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Total air temperature

Total air temperature is a term used generally in aviation. It is measured by a specially designed temperature probe mounted on the surface of the aircraft. The probe is designed to bring the air to rest relative to the aircraft. As the air is brought to rest kinetic energy is converted to internal energy. The air is compressed and experiences an adiabatic increase in temperature. Therefore total air temperature is higher than the static (or ambient) air temperature.

Total air temperature is an essential input to an air data computer in order to enable computation of static air temperature and hence true airspeed.

The relationship between static and total air temperatures is given by:

$\frac{T_\mathrm{total}}{T_{0}}={1+\frac{\gamma -1}{2}M_a^2}$

where:

T0 = static air temperature (kelvin or degree Rankine)
Ttotal = total air temperature (kelvin or degree Rankine)
Ma = Mach number
$\gamma\ =\,$ ratio of specific heats = approx 1.4 for air

In practice the total air temperature probe will not perfectly recover the energy of the airflow and the temperature rise may not be entirely due to adiabatic process. In this case an empirical recovery factor (less than 1) may be introduced to compensate:

$\frac{T_\mathrm{total}}{T_{0}}={1+\frac{\gamma -1}{2}eM_a^2}$

Where:

e = recovery factor (also noted Ct)

Typical recovery factors

Platinum wire ratiometer thermometer ("flush bulb type"): e ≈ 0.75 - 0.9

Double platinum tube ratiometer thermometer ("TAT probe"): e ≈ 1

Other notations

Total air temperature (TAT) is also called: indicated air temperature (IAT) or ram air temperature (RAT)
Static air temperature (SAT) is also called: outside air temperature (OAT) or true air temperature

The difference between TAT & SAT is called ram rise (RR)

$RR=TAT-SAT \,$

In practice the ram rise is negligible for aircraft flying at (true) airspeeds under Mach 0.2