Beneficial wake-capture effect for forward propulsion with a restrained wing-pitch motion of a butterfly

Abstract

Unlike other insects, a butterfly uses a small amplitude of the wing-pitch motion for flight. From an analysis of the dynamics of real flying butterflies, we show that the restrained amplitude of the wing-pitch motion enhances the wake-capture effect so as to enhance forward propulsion. A numerical simulation refined with experimental data shows that, for a small amplitude of the wing-pitch motion, the shed vortex generated in the downstroke induces air in the wake region to flow towards the wings. This condition enables a butterfly to capture an induced flow and to acquire an additional forward propulsion, which accounts for more than 47% of the thrust generation. When the amplitude of the wing-pitch motion exceeds 45°, the flow induced by the shed vortex drifts away from the wings; it attenuates the wake-capture effect and causes the butterfly to lose a part of its forward propulsion. Our results provide one essential aerodynamic feature for a butterfly to adopt a small amplitude of the wing-pitch motion to enhance the wake-capture effect and forward propulsion. This work clarifies the variation of the flow field correlated with the wing-pitch motion, which is useful in the design of wing kinematics of a micro-aerial vehicle.

Lift enhancement of a butterfly-like flapping wing vehicle by reinforcement learning algorithm

“…As a result, at the beginning of the experiment, the average aerodynamic lift in one period is 0.044 N, and the motion parameters are (51 • , −14 • , 0.35, 1.7 Hz), the agent finds the appropriate motion parameters that the amplitude, the middle position, the downstroke ratio and the flapping frequency are (73 • , −12 • , 0.3, 2 Hz), respectively. The flapping amplitude is evidently different from the real butterfly [30]. Under this setting, the average aerodynamic lift in one period reaches 0.861 N and the lift force curves in figure 6 show that a conventional lift peak is generated in the downstroke stage, but an unexpected strong lift peak is generated in the upstroke stage.…”

Flight dynamics in forward flights of cabbage white butterfly

“…While some studies (e.g., Zheng et al, 2013;Johansson and Henningsson, 2020) suggested the importance of wing deformation in terms of aerodynamic performance, many authors presented satisfactory results using rigid flat plates (e.g., Bimbard et al 2013;Yokoyama et al 2013;Yang 2015, 2016;Chang et al 2020;Suzuki et al, 2022). As Lin et al (2021) also suggested, it can be expected that the use of rigid flat plates does not affect a butterfly's natural flight trend. We assume the left wing has the same shape as the right wing.…”

“…In addition to the above-mentioned experimental measurements, some numerical simulations using computational fluid dynamics (CFD) aided by experimental measurements have been conducted (e.g., takeoff of Pieris melete by Sunada et al, 1993; forward flight of Vanessa cardui by Zheng et al, 2013; forward flight of Chilasa clytia by Zhang et al, 2021; forward-climbing flight of Danaus plexipus by Tejaswi et al, 2021; forward flight of Tirumala septentrionis by Lin et al, 2021). Among such numerical simulations, only a few studies have considered the interaction among the wings, body, and ambient air by directly calculating the incompressible Navier-Stokes equations and the equations of the butterfly motion.…”

Experimental Analyses of Aerodynamic Force Generation and Wing Motion Associated with a Single-motor-driven Butterfly-inspired Flapping-wing Robot

“…In addition, the aspect ratio, wing loading, and flapping frequency were chosen so that these were close to the range of real butterflies. (26,27) Moreover, the effects of the vein structures of the real butterfly wings were not considered and are one of our on-going research topics. (28,29) The body frame is constructed using an acrylic resin (AR-M2), designed with CAD software (Fusion360, Autodesk), and fabricated using a 3D printer (AGILISTA-3200, Keyence).…”