Dynamic flight stability in the desert locust Schistocerca gregaria.

Here we provide the first formal quantitative analysis of dynamic stability in a flying animal. By measuring the longitudinal static stability derivatives and mass distribution of desert locusts Schistocerca gregaria, we find that their static stability and static control responses are insufficient to provide asymptotic longitudinal dynamic stability unless they are sensitive to pitch attitude (measured with respect to an inertial or earth-fixed frame) as well as aerodynamic incidence (measured relative to the direction of flight). We find no evidence for a 'constant-lift reaction', previously supposed to keep lift production constant over a range of body angles, and show that such a reaction would be inconsequential because locusts can potentially correct for pitch disturbances within a single wingbeat. The static stability derivatives identify three natural longitudinal modes of motion: one stable subsidence mode, one unstable divergence mode, and one stable oscillatory mode (which is present with or without pitch attitude control). The latter is identified with the short period mode of aircraft, and shown to consist of rapid pitch oscillations with negligible changes in forward speed. The frequency of the short period mode (approx. 10 Hz) is only half the wingbeat frequency (approx. 22 Hz), so the mode would become coupled with the flapping cycle without adequate damping. Pitch rate damping is shown to be highly effective for this purpose - especially at the small scales associated with insect flight - and may be essential in stabilising locust flight. Although having a short period mode frequency close to the wingbeat frequency risks coupling, it is essential for control inputs made at the level of a single wingbeat to be effective. This is identified as a general constraint on flight control in flying animals.