Discussion
For an aeroplane cruising at a lift-to-drag ratio of 12, the estimate \( \zeta_{ph} \approx C_D/(\sqrt{2}\,C_L) \) gives a phugoid damping ratio of about
Answer: C
With \( C_D/C_L = 1/12 \), the damping ratio is \( 1/(\sqrt{2} \times 12) = 0.059 \). That is about six per cent of critical, which is why a phugoid takes so many cycles to disappear. 0.083 is \( 1/12 \) with the root two forgotten, 0.042 divides by two rather than by \( \sqrt{2} \), and 0.118 is twice the correct figure. The formula carries a design warning: damping is inversely proportional to lift-to-drag ratio, so the cleaner and more efficient the aeroplane, the more poorly damped its phugoid.
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