Bistability in the rotational motion of rigid and flexible flyers

TL;DR

This paper investigates the rotational stability and bistability of rigid and flexible flyers in oscillating airflow, revealing how passive flapping and flexibility influence stability regimes relevant to biological and engineered flight.

Contribution

It introduces a model of a lambda-shaped flyer demonstrating bistability and explores how passive flapping and flexibility affect stability, providing new insights into passive flight mechanisms.

Findings

Flyers exhibit stable concave-up and concave-down configurations.

Bistability occurs over a range of flow conditions.

Flexibility and passive flapping influence stability transitions.

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.