Airspeed

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For the British aircraft manufacturer, see Airspeed Ltd.

Airspeed is the speed of an aircraft relative to the air. There are several different measures of airspeed: indicated airspeed, calibrated airspeed, equivalent airspeed and true airspeed.

1 Indicated airspeed
2 Calibrated airspeed
3 Equivalent airspeed
4 True airspeed
5 Groundspeed
6 References
7 External links

[edit] Indicated airspeed

Indicated airspeed (IAS) is the airspeed indicator reading (ASIR) corrected only for instrument error. (Source BCAR Section D Aeroplanes)

Outside of the former Soviet bloc, most airspeed indicators show the speed in knots i.e. nautical miles per hour. Some light aircraft have airspeed indicators showing speed in miles per hour.

An airspeed indicator is a differential pressure gauge with the pressure reading expressed in units of speed, rather than pressure. The airspeed is derived from the difference between the total pressureand the static air pressure. The total pressure is usually detected by a pitot tube which is mounted facing forward; the static pressure is usually detected at static ports on one or both sides of the aircraft. Sometimes both pressure sources are combined in a single probe, a pitot-static tube. The static pressure measurement is subject to error due to inability to place the static ports at positions where the pressure is true static pressure. The correction for this error is the position error correction (PEC).

The airspeed indicator is shown the airspeed calculated as follows:

Where: <math>V_i \, </math> is the indicated airspeed,; <math>p_t \,</math> is the total air pressure sensed by the pitot tube,; <math>p \, </math> is the static air pressure sensed at the static source,; <math>\rho_0 \, </math> is 1.225 kg/m³, the air density at sea level, ISA conditions.

This expression is based on the form of Bernoulli's equation applicable to a perfect, incompressible, gas. The air density used is that at SL, ISA i.e. the conditions under which airspeed indicators are calibrated.

(Modern airspeed indicators are calibrated for compressible flow at sea level ISA, see link to calibrated airspeed)

[edit] Calibrated airspeed

Calibrated airspeed (CAS) is indicated airspeed corrected for position error and installation errors.

[edit] Equivalent airspeed

Equivalent airspeed (EAS) is calibrated airspeed corrected for error due to air compressibility which arises at high altitudes and mach numbers. Under standard sea level conditions EAS is the same as CAS.

Let <math>q \,</math> represent the dynamic pressure <math>\frac {1}{2} \rho V^2 = \frac {1}{2} \rho_0 V_e^2</math>.

Then the relationship between the pressure difference <math>p_t \, - \, p </math> sensed by a pitot-static system and the dynamic pressure is given by:

<math> \frac{p_t - p}{q} = \frac{V_i^2}{V_e^2} = 1 + \frac{1}{4} M^2 + \frac{ (2 - \gamma )}{24} M^4 + \frac{(2 - \gamma )( 3 - 2 \gamma )}{192} M^6 + ... </math>

Where: <math>M \,</math> is the Mach number,; <math>V \, </math> is the true airspeed,; <math>V_e \,</math> is the equivalent airspeed,; <math>\gamma \,</math> is the ratio of the specific heats of air and; <math>\rho \, </math> is the air density.

The ratio of the specific heats, <math>\gamma \, </math> , is 1.4 in air. Substituting this value gives:

(This section needs editing due to confusion between V (TAS) and Vi (CAS) and ambiguity regarding ASI calibration - incompressible flow equation above or compressible flow equation under calibrated airspeed? If the ASI is calibrated to the CAS calibration equation which (for subsonic speeds) eliminates compressibility error at standard sea level then the compressibility correction above is not valid. See also link to equivalent airspeed)

This approximation is valid up to about Mach 2.3.

Source: Aerodynamics of a Compressible Fluid. Liepmann and Puckett 1947. Publishers John Wiley & Sons Inc.

The difference between calibrated airspeed and equivalent airspeed is negligible at low Mach numbers rising to 3% at Mach 0.5 and 13% at Mach 1 depending on altitude.

The significance of equivalent airspeed is that at Mach numbers below the onset of wave drag, all of the aerodynamic forces and moments on an aircraft scale with the square of the equivalent airspeed. The equivalent airspeed is closely related to the Indicated airspeed speed shown by the airspeed indicator. Thus, the handling and 'feel' of an aircraft, and the aerodynamic loads upon it, at a given equivalent airspeed, are very nearly constant and equal to those at SL, ISA irrespective of the actual flight conditions.

[edit] True airspeed

True airspeed (TAS) is the true speed of the aircraft relative to the air. It differs from the equivalent airspeed because the airspeed indicator is calibrated at SL,ISA conditions, where the air density is 1.225 kg/m³ , whereas the air density in flight normally differs from this value.

Thus

Where: <math>\rho \,</math> is the air density at the flight condition.

The air density may be calculated from:

Where: <math>p \,</math> is the air pressure at the flight condition,; <math>p_0 \,</math> is the air pressure at sea level = 1013.2 hPa,; <math>T \,</math> is the air temperature at the flight condition,; <math>T_0 \,</math> is the air temperature at sea level, ISA = 288.15 K.

Source: Aerodynamics of a Compressible Fluid. Liepmann and Puckett 1947. Publishers John Wiley & Sons Inc.

[edit] Groundspeed

Groundspeed is the speed of the aircraft relative to the ground rather than through the air, which can itself be moving.

[edit] References

Glauert H : The Elements of Aerofoil and Airscrew Theory, Chapter 2, Cambridge University Press, 1947
Liepmann H W and A E Pucket : Introduction to Aerodynamics of a Compressible Fluid, John Wiley and Sons, Inc. 1947