Air Temperature Measurement — Page 39, Lesson 42

Let’s start with the accurate formula, because that is the heart of this whole section. The formula is: SAT = TAT / (1 + 0.2 × Kr × M²) Here, SAT is Static Air Temperature, TAT is Total Air Temperature, M is the Mach Number, and Kr is the Recovery Factor. I’ll define each of those properly in a moment, but first, let’s look at the formula itself. The denominator, 1 + 0.2 Kr M², is the correction that converts the temperature you measure at the probe into the true outside air temperature. Now, the formula assumes that temperature is quoted in degrees Absolute, which is the same as Kelvin. So before we can use the formula, we need to understand the Kelvin scale. When Celsius designed his scale, he chose the boiling point of water as 100°C and the freezing point as 0°C. That seemed reasonable at the time, but the problem is that the Celsius scale changes sign at 0°C — numbers above zero are positive, numbers below are negative. To measure hotness meaningfully, we need a baseline of absolute zero — no heat at all. That occurs at -273°C on the Celsius scale. So -273°C is 0 K on the Kelvin scale. One kelvin is the same amount of temperature change as one degree Celsius, so the freezing point of water is 273 K, and the boiling point is 373 K. Now let’s apply this with a worked example. Assume the indicated TAT — which is actually RAT, Recovery Air Temperature — is -20°C. The Mach Number is 0.73, which is a typical cruise speed for a B737 in Long Range Cruise. The Recovery Factor is 0.98, a typical value for a modern TAT probe. Kr is determined by flight testing and is published in the operating instructions for the aircraft. First, convert -20°C to Kelvin: that’s 253 K. Now substitute into the formula: SAT = 253 / (1 + 0.2 × 0.98 × 0.73²) Let’s work the denominator. 0.73² is 0.5329. Multiply by 0.98 gives 0.5222. Multiply by 0.2 gives 0.1044. So the denominator is 1 + 0.1044 = 1.1044. Now divide: 253 / 1.1044 = 229 K. And 229 K is -44°C on the Celsius scale. So the measured TAT of -20°C corresponds to a true static air temperature of -44°C. That’s the whole point of the correction — the probe heats the air through compression, so the measured temperature is higher than the true outside temperature. Now, calibration. Because the atmosphere varies with temperature and pressure, we need a standard calibration for the instruments. The conditions used for calibration are those of the International Standard Atmosphere, or ISA. The ISA assumptions are: at Mean Sea Level, pressure is 1013.25 hectopascals, temperature is +15°C, and density is 1225 grams per cubic metre. From MSL up to 11 km, which is 36,090 feet, temperature falls at 6.5°C per km, or 1.98°C per 1000 feet. From 11 km to 20 km, which is 65,617 feet, temperature is constant at -56.5°C. From 20 km to 32 km, which is 104,987 feet, temperature rises at 1°C per km, or 0.3° per 1000 feet. With these assumptions, the pressure corresponding to any given level in the ISA can be calculated from the calibration formulae. Graphs or tables can be produced showing height in terms of pressure under standard conditions. These tables are used for the manufacturer’s calibration of the altimeter scale. Any discrepancies, if within certain agreed tolerances, are listed over the operating height ranges as instrument errors. And importantly, the calibration is carried out with increasing and decreasing readings, so that the amount of lag at calibration conditions can be determined. So to tie it together: the accurate formula converts measured TAT into true SAT using the Mach number and recovery factor, and the Kelvin scale is essential because it starts from absolute zero. Then the ISA provides the standard atmosphere against which all instruments are calibrated.