Editing Calibrated airspeed (section)

==Calculation from impact pressure==

Since the airspeed indicator capsule responds to [[impact pressure]],<ref>Some authors in the field of compressible flows use the term dynamic pressure or compressible dynamic pressure instead of impact pressure.</ref> 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 the [[speed of sound]] is a direct function of temperature, so instead of a standard temperature, we can define a standard speed of sound.

For [[Speed of sound|subsonic]] speeds, CAS is calculated as:

<math>CAS=a_{0}\sqrt{5\left[\left(\frac{q_c}{P_{0}}+1\right)^\frac{2}{7}-1\right]}</math>

where:
* <math>q_c</math> = impact pressure
* <math>P_{0}</math> = standard pressure at sea level
* <math>{a_{0}}</math> is the standard speed of sound at 15&nbsp;°C

For [[supersonic]] airspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies:

<math>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)} </math>

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

These formulae work in any units provided the appropriate values for <math>P_{0}</math> and <math>a_{0}</math> are selected. For example, <math>P_{0}</math> = 1013.25 hPa, <math>a_{0}</math> = {{cvt|1225|km/h|kn|sigfig=5}}. The [[ratio of specific heats]] for air is assumed to be 1.4.

These formulae can then be used to calibrate an airspeed indicator when impact pressure (<math>q_c</math>) is measured using a water [[manometer]] or accurate pressure gauge. If using a water manometer to measure millimeters of water the reference pressure (<math>P_{0}</math>) may be entered as 10333&nbsp;mm <math>H_2O</math>.

At higher altitudes CAS can be corrected for compressibility error to give [[equivalent airspeed]] (EAS). In practice compressibility error is negligible below about {{cvt|10000|ft|m|order=flip|sigfig=2}} and {{cvt|200|kn|km/h|order=flip}}.