Discussion
An aeroplane climbs from sea level to \( 10 \ \mathrm{km} \) while holding true airspeed constant. By Lanchester's relation its phugoid period changes by a factor of
Answer: C
Lanchester's period \( T = \sqrt{2}\pi u_0/g \) contains only true airspeed and gravity, so holding true airspeed fixed leaves the period unchanged, even though the air is a third as dense at the top of the climb. This is a sharp contrast with the short period, whose frequency falls with the square root of density in the same climb, and it is a good check on whether the two formulae are being kept apart. The factors 0.5, 1.4 and 2.0 are all density-driven, and would be right if the phugoid depended on dynamic pressure, which it does not.
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