Low-speed flight

At low speeds and altitudes, IAS and CAS are close to equivalent airspeed (EAS).

${\displaystyle \rho _{0}(EAS)^{2}=\rho (TAS)^{2}}$ ^[1]

TAS can be calculated as a function of EAS and air density: ^[1]

${\displaystyle \mathrm {TAS} ={\frac {\mathrm {EAS} }{\sqrt {\frac {\rho }{\rho _{0}}}}}}$

where

${\displaystyle \mathrm {TAS} }$ is true airspeed,

${\displaystyle \mathrm {EAS} }$ is equivalent airspeed,

${\displaystyle \rho _{0}}$ is the air density at sea level in the International Standard Atmosphere (15 °C and 1013.25 hectopascals, corresponding to a density of 1.225 kg/m³),

${\displaystyle \rho }$ is the density of the air in which the aircraft is flying.

High-speed flight

TAS can be calculated as a function of Mach number and static air temperature:

${\displaystyle \mathrm {TAS} ={a_{0}}M{\sqrt {T \over T_{0}}},}$

where

${\displaystyle {a_{0}}}$ is the speed of sound at standard sea level (661.47 knots (1,225.04 km/h; 340.29 m/s)),

${\displaystyle M}$ is Mach number,

${\displaystyle T}$ is static air temperature in kelvins,

${\displaystyle T_{0}}$ is the temperature at standard sea level (288.15 K).

For manual calculation of TAS in knots, where Mach number and static air temperature are known, the expression may be simplified to

${\displaystyle \mathrm {TAS} =39M{\sqrt {T}}}$

(remembering temperature is in kelvins).

Combining the above with the expression for Mach number gives an expression for TAS as a function of impact pressure, static pressure and static air temperature (valid for subsonic flow):

${\displaystyle \mathrm {TAS} =a_{0}{\sqrt {{\frac {5T}{T_{0}}}\left[\left({\frac {q_{c}}{P}}+1\right)^{\frac {2}{7}}-1\right]}},}$

where:

${\displaystyle q_{c}}$ is impact pressure,

${\displaystyle P}$ is static pressure.

Electronic flight instrument systems (EFIS) contain an air data computer with inputs of impact pressure, static pressure and total air temperature. In order to compute TAS, the air data computer must convert total air temperature to static air temperature. This is also a function of Mach number:

${\displaystyle T={\frac {T_{\text{t}}}{1+0.2M^{2}}},}$

where

${\displaystyle T_{\text{t}}=}$ total air temperature.

In simple aircraft, without an air data computer or machmeter, true airspeed can be calculated as a function of calibrated airspeed and local air density (or static air temperature and pressure altitude, which determine density). Some airspeed indicators incorporate a slide rule mechanism to perform this calculation. Otherwise, it can be performed using this applet or a device such as the E6B (a handheld circular slide rule).

Bibliography

• Air Navigation. Department of the Air Force. 1 December 1989. AFM 51-40.
• Clancy, L.J.(1975), Aerodynamics, Chapter 3. Pitman Publishing Limited, London. ISBN 0-273-01120-0
• Kermode, A.C., Mechanics of Flight, Chapter 2. (Eighth edition 1972) Pitman Publishing Limited, London. ISBN 0-273-31623-0
• Gracey, William (1980), "Measurement of Aircraft Speed and Altitude" Archived 2021-09-26 at the Wayback Machine (11 MB), NASA Reference Publication 1046.