Mach = TAS/LSS so the higher the Mach number the higher the TAS. For TAS greater than 300 kts compressibility has to be taken into account.

 

This can be shown on the CRP5:

 

For example if an aircraft is flying at a CAS of 250kts at FL 400. If the OAT is -56.5o C calculate the TAS.

In the airspeed window enter FL400 against the OAT. Set 250kts CAS on the inner ring and read off the TAS on the outer ring = 492kts. This is greater than 300kt so compressibility has to be corrected for. (492/100) - 3 = 1.92 divisions. Rotate the ring 1.92 divs to the left. Now read off TAS against 250kt CAS = 470kts. The greater the TAS the greater the compressibility and the greater the negative affect it has on TAS.

 

Notably CAS to EAS takes account of compressibility error. The ASI is calibrated for ISA SL density and the reading is dependent on the dynamic pressure 1/2 x rho x V^2. At higher speeds the instrument will over read since dynamic pressure is greater than 1/2 x rho x V^2, so a compressibility correction has to be applied.

 

It follows that Dynamic pressure = 1/2 x rho x V^2 x[1 + (1/4 x M^2)]

 

The compressibility factor is therefore always negative and dependent on Mach number.