Experimental Characterization of a Butterfly in Climbing Flight

Abstract

An optical tracking facility was used to record the free flight of the Monarch butterfly for a large number of sequential flaps. The system automatically tracked reflective markers, which were modified to reduce the effects of additional mass on the flight characteristics. Measurements were analyzed over 75 flights of 9 butterflies in a climbing trajectory covering a large range of climbing rates. The flapping frequency remained fairly constant at 9.8 Hz. The peak-to-peak flapping amplitude varied more significantly with an average of 246.4°. The phase offset between flapping and body undulation averaged 89°. The body oscillation amplitude was 4.9 mm. Simulations using Theodorsen’s equation coupled with a single mass dynamics equation resulted in a body motion that closely agreed with the observed data. The undulation amplitude increased with the flapping amplitude, but decreased with wing loading. Butterflies have the lowest wing loading among insects, consistent with their large body undulation amplitudes. The wing–body phase offset solely depends on the reduced frequency, a consequence of the timing between the noncirculatory and circulatory forces. These results suggest that this novel experimental framework can increase our understanding of biological flight and development of micro flapping robots.