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GATE 2025 AE – Question 38

Flight Mechanics & Space Dynamics · Static stability: stability and control derivatives, longitudinal, directional and lateral stability, hinge moments and stick forces · 2 marks · Multiple select

A general aviation airplane is initially in steady and level flight. The stability coefficient $\frac{\partial C_m}{\partial q}$ ($C_m$ is the airplane pitching moment coefficient and $q$ is the pitch rate) is negative. The airplane is perturbed with a small nose-up constant pitch rate. Assume that the horizontal tail does not stall during the perturbation, and unsteady effects are neglected. When compared to steady and level flight condition, which of the following statements is/are true during the perturbed motion?

  1. The angle of attack of the horizontal tail increases.
  2. The contribution of the horizontal tail to the airplane's pitching moment about the center of gravity is more stabilizing.
  3. The lift generated by the horizontal tail increases.
  4. The contribution of the horizontal tail to the airplane's pitching moment about the center of gravity is less stabilizing.

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Correct answer: (A) The angle of attack of the horizontal tail increases.; (B) The contribution of the horizontal tail to the airplane's pitching moment about the center of gravity is more stabilizing.; (C) The lift generated by the horizontal tail increases.

Explanation

A nose-up pitch rate makes the tail, which is behind the centre of gravity, move downwards relative to the air. Its local angle of attack rises by about $\frac{q\,l_t}{V}$ (A), so the tail lift grows (C). That extra upward tail force gives a nose-down moment that opposes the nose-up rotation, so the tail's contribution is more stabilizing (B). This is the pitch damping, which is why $\frac{\partial C_m}{\partial q}$ is negative.