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At 1400 UTC an aircraft 550 NM from point X is requested to reach point X at 1525 UTC. Current cruise conditions are FL290, OAT -43º C, wind component -70kt. What is the required Mach Number to comply with specified time?
  • A
    0.57
  • B
    0.68
  • C
    0.77
  • D
    0.85

Formulas needed:

M = TAS / LSS; where M stands for Mach number, TAS is True Air Speed and LSS is Local Speed of Sound.
LSS = 38.95 x Absolute temperature (K)


1) Determine the Ground Speed:

Aircraft is requested to cover a distance of 550 NM in 1 h 25 (15 h 25 - 14 h 00). Therefore, its Ground Speed must be = 550 NM / 1h 25 = 388 kt


2) Calculate TAS (for a wind component of -70 kt, 70 kt Head):

TAS = GS + Headwind
TAS = 388 + 70 = 458 kt


3) Calculate the Mach number for a TAS of 458 kt and OAT of -43ºC:
  • LSS = 38.95 x (-42 + 273)
    LSS = 591 kt
  • M = TAS / LSS
    M = 458 / 591
    M = 0.77

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