Post-Stall Motions Evolving Toward Chaos

Abstract

The spin of an airplane occurs for angles of attack beyond stall, where nonlinear aerodynamics dominates and where complex and unpredictable behaviors might induce to question whether or not such a motion is chaotic. To find an answer to this issue, wind-tunnel tests are carried out on a model of a fighter attached by its center of gravity through an universal joint that allows only the three rotations. These degrees of freedom are analyzed according to modern techniques for the study of "supposedly chaotic data." It is found that, for increasing Reynolds number, successive bifurcations take place with a consequent more complex structure of the attractor, which reveals some features typical of quasi-periodic systems evolving toward chaos. The model is tested also in other configurations (different nose and/or leading-edge extensions, presence or absence of tail planes) so as to verify the dependence of the motion on some details. It is found that unpredictability and strong dependence on the initial conditions characterize the basic configuration, whereas a blunt nose and leading-edge extensions make the motion extremely regular. Even though the system might be on its route to chaos, a fully developed chaotic behavior is not observed.

An investigation into aircraft loss of control and recovery solutions

“…Even though previous works establishes the existence of chaotic solutions, their existence is justified by considering the inherent nonlinear behavior of aircraft systems. The possibility of existence of a chaotic attractor for spin has been investigated by Zuccher and Ponte 40 and wind tunnel tests corroborated their claims. They were able to present some quasi-periodic spin behavior for the post-stall motions.…”