Discussion
An aeroplane rolls at a steady \( 0.30 \ \mathrm{rad/s} \) with a roll mode time constant of \( 0.50 \ \mathrm{s} \). Approximately how long after the aileron input does the roll rate reach 63 per cent of its final value?
Answer: A
For a first-order response the time to reach \( 1 - 1/e \), that is 63 per cent, of the final value is exactly one time constant, 0.50 seconds. Three time constants take it to 95 per cent, which is why a roll feels established almost at once on an aeroplane with a short constant. 0.32 s multiplies the constant by 0.63, confusing the fraction of the response with the fraction of the time. 1.50 s is three time constants, the 95 per cent figure. 0.15 s does not follow at all.
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