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GATE 2024 AE – Question 48

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

For an airplane having directional / weathercock static stability, which of the following options is/are correct?

(B) The variation of yawing moment coefficient ($C_n$) with sideslip angle ($\beta$) for the airplane will look like [Figure: a straight line through the origin with $C_n$ increasing as $\beta$ increases].

Diagram for GATE 2024 AE question 48
  1. The airplane when disturbed in yaw, from an equilibrium state, will experience a restoring moment
  2. The variation of yawing moment coefficient ($C_n$) with sideslip angle ($\beta$) for the airplane will look like a straight line through the origin with a positive slope
  3. The airplane will always tend to point into the relative wind
  4. The airplane when disturbed in yaw will return to equilibrium state in a finite amount of time after removing the disturbance

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Show answer and explanation

Correct answer: (A) The airplane when disturbed in yaw, from an equilibrium state, will experience a restoring moment; (B) The variation of yawing moment coefficient ($C_n$) with sideslip angle ($\beta$) for the airplane will look like a straight line through the origin with a positive slope; (C) The airplane will always tend to point into the relative wind

Explanation

Directional static stability means $C_{n_\beta} > 0$: a sideslip produces a yawing moment that turns the nose into the relative wind, so the moment is restoring (A), the plot of $C_n$ against $\beta$ is an upward-sloping line through the origin (B), and the airplane points into the wind like a weathercock (C). Static stability does not say how long the return takes, since the motion can be a decaying oscillation that never exactly stops (D).