FAA Airline Transport Pilot (ATM)Aircraft Performance and Weight and BalanceEasy
A turbojet is cruising at a constant Mach 0.80 and climbs into a layer of air that is colder than the temperature it was flying in previously, with Mach number held constant. How does the airplane's true airspeed (TAS) change?
- ATAS increases because Mach number and TAS are directly proportional at all temperatures
- BTAS remains unchanged because Mach number alone determines TAS
- CTAS decreases because the local speed of sound decreases as temperature decreases
- DTAS increases because colder, denser air increases true airspeed for a given power setting
Show answer & explanationAnswer & explanation
Correct answer: C. TAS decreases because the local speed of sound decreases as temperature decreases
TAS = Mach number × local speed of sound, and the speed of sound is proportional to the square root of absolute temperature. In colder air, the speed of sound is lower, so holding Mach constant results in a lower TAS even though indicated Mach has not changed.
Why the other options are wrong
- A. Mach and TAS are related through temperature, not a fixed constant proportion.
- B. Mach alone does not determine TAS; temperature (speed of sound) is also required.
- D. Air density affects performance but TAS at constant Mach is governed by temperature via speed of sound, not density directly.
Mach/TAS/Temperature Relationship
True airspeed equals Mach number multiplied by the local speed of sound, which decreases with decreasing outside air temperature.
- Speed of sound ∝ √(absolute temperature)
- Colder air = lower speed of sound = lower TAS at same Mach
- This is why TAS can vary along a route even at constant Mach cruise
Memory trick: Cold air slows sound, so the same Mach buys you less true speed.