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Mach number

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Mach number

The Mach number (M or Ma), often only Mach, (; German: [max]) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after Austrian physicist and philosopher Ernst Mach.

M = u c , {\displaystyle \mathrm {M} ={\frac {u}{c}},}

where:

M is the local Mach number, u is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and c is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach 1, the local flow velocity u is equal to the speed of sound. At Mach 0.65, u is 65% of the speed of sound (subsonic), and, at Mach 1.35, u is 35% faster than the speed of sound (supersonic). The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium can be a gas or a liquid. The boundary can be travelling in the medium, or it can be stationary while the medium flows along it, or they can both be moving, with different velocities: what matters is their relative velocity with respect to each other. The boundary can be the boundary of an object immersed in the medium, or of a channel such as a nozzle, diffuser or wind tunnel channelling the medium. As the Mach number is defined as the ratio of two speeds, it is a dimensionless quantity. If M < 0.2–0.3 and the flow is quasi-steady and isothermal, compressibility effects will be small and simplified incompressible flow equations can be used.

Tables

· Classification of Mach regimes
(Mach)
(Mach)
Regime
(Mach)
Flight speed
(knots)
Flight speed
(mph)
Flight speed
(km/h)
Flight speed
(m/s)
Subsonic
Subsonic
Regime
Subsonic
Flight speed
<0.8
Flight speed
<530
Flight speed
<609
Flight speed
<980
Flight speed
<273
General plane characteristics
Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges. The subsonic speed range is that range of speeds within which, all of the airflow over an aircraft is less than Mach 1. The critical Mach number (Mcrit) is lowest free stream Mach number at which airflow over any part of the aircraft first reaches Mach 1. So the subsonic speed range includes all speeds that are less than Mcrit.
Transonic
Transonic
Regime
Transonic
Flight speed
0.8–1.2
Flight speed
530–794
Flight speed
609–914
Flight speed
980–1,470
Flight speed
273–409
General plane characteristics
Transonic aircraft nearly always have swept wings, causing the delay of drag-divergence, and often feature a design that adheres to the principles of the Whitcomb area rule. The transonic speed range is that range of speeds within which the airflow over different parts of an aircraft is between subsonic and supersonic. So the regime of flight from Mcrit up to Mach 1.3 is called the transonic range.
Supersonic
Supersonic
Regime
Supersonic
Flight speed
1.2–5.0
Flight speed
794–3,308
Flight speed
915–3,806
Flight speed
1,470–6,126
Flight speed
410–1,702
General plane characteristics
The supersonic speed range is that range of speeds within which all of the airflow over an aircraft is supersonic (more than Mach 1). But airflow meeting the leading edges is initially decelerated, so the free stream speed must be slightly greater than Mach 1 to ensure that all of the flow over the aircraft is supersonic. It is commonly accepted that the supersonic speed range starts at a free stream speed greater than Mach 1.3. Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1. Sharp edges, thin aerofoil sections, and all-moving tailplane/canards are common. Modern combat aircraft must compromise in order to maintain low-speed handling.
Hypersonic
Hypersonic
Regime
Hypersonic
Flight speed
5.0–10.0
Flight speed
3,308–6,615
Flight speed
3,806–7,680
Flight speed
6,126–12,251
Flight speed
1,702–3,403
General plane characteristics
The X-15, at Mach 6.72, is one of the fastest crewed aircraft. Cooled nickel-titanium skin; highly integrated (due to domination of interference effects: non-linear behaviour means that superposition of results for separate components is invalid), small wings, such as those on the Mach 5 X-51A Waverider.
High-hypersonic
High-hypersonic
Regime
High-hypersonic
Flight speed
10.0–25.0
Flight speed
6,615–16,537
Flight speed
7,680–19,031
Flight speed
12,251–30,626
Flight speed
3,403–8,508
General plane characteristics
The NASA X-43, at Mach 9.6, is one of the fastest aircraft. Thermal control becomes a dominant design consideration. Structure must either be designed to operate hot, or be protected by special silicate tiles or similar. Chemically reacting flow can also cause corrosion of the vehicle's skin, with free-atomic oxygen featuring in very high-speed flows. Hypersonic designs are often forced into blunt configurations because of the aerodynamic heating rising with a reduced radius of curvature.
Re-entry speeds
Re-entry speeds
Regime
Re-entry speeds
Flight speed
>25.0
Flight speed
>16,537
Flight speed
>19,031
Flight speed
>30,626
Flight speed
>8,508
General plane characteristics
Ablative heat shield; small or no wings; blunt shape. Russia's Avangard is claimed to reach up to Mach 27.
Regime
Flight speed
General plane characteristics
(Mach)
(knots)
(mph)
(km/h)
(m/s)
Subsonic
<0.8
<530
<609
<980
<273
Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges. The subsonic speed range is that range of speeds within which, all of the airflow over an aircraft is less than Mach 1. The critical Mach number (Mcrit) is lowest free stream Mach number at which airflow over any part of the aircraft first reaches Mach 1. So the subsonic speed range includes all speeds that are less than Mcrit.
Transonic
0.8–1.2
530–794
609–914
980–1,470
273–409
Transonic aircraft nearly always have swept wings, causing the delay of drag-divergence, and often feature a design that adheres to the principles of the Whitcomb area rule. The transonic speed range is that range of speeds within which the airflow over different parts of an aircraft is between subsonic and supersonic. So the regime of flight from Mcrit up to Mach 1.3 is called the transonic range.
Supersonic
1.2–5.0
794–3,308
915–3,806
1,470–6,126
410–1,702
The supersonic speed range is that range of speeds within which all of the airflow over an aircraft is supersonic (more than Mach 1). But airflow meeting the leading edges is initially decelerated, so the free stream speed must be slightly greater than Mach 1 to ensure that all of the flow over the aircraft is supersonic. It is commonly accepted that the supersonic speed range starts at a free stream speed greater than Mach 1.3. Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1. Sharp edges, thin aerofoil sections, and all-moving tailplane/canards are common. Modern combat aircraft must compromise in order to maintain low-speed handling.
Hypersonic
5.0–10.0
3,308–6,615
3,806–7,680
6,126–12,251
1,702–3,403
The X-15, at Mach 6.72, is one of the fastest crewed aircraft. Cooled nickel-titanium skin; highly integrated (due to domination of interference effects: non-linear behaviour means that superposition of results for separate components is invalid), small wings, such as those on the Mach 5 X-51A Waverider.
High-hypersonic
10.0–25.0
6,615–16,537
7,680–19,031
12,251–30,626
3,403–8,508
The NASA X-43, at Mach 9.6, is one of the fastest aircraft. Thermal control becomes a dominant design consideration. Structure must either be designed to operate hot, or be protected by special silicate tiles or similar. Chemically reacting flow can also cause corrosion of the vehicle's skin, with free-atomic oxygen featuring in very high-speed flows. Hypersonic designs are often forced into blunt configurations because of the aerodynamic heating rising with a reduced radius of curvature.
Re-entry speeds
>25.0
>16,537
>19,031
>30,626
>8,508
Ablative heat shield; small or no wings; blunt shape. Russia's Avangard is claimed to reach up to Mach 27.
· High-speed flow around objects
Mach
Mach
Regime
Mach
Subsonic
<0.8
Transonic
0.8–1.2
Speed of sound
1.0
Supersonic
1.2–5.0
Hypersonic
5.0–10.0
Hypervelocity
>8.8
Regime
Subsonic
Transonic
Speed of sound
Supersonic
Hypersonic
Hypervelocity
Mach
<0.8
0.8–1.2
1.0
1.2–5.0
5.0–10.0
>8.8

References

  1. A Brief Introduction to Fluid Mechanics
    https://lccn.loc.gov/2010038482
  2. Engineering Fluid Mechanics
    https://search.worldcat.org/oclc/1034989004
  3. Encyclopædia Britannica
    https://www.britannica.com/biography/Ernst-Mach
  4. Jakob Ackeret: Der Luftwiderstand bei sehr großen Geschwindigkeiten. Schweizerische Bauzeitung 94 (Oktober 1929), pp. 17
  5. Bodie, Warren M., The Lockheed P-38 Lightning, Widewing Publications ISBN 0-9629359-0-5.
  6. NASA
    https://www.grc.nasa.gov/WWW/k-12/airplane/mach.html
  7. Clancy, L.J. (1975), Aerodynamics, Table 1, Pitman Publishing London, ISBN 0-273-01120-0
  8. Fluid Mechanics
  9. Olson, Wayne M. (2002). "AFFTC-TIH-99-02, Aircraft Performance Flight Testing". Air Force Flight Test Center, Edwards Ai
    http://www.aviation.org.uk/pdf/Aircraft_Performance_Flight_Testing.pdf
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