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Mach number

Contents

  • Taxonavigation 1
  • Name 2
  • Overview 3
  • Classification of Mach regimes 4
  • Overview 5
  • Classification of Mach regimes 6
  • Name 7

Taxonavigation

Species (3):


[Source: WoRMS]

Name

Brochiverruca :bn=978-0-470-59679-1|edition=5|author2=Bruce R. Munson |author3=Theodore H. Okiishi |author4=Wade W. Huebsch |page=95}}[1]

\mathrm{M} = \frac }}

where

M is the Mach number,
v is the velocity of the source relative to the medium, and
vsound is the speed of sound in the medium.

Mach number depends on the condition of the surrounding medium, in particular the temperature and pressure. The Mach number can be used to determine if a flow can be treated as an incompressible flow. If M < 0.2–0.3 and the flow is (quasi) steady and isothermal, compressibility effects will be small and a simplified incompressible flow equations can be used.[2][1]

The Mach number is named after Austrian physicist and philosopher Ernst Mach, a designation proposed by aeronautical engineer Jakob Ackeret. As the Mach number is a dimensionless quantity rather than a unit 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. In the decade preceding faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1."[3]

Overview

The Mach number is commonly used 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 Standard Sea Level conditions (corresponding to a temperature of 15 degrees Celsius), the speed of sound is 340.3 m/s[4] (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature.

Since the speed of sound increases as the ambient temperature increases, the actual speed of an object traveling at Mach 1, will depend on the temperature of the fluid temperature through which is passing. Mach number is useful because the fluid behaves in the same manner at the similar Mach number. So, an aircraft traveling at Mach 1 at 20°C ( or 68°F), at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft) altitude, at −50°C (−58°F), even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F.[5]

Classification of Mach regimes

While the terms "subsonic" and "supersonic," in the purest sense, refer to speeds below and above the local speed of sound respectively, aerodynamicists often use the same terms to talk about particular ranges of Mach values. This occurs because of the presence of a "transonic regime" around M = 1 where approximations of the Navier-Stokes equations used for subsonic design actually no longer apply, the simplest explanation is that the flow locally begins to exceed M = 1 even though the freestream Mach number is below this value.

Meanwhile, the "supersonic regime" is usually used to talk about the set of Mach numbers for which linearised theory may be used, where for example the (air) flow is not chemically reacting, and where heat-transfer between air and vehicle may be reasonably neglected in calculations.

In the following table, the "regimes" or "ranges of Mach values" are referred to, and not the "pure" meanings of the words "subsonic" and "supersonic".

Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Aircraft operating in this regime include the Space Shuttle and various space planes in development.

Regime Mach mph km/h m/s General plane characteristics
Subsonic <0.8 <610 <980 <270 Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges.
Transonic 0.8-1.2 610-915 980-1,470 270-410 Transonic aircraft nearly always have swept wings, causing the delay of drag-divergence, and often features a design that adheres to the principles of the Whitcomb Area rule.
Supersonic 1.2–5.0 915-3,840 1,470–6,150 410–1,710 Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behaviour 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; "true" supersonic designs include the F-104 Starfighter, SR-71 Blackbird and BAC/Aérospatiale Concorde.
Hypersonic 5.0–10.0 3,840–7,680 6,150–12,300 1,710–3,415 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 X-51A Waverider
High-hypersonic 10.0–25.0
An F/A-18 Hornet creating a vapor cone at transonic speed just before reaching the speed of sound

In fluid mechanics, Mach number (M or Ma) is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local speed of sound.[2][1]

\mathrm{M} = \frac }}

where

M is the Mach number,
v is the velocity of the source relative to the medium, and
vsound is the speed of sound in the medium.

Mach number depends on the condition of the surrounding medium, in particular the temperature and pressure. The Mach number can be used to determine if a flow can be treated as an incompressible flow. If M < 0.2–0.3 and the flow is (quasi) steady and isothermal, compressibility effects will be small and a simplified incompressible flow equations can be used.[2][1]

The Mach number is named after Austrian physicist and philosopher Ernst Mach, a designation proposed by aeronautical engineer Jakob Ackeret. As the Mach number is a dimensionless quantity rather than a unit 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. In the decade preceding faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1."[6]

Overview

The Mach number is commonly used 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 Standard Sea Level conditions (corresponding to a temperature of 15 degrees Celsius), the speed of sound is 340.3 m/s[7] (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature.

Since the speed of sound increases as the ambient temperature increases, the actual speed of an object traveling at Mach 1, will depend on the temperature of the fluid temperature through which is passing. Mach number is useful because the fluid behaves in the same manner at the similar Mach number. So, an aircraft traveling at Mach 1 at 20°C ( or 68°F), at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft) altitude, at −50°C (−58°F), even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F.[5]

Classification of Mach regimes

While the terms "subsonic" and "supersonic," in the purest sense, refer to speeds below and above the local speed of sound respectively, aerodynamicists often use the same terms to talk about particular ranges of Mach values. This occurs because of the presence of a "transonic regime" around M = 1 where approximations of the Navier-Stokes equations used for subsonic design actually no longer apply, the simplest explanation is that the flow locally begins to exceed M = 1 even though the freestream Mach number is below this value.

Meanwhile, the "supersonic regime" is usually used to talk about the set of Mach numbers for which linearised theory may be used, where for example the (air) flow is not chemically reacting, and where heat-transfer between air and vehicle may be reasonably neglected in calculations.

In the following table, the "regimes" or "ranges of Mach values" are referred to, and not the "pure" meanings of the words "subsonic" and "supersonic".

Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Aircraft operating in this regime include the Space Shuttle and various space planes in development.

Regime Mach mph km/h m/s General plane characteristics
Subsonic <0.8 <610 <980 <270 Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges.
Transonic 0.8-1.2 610-915 980-1,470 270-410 Transonic aircraft nearly always have swept wings, causing the delay of drag-dive==Taxonavigation==

Species (3):
[Source: WoRMS]

Name

Brochiverruca :

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