Measuring Air Temperature
Dave Jesse on February 6, 2013

OK, it’s really easy. You stick a thermometer out of the side of the aircraft and read what it says.

Nothing could be simpler, until you fly through a cloud. I’ll take these two parts – “fly” and “cloud” in turn.

To fly, we are inherently moving through the air, and the thermometer has to bash the air out of the way. At low speeds this barely makes any difference (think about it – the
weatherman doesn’t say “tomorrow will be warmer due to the wind”, does he?).

The problem is that we do insist on flying fast. Fast is good for making the journey go quickly, but the faster we fly, the more the effect of hitting the outside air becomes. Here come two explanations; take your pick…

Easy explanation: Think of some air molecules sitting quietly at 35,000 ft minding their own business. Suddenly they get hit by a temperature probe and – because they can’t get out of the way quickly enough – they squash up against their neighbours and, just like being in a mosh pit, they all get hot and bothered.

Harder explanation: Stationary air undergoes adiabatic compression with a ram rise temperature increase related to the local speed of sound by:

(See http://en.wikipedia.org/wiki/Total_air_temperature for details of the formula).

At this stage, we have two temperature measurements and we need to give them clear names. The Static Air Temperature (SAT) is the temperature of the air molecules sitting quietly, while the Total Air Temperature (TAT) is the temperature of the air when we hit it with the temperature probe. The difference is the “ram rise” so TAT = SAT + RR.

Of course, only two names would be easy, so confuse matters by sometimes calling the Static Air Temperature the Outside Air Temperature.

Still, life’s not that easy, and as well as flying fast, we want to fly through clouds. Clouds are wet and very cold. Supercooled water droplets freeze on the probe and coat the probe in rime ice, after which the temperature probe will no longer measure the air temperature properly.

Now here comes the really tricky part of the explanation, and one which I have to admit still makes my head hurt. To stop ice forming on the temperature probe, temperature probes are heated. In fact they get so hot that you can burn your hand if you touch them (as I learned in the hangar one day).

When the air is flowing through the probe the probe measures the air temperature correctly, but at low speeds it indicates how hot the heater has made the probe. Here is the POLARIS graph of TAT and Airspeed for the taxi out phase of a flight, and the red trace shows temperature variations. Sometimes the probe is cooled as the aircraft taxis, but when it is stationary the temperature rises swiftly to indicate almost 60C. The local temperature on that day was about freezing.

You can see the probe start to work properly as the airspeed builds during the takeoff run.

Now that we know the Total Temperature, the indicated airspeed and pressure altitude (see an earlier blog) we can do some sums involving gas constants, adiabatic exponents and the speed of sound to calculate useful things like the Static Air Temperature, the True Airspeed and the Mach number. This is what an Air Data Computer does.