FAA Airline Transport Pilot (ATM)Transport Aerodynamics and High-Altitude OperationsMedium
A transport aircraft is cruising at FL370 where the SAT is -56.5°C (216.5 K) at Mach 0.82. Using the approximation ΔT(K) = SAT(K) × 0.2 × M², what is the approximate total air temperature (TAT)?
- A-40°C
- B-56°C
- C-27°C
- D-10°C
Show answer & explanationAnswer & explanation
Correct answer: C. -27°C
ΔT = 216.5 × 0.2 × (0.82)² = 216.5 × 0.2 × 0.6724 ≈ 29.1 K. TAT = 216.5 + 29.1 = 245.6 K ≈ -27.5°C, closest to -27°C.
Why the other options are wrong
- A. Underestimates the ram temperature rise from compressibility heating.
- B. This is the SAT, ignoring ram rise entirely.
- D. Overstates the ram rise beyond what Mach 0.82 produces.
Ram Rise (TAT vs SAT)
Total Air Temperature (TAT) is higher than Static Air Temperature (SAT) due to adiabatic compression heating of air at the probe as speed increases, approximated by ΔT(K) ≈ SAT(K) × 0.2 × M².
- TAT sensed by probe, SAT is true ambient temp
- Ram rise increases with the square of Mach number
- Used to correct for engine performance and TAS calculations
Memory trick: Faster air, hotter probe — squeeze the air, feel the heat