The thrust balance model during the dragonfly hovering flight

In recent years, the micro air vehicle (MAV) oscillations caused by thrust imbalances have received more attention. This paper proposes a dual-wing thrust balance model (DTBM) that can solve the above problem by iterating the modified rotation angle formula. The core control parameter of the DTBM model is the au angle, which refers to the angle between the wing surface and the stroke plane at the mid-stroke position during the upstroke. For each degree change in the au angle, the range of variation in the dimensionless average thrust coefficient is between 0.0225-0.0268. A thrust coefficient of 0.0225 causes the dragonfly to move forward by 9.037 cm in one second, which is equivalent to 1.29 times its body length. By using DTBM, the average thrust coefficient can be reduced to below 0.001 in just a few iterations. No matter how complex the motion pattern is, the DTBM can achieve thrust balance within 0.278 s. Through our research, when selecting the deviation angle motion of real dragonflies, the dual-wing au angles exhibit a highly linear correlation with wing spacing, called linear motion. In contrast, the nonlinear variation of the au angle appears in the hindwing of the no-deviation motion and the forewing of the elliptical deviation motion. All of the nonlinear changes are referred to as nonlinear motion. Nonlinear variation of the au angle arises from larger disturbances of the lateral force during the upstroke. The stronger lateral force is closely related to the flapping trajectory. When the flapping trajectory causes the dual-wing to closely approach each other in the mid-stroke, a continuous positive pressure zone forms between the dual-wing. The collision of the leading-edge vortex and the shedding of the trailing-edge vortex is the special flow field structure in the nonlinear motion. Guided by the DTBM, future designs of MAVs will be able to better achieve thrust balance during hovering flight, requiring only the embedding of the iteration algorithm and prediction function of the DTBM in the internal chip.