Confusion reigns...
Right, lets get to the bottom of this.
IAS = speed calculated from dynamic pressure (i.e. total - static), assuming ISA SEA LEVEL air density. IAS is therefore a representation of DYNAMIC PRESSURE, not actual speed though the air in the sense of speed = distance/time. IAS also has errors because there is no pressure error correction on the static source(s).
CAS is IAS with the static pressure errors corrected, but it is only valid up to about Mach 0.3 because it assumes zero compressibility error. CAS will over-read once compressibility of the air in the pitot tube becomes significant; this discrepancy increases with altitude.
EAS is CAS with a compressibility correction, but still assumes ISA sea level density when deriving the speed from the dynamic pressure.
In a perfect aircraft with no static pressure errors and no compressibility errors, IAS = CAS = EAS, but these still only represent dynamic pressure, not the actual speed of the aircraft through the air. So why use them? Well, all your limiting speeds (e.g. stall, flaps/slats, gear, Vne, etc) are dynamic pressure related and will be constant regardless of actual local air density provided they are expressed in terms of EAS, which means they are easier to remember and comply with throughout the flight envelope. If they were expressed in TAS you would have to recalculate the limits frequently as temperature and altitude changed.
TAS = EAS corrected for density. See below:
0.5 * density(ISA sea level) * EAS^2 = 0.5 * density(actual) * TAS ^2
thus:
TAS = EAS / SQRT(sigma) where sigma = Rho(actual) / Rho(ISA sea level)
Clearly we need to know TAS for navigation, and also because speed of sound is a true air speed. Both TAS and speed of sound depend on temperature, so when you calculate Mach Number the temperature dependency cancels out.
Mach No = TAS / Local Speed of Sound
If you plot a graph showing a constant EAS climb, TAS increases with height but speed of sound decreases with height. Therefore there will be a height where a given Mach No will be equivalent in TAS to a given EAS expressed as TAS. Therefore at low altitude Vmo takes precedence (dynamic pressure limit), but at a certain height Mmo becomes more limiting (e.g. wave drag, mach tuck and possible control problems).
Hope this helps.
Last edited by Jetdriver; 20th Jun 2013 at 17:40.