Discussion
A phugoid has a damping ratio of 0.04. The number of cycles needed for the amplitude to halve, from \( N_{1/2} = 0.110\sqrt{1-\zeta^{2}}/\zeta \), is about
Answer: B
Substituting \( \zeta = 0.04 \) gives \( N_{1/2} = 0.110 \times 0.9992 / 0.04 = 2.75 \), so between two and three full cycles. With a period of a minute or so that is several minutes of oscillation, which is exactly the pilot complaint the requirement on phugoid damping exists to control. 1.4 cycles would need a damping ratio nearer 0.08, twice what was given. 5.5 halves the damping instead. 0.11 cycles is the constant in the formula quoted back without the division, and would describe a very heavily damped mode.
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