Study on Flapping-of-Wings Flight of Butterfly with Numerical and Experimental Analysis

Abstract

This paper treats the flapping-of-wings flight of a butterfly, which is rhythmic and cyclic motion. The objective of this paper is to clarify the principle of stabilization of the flapping-of-wings flight. For the purpose, this study performs the experiment for the quantitative data acquisition and qualitative observation, derives models of a butterfly, and compares the actual and modeled butterflies. 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 by a measure and a optical measurement system. The measured data of flapping motion shows what degreeof-freedom are used for butterfly control. A dynamics model of a butterfly is derived for analyses 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 model is examined by comparing the measured data with the numerical results. A periodic orbit of a flapping-of-wings flight is searched so as to fly the butterfly model. Both models in the flapping-of-wings flight are unstable. The unstable level of the panel method model becomes small by considering free-vortices in wakes. It is shown that the wake-induced flow of the panel method has a kind of feedback stabilization eect.