Air Speed Measurements

True Air Speed (TAS)

True airspeed is equivalent airspeed corrected for temperature and pressure altitude. True airspeed is the speed of your aircraft relative to the air it’s flying through. As you climb, true airspeed is higher than your indicated airspeed. Pressure decreases with higher altitudes, so for any given true airspeed, as you climb, fewer and fewer air molecules will enter the pitot tube. Because of that, indicated airspeed will be less than true airspeed. (Indicated air speed, is usually what you’ll reference in the cockpit for speed changes.)

(1)   \begin{equation*}V_{true} = \sqrt{\frac{2 \gamma P_{static}}{(\gamma -1) \rho_{static}} \left[ \left( \frac{P_{total}-P_{static}}{P_{static}} + 1 \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]}\end{equation*}

Calibrated Air Speed (CAS)

Calibrated airspeed is indicated airspeed corrected for instrument and positional errors. This error is generally greatest at low airspeeds, with nose high pitch attitudes.

(2)   \begin{equation*}V_{calibrated} = \sqrt{\frac{2 \gamma P_{0}}{(\gamma -1) \rho_{0}} \left[ \left( \frac{P_{total}-P_{static}}{P_{0}} + 1 \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]} = a_0 \sqrt{5 \left[ \left( \frac{P_{total}-P_{static}}{P_0} + 1 \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]}\end{equation*}


If an airplane is operating at exactly sea level standard day pressure and density conditions, the calibrated air speed and aircraft’s true velocity will be the same.

Equivalent Air Speed (EAS)

Equivalent Airspeed is calibrated airspeed corrected for compressibility.

(3)   \begin{equation*}V_{equivalent} = \sqrt{\frac{2 \gamma P_{static}}{(\gamma -1) \rho_{0}} \left[ \left( \frac{P_{total}-P_{static}}{P_{static}} + 1 \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right]} = \sqrt{\sigma} V_{true}\end{equation*}

Mach Number

(4)   \begin{equation*}M = \frac{V_{true}}{a} = \frac{V_{true}}{a_0 \sqrt{\theta}}\end{equation*}