FAA Airline Transport Pilot (ATM)Transport Aerodynamics and High-Altitude OperationsHard
An aircraft is cruising above the tropopause at FL370, where the ISA temperature is -56.5°C, giving a speed of sound of approximately 573 knots. The aircraft is flying at Mach 0.80. If the actual outside air temperature is ISA+15°C instead, what is the approximate change in true airspeed (TAS) at the same Mach number?
- ANo change in TAS
- BAn increase of approximately 15 knots
- CA decrease of approximately 15 knots
- DAn increase of approximately 50 knots
Show answer & explanationAnswer & explanation
Correct answer: B. An increase of approximately 15 knots
Speed of sound depends on absolute temperature: a ≈ 39×√T(K). At -56.5°C (216.65K), a ≈ 573 kt; at ISA+15 (-41.5°C, 231.65K), a ≈ 593 kt. TAS = Mach × a: standard TAS = 0.80×573 ≈ 458 kt; warmer TAS = 0.80×593 ≈ 474 kt, an increase of about 15-16 knots for the same indicated Mach number.
Why the other options are wrong
- A. TAS does change because speed of sound is temperature-dependent, even at constant Mach.
- C. TAS increases, not decreases, in warmer-than-standard air at constant Mach.
- D. This overstates the change; the actual increase is roughly 15-16 knots based on the calculation.
Temperature Effect on TAS at Constant Mach
Because the speed of sound varies with the square root of absolute temperature, TAS at a given Mach number increases in warmer-than-standard air and decreases in colder-than-standard air.
- Speed of sound formula: a ≈ 39 × √T(Kelvin) in knots
- TAS = Mach number × local speed of sound
- Warmer air increases both speed of sound and TAS for the same Mach number
Memory trick: Warmer air, faster sound, faster TAS at the same Mach