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At high subsonic Mach numbers a large transport can develop an aperiodic longitudinal divergence known as the tuck mode. Its dynamic signature is

  • A.A sign change in the last coefficient of the quartic
  • B.A sudden rise in short-period frequency
  • C.A collapse of the phugoid period to a few seconds
  • D.A pair of purely imaginary roots

Answer: A

Tuck appears when the pitching moment derivative with speed turns negative as the aerodynamic centre moves aft with Mach number. That drives \( E \) through zero and negative, producing a real positive root and a nose-down divergence with no oscillation, which is why a Mach trim system is fitted to sense the condition and apply compensating trim. Short-period frequency is set by stiffness in incidence and is not what changes here. The phugoid period is tied to trim speed and does not collapse. Purely imaginary roots would be the boundary of an oscillatory instability, a different case entirely.

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