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at
transonic speed and displaying the Prandtl-Glauert singularity just before breaking the
sound barrier.
Mach number (
Ma) (pronounced: , 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:
\ M = \frac
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
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 Austria 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 Sound barrier#Attempts to break the sound barrier, aeronautical engineers referred to the speed of sound as
Mach's number, never "Mach 1".Bodie, Warren M.,
The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5
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 knot (speed)) 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
foot (length)), 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:
- sonic: Ma=1
- Subsonic: Ma < 1
- Transonic: 0.8 < Ma < 1.2
- Supersonic: 1.2 < Ma < 5
- Hypersonic: Ma > 5
(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 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
at
transonic speed and displaying the Prandtl-Glauert singularity just before breaking the sound barrier.
Mach number (
Ma) (pronounced: , 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:
\ M = \frac
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
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 Austria 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
Sound barrier#Attempts to break the sound barrier, aeronautical engineers referred to the speed of sound as
Mach's number, never "Mach 1".Bodie, Warren M.,
The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5
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
knot (speed)) 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 foot (length)), 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:
- sonic: Ma=1
- Subsonic: Ma < 1
- Transonic: 0.8 < Ma < 1.2
- Supersonic: 1.2 < Ma < 5
- Hypersonic: Ma > 5
(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 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
Mach number - Wikipedia, the free encyclopedia
Mach number (Ma or M) (generally pronounced /ˈmɑːk/, sometimes /ˈmɑːx/ or /ˈmæk/) is the speed of an object moving through air, or any fluid substance, divided by the speed ...
Mach Number
As an aircraft moves through the air, the air molecules near the aircraft are disturbed and move around the aircraft. If the aircraft passes at a low speed, typically less than 250 ...
Mach number
Ratio of the speed of a body to the speed of sound in the medium through which the body travels ... Tiscali Quicklinks. Please visit our Accessibility Page for a list of the Access ...
Definition: Mach number from Online Medical Dictionary
The Online Medical Dictionary is a searchable dictionary of definitions from medicine, science and technology.
Mach Number
As a rocket moves through the air, the air molecules near the rocket are disturbed and move around the rocket. If the rocket passes at a low speed, typically less than 250 mph ...
The effect of Mach number on unstable disturbances in shock/boundary ...
The effect of Mach number on unstable disturbances in shock/boundary-layer interactions
e-Prints Soton - The effect of Mach number on unstable disturbances in ...
The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct ...
Mach number - Hutchinson encyclopedia article about Mach number
Mach number. Ratio of the speed of a body to the speed of sound in the medium through which the body travels. In the Earth's atmosphere, Mach 1 is reached when a body (such as an ...
Mach number definition of Mach number in the Free Online Encyclopedia.
Mach number (mäk) [for E. Mach Mach, Ernst (ĕrnst mäkh), 1838–1916, Austrian physicist and philosopher, b. Moravia..... Click the link for more information.], ratio between ...
e-Prints Soton - Effect of Mach number on the structure of turbulent ...
Direct numerical simulations have been performed to study the dynamics of isolated turbulent spots in compressible isothermal-wall boundary layers. Results of a bypass transition ...
