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 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: static air temperature, SAT total air temperature,
TAT Mach number ratio of specific heats, approx 1.400 for dry 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 may be introduced to compensate:
(1) : Where:
e = recovery factor Typical recovery factors
Platinum wire ratiometer thermometer: e ≈ 0.75 - 0.9
Double platinum tube ratiometer thermometer: e ≈ 1
Other notations Total air temperature is also called: indicated
air temperature or ram air temperatureStatic air temperature is also called: outside air
temperature or true air temperature Ram rise
The difference between TAT and SAT is called ram rise and is caused by compressibility
and friction of the air at high velocities. (2) :
In practice the ram rise is negligible for aircraft flying at airspeeds under Mach 0.2
For airspeeds over Mach 0.2, as airspeed increases the temperature exceeds that of still air.
This is caused by a combination of kinetic heating and adiabatic compression
Kinetic heating. As the airspeed increases, more and more molecules of air per second
hit the aircraft. This causes a temperature rise in the Direct Reading thermometer probe
of the aircraft due to friction. Because the airflow is thought to be compressible and
isentropic, which, by definition, is adiabatic and reversible, the equations used in this
article do not take account of friction heating. This is why the calculation of static air
temperature requires the use of the recovery factor, . Kinetic heating for modern passenger
jets is almost negligible. Adiabatic compression. As described above,
this is caused by a conversion of energy and not by direct application of heat. At airspeeds
over Mach 0.2, in the Remote Reading temperature probe, the outside airflow, which may be several
hundred knots, is brought virtually to rest very rapidly. The energy of the moving air
is then released in the form of a temperature rise. Energy cannot be destroyed but only
transformed; this means that according to the first law of thermodynamics, the total
energy of an isolated system must remain constant. The total of kinetic heating and adiabatic
temperature change is the Total Ram Rise. Combining equations &, we get:
If we use the Mach number equation for dry air:
where
we get (3) :
Which can be simplified to:
by using
and
local speed of sound. adiabatic index and is assumed for aviation
purposes to be 7/5 = 1.400. specific gas constant. The approximate value
of for dry air is 286.9 J·kg−1·K−1. heat capacity constant for constant pressure.
heat capacity constant for constant volume. static air temperature, SAT, measured in Kelvin.
true airspeed of the aircraft, TAS. recovery factor, which has an approximate
value of 0.98, typical for a modern TAT-probe. By solving for the above values with TAS in
knots, a simple accurate formula for ram rise is then:
See also Stagnation point
Stagnation temperature Outside Air Temperature
Mach number Speed of sound
Adiabatic process Isentropic process
Specific enthalpy External links
In-Flight Temperature Measurements Measurement of Temperature on Aircraft
TAT Sensor Operation and Equations TAT Sensor Heater Error Effect
High speed flight - Viscous Interaction