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A spiral mode has a real root of \( +0.035 \ \mathrm{s^{-1}} \). Against a requirement that the time to double amplitude be at least 20 seconds, the aeroplane is

  • A.Compliant, with about 35 s
  • B.Non-compliant, with about 14 s
  • C.Compliant, with about 20 s
  • D.Non-compliant, with about 7 s

Answer: C

The doubling time is \( t_2 = \ln 2/\sigma = 0.693/0.035 = 19.8 \ \mathrm{s} \), so the aeroplane sits right on the 20-second requirement and is compliant to the accuracy of the measurement. A divergent spiral is acceptable precisely because it is slow: twenty seconds is many times a pilot's reaction time, and any autopilot holds wings level without effort. The other options come from using the root directly, or from confusing the doubling time with the time constant \( 1/\sigma = 28.6 \) seconds.

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