# What is the difference between OAT, RAT, TAT, and SAT?

When I first started flying jet aircraft, I found different instruments that measure temperature in different ways and it was quite confusing.

What is the difference between Outside Air Temperature, Ram Air Temperature (RAT), Total Air Temperature (TAT), Static Air Temperature (SAT), and any that I might have missed?

• Jeppesen ATPL book for Instruments (pg 1-5) mentions as well RAT as a name for TAT when the recovery factor is less than 1
– user5639
Dec 27 '14 at 13:59

As you measure temperature moving at high velocities, your outside thermometer will measure a higher temp than what is actually outside (what a non-moving thermometer would get). That's because as the air rams into your thermometer it gets a little bit compressed, and that makes it heat up a little bit.

Amazingly, some smart people have even calculated how much that "ram rise" is, and you can actually compensate (well, in theory) from the indicated temperature to calculate what the actual outside air temp is:

$$Ram~Rise=SAT\times0.2\times{M}^2$$

Where $SAT$ is Static Air Temperature in Kelvin, $M$ is Mach number

Problem is, not all instruments will compress that air in the same way, and not all of them will pick up this Ram Rise entirely. So they will publish a $K$, a ram-rise-coefficient (also called recovery factor) meaning how much of from the theoretical Ram Rise they actually pick up.

(OAT/SAT) Static Air Temperature = noted as $T_S$, actual temperature of the air outside, the same your thermometer will pick up if you were not moving (say, in a balloon?)

(RAT) Ram Air Temperature = noted as $T_M$, actual measured temperature by your instrument.

$$RAT=SAT+k\times{Ram~Rise}$$

(TAT) Total Air Temperature = noted as $T_T$, total temperature as measured by an instrument with $K$-coefficient of $1$.

$$TAT=SAT+Ram~Rise$$