Forward flight stability in a drone-fly.

Previous studies on forward flight stability in insects are for low to medium flight-speeds. In the present work, we investigated the stability problem for the full range of flight speeds (0-8.6 m/s) of a drone-fly. Our results show the following: The longitudinal derivatives due to the lateral motion are approximately 3 orders of magnitude smaller than the other longitudinal derivatives. Thus, we can decouple these two motions of the insect, as commonly done for a conventional airplane. At hovering flight, the motion of the dronefly is weakly unstable owing to two unstable natural modes of motion, a longitudinal one and a lateral one. At low (1.6 m/s) and medium (3.1 m/s) flight-speeds, the unstable modes become even weaker and the flight is approximately neutral. At high flight-speeds (4.6 m/s, 6.9 m/s and 8.6 m/s), the flight becomes more and more unstable due to an unstable longitudinal mode. At the highest flight speed, 8.6 m/s, the instability is so strong that the time constant representing the growth rate of the instability (disturbance-doubling time) is only 10.1 ms, which is close to the sensory reaction time of a fly (approximately 11 ms). This indicates that strong instability may play a role in limiting the flight speed of the insect.