Total air temperature

In aviation, stagnation temperature is known as total air temperature and is measured by a 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:
where:
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:
(1) :formula_6
Where:
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
Ram rise.
The difference between TAT and SAT is called ram rise (RR) and is caused by compressibility and friction of the air at high velocities.
(2) :formula_7
In practice the ram rise is negligible for aircraft flying at (true) airspeeds under Mach 0.2
For airspeeds (TAS) over Mach 0.2, as airspeed increases the temperature exceeds that of still air. This is caused by a combination of kinetic (friction) heating and adiabatic compression
The total of kinetic heating and adiabatic temperature change (caused by adiabatic compression) is the Total Ram Rise.
Combining equations (1) & (2), we get:
If we use the Mach number equation for dry air:
where formula_11
we get
(3) :formula_12
Which can be simplified to:
by using formula_14
and
By solving (3) for the above values with TAS in knots, a simple accurate formula for ram rise is then: