Is CAS describing an “aerodynamic” speed, what you would see if you model the speed/density of the air going past the wings? And then IAS is the inaccurate measurement of CAS?
Essentially. Dynamic pressure (q) is the difference between total pressure and ambient pressure (Pt-Pa). A pitot tube measures total pressure Pt (with some small error at high angles of attack) and a static port measures ambient pressure Pa with larger errors due to airflow entering the port and introducing some dynamic pressure component.
Dynamic pressure is also equal to the familiar 1/2*rho*V^2, where rho is density and V is speed, but if you use calibrated airspeed Vc the equation becomes:
q = 1/2*rho_ssl*Vc^2, where rho_ssl is the density of air at sea level standard day conditions, or Vc = sqrt(2q/rho_ssl). The nice thing about this relationship is you don't need to know any local atmospheric properties to get airspeed from dynamic pressure. Since the pitot-static system has errors (see above) it doesn't really give you this exact quantity, the resulting dynamic pressure measurement and airspeed calculation gives you indicated dynamic pressure (qci) and indicated airspeed Vi. Since it's all referred by standard day sea level conditions you can test to find the corrections to airspeed as a function of airspeed and not have to worry about (e.g.) temp or pressure when testing.
In terms of true airspeed (Vt) and the same dynamic pressure,
q = 1/2*rho_a*Vt^2, where rho_a is atmospheric density at the point where the measurement was taken, and Vt is true airspeed. With a little math you can also show that Vt = sqrt(T_ssl/T_a) *Vc (for low subsonic speeds) where T_ssl = temp at sea level standard day and T_a = ambient temp where the measurement is taken. Watch units, with no conversion factors temps must be absolute (R or K) and speeds ft/s.
Also note that the static errors also result in an altimeter error since your static port isn't reading the exact ambient pressure. A good source error correction test will get the corrections for both indicated airspeed and indicated altitude (there are requirements for both). Also note that if the errors were due solely to pitot errors there would be no altitude correction required. Hmmm...
The Naval Test Pilot School fixed wing flight test performance manual (search for USNTPS FTM-108) has a really good writeup on all of this if you want gory details including different test techniques.
Nauga,
pneumatically