Effects of structural flexibility of wings in flapping flight of butterfly

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.

Shape Morphing by Topological Patterns and Profiles in Laser-Cut Liquid Crystal Elastomer Kirigami

Programming shape changes in soft materials requires precise control of the directionality and magnitude of their mechanical response. Among ordered soft materials, liquid crystal elastomers (LCEs) exhibit remarkable and programmable shape shifting when their molecular order changes. In this work, we synthesized, remotely programmed, and modeled reversible and complex morphing in monolithic LCE kirigami encoded with predesigned topological patterns in its microstructure. We obtained a rich variety of out-of-plane shape transformations, including auxetic structures and undulating morphologies, by combining different topological microstructures and kirigami geometries. The spatiotemporal shape-shifting behaviors are well recapitulated by elastodynamics simulations, revealing that the complex shape changes arise from integrating the custom-cut geometry with local director profiles defined by topological defects inscribed in the material. Different functionalities, such as a bioinspired fluttering butterfly, a flower bud, dual-rotation light mills, and dual-mode locomotion, are further realized. Our proposed LCE kirigami with topological patterns opens opportunities for the future development of multifunctional devices for soft robotics, flexible electronics, and biomedicine.

Revisiting the flight dynamics of take-off of a butterfly: experiments and CFD simulations for a cabbage white butterfly

We conducted measurements of the taking-off motion of a butterfly (Pieris rapae) and numerical simulations using a computational model reflecting its motion. The computational butterfly model is composed of a thorax, an abdomen, and four wings (left and right wings with fore and hind parts), i.e., a six-link rigid-body system. The present model is more sophisticated than the models which have ever constructed in existing studies. In the butterfly model, the body trajectory and thoracic pitching angle can be calculated from the equations of motion, whereas the abdominal angle and wings' joint angles are prescribed by the measured data. We calculated the flow field and aerodynamic force and torque generated by the butterfly model using the immersed boundary-lattice Boltzmann method． As a result, the butterfly generates the horizontal and vertical vortex rings as well as the aerodynamic lift and thrust forces during the downstroke and upstroke, respectively. The leg impulsion is essential in the upward motion of the taking-off butterfly rather than the aerodynamic lift force by the flapping wings. The inertial forces of the abdomen and wings are comparable in magnitude with the aerodynamic forces, but the net influence of the inertial forces on the position of the butterfly is not significant due to the offsetting of the body and wing inertia. The net aerodynamic and gravitational torques raise the thorax of the butterfly, and the net inertial torques suppress the rise of the thorax.

Fully-printed metamaterial-type flexible wings with controllable flight characteristics

Insect wings are an outstanding example of how a proper interplay of rigid and flexible materials enables an intricate flapping flight accompanied by sound. The understanding of the aerodynamics and acoustics of insect wings has enabled the development of man-made flying robotic vehicles and explained basic mechanisms of sound generation by natural flyers. This work proposes the concept of artificial wings with a periodic pattern, inspired by metamaterials, and explores how the pattern geometry can be used to control the aerodynamic and acoustic characteristics of a wing. For this, we analyzed bio-inspired wings with anisotropic honeycomb patterns flapping at a low frequency and developed a multi-parameter optimization procedure to tune the pattern design in order to increase lift and simultaneously to manipulate the produced sound. Our analysis is based on the finite-element solution to a transient three-dimensional fluid-structure interactions problem. The two-way coupling is described by incompressible Navier-Stokes equations for viscous air and structural equations of motion for a wing undergoing large deformations. We 3D-printed three wing samples and validated their robustness and dynamics experimentally. Importantly, we showed that the proposed wings can sustain long-term resonance excitation that opens a possibility to implement resonance-type flights inherent to certain natural flyers. Our results confirm the feasibility of metamaterial patterns to control the flapping flight dynamics and can open new perspectives for applications of 3D-printed patterned wings, e.g. in the design of drones with target sound.

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

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.

Enhanced lift and thrust via the translational motion between the thorax-abdomen node and the center of mass of a butterfly with a constructive abdominal oscillation

Butterflies fly with an abdomen oscillating relative to the thorax; the abdominal oscillation causes body parts to undulate translationally relative to the center of mass of a butterfly, which could generate a significant effect on flight. Based on experimental measurements, we created a numerical model to investigate this effect in a free-flying butterfly (Idea leuconoe). We fixed the motions of wing-flapping and thorax-pitching, and parametrized the abdominal oscillation by varied oscillating phase. To concentrate the analysis on translational dynamics, we used a motion of a thorax-abdomen node, a joint that the thorax and the abdomen rotate about, to express the translational motion of body parts relative to the center of mass. The results show that the abdominal oscillation enhances lift and thrust via the translational motion of the thorax-abdomen node relative to the center of mass. With the abdominal oscillating phase recorded from real butterflies, the abdominal oscillation causes the thorax-abdomen node to move downward relative to the center of mass in downstroke and move upward relative to the center of mass in upstroke. This constructive movement amplifies the wing-flapping speed relative to the center of mass, which enhances the angle of attack and the strength of leading- and trailing-edge vortices on the wings. The wings thereby generate increased values of instantaneous lift and thrust by 50.32% and 32.57% compared to the case of no abdominal oscillation. Natural butterflies are stated to utilize a particular phase offset of abdominal oscillation to fly. With comparing varied oscillating phases, only the abdominal oscillating phase recorded from natural butterflies produces the best constructive effect on the translational motion of thorax-abdomen node, which maximizes the lift and thrust generated on the wings. It clarifies that butterflies use this specific range of abdominal oscillating phase to regulate the translational motion between the thorax-abdomen node and the center of mass to enhance flight. Our work reveals the translational mechanism of the abdominal oscillation, which is as important as the thorax-pitching effect. The findings in this work provide insight into the flight of butterflies and the design of micro aerial vehicles.

Structure, properties and functions of the forewing-hindwing coupling of honeybees

Worker honeybees (Apis mellifera) are morphologically four-winged, but are functionally dipterous insects. During flight, their fore- and hindwings are coupled by means of the forewing posterior rolled margin (PRM) and hindwing hamuli. Morphological analysis shows that the PRM can be connected to the hamuli, so that the fore- and hindwing are firmly hinged, and can rotate with respect to each other. In the present study, using a combination of scanning electron microscopy (SEM) and confocal laser scanning microscopy (CLSM), we investigate the micromorphology and material composition of the coupling structures on both fore- and hindwings. High-speed filming is utilized to determine the angle variation between the fore- and hindwings in tethered flight. Using sets of two-dimensional (2D) computation fluid dynamic analyses, we further aim to understand the influence of the angle variation on the aerodynamic performance of the coupled wings. The results of the morphological investigations show that both PRM and hamuli are made up of a strongly sclerotized cuticle. The sclerotized hinge-like connection of the coupling structure allows a large angle variation between the wings (135°-235°), so that a change is made from an obtuse angle during the pronation and downstroke to a reflex angle during the supination and upstroke. Our computational results show that in comparison to a model with a rigid coupling hinge, the angle variation of a model having a flexible hinge results in both increased lift and drag with a higher rate of drag increase. This study deepens our understanding of the wing-coupling mechanism and functioning of coupled insect wings.

Effect of body aerodynamics on the dynamic flight stability of the hawkmoth Manduca sexta

This study explores the effects of the body aerodynamics on the dynamic flight stability of an insect at various different forward flight speeds. The insect model, whose morphological parameters are based on measurement data from the hawkmoth Manduca sexta, is treated as an open-loop six-degree-of-freedom dynamic system. The aerodynamic forces and moments acting on the insect are computed by an aerodynamic model that combines the unsteady panel method and the extended unsteady vortex-lattice method. The aerodynamic model is then coupled to a multi-body dynamic code to solve the system of motion equations. First, the trimmed flight conditions of insect models with and without consideration of the body aerodynamics are obtained using a trim search algorithm. Subsequently, the effects of the body aerodynamics on the dynamic flight stability are analysed through modal structures, i.e., eigenvalues and eigenvectors in this case, which are based on linearized equations of motion. The solutions from the nonlinear and linearized equations of motion due to gust disturbances are obtained, and the effects of the body aerodynamics are also investigated through these solutions. The results showed the important effect of the body aerodynamics at high-speed forward flight (in this paper at 4.0 and 5.0 m s^-1) and the movement trends of eigenvalues when the body aerodynamics is included.

Importance of body rotation during the flight of a butterfly

In nature the body motion of a butterfly is clearly observed to involve periodic rotation and varied flight modes. The maneuvers of a butterfly in flight are unique. Based on the flight motion of butterflies (Kallima inachus) recorded in free flight, a numerical model of a butterfly is created to study how its flight relates to body pose; the body motion in a simulation is prescribed and tested with varied initial body angle and rotational amplitude. A butterfly rotates its body to control the direction of the vortex rings generated during flapping flight; the flight modes are found to be closely related to the body motion of a butterfly. When the initial body angle increases, the forward displacement decreases, but the upward displacement increases within a stroke. With increased rotational amplitudes, the jet flows generated by a butterfly eject more downward and further enhance the generation of upward force, according to which a butterfly executes a vertical jump at the end of the downstroke. During this jumping stage, the air relative to the butterfly is moving downward; the butterfly pitches up its body to be parallel to the flow and to decrease the projected area so as to avoid further downward force generated. Our results indicate the importance of the body motion of a butterfly in flight. The inspiration of flight controlled with body motion from the flight of a butterfly might yield an alternative way to control future flight vehicles.

Enhanced thrust and speed revealed in the forward flight of a butterfly with transient body translation

A butterfly with broad wings, flapping at a small frequency, flies an erratic trajectory at an inconstant speed. A large variation of speed within a cycle is observed in the forward flight of a butterfly. A self-propulsion model to simulate a butterfly is thus created to investigate the transient translation of the body; the results, which are in accordance with experimental data, show that the shape of the variation of the flight speed is similar to a sinusoidal wave with a maximum (J=0.89) at the beginning of the downstroke, and a decrease to a minimum (J=0.17) during a transition from downstroke to upstroke; the difference between the extrema of the flight speed is enormous in a flapping cycle. At a high speed, a clapping motion of the butterfly wings decreases the generation of drag. At a small speed, a butterfly is able to capture the induced wakes generated in a downstroke, and effectively generates a thrust at the beginning of an upstroke. The wing motion of a butterfly skillfully interacts with its speed so as to enable an increased speed with the same motion. Considering a butterfly to fly in a constant inflow leads to either an underestimate of its speed or an overestimate of its generated lift, which yields an inaccurate interpretation of the insect's flight. Our results reveal the effect of transient translation on a butterfly in forward flight, which is especially important for an insect with a small flapping frequency.

The function of resilin in honeybee wings

The present work aimed to reveal morphological characteristics of worker honeybee (Apis mellifera) wings and demonstrate the function of resilin on camber changes during flapping flight. Detailed morphological investigation of the wings showed that different surface characteristics appear on the dorsal and ventral side of the honeybee wings and the linking structure connecting the forewing and hindwing plays an indispensable role in honeybee flapping flight. Resilin stripes were found on both the dorsal and ventral side of the wings, and resilin patches mostly existed on the ventral side. On the basis of resilin distribution, five flexion lines and three cambered types around the lines of passive deformation of the coupled-wing profile were obtained, which defined the deformation mechanism of the wing along the chord, i.e. concave, flat plate and convex. From a movie obtained using high-speed photography from three orthogonal views of free flight in honeybees, periodic changes of the coupled-wing profile were acquired and further demonstrated that the deformation mechanism is a fundamental property for variable deformed shapes of the wing profile during flapping flight, and, in particular, the flat wing profile achieves a nice transition between downstrokes and upstrokes.