Stability of falling flyers

The motion of falling $\vee$-flyers is studied using an inviscid vortex shedding model. The body and vortices separated from the edge of the body are described by vortex sheets. The model provides a highly resolved vorticity field of the flow. We investigate the stability of falling flyers for various physical parameters. At high Reynolds numbers, the dynamics of falling bodies are characterized by the Froude number, which represents the relative importance of body inertia. We consider four folding angles of the wings: ${\varphi }_0=10^{\circ },20^{\circ },30^{\circ }$, and 45°, with the Froude number $\text{Fr}=1$. Our results show significant differences in the stability of flyers for varying the folding angle. For ${\varphi }_0=10^{\circ }$, the oscillation of the side-to-side motion increases rapidly, whereas for ${\varphi }_0=20^{\circ }$ and 30°, the flyers fall similarly and the oscillation increases much more slowly than in the case of ${\varphi }_0=10^{\circ }$. For ${\varphi }_0=45^{\circ }$, the flyer falls stably at early times, but the oscillation later grows rapidly. We also examine the effects of varying the Froude number and the center of mass of the body, with a fixed angle of ${\varphi }_0=20^{\circ }$. The flyer maintains a side-to-side oscillation for $\text{Fr}=0.5$, whereas it becomes unstable and eventually flips for $\text{Fr}=2$. It is found that lowering the center of mass stabilizes the flyer, whereas heightening the center of mass destabilizes it. The results on the flyer’s stability have practical implications in real-world applications such as air-gliders and bio-inspired flyers.