 2 < Ma < 5
Hypersonic: Ma > 5

(For comparison: the required speed for low Earth orbit is ca. In Aerodynamics, hypersonic speeds are speeds that are highly Supersonic. A Low Earth Orbit (LEO is generally defined as an Orbit within the locus extending from the Earth’s surface up to an altitude of 2000 km 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. WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called It is this shock wave that causes the sonic boom heard as a fast moving aircraft travels overhead. The term sonic boom is commonly used to refer to the shocks caused by the Supersonic flight of an aircraft 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. For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called 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). 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 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. A Machmeter is an Aircraft Pitot-static system Flight instrument thatshows the Ratio of the True airspeed to the Speed of An electronic flight instrument system, or EFIS is a flight deck instrument display system in which the display technology used is electronic rather than electromechanical A Pitot (ˈpiːtoʊ tube is a Pressure measurement instrument used to measure Fluid flow Velocity.

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:^[3]

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

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:

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

where:

$\ q_c$ is now impact pressure measured behind a normal shock

As can be seen, M appears on both sides of the equation. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in Impact pressure is the difference between pitot pressure (also known as Stagnation pressure) and Static pressure. In the design and operation of Aircraft, static pressure is the air pressure in the aircraft’s static pressure system. In Fluid mechanics, the Rayleigh number for a fluid is a Dimensionless number associated with buoyancy driven flow (also known as Free convection or natural Impact pressure is the difference between pitot pressure (also known as Stagnation pressure) and Static pressure. The easiest method to solve the supersonic M calculation is to enter both the subsonic and supersonic equations into a computer spreadsheet. A spreadsheet is a Computer application that simulates a paper worksheet 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. ^[3]

References

^ Bodie, Warren M. A Machmeter is an Aircraft Pitot-static system Flight instrument thatshows the Ratio of the True airspeed to the Speed of Sound is a vibration that travels through an elastic medium as a Wave. True airspeed ( TAS) is the speed of an aircraft relative to the airmass in which it flies i , The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5
^ Clancy, L. J. (1975), Aerodynamics, Table 1, Pitman Publishing London, ISBN 0 273 01120 0
^ ^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.

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 Calculate Mach number.
NewByte standard atmosphere calculator and speed converter

Dictionary

-noun

(physics) The ratio of the velocity of a body to that of sound in the surrounding medium.

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