Airspeed

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For the British aircraft manufacturer, see Airspeed Ltd. For the defunct American airline, see Air-Speed Inc.

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

Main article: 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, or stagnation pressure and the static 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) and varies for different aircraft.

Indicated airspeed values less than the speed of sound at standard sea level (661.4788 knots) are calculated as follows:

$V_i=A_o\sqrt{5\Bigg[\bigg(\frac{Q_c}{P_o}+1\bigg)^\frac{2}{7}-1\Bigg]}$ minus PEC

Where: $V_i \,$ is the indicated airspeed,; $Q_c \,$ is the differential air pressure (inches Hg) sensed by the pitot tube,; $P_o \,$ is 29.92126 inches Hg; static air pressure at standard sea level,; $A_o \,$ is 661.4788 knots;, speed of sound at standard sea level.

This expression is based on the form of Bernoulli's equation applicable to a perfect, compressible gas. The values for $P o$ and $A o$ are consistent with the ISA i.e. the conditions under which airspeed indicators are calibrated.

Main article: Calibrated airspeed

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

Main article: Equivalent airspeed

Equivalent airspeed (EAS) is defined as the speed at sea level that would produce the same incompressible dynamic pressure as the true airspeed at the altitude at which the vehicle is flying. An aircraft in forward flight is subject to the effects of compressiblity. Likewise, the calibrated airspeed is a function of the compressible impact pressure. EAS, on the other hand, is a measure of airspeed that is a function of incompressible dynamic pressure. Structural analysis is often in terms of incompressible dynamic pressure, so that equivalent airspeed is a useful speed for structural testing. At sea level, standard day, calibrated airspeed and equivalent airspeed are equal (or equivalent), but only at that condition. For the performance engineer, there is no practical reason to use equivalent airspeed for anything. However, structural analysis is often performed in terms of equivalent airspeed (since it is a direct function of the incompressible dynamic pressure), so the performance engineer needs to be able to convert $V e$ to parameters that are more useful.:^[1]

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

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

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

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

The ratio of the specific heats, $\gamma \,$ , is 1.4 in air. Substituting this value gives:

$\frac{p_t \, - \, p}{q} = \frac{V_i^2}{V_e^2} = 1 + \frac{1}{4} M^2 + \frac{1}{40} M^4 + \frac{1}{1600} M^6 +...$

(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.

Main article: True airspeed

True airspeed (TAS) is the physical speed of the aircraft relative to the moving air mass. The true airspeed is a vector quantity. The relationship between the true airspeed and the speed with respect to the ground $(V g)$ is:

$V_t \ = \ V_g + V_w$

Where:

V w

= Windspeed vector

Aircraft flight instruments, however, don't compute true airspeed as a function of groundspeed and windspeed. They use impact and static pressures as well as a temperature input. Basically, true airspeed is calibrated airspeed that is corrected for altitude and temperature. The result is the true physical speed of the aircraft minus the wind component. True Airspeed is equal to calibrated airspeed at standard sea level conditions.

The simplest way to compute true airspeed is using a function of Mach number:

$V_t \ = \ A_o \cdot M \sqrt{\frac{T}{T_o}}$

Where:

A o

= Speed of sound at standard sea level (661.4788 knots)

M

= Mach number

T

= Temperature (Kelvins)

T o

= Standard sea level temperature (288.15 Kelvin)

Or if Mach number is not known:

$V_t \ = \ A_o \cdot \sqrt{5\left[\left(\frac{q_c}{P}+1\right)^\frac{2}{7}-1\right] \cdot \frac{T}{T_o}}$

Where:

A o

= Speed of sound at standard sea level (661.4788 knots)

Q c

= Impact pressure (inHg)

P

= Static pressure (inHg)

T

= Temperature (Kelvins)

T o

= Standard sea level temperature (288.15 Kelvin)

The above equation is only for Mach numbers less than 1.0.

True airspeed 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.

$\frac {1}{2} \rho V^2 = q = \frac {1}{2} \rho_0 V_e^2$

Thus

$\frac {V}{V_e} = \sqrt{ \frac {\rho_0 }{ \rho}}$

Where: $\rho \,$ is the air density at the flight condition.

The air density may be calculated from:

$\frac {\rho }{\rho_0 } = \frac {p \, T_0}{p_0 \, T}$

Where: $p \,$ is the air pressure at the flight condition,; $p_0 \,$ is the air pressure at sea level = 1013.2 hPa,; $T \,$ is the air temperature at the flight condition,; $T_0 \,$ 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.

Main article: Groundspeed

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

^ 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.

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

Retrieved from "http://en.wikipedia.org../../../a/i/r/Airspeed.html"

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