Discussion
A Dutch roll with a damping ratio of 0.10 halves its amplitude in about how many cycles, from \( N_{1/2} = 0.110\sqrt{1-\zeta^{2}}/\zeta \)?
Answer: A
Substituting, \( N_{1/2} = 0.110 \times 0.995/0.10 = 1.09 \), so a little over one cycle. That is the practical meaning of a damping ratio of a tenth: the aeroplane completes roughly one visible wag and rock before the motion is halved, which passengers notice but pilots can live with. 0.11 cycles is the formula's constant returned without the division and would describe a heavily damped mode. 11 cycles is a decade out. 2.2 cycles corresponds to a damping ratio near 0.05.
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