Calibrated airspeed

Inaviation,calibrated airspeed(CAS) is indicatedairspeedcorrected for instrument andposition error.

When flying atsea levelunderInternational Standard Atmosphereconditions (15 °C, 1013 hPa, 0% humidity) calibrated airspeed is the same asequivalent airspeed(EAS) andtrue airspeed(TAS). If there is no wind it is also the same asground speed(GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS.

Calibrated airspeed inknotsis usually abbreviated asKCAS,while indicated airspeed is abbreviated asKIAS.

In some applications, notably British usage, the expressionrectified airspeedis used instead of calibrated airspeed.^[1]

Practical applications of CAS

CAS has two primary applications in aviation:

for navigation, CAS is traditionally calculated as one of the steps between indicated airspeed and true airspeed;
for aircraft control, CAS (and EAS) are the primary reference points, since they describe the dynamic pressure acting on aircraft surfaces regardless of density, altitude, wind, and other conditions. EAS is used as a reference by aircraft designers, but EAS cannot be displayed correctly at varying altitudes by a simple (single capsule) airspeed indicator. CAS is therefore a standard for calibrating the airspeed indicator such that CAS equals EAS at sea level pressure and approximates EAS at higher altitudes.

With the widespread use ofGPSand other advanced navigation systems in cockpits, the first application is rapidly decreasing in importance – pilots are able to read groundspeed (and often true airspeed) directly, without calculating calibrated airspeed as an intermediate step. The second application remains critical, however – for example, at the same weight, an aircraft will rotate and climb at approximately the same calibrated airspeed at any elevation, even though the true airspeed and groundspeed may differ significantly. TheseV speedsare usually given as IAS rather than CAS, so that a pilot can read them directly from the airspeed indicator.

Calculation from impact pressure

Since the airspeed indicator capsule responds toimpact pressure,^[2]CAS is defined as a function of impact pressure alone. Static pressure and temperature appear as fixed coefficients defined by convention as standard sea level values. It so happens that thespeed of soundis a direct function of temperature, so instead of a standard temperature, we can define a standard speed of sound.

Forsubsonicspeeds, CAS is calculated as:

$CAS=a_{0}{\sqrt {5\left[\left({\frac {q_{c}}{P_{0}}}+1\right)^{\frac {2}{7}}-1\right]}}$

where:

$q_{c}$ = impact pressure
$P_{0}$ = standard pressure at sea level
${a_{0}}$ is the standard speed of sound at 15 °C

Forsupersonicairspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies:

$CAS=a_{0}\left[\left({\frac {q_{c}}{P_{0}}}+1\right)\times \left(7\left({\frac {CAS}{a_{0}}}\right)^{2}-1\right)^{2.5}/\left(6^{2.5}\times 1.2^{3.5}\right)\right]^{(1/7)}$

The supersonic formula must be solved iteratively, by assuming an initial value for $CAS$ equal to $a_{0}$ .

These formulae work in any units provided the appropriate values for $P_{0}$ and $a_{0}$ are selected. For example, $P_{0}$ = 1013.25 hPa, $a_{0}$ = 1,225 km/h (661.45 kn). Theratio of specific heatsfor air is assumed to be 1.4.

These formulae can then be used to calibrate an airspeed indicator when impact pressure ( $q_{c}$ ) is measured using a watermanometeror accurate pressure gauge. If using a water manometer to measure millimeters of water the reference pressure ( $P_{0}$ ) may be entered as 10333 mm $H_{2}O$ .

At higher altitudes CAS can be corrected for compressibility error to giveequivalent airspeed(EAS). In practice compressibility error is negligible below about 3,000 m (10,000 ft) and 370 km/h (200 kn).

References

^Clancy, L. J. (1975)Aerodynamics,pp 31, 32. Pitman Publishing Limited, London.ISBN 0 273 01120 0
^Some authors in the field of compressible flows use the term dynamic pressure or compressible dynamic pressure instead of impact pressure.

Bibliography

Blake, Walt (2009).Jet Transport Performance Methods.Seattle:Boeing Commercial Airplanes.
Gracey, William (1980),"Measurement of Aircraft Speed and Altitude"(12 MB), p. 15, NASA Reference Publication 1046.

External links

[1] Clancy, L. J. (1975)Aerodynamics,pp 31, 32. Pitman Publishing Limited, London.ISBN 0 273 01120 0

[2] Some authors in the field of compressible flows use the term dynamic pressure or compressible dynamic pressure instead of impact pressure.

[1]

[2]

Practical applications of CAS

Calculation from impact pressure

See also

References

Bibliography

External links