Linear control of lift in dragonfly vertical flight

Abstract The lift generation mechanisms of dragonflies have been extensively and deeply studied. As research advances, controlling the lift coefficient faces significant challenges. How the lift coefficient varies and whether a unified model can predict lift tendency remains unresolved. In this study, we propose a flapping amplitude partial advanced model (FAPAM) to control the linear variation of lift in dragonfly vertical flight. The FAPAM model can predict the average lift coefficient by the spatial plane and control the dragonfly lift coefficient over a large range. In this model, the maximum lift coefficient is 2.01 times higher than the weight of a dragonfly. The control parameters of the FAPAM are flapping amplitude (FA) and partial lead percent (PLP). Any linear combination of FA and PLP ensures a linear variation of the average lift coefficient. When FA and advanced rotation angle (ARA) increase by one degree, respectively, the increased lift coefficient of FA is 5.38–9.52 times higher than that of ARA, which is closely related to the leading-edge vortex, trailing edge vortex, and positive pressure zone. The FAPAM model seamlessly integrates vertical ascending mode and vertical climbing mode by introducing transition mode. Additionally, FAPAM can effectively simulate the lift coefficient required for the vertical undulating motion of dragonflies during their oviposition process on water. Most importantly, the FAPAM model can maximize the energy efficiency of different motion modes.