Discussion
The roll mode time constant is given by \( \tau_R = -1/L_p \). For \( L_p = -2.5 \ \mathrm{s^{-1}} \) it is
Answer: C
The reciprocal of 2.5 is 0.40, so four tenths of a second: an aileron input reaches about 63 per cent of its steady roll rate in that time and is essentially complete in three time constants. 2.5 s is the derivative read back as a time. 1.73 s and 0.28 s come from folding in a logarithm of two that does not belong: the time to half amplitude is \( 0.693\tau_R = 0.28 \ \mathrm{s} \), which is a different measure and is worth keeping distinct from the time constant itself.
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