Discussion
Consider the following pairs of derivative and the mode whose damping it chiefly supplies.
Pitching moment with pitch rate - Short period
Axial force with forward speed - Phugoid
Pitching moment with rate of change of incidence - Short period
Normal force with incidence - Phugoid
How many of the pairs given above are correctly matched?
Answer: D
The first three are correctly paired and the fourth is not, so three match. Pitch damping and the downwash-lag term both damp the short period, and the axial force derivative with speed, dominated by drag, damps the phugoid. The normal force derivative with incidence appears as \( Z_\alpha/u_0 \) in the short-period damping, not the phugoid's, and it is one of the three terms in \( 2\zeta\omega_n \). Keeping the two force derivatives apart is the point of the question: one acts along the flight path and slowly, the other across it and fast.
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