Discussion
Which pair of aerodynamic derivatives sets the damping of the short-period mode?
Answer: C
Short-period damping comes from \( 2\zeta\omega_n = -(M_q + M_{\dot\alpha} + Z_\alpha/u_0) \), so the contributors are the pitch damping \( M_q \), the downwash-lag term \( M_{\dot\alpha} \) and the lift term \( Z_\alpha/u_0 \). All three are negative on a conventional aeroplane and all three therefore damp the motion. The speed derivatives of drag and thrust damp the phugoid, not this mode. Sideslip and yaw derivatives belong to the lateral problem entirely. Elevator effectiveness sets how hard the mode can be excited and where the aeroplane trims, but it does not appear in the damping term.
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