Calibrated airspeed

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Calibrated airspeed (CAS) is indicated airspeed, corrected for instrument error and position error. At high speeds and altitudes, calibrated airspeed is further corrected for compressibility errors and becomes equivalent airspeed (EAS).

When flying at sea level under International Standard Atmosphere conditions (15°C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed and true airspeed (TAS). If there is no wind it is also the same as ground speed (GS). Under any other conditions, CAS differs from the aircraft's TAS and GS.

Calibrated airspeed in knots is usually abbreviated as KCAS, while indicated airspeed is abbreviated as KIAS.

[edit] 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.

With the widespread use of GPS and 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 the same calibrated airspeed at any elevation, even though the true airspeed and groundspeed may differ significantly. These V speeds are usually given as IAS rather than CAS, so that a pilot can read them directly from the airspeed indicator.

[edit] Spreadsheet calculation

A simple airspeed indicator has only one capsule measuring impact pressure (pitot - static differential). CAS must therefore be defined as a function of impact pressure alone. The instrument does not "know" the absolute static pressure or the static air temperature. Static pressure and temperature are therefore defined by convention as standard sea level values. It so happens that the speed of sound is a direct function of temperature, so instead of a reference temperature, we can define a reference speed of sound. This makes the math easier.

In a spreadsheet CAS can be computed as: $CAS=a_{sl}\sqrt{5\left[\left(\frac{q_c}{P_{sl}}+1\right)^\frac{2}{7}-1\right]}$

where:

$q c$ = impact pressure
$P s l$ = standard pressure at sea level
$a s l$ is the standard speed of sound at 15 °C

The above is based on the Saint-Venant formula for subsonic airspeeds. For supersonic airspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies:

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

The supersonic formula must be solved iteratively, by assuming an initial value for $C A S$ equal to $a s l$ .

The formula works in any units, just select the appropriate values for $P s l$ and $a s l$ . For example $P s l$ = 1013.25 hPa, $a s l$ = 661.48 knots.

This can then be used to calibrate an airspeed indicator when pitot pressure ( $q c$ ) is measured using a water manometer or accurate pressure gauge. If using a water manometer to measure millimeters of water the reference pressure ( $P s l$ ) may be entered as 10333 mm $H 20$ .

The definition is based on a model of the air as a compressible fluid. CAS therefore represents true airspeed (TAS) at all subsonic speeds under the reference conditions, i.e. standard sea level pressure and temperature.

At higher altitudes CAS can be corrected for compressibility error to give equivalent airspeed (EAS). In practice compressibility error is negligible below about 10,000 feet and 200 knots.