Total air temperature
Encyclopedia
Total air temperature is a term used generally in aviation. In other applications it is called stagnation temperature
. Total air temperature 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:
where:
static air temperature, SAT (kelvin
or degree Rankine)
total air temperature, TAT (kelvin or degree Rankine)
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 (less than 1) may be introduced to compensate:
(1) :
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
(2) :
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
we get
(3) :
Which can be simplified to:
by using
and
is the local speed of sound
.
is the adiabatic index
and is assumed for aviation purposes to be 7/5 = 1.400.
is the specific gas constant
. The approximate value of
for dry air is 286.9 J·mol−1·K−1.
, is the heat capacity
constant for constant pressure.
, is the heat capacity
constant for constant volume.
is the Static Air Temperature, SAT, measured in Kelvin.
is the true airspeed
of the aircraft, TAS.
recovery factor, which has an approximate value of 0.98, typical for a modern TAT-probe.
By solving (3) for the above values, a simple accurate formula for ram rise is then:
Stagnation temperature
In thermodynamics and fluid mechanics, stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy...
. Total air temperature 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
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
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
Air data computer
An air data computer is an essential avionics component found in modern glass cockpits. This computer, rather than individual instruments, can determine the calibrated airspeed, Mach number, altitude, and altitude trend from input data from sensors such as an aircraft's pitot-static system,...
in order to enable computation of static air temperature and hence true airspeed
True airspeed
True airspeed of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.-Performance:...
.
The relationship between static and total air temperatures is given by:
where:
static air temperature, SAT (kelvinKelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
or degree Rankine)
total air temperature, TAT (kelvin or degree Rankine) Mach numberMach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
ratio of specific heats = approx 1.400 for dry airIn 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) :
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)
Outside air temperature
In aviation terminology, the outside air temperature or static air temperature refers to the temperature of the air around an aircraft, but unaffected by the passage of the aircraft through it.-Aviation usage:...
is also called: outside air temperature (OAT)
Outside air temperature
In aviation terminology, the outside air temperature or static air temperature refers to the temperature of the air around an aircraft, but unaffected by the passage of the aircraft through it.-Aviation usage:...
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) :
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
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
- 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 isentropicIsentropic processIn thermodynamics, an isentropic process or isoentropic process is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the...
and compressible, which by definition is adiabatic and reversible, the equations used in this article do not take account for friction heating. This is why we have to use the recovery factor
. Kinetic heating for modern passenger jets is almost negligible.
- Adiabatic compressionAdiabatic processIn thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
. 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 (TAT-probe), the outside airflow which may be several hundred knots, is brought virtually to rest very rapidly. The energy (Specific Kinetic Energy) of the moving air is then released (converted) in the form of a temperature rise (Specific Enthalpy). Energy can not be destroyed but only transformed, this means that according to the first law of thermodynamicsFirst law of thermodynamicsThe first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
, the internal energy of an isolated system must remain constant.
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
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
equation for dry air:
where
we get
(3) :
Which can be simplified to:
by using
and
is the local speed of soundSpeed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
.
is the adiabatic indexHeat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...
and is assumed for aviation purposes to be 7/5 = 1.400.
is the specific gas constantGas constant
The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...
. The approximate value of
for dry air is 286.9 J·mol−1·K−1., is the heat capacityHeat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
constant for constant pressure.
, is the heat capacityHeat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
constant for constant volume.
is the Static Air Temperature, SAT, measured in Kelvin. is the true airspeedTrue airspeed
True airspeed of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.-Performance:...
of the aircraft, TAS.
recovery factor, which has an approximate value of 0.98, typical for a modern TAT-probe.By solving (3) for the above values, a simple accurate formula for ram rise is then:
See also
- Stagnation pointStagnation pointIn fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object...
- Stagnation temperatureStagnation temperatureIn thermodynamics and fluid mechanics, stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy...
- Outside Air TemperatureOutside air temperatureIn aviation terminology, the outside air temperature or static air temperature refers to the temperature of the air around an aircraft, but unaffected by the passage of the aircraft through it.-Aviation usage:...
- Mach numberMach numberMach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
- Speed of soundSpeed of soundThe speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
- Adiabatic processAdiabatic processIn thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
- Isentropic processIsentropic processIn thermodynamics, an isentropic process or isoentropic process is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the...
- Specific enthalpy