Asymmetric pitching and intermittent flapping of the hindwing enhance force-vectoring propulsion of tandem flapping wings

Natural flyers and swimmers exploit unsteady flow interactions in tandem wings or fins and thus achieve force-vectoring propulsion. However, efficient control strategies lie in a wide parameter space of both wings and fins. This study focuses on independent motion modulation of the hindwing to enhance the force-vectoring propulsion. The system is simplified as two-dimensional tandem airfoils, with the forewing performing continuous symmetric pitching–plunging motions while the hindwing undergoes asymmetric pitching (non-zero mean pitch angle, α0) and intermittent flapping. The results show that introducing α0 shifts the system from a pure propelling mode to an integrated lift-propelling mode. This transition is primarily attributed to the enhanced leading-edge vortex (LEV) and altered projection of the aerodynamic force vector on the hindwing. More importantly, an intermittent flapping hindwing with a duty cycle of 0.5 can improve lift generation while substantially reducing power, thereby enhancing lift efficiency at propulsion equilibrium. This surprising enhancement benefits from the stronger starting vortex in the burst phase and the sustained but energy-free LEV-induced lift during the coast phase. Overall, this study demonstrates that, by combining asymmetric pitching and intermittent flapping, individual control of hindwing motion can efficiently manipulate the force vectoring of a tandem flapping-wing system. This may simplify the control of aerial and underwater vehicles with multiple flapping wings.