Airspeed: Wikis

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An airspeed indicator is a flight instrument that displays airspeed. This airspeed indicator has standardized markings for a multiengine airplane
Airliners have pitot probes for measuring airspeed

Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed ("IAS"), calibrated airspeed ("CAS"), true airspeed ("TAS"), equivalent airspeed ("EAS") and density airspeed.

The measurement and indication of airspeed is ordinarily accomplished on board an aircraft by an airspeed indicator ("ASI") connected to a pitot-static system. The pitot-static system comprises one or more pitot probes (or tubes) facing the on-coming air flow to measure pitot pressure (also called stagnation, total or ram pressure) and one or more static ports to measure the static pressure in the air flow. These two pressures are compared by the ASI to give an IAS reading.

Contents

Indicated airspeed

Indicated airspeed (IAS) is the airspeed indicator reading (ASIR) uncorrected for instrument, position, and other errors. From current EASA definitions: Indicated airspeed means the speed of an aircraft as shown on its pitot static airspeed indicator calibrated to reflect standard atmosphere adiabatic compressible flow at sea level uncorrected for airspeed system errors. [1]

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 ram air pressure from the pitot tube, or stagnation pressure, and the static pressure. The pitot tube is mounted facing forward; the static pressure is frequently 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 at all airspeeds and attitudes. The correction for this error is the position error correction (PEC) and varies for different aircraft and airspeeds. Further errors of 10% or more are common if the airplane is flown in “uncoordinated” flight.

Calibrated airspeed

Calibrated airspeed (CAS) is indicated airspeed corrected for instrument errors, position error (due to incorrect pressure at the static port) and installation errors.

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

V_c=A_0\sqrt{5\Bigg[\bigg(\frac{Q_c}{P_0}+1\bigg)^\frac{2}{7}-1\Bigg]} minus position and installation error correction.

Where 
V_c \, is the calibrated airspeed,
Q_c \, is the impact pressure (inches Hg) sensed by the pitot tube,
P_0 \, is 29.92126 inches Hg; static air pressure at standard sea level,
A_0 \, is 661.4788 knots;, speed of sound at standard sea level.

Units other than knots and inches of mercury can be used, if used consistently.

This expression is based on the form of Bernoulli's equation applicable to a perfect, compressible gas. The values for P0 and A0 are consistent with the ISA i.e. the conditions under which airspeed indicators are calibrated.

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 compressibility. 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 Ve 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.

True airspeed

True airspeed (TAS) is the physical speed of the aircraft relative to the air surrounding the aircraft. The true airspeed is a vector quantity. The relationship between the true airspeed and the speed with respect to the ground (Vg)is:

V_t \ = \ V_g - V_w

Where:

Vw = 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 pressure altitude and temperature. The result is the true physical speed of the aircraft plus or 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_0 \cdot M \sqrt{\frac{T}{T_0}}

Where:

A0 = Speed of sound at standard sea level (661.4788 knots)
M = Mach number
T = Temperature (kelvins)
T0 = Standard sea level temperature (288.15 kelvin)


Or if Mach number is not known:

V_t \ = \ A_0 \cdot \sqrt{5\left[\left(\frac{q_c}{P}+1\right)^\frac{2}{7}-1\right] \cdot \frac{T}{T_0}}

Where:

A0 = Speed of sound at standard sea level (661.4788 knots)
Qc = Impact pressure (inHg)
P = Static pressure (inHg)
T = Temperature (kelvin)
T0 = 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.

Groundspeed

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

See also

References

  1. ^ 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

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