True airspeed

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True airspeed (TAS) is the speed of an aircraft relative to the airmass in which it flies, i.e. the magnitude of the vector difference of the velocity of the aircraft and the velocity of the air. Under zero wind conditions and in horizontal flight, this is equal to the speed over the ground. Under wind conditions an estimation of the wind is used to make a windspeed vector calculation that computes an estimated ground speed from the true air speed and a wind correction angle to maintain the desired ground track.

Aircraft display an indicated airspeed on an instrument called an airspeed indicator. Indicated airspeed will differ from true airspeed at air densities other than some reference density. Air density is affected by temperature, moisture content, and altitude. Indicated airspeed is used in aircraft operation as the aircraft stalling speed and structural limiting speeds are dependent on indicated airspeed, irrespective of true airspeed. However, proper navigation via dead reckoning (without constant ground reference) requires the use of true airspeed and wind corrections.

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

$TAS ={a_{sl}} M_a \sqrt{T\over T_{sl}}$

Where: $T A S =$ true airspeed; $a s l$ is the standard speed of sound at 15 °C (661.47 knots); $M a$ is Mach number,; $T$ is static air temperature in Kelvin,; $T s l$ is standard sea level temperature (288.15 K)

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

$TAS={a_{sl}}\sqrt{{5T\over T_{sl}}[(\frac{q_c}{P}+1)^\frac{2}{7}-1]}$

Where: $q c$ is impact pressure; $P$ 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 a function of Mach number:

$T={\frac{T_{t}}{1+0.2M_a^2}}$

Where: $T t =$ total air temperature

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

$\mathrm{TAS} = 39M_a\sqrt{T}$

remembering that temperature is in Kelvin.

In simple aircraft, without an air data computer or Mach meter, 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 with a calculator such as the E6B handheld circular slide rule.