Calibrated airspeed from impact pressure - Supersonic speed

Description

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

When flying at sea level under International Standard Atmosphere conditions (15 °C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed (EAS) and true airspeed (TAS). If there is no wind it is also the same as ground speed (GS). Under any other conditions, CAS may differ from the aircraft’s TAS and GS. Calibrated airspeed in knots is usually abbreviated as KCAS, while indicated airspeed is abbreviated as KIAS. In some applications, notably British usage, the expression rectified airspeed is used instead of calibrated airspeed.

Since the airspeed indicator capsule responds to impact pressure, 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 supersonic airspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies.

Related formulas

Variables

CAScalibrated airspeed (m/s)
a0standard speed of sound at 15 °C (m/s)
qcimpact pressure (Pa)
P0standard pressure at sea level (Pa)