Bistability in the rotational motion of rigid and flexible flyers

Abstract

We explore the rotational stability of hovering flight. Our model is motivated by an experimental pyramid-shaped object and a computational lambda-shaped analog hovering passively in oscillating airflows; both systems have been shown to maintain rotational balance during free flight. Here, we attach the lambda-shaped flyer at its apex, allowing it to rotate freely akin to a pendulum. We find that the flyer exhibits stable concave-down and concave-up behavior. Importantly, the down and up configurations are bistable and co-exist for a range of background flow properties. We explain the aerodynamic origin of this bistability and compare it to the inertia-induced stability of an inverted pendulum oscillating at its base. We then allow the flyer to flap passively by introducing a rotational spring at its apex. For stiff springs, flexibility diminishes upward stability but as stiffness decreases, a new transition to upward stability is induced by flapping. We conclude by commenting on the implications of these findings for biological and man-made aircraft.