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

Measurement of wing motion, deformation, and inertial forces of a biomimetic butterfly

This paper introduces a method for measuring wing motion, deformation, and inertial forces in bio-inspired aircraft research using a camera motion capture system. The method involves placing markers on the wing surface and fitting rigid planes to determine the wing's spatial axis. This allows for describing the wing's rigid motion and obtaining deformation characteristics, such as deflection, twist angle, and gap distance of the forewing and hindwing. An image-based method is proposed for determining wing mass distribution, mass blocks, and mass points for inertial force measurement. The study addresses wing motion, deformation, and inertial force measurement in a real butterfly-like flapping wing vehicle and demonstrates the effectiveness of the approach. The results reveal that inertial forces play a negligible role in the generation of lift peaks and contribute minimal lift during the entire flapping cycle. Furthermore, a transitional phase between downstroke and upstroke is found in flexible wing motion, which has high lift production. This measurement approach offers a rapid and effective solution to experimental challenges in bio-inspired aircraft design and optimization.

Bottom-up butterfly model with thorax-pitch control and wing-pitch flexibility

The diversity in butterfly morphology has attracted many people around the world since ancient times. Despite morphological diversity, the wing and body kinematics of butterflies have several common features. In the present study, we constructed a bottom-up butterfly model, whose morphology and kinematics are simplified while preserving the important features of butterflies. The present bottom-up butterfly model is composed of two trapezoidal wings and a rod-shaped body with a thorax and abdomen. Its wings are flapped downward in the downstroke and backward in the upstroke by changing the geometric angle of attack (AOA). The geometric AOA is determined by the thorax-pitch and wing-pitch angles. The thorax-pitch angle is actively controlled by abdominal undulation, and the wing-pitch angle is passively determined because of a rotary spring representing the basalar and subalar muscles connecting the wings and thorax. We investigated the effectiveness of abdominal undulation for thorax-pitch control and how wing-pitch flexibility affects aerodynamic-force generation and thorax-pitch control, through numerical simulations using the immersed boundary-lattice Boltzmann method. As a result, the thorax-pitch angle perfectly follows the desired angle through abdominal undulation. In addition, there is an optimal wing-pitch flexibility that maximizes the flying speed in both the forward and upward directions, but the effect of wing-pitch flexibility on thorax-pitch control is not significant. Finally, we compared the flight behavior of the present bottom-up butterfly model with that of an actual butterfly. It was found that the present model does not reproduce reasonable body kinematics but can provide reasonable aerodynamics in butterfly flights.

The Lift Effects of Chordwise Wing Deformation and Body Angle on Low-Speed Flying Butterflies

This work investigates the effects of body angle and wing deformation on the lift of free-flying butterflies. The flight kinematics were recorded using three high-speed cameras, and particle-image velocimetry (PIV) was used to analyze the transient flow field around the butterfly. Parametric studies via numerical simulations were also conducted to examine the force generation of the wing by fixing different body angles and amplifying the chordwise deformation. The results show that appropriately amplifying chordwise deformation enhances wing performance due to an increase in the strength of the vortex and a more stabilized attached vortex. The wing undergoes a significant chordwise deformation, which can generate a larger lift coefficient than that with a higher body angle, resulting in a 14% increase compared to a lower chordwise deformation and body angle. This effect is due to the leading-edge vortex attached to the curved wing, which alters the force from horizontal to vertical. It, therefore, produces more efficient lift during flight. These findings reveal that the chordwise deformation of the wing and the body angle could increase the lift of the butterfly. This work was inspired by real butterfly flight, and the results could provide valuable knowledge about lift generation for designing microaerial vehicles.

Decoupling wing-shape effects of wing-swept angle and aspect ratio on a forward-flying butterfly

The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.

Downstroke and upstroke conflict during banked turns in butterflies

For all flyers, aeroplanes or animals, making banked turns involve a rolling motion which, due to higher induced drag on the outer than the inner wing, results in a yawing torque opposite to the turn. This adverse yaw torque can be counteracted using a tail, but how animals that lack tail, e.g. all insects, handle this problem is not fully understood. Here, we quantify the performance of turning take-off flights in butterflies and find that they use force vectoring during banked turns without fully compensating for adverse yaw. This lowers their turning performance, increasing turn radius, since thrust becomes misaligned with the flight path. The separation of function between downstroke (lift production) and upstroke (thrust production) in our butterflies, in combination with a more pronounced adverse yaw during the upstroke increases the misalignment of the thrust. This may be a cost the butterflies pay for the efficient thrust-generating upstroke clap, but also other insects fail to rectify adverse yaw during escape manoeuvres, suggesting a general feature in functionally two-winged insect flight. When lacking tail and left with costly approaches to counteract adverse yaw, costs of flying with adverse yaw may be outweighed by the benefits of maintaining thrust and flight speed.