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GATE 2022 AE – Question 19

Flight Mechanics & Space Dynamics · Static stability: stability and control derivatives, longitudinal, directional and lateral stability, hinge moments and stick forces · 1 mark · Multiple choice

Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

  1. It contributes to $C_{m_\alpha}<0$
  2. It makes $C_{m_\alpha}=0$
  3. It makes $C_{m_\alpha}>0$
  4. It makes $C_{m0}>0$ and $C_{m_\alpha}>0$

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Correct answer: (A) It contributes to $C_{m_\alpha}<0$

Explanation

Static longitudinal stability needs a **negative** slope of the pitching-moment curve about the centre of gravity, $C_{m_\alpha}<0$: if the nose pitches up, the aircraft must develop a nose-down moment.

**The horizontal tail.** It sits well behind the centre of gravity. When the angle of attack increases, the tail's angle of attack increases too, so it creates an **upward lift increment** at a point behind the CG. That lift gives a **nose-down** moment about the CG, i.e. a negative contribution to $C_{m_\alpha}$.

$$C_{m_\alpha,tail}=-a_t\,\eta\,V_H\left(1-\frac{d\varepsilon}{d\alpha}\right)<0 .$$

The wing alone is usually destabilising, so the tail is what gives the airplane its stability. Answer **A**.