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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 = asl*SQRT(5*((qc/psl+1)^(2/7)-1))
where qc is the impact pressure, psl is the standard pressure at sea level and asl is the standard speed of sound at sea level. The formula works in any units, just select the appropriate values for psl and asl. For example psl = 1013.25 hPa, asl = 661.48 knots.
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 must be corrected for compressibility error to give equivalent airspeed (EAS), and EAS must in turn be corrected for density to give TAS. In practice compressibility error is negligible below about 10000 feet and 200 knots.
With the advent of the glass cockpit, even in small aircraft, the mechanical airspeed indicator may become obsolete, being replaced by an air data computer. An air data computer which has inputs of static pressure and total air temperature as well as impact pressure can compute EAS and TAS directly, as well as mach number, pressure altitude etc. CAS may also therefore become obsolete.
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