Gliding simulations of a butterfly wing and potential applications to Danaus plexippus (Lepidoptera: Danaidae) migration

Monarch butterflies are known to make much use of gliding and soaring during their annual fall migration from southern Canada and the U.S. to Mexico. In previous studies, wind tunnels were constructed to measure aerodynamic forces on insects. In recent years, computational fluid dynamics (CFD) have been employed, which can often replace wind tunnel studies for aerodynamic measurements. CFD is a popular method in aerospace engineering. In this study, CFD was used for the first time in order to obtain lift and drag coefficients of a gliding monarch butterfly wing. The CFD package utilized for the simulations was FLUENT 6.2.12. The simulation demonstrated what effects variations in angle of attack, wind velocity, and wing area have on lift and drag coefficients (Cl, Cd). Differences in these parameters might influence the migration success of monarch butterflies. Angle of attack had the largest effect on Cl and Cd, which increased from 2.0 to almost 4.1 and from 0.03 to 0.1 respectively, as angle of attack doubled. Lift and drag forces increased proportional to an increase in angle of attack and wing area; lift increased proportional to velocity-squared, and drag increased in a non-proportional fashion with velocity. Even though the simulations do not allow the measurement of absolute lift and drag forces, the influence of different parameters can be determined. A potential further application would be to compare lift and drag forces of migratory versus resident monarch butterflies, which have significantly different wing shapes.