Discussion
Statement I: Moving the centre of gravity aft reduces the magnitude of the pitching moment derivative with angle of attack.
Statement II: Moving the centre of gravity aft raises the short-period natural frequency.
In the light of the above statements, choose the correct answer.
Answer: D
The first statement is right and the second is exactly backwards. An aft centre of gravity shortens the moment arm between it and the aerodynamic centre, so \( C_{m_\alpha} \) becomes less negative and the pitch stiffness falls. Since frequency follows the square root of that stiffness, the short period gets slower, not faster. What does rise is the damping ratio, because the real part of the root stays roughly fixed while the frequency drops, so \( \zeta = \sigma/\omega_n \) increases. An aft centre of gravity therefore buys damping at the price of frequency, and eventually of stability altogether.
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