Stabilization of Flapping-of-Wings Flight of a Butterfly, Considering Wakes

Abstract

This paper studies the flapping-of-wings flight of a butterfly, which is rhythmic and cyclic in motion. The objective is to clarify the principle of stabilization of the flapping-of-wings flight. For this purpose, an experimental system with a low-speed wind tunnel is constructed for fundamental data of flapping-of-wings motion, where the system measures the aerodynamic force and the motion simultaneously using a measure and an optical measurement system. A dynamics model of a butterfly is derived by Lagrange’s method, where the butterfly is considered as a rigid body system. For the aerodynamic forces, a lumped-vortex method and a panel method are applied. Validity of the mathematical models is examined by the good agreement of the numerical results with the measured data. Then, periodic orbits of a flapping-of-wings flight are searched in order to fly the butterfly models. Almost periodic orbits are obtained, but both models in the flapping-of-wings flight are unstable. The unstable level of the panel method model is smaller by considering free-vortices in wakes. Meaning that the wake-induced flow has a type of feedback stabilization effect.