Computational investigation of cicada aerodynamics in forward flight

Kinematics and Flow Field Analysis of Allomyrina dichotoma Flight

In recent years, bioinspired insect flight has become a prominent research area, with a particular focus on beetle-inspired aerial vehicles. Studying the unique flight mechanisms and structural characteristics of beetles has significant implications for the optimization of biomimetic flying devices. Among beetles, Allomyrina dichotoma (rhinoceros beetle) exhibits a distinct wing deployment-flight-retraction sequence, whereby the interaction between the hindwings and protective elytra contributes to lift generation and maintenance. This study investigates A. dichotoma's wing deployment, flight, and retraction behaviors through motion analysis, uncovering the critical role of the elytra in wing folding. We capture the kinematic parameters throughout the entire flight process and develop an accurate kinematic model of A. dichotoma flight. Using smoke visualization, we analyze the flow field generated during flight, revealing the formation of enhanced leading-edge vortices and attached vortices during both upstroke and downstroke phases. These findings uncover the high-lift mechanism underlying A. dichotoma's flight dynamics, offering valuable insights for optimizing beetle-inspired micro aerial vehicles.

Enhanced flight performance and adaptive evolution of Mesozoic giant cicadas

Insects have evolved diverse ecological flight behaviors and adaptations that played a key role in their large-scale evolutionary patterns. However, the evolution of their flight performance is poorly understood because reconstructing flight abilities of extinct insects is highly challenging. Here, we propose an integrated approach to reveal the evolution of flight performance of Palaeontinidae (giant cicadas), a Mesozoic arboreal insect clade with large bodies and wings. Our analyses unveil a faunal turnover from early to late Palaeontinidae during the latest Jurassic-earliest Cretaceous, accompanied by a morphological adaptive shift and remarkable improvement in flight abilities including increased flight speed and enhanced maneuverability. The adaptive aerodynamic evolution of Palaeontinidae may have been stimulated by the rise of early birds, supporting the hypothesis of an aerial evolutionary arms race (Air Race) between Palaeontinidae and birds. Our results provide a potential example of predator-induced morphological and behavioral macroevolution and contribute to our understanding of how powered flight has shaped animal evolution.

Structural response and mechanical properties of the hind wing of the beetle Protaetia brevitarsis

The folding/unfolding mechanism and collision recovery effect of the beetle's hind wings can provide biomimetic inspiration for the optimization of wing deplorability and the investigation of collision prevention recovery mechanism of new amphibious morphing vehicle. In this study, a method is described to investigate the structural response and mechanical properties of the hind wings of the beetle Protetia brevitarsis under natural conditions. The specially processed test samples were conducted to tensile testing, which facilitates the evaluation of the mechanical properties of specific areas of the hind wing. The micro geometric morphological characteristics of the cross-section of the specimen after tensile fracture were observed by scanning electron microscopy. The three-dimensional morphology of the ventral and dorsal sides of the hind wing was characterized using three-dimensional scanning and reverse modeling methods. The finite element model of the hind wing is developed to investigate the structural deformation and modal response characteristics of its flapping. The uniformly distributed load on the hind wing surface is derived from the lift characteristics obtained from the computational fluid dynamics simulation of flapping wing motion. RESEARCH HIGHLIGHTS: Scanning electron microscope is used to observe the cross-sectional characteristics of the veins and membranes. The material properties of the wing membranes and veins of the hind wings were measured using the tensile testing system. The three-dimensional morphology of the hind wing was characterized using 3D scanning and reverse modeling methods. The finite element model of the hind wing is developed to investigate the structural deformation and modal response characteristics of its flapping.

Towards silent and efficient flight by combining bioinspired owl feather serrations with cicada wing geometry

As natural predators, owls fly with astonishing stealth due to the serrated feather morphology that produces advantageous flow characteristics. Traditionally, these serrations are tailored for airfoil edges with simple two-dimensional patterns, limiting their effect on noise reduction while negotiating tradeoffs in aerodynamic performance. Conversely, the intricately structured wings of cicadas have evolved for effective flapping, presenting a potential blueprint for alleviating these aerodynamic limitations. In this study, we formulate a synergistic design strategy that harmonizes noise suppression with aerodynamic efficiency by integrating the geometrical attributes of owl feathers and cicada forewings, culminating in a three-dimensional sinusoidal serration propeller topology that facilitates both silent and efficient flight. Experimental results show that our design yields a reduction in overall sound pressure levels by up to 5.5 dB and an increase in propulsive efficiency by over 20% compared to the current industry benchmark. Computational fluid dynamics simulations validate the efficacy of the bioinspired design in augmenting surface vorticity and suppressing noise generation across various flow regimes. This topology can advance the multifunctionality of aerodynamic surfaces for the development of quieter and more energy-saving aerial vehicles.

Postural Change of the Annual Cicada (Tibicen linnei) Helps Facilitate Backward Flight

Cicadas are heavy fliers well known for their life cycles and sound production; however, their flight capabilities have not been extensively investigated. Here, we show for the first time that cicadas appropriate backward flight for additional maneuverability. We studied this flight mode using computational fluid dynamics (CFD) simulations based on three-dimensional reconstructions of high-speed videos captured in a laboratory. Backward flight was characterized by steep body angles, high angles of attack, and high wing upstroke velocities. Wing motion occurred in an inclined stroke plane that was fixed relative to the body. Likewise, the directions of the half-stroke-averaged aerodynamic forces relative to the body (local frame) were constrained in a narrow range (<20°). Despite the drastic difference of approximately 90° in body posture between backward and forward flight in the global frame, the aerodynamic forces in both flight scenarios were maintained in a similar direction relative to the body. The forces relative to the body were also oriented in a similar direction when observed during climbs and turns, although the body orientation and motions were different. Hence, the steep posture appropriated during backward flight was primarily utilized for reorienting both the stroke plane and aerodynamic force in the global frame. A consequence of this reorientation was the reversal of aerodynamic functions of the half strokes in backward flight when compared to forward flight. The downstroke generated propulsive forces, while the upstroke generated vertical forces. For weight support, the upstroke, which typically generates lesser forces in forward flight, is aerodynamically active in backward flight. A leading-edge vortex (LEV) was observed on the forewings during both half strokes. The LEV's effect, together with the high upstroke velocity, increased the upstroke's force contribution from 10% of the net forces in forward flight to 50% in backward flight. The findings presented in this study have relevance to the design of micro-aerial vehicles (MAVs), as backward flight is an important characteristic for MAV maneuverability or for taking off from vertical surfaces.

Hydrodynamic analysis of fin-fin interactions in two-manta-ray schooling in the vertical plane

This study investigates the interaction of a two-manta-ray school using computational fluid dynamics simulations. The baseline case consists of two in-phase undulating three-dimensional manta models arranged in a stacked configuration. Various vertical stacked and streamwise staggered configurations are studied by altering the locations of the top manta in the upstream and downstream directions. Additionally, phase differences between the two mantas are considered. Simulations are conducted using an in-house developed incompressible flow solver with an immersed boundary method. The results reveal that the follower will significantly benefit from the upstroke vortices (UVs) and downstroke vortices depending on its streamwise separation. We find that placing the top manta 0.5 body length (BL) downstream of the bottom manta optimizes its utilization of UVs from the bottom manta, facilitating the formation of leading-edge vortices (LEVs) on the top manta's pectoral fins during the downstroke. This LEV strengthening mechanism, in turn, generates a forward suction force on the follower that results in a 72% higher cycle-averaged thrust than a solitary swimmer. This benefit harvested from UVs can be further improved by adjusting the phase of the top follower. By applying a phase difference ofπ/3to the top manta, the follower not only benefits from the UVs of the bottom manta but also leverages the auxiliary vortices during the upstroke, leading to stronger tip vortices and a more pronounced forward suction force. The newfound interaction observed in schooling studies offers significant insights that can aid in the development of robot formations inspired by manta rays.

Numerical Simulations of the Effect of the Asymmetrical Bending of the Hindwings of a Hovering C. buqueti Bamboo Weevil with Respect to the Aerodynamic Characteristics

The airfoil structure and folding pattern of the hindwings of a beetle provide new transformation paths for improvements in the aerodynamic performance and structural optimization of flapping-wing flying robots. However, the explanation for the aerodynamic mechanism of the asymmetrical bending of a real beetle's hindwings under aerodynamic loads originating from the ventral and dorsal sides is unclear. To address this gap in our understanding, a computational investigation into the aerodynamic characteristics of the flight ability of C. buqueti and the large folding ratio of their hindwings when hovering is carried out in this article. A three-dimensional (3D) pressure-based SST k-ω turbulence model with a biomimetic structure was used for the detailed analysis, and a refined polyhedral mesh was used for the simulations. The results show that the fluid around the hindwings forms a vortex ring consisting of a leading-edge vortex (LEV), wing-tip vortex (TV) and trailing-edge vortex (TEV). Approximately 61% of the total lift is generated during the downstroke, which may be closely related to the asymmetric bending of the hindwings when they are subjected to pressure load.

Wing Kinematics and Unsteady Aerodynamics of a Hummingbird Pure Yawing Maneuver

As one of few animals with the capability to execute agile yawing maneuvers, it is quite desirable to take inspiration from hummingbird flight aerodynamics. To understand the wing and body kinematics and associated aerodynamics of a hummingbird performing a free yawing maneuver, a crucial step in mimicking the biological motion in robotic systems, we paired accurate digital reconstruction techniques with high-fidelity computational fluid dynamics (CFD) simulations. Results of the body and wing kinematics reveal that to achieve the pure yaw maneuver, the hummingbird utilizes very little body pitching, rolling, vertical, or horizontal motion. Wing angle of incidence, stroke, and twist angles are found to be higher for the inner wing (IW) than the outer wing (OW). Unsteady aerodynamic calculations reveal that drag-based asymmetric force generation during the downstroke (DS) and upstroke (US) serves to control the speed of the turn, a characteristic that allows for great maneuvering precision. A dual-loop vortex formation during each half-stroke is found to contribute to asymmetric drag production. Wake analysis revealed that asymmetric wing kinematics led to leading-edge vortex strength differences of around 59% between the IW and OW. Finally, analysis of the role of wing flexibility revealed that flexibility is essential for generating the large torque necessary for completing the turn as well as producing sufficient lift for weight support.

Functional characteristics of the rigid elytra in a bamboo weevil beetle Cyrtotrachelus buqueti

The bamboo weevil beetle, Cyrtotrachelus buqueti, has evolved a particular flight pattern. When crawling, the beetle folds the flexible hind wings and stuffs under the rigid elytra. During flight, the hind wings are deployed through a series of deployment joints that are passively driven by flapping forces. When the hind wings are fully expanded, the unfolding joint realises self‐locking. At this time, the hind wings act as a folded wing membrane and flap simultaneously with the elytra to generate aerodynamics. The functional characteristics of the elytra of the bamboo weevil beetle were investigated, including microscopic morphology, kinematic properties and aerodynamic forces of the elytra. In particular, the flapping kinematics of the elytra were measured using high‐speed cameras and reconstructed using a modified direct linear transformation algorithm. Although the elytra are passively flapped by the flapping of the hind wings, the analysis shows that its flapping wing trajectory is a double figure‐eight pattern with flapping amplitude and angle of attack. The results show that the passive flapping of elytra produces aerodynamic forces that cannot be ignored. The kinematics of the elytra suggest that this beetle may use well‐known flapping mechanisms such as a delayed stall and clap and fling.

The forewing of a black cicada Cryptotympana atrata (Hemiptera, Homoptera: Cicadidae): Microscopic structures and mechanical properties

Insects in nature flap their wings to generate lift force and driving torque to adjust their attitude and control stability. An insect wing is a biomaterial composed of flexible membranes and tough veins. In this paper, we study the microscopic structures and mechanical properties of the forewing of the black cicada, Cryptotympana atrata. The thickness of the wing membranes and the diameter of veins varied from the wing root to the tip. The thickness of the wing membranes ranged from 6.0 to 29.9 μm, and the diameter of the wing veins decreased in a gradient from the wing root to the tip, demonstrating that the forewing of the black cicada is a nonuniform biomaterial. The elastic modulus of the membrane near the wing root ranged from 4.45 to 5.03 GPa, which is comparable to that of some industrial membranes. The microstructure of the wing vein exhibited a hollow tubular structure with flocculent structure inside. The "fresh" sample stored more water than the "dry" sample, resulting in a significant difference in the elastic modulus between the fresh and dried veins. The different membrane thicknesses and elastic moduli of the wing veins near the root and tip resulted in varied degrees of deformation on both sides of the flexion line of the forewing during twisting. The measurements of the forewing of the cicada may serve as a guide for selecting airfoil materials for the bionic flapping-wing aircraft and promote the design and manufacture of more durable bionic wings in the future.

Turning-ascending flight of a Hipposideros pratti bat

Bats exhibit a high degree of agility and provide an excellent model system for bioinspired flight. The current study investigates an ascending right turn of a Hipposideros pratti bat and elucidates on the kinematic features and aerodynamic mechanisms used to effectuate the manoeuvre. The wing kinematics captured by a three-dimensional motion capture system is used as the boundary condition for the aerodynamic simulations featuring immersed boundary method. Results indicate that the bat uses roll and yaw rotations of the body to different extents synergistically to generate the centripetal force to initiate and sustain the turn. The turning moments are generated by drawing the wing inside the turn closer to the body, by introducing phase lags in force generation between the wings and redirecting force production to the outer part of the wing outside of the turn. Deceleration in flight speed, an increase in flapping frequency, shortening of the upstroke and thrust generation at the end of the upstroke were observed during the ascending manoeuvre. The bat consumes about 0.67 W power to execute the turning-ascending manoeuvre, which is approximately two times the power consumed by similar bats during level flight. Upon comparison with a similar manoeuvre by a Hipposideros armiger bat (Windes et al. 2020 Bioinspir. Biomim. 16, abb78d. (doi:10.1088/1748-3190/abb78d)), some commonalities, as well as differences, were observed in the detailed wing kinematics and aerodynamics.

A nondestructive method of calculating the wing area of insects

Most insects engage in winged flight. Wing loading, that is, the ratio of body mass to total wing area, has been demonstrated to reflect flight maneuverability. High maneuverability is an important survival trait, allowing insects to escape natural enemies and to compete for mates. In some ecological field experiments, there is a need to calculate the wing area of insects without killing them. However, fast, nondestructive estimation of wing area for insects is not available based on past work. The Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, is frequently used to calculate leaf area of plants, in crops with entire linear, lanceolate leaves. Recently, the ME was proved to apply to leaves with more complex shapes from plants that do not have any needle leaves. Given that the wings of insects are similar in shape to broad leaves, we tested the validity of the ME approach in calculating the wing area of insects using three species of cicadas common in eastern China. We compared the actual area of the cicadas' wings with the estimates provided by six potential models used for wing area calculation, and we found that the ME performed best, based on the trade-off between model structure and goodness of fit. At the species level, the estimates for the proportionality coefficients of ME for three cicada species were 0.686, 0.693, and 0.715, respectively. There was a significant difference in the proportionality coefficients between any two species. Our method provides a simple and powerful approach for the nondestructive estimation of insect wing area, which is also valuable in quantifying wing morphological features of insects. The present study provides a nondestructive approach to estimating the wing area of insects, allowing them to be used in mark and recapture experiments.

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.

Flight Maneuver of a Damselfly with Phase Modulation of the Wings

We developed a numerical model for four-wing self-propulsion to calculate effectively the flight velocity generated with varied wing motions, which satisfactorily verified biological experiments. Through this self-propulsion model, we analyzed the flight velocity of a damselfly (Matrona cyanoptera) at varied phases. The results show that after phase modulation of the wings, the aerodynamic performance of the forewing (FW) is affected by the incoming flow and an effective angle of attack, whereas that of the hindwing (HW) is dominated by the vortex interaction and induced flow generated by the shed vortex of the FW. Cooperating with the flow interaction, in stable flight, the HW in the lead phase has a larger vertical velocity, whereas the FW in the lead phase has a larger horizontal velocity. Regarding the aerodynamic efficiency, the FW in the lead phase has greater horizontal efficiency, whereas the HW in the lead phase has greater vertical efficiency; the overall efficiency does not vary with the phase. This work interprets that a dragonfly adopts the HW in the lead phase to generate a larger lift, thus supporting the larger body weight, whereas a damselfly adopts the FW in the lead phase to have a greater forward velocity, which can supplement the lack of flapping frequency.

Effects of flight altitude on the lift generation of monarch butterflies: from sea level to overwintering mountain

Aerodynamic efficiency behind the annual migration of monarch butterflies, the longest among insects, is an unsolved mystery. Monarchs migrate 4000 km at high-altitudes to their overwintering mountains in Central Mexico. The air is thinner at higher altitudes, yielding reduced aerodynamic drag and enhanced range. However, the lift is also expected to reduce in lower density conditions. To investigate the ability of monarchs to produce sufficient lift to fly in thinner air, we measured the climbing motion of freely flying monarchs in high-altitude conditions. An optical method was used to track the flapping wing and body motions inside a large pressure chamber. The air density inside the chamber was reduced to recreate the higher altitude densities. The lift coefficient generated by monarchs increased from 1.7 at the sea-level to 9.4 at 3000 m. The correlation between this increase and the flapping amplitude and frequency was insignificant. However, it strongly correlated to the effective angle of attack, which measures the wing to body velocity ratio. These results support the hypothesis that monarchs produce sufficiently high lift coefficients at high altitudes despite a lower dynamic pressure.

Kinematic and Aerodynamic Investigation of the Butterfly in Forward Free Flight for the Butterfly-Inspired Flapping Wing Air Vehicle

To ensure the stability of flight, the butterfly needs to flap its wings and simultaneously move its main body to achieve all kinds of flying motion, such as taking off, hovering, or reverse flight. The high-speed camera is used to record the swing of the abdomen, the movement of the wings, and the pitch angle of the body for butterflies during their free flight; the comprehensive biokinetic observations show that the butterfly’s wings and body are coupled in various flight states. The swing of the abdomen and the flap of the fore wing affect the pitch motion significantly. For theoretical analysis of the butterfly flight, a three-dimensional multi-rigid butterfly model based on real butterfly dimension is established, and the aerodynamic of the butterfly flight is simulated and analyzed via computational fluid dynamics methods to obtain an optimal kinematic model of butterfly forward flight. Moreover, the formation and development of three-dimensional vortex structures in the forward flight are also presented. The detailed structures of vortices and their dynamic behavior show that the wing’s flap and the abdominal swing play a key role in reorienting and correcting the “clap and peel” mechanism, and the force generation mechanisms are evaluated. The research indicates that longitudinal flight performance is mainly related to the kinematic parameters of the wing and body, and it can lead to the development of butterfly-inspired flapping wing air vehicles.

Extracting signature responses from respiratory flows: Low-dimensional analyses on Direct Numerical Simulation-predicted wakes of a flapping uvula

Uvula-induced snoring and associated obstructive sleep apnea is a complex phenomenon characterized by vibrating structures and highly transient vortex dynamics. This study aimed to extract signature features of uvula wake flows of different pathological origins and develop a linear reduced-order surrogate model for flow control. Six airway models were developed with two uvula kinematics and three pharynx constriction levels. A direct numerical simulation (DNS) flow solver based on the immersed boundary method was utilized to resolve the wake flows induced by the flapping uvula. Key spatial and temporal responses of the flow to uvula kinematics and pharynx constriction were investigated using continuous wavelet transform (CWT), proper orthogonal decomposition (POD), and dynamic mode decomposition (DMD). Results showed highly complex patterns in flow topologies. CWT analysis revealed multiscale correlations in both time and space between the flapping uvular and wake flows. POD analysis successfully separated the flows among the six models by projecting the datasets in the vector space spanned by the first three eigenmodes. Perceivable differences were also captured in the time evolution of the DMD modes among the six models. A linear reduced-order surrogate model was constructed from the predominant eigenmodes obtained from the DMD analysis and predicted vortex patterns from this surrogate model agreed well with the corresponding DNS simulations. The computational and analytical platform presented in this study could bring a variety of applications in breathing-related disorders and beyond. The computational efficiency of surrogate modeling makes it well suited for flow control, forecasting, and uncertainty analyses.

The reverse flight of a monarch butterfly (Danaus plexippus) is characterized by a weight-supporting upstroke and postural changes

Butterflies are agile fliers which use inactive and active upstrokes (US). The active US plays a secondary role to the downstroke (DS), generating both thrust and negative vertical force. However, whether their active halfstroke function is fixed or facultative has not been clarified. We showed that during multiple backward flights of an individual, postural adjustments via body angles greater than 90°, with pitch-down and pitch-up motions in the DS and US, respectively, reoriented the stroke plane and caused the reversal of the aerodynamic functions of the halfstrokes compared with forward flight. The US and DS primarily provided weight support and horizontal force, respectively, and a leading edge vortex (LEV) was formed in both halfstrokes. The US's LEV was a Class II LEV extending from wingtip to wingtip, previously reported albeit during the DS in forward flight. The US's net force contribution increased from 32% in forward to 60% in backward flight. Likewise, US weight support increased from 8 to 85%. Despite different trajectories, body postures and force orientations among flight sequences in the global frame, the halfstroke-average forces pointed in a uniform direction relative to the body in both forward and backward flight.

Wing-kinematics measurement and flight modelling of the bamboo weevil C. buqueti

Insects are one of the most agile flyers in nature, and studying the kinematics of their wings can provide important data for the design of insect-like wing-flapping micro aerial vehicles. This study integrates high-speed photogrammetry and three-dimensional (3D) force measurement system to explore the kinematics of Cyrtotrachelus buqueti during the wing-flapping flight. The tracking point at the wing tip of the hind wing was recorded using high-speed videography. The lift-thrust force characteristic of wing-flapping motion was obtained by the 3D force sensor. Quantitative measurements of wing kinematics show that the wing-flapping pattern of the hind wing of C. buqueti was revealed as a double figure-eight trajectory. The kinematic modelling of the wing-flapping pattern was then established by converting the flapping motion into rotational motion about the pivoting wing base in the reference coordinate system. Moreover, the lift force generated by C. buqueti during the wing-flapping flight is sufficient to support its body weight without the need to use thrust force to compensate for the lack of lift force.

Experimental Force and Deformation Measurements of Bioinspired Flapping Wings in Ultra-Low Martian Density Environment

A Mars flight vehicle could provide a third-dimension for ground-based rovers and supplement orbital observation stations, providing a much more detailed aerial view of the landscape as well as unprecedented survey of the atmosphere of Mars. However, flight on Mars is a difficult proposition due to the very low atmospheric density, which is approximately 1.3% of sea level density on Earth. While traditional aircraft efficiency suffers in the low Reynolds number environment, insect inspired flapping wing flyers on Mars might be able to take advantage of the same lift enhancing effects as insects on Earth. The present work investigates the feasibility of using a bioinspired, flapping wing flight vehicle to produce lift in an ultra-low-density Martian atmosphere. A four-wing prototype, inspired by a prior computational study, was placed in an atmospheric chamber to simulate Martian density. Lift and wing deformation were simultaneously recorded. In Earth density conditions, the passive pitch wing deflection increased monotonically with flapping frequency. On the other hand, in the Martian density environment, the passive pitch deflection angles were very erratic. The measured lift peaked at around 8 grams at 16 Hz. These measurements suggest that sufficient aerodynamic forces for hover on Mars can be generated for a 6-gram flapping wing vehicle. Also, the performance can potentially be improved by better understanding the fluid-structure interaction in ultra-low Mars density condition.

Determination of spatial fidelity required to accurately mimic the flight dynamics of a bat

Bats possess unique flight capabilities enabled by their wing morphology. While the articulated bone structure and flexible membrane constituting the wing are known to play a critical role in aerodynamic performance, the relationship has never been robustly quantified. Characterization of the sensitivity between precise wing contour and aerodynamic performance is important when designing a biomimetic flight vehicle based on experimentally measured wing kinematics. 3D optical motion capture, a standard method for obtaining wing kinematic measurements, discretely samples the smooth surface of a bat wing during flight. If the constellation of tracked 3D points is too sparse, a loss of critical information occurs. Here, we have explored the relationship between the density of wing surface points and several aerodynamic metrics, specifically, wing surface area variation, aerodynamic loads, and power expenditure. Loads and power were calculated using an incompressible Navier-Stokes solver. Of the metrics examined, aerodynamic power was found to be most sensitive to the spatial fidelity of the wing-the normalized root mean squared difference (NRMSD) between the 10- and 238-point cases was 35%. Load calculations varied slightly less with a peak NRMSD of 24% between the highest and lowest fidelity cases. Lastly, the wing surface area was least sensitive to the spatial fidelity of the wing kinematics, with a maximum NRMSD surface area of 8%. Close similarity in aerodynamic behavior was observed when using either a 120- and 238-point surface representation, establishing a bound to the sensitivity between wing shape and aerodynamics. The results from the 10- and 22-point configurations demonstrate that sparse representation of a wing surface can lead to a loss of information. The characterization of kinematic complexity of the wings both informs how many degrees of freedom are important to measure and also informs how many degrees of freedom are required to robotically reproduce the flapping flight.

Flying in reverse: kinematics and aerodynamics of a dragonfly in backward free flight

In this study, we investigated the backward free flight of a dragonfly, accelerating in a flight path inclined to the horizontal. The wing and body kinematics were reconstructed from the output of three high-speed cameras using a template-based subdivision surface reconstruction method, and numerical simulations using an immersed boundary flow solver were conducted to compute the forces and visualize the flow features. During backward flight, the dragonfly maintained an upright body posture of approximately 90° relative to the horizon. The upright body posture was used to reorient the stroke plane and the flight force in the global frame; a mechanism known as 'force vectoring' which was previously observed in manoeuvres of other flying animals. In addition to force vectoring, we found that while flying backward, the dragonfly flaps its wings with larger angles of attack in the upstroke (US) when compared with forward flight. Also, the backward velocity of the body in the upright position enhances the wings' net velocity in the US. The combined effect of the angle of attack and wing net velocity yields large aerodynamic force generation in the US, with the average magnitude of the force reaching values as high as two to three times the body weight. Corresponding to these large forces was the presence of a strong leading edge vortex (LEV) at the onset of US which remained attached up until wing reversal. Finally, wing-wing interaction was found to enhance the aerodynamic performance of the hindwings (HW) during backward flight. Vorticity from the forewings' trailing edge fed directly into the HW LEV to increase its circulation and enhance force production.

Computational investigation of wing-body interaction and its lift enhancement effect in hummingbird forward flight

A lift enhancement mechanism due to wing-body interaction (WBI) was previously proved to be significant in the forward flight of insect flyers with wide-shape bodies, such as cicada. In order to further explore WBI and its lift enhancement effect in a flapping flight platform with different wing and body shapes, numerical investigations of WBI were performed on the forward flight of a hummingbird in this paper. A high-fidelity computational model of a hummingbird in forward flight was modeled with its geometric complexity. The wing kinematics of flapping flight were prescribed using experimental data from previous literature. An immersed-boundary-method-based incompressible Navier‒Stokes solver was used for the 3D flow simulations of the wing-body system. Analyses on aerodynamic performances and vortex dynamics of three models, including the wing-body (WB), wing-only (WO), and body-only (BO) models, were made to examine the effect of WBI. Results have shown significant overall lift enhancement (OLE) due to WBI. The total lift force of the WB model increased by 29% compared with its WO/BO counterparts. Vortex dynamics results showed formations of unique body vortex pairs on the dorsal thorax of hummingbird where low-pressure zones were created to generate more body lift. Significant interactions between body vortex and leading-edge vortex (LEV) were observed, resulting in strengthened LEVs near the wing root and enhanced wing lift generation during downstroke. Parametric studies showed strong OLEs over wide ranges of body angle and advance ratio, respectively. The contribution of OLE from the hummingbird body increased with increasing body angle, and the wing pair's contribution increased as advance ratio increased. Results from this paper supported that lift enhancement due to WBI is potentially a general mechanism adopted by different kinds of flapping-wing flyers, and demonstrated the potential of WBI in the design of flapping-wing micro aerial vehicle (MAV) that pursue higher performance.

A computational investigation of lift generation and power expenditure of Pratt's roundleaf bat (Hipposideros pratti) in forward flight

The aerodynamic mechanisms of bat flight have been studied using a numerical approach. Kinematic data acquired using a high resolution motion capture system was employed to simulate the unsteady air flow around a bat’s wings. A flapping bat wing contains many degrees of freedom, which make 3D motion tracking challenging. In order to overcome this challenge, an optical motion capture system of 21 cameras was used to reduce wing self-occlusion. Over the course of a meter-long flight, 108 discrete marker points on the bat’s wings (Pratt’s roundleaf bat, Hipposideros pratti) were tracked. The time evolution of the surface of each wing was computationally reconstructed in 3D space. The resulting kinematic model was interfaced with an unsteady incompressible flow solver using the immersed boundary method (IBM) and large eddy simulation (LES). Verification and validation of the flow simulation were conducted to establish accuracy. The aerodynamic forces calculated from the simulation compared well to the forces theoretically needed to sustain the observed flight trajectory. The transient flow field generated by the simulation allowed for the direct calculation of lift, drag, and power output of the bat during flight. The mean lift coefficient was found to be 3.21, and the flap cycle averaged aerodynamic power output was 1.05 W. Throughout the flap cycle, the planform area of the wings varied up to 46% between the largest and smallest values. During the upstroke, wing rotation was found to mitigate negative lift thereby improving overall flight efficiency. The high resolution motion capture and flow simulation framework presented here has the potential to facilitate the understanding of complex bat flight aerodynamics for both straight and maneuvering flight modes.

A Numerical Study of the Sound and Force Production of Flexible Insect Wings

We numerically solved the acoustic and flow field around cicada wing models with parametrically varied flexibility using the hydrodynamic/acoustic splitting method. We observed a gradual change of sound directivity with flexibility. We found that flexible wings generally produce lower sound due to reduced aerodynamic forces, which were further found to scale with the dynamic pressure force defined as the integration of dynamic pressure over the wing area. Unlike conventional scaling where the incoming flow velocity is used as the reference to calculate the force coefficients, here only the normal component of the relative velocity of the wing to the flow was used to calculate the dynamic pressure, putting kinematic factors into the dynamic pressure force and leaving the more fundamental physics to the force coefficients. A high correlation was found between the aerodynamic forces and the dynamic pressure. The scaling is also supported by previously reported data of revolving wing experiments.

The leading-edge vortex on a rotating wing changes markedly beyond a certain central body size

Stable attachment of a leading-edge vortex (LEV) plays a key role in generating the high lift on rotating wings with a central body. The central body size can affect the LEV structure broadly in two ways. First, an overall change in the size changes the Reynolds number, which is known to have an influence on the LEV structure. Second, it may affect the Coriolis acceleration acting across the wing, depending on the wing-offset from the axis of rotation. To investigate this, the effects of Reynolds number and the wing-offset are independently studied for a rotating wing. The three-dimensional LEV structure is mapped using a scanning particle image velocimetry technique. The rapid acquisition of images and their correlation are carefully validated. The results presented in this paper show that the LEV structure changes mainly with the Reynolds number. The LEV-split is found to be only minimally affected by changing the central body radius in the range of small offsets, which interestingly includes the range for most insects. However, beyond this small offset range, the LEV-split is found to change dramatically.

The effect of wing flexibility on sound generation of flapping wings

In this study, the unsteady flow and acoustic characteristics of a three-dimensional (3D) flapping wing model of a Tibicen linnei cicada in forward-flight are numerically investigated. A single cicada wing is modelled as a membrane with a prescribed motion reconstructed from high-speed videos of a live insect. The numerical solution takes a hydrodynamic/acoustic splitting approach: the flow field is solved with an incompressible Navier-Stokes flow solver based on an immersed boundary method, and the acoustic field is solved with linearized perturbed compressible equations. The 3D simulation allows for the examination of both the directivity and frequency compositions of the flapping wing sound in a full space. Along with the flexible wing model, a rigid wing model that is extracted from real motion is also simulated to investigate the effects of wing flexibility. The simulation results show that the flapping sound is directional; the dominant frequency varies around the wing. The first and second frequency harmonics show different radiation patterns in the rigid and flexible wing cases, which are demonstrated to be highly associated with wing kinematics and loadings. Furthermore, the rotation and deformation in the flexible wing is found to help lower the sound strength in all directions.

Aerodynamics and flow features of a damselfly in takeoff flight

Flight initiation is fundamental for survival, escape from predators and lifting payload from one place to another in biological fliers and can be broadly classified into jumping and non-jumping takeoffs. During jumping takeoffs, the legs generate most of the initial impulse. Whereas the wings generate most of the forces in non-jumping takeoffs, which are usually voluntary, slow, and stable. It is of great interest to understand how these non-jumping takeoffs occur and what strategies insects use to generate large amount of forces required for this highly demanding flight initiation mode. Here, for the first time, we report accurate wing and body kinematics measurements of a damselfly during a non-jumping takeoff. Furthermore, using a high fidelity computational fluid dynamics simulation, we identify the 3D flow features and compute the wing aerodynamics forces to unravel the key mechanisms responsible for generating large flight forces. Our numerical results show that a damselfly generates about three times its body weight during the first half-stroke for liftoff. In generating these forces, the wings flap through a steeply inclined stroke plane with respect to the horizon, slicing through the air at high angles of attack (45°-50°). Consequently, a leading edge vortex (LEV) is formed during both the downstroke and upstroke on all the four wings. The formation of the LEV, however, is inhibited in the subsequent upstrokes following takeoff. Accordingly, we observe a drastic reduction in the magnitude of the aerodynamic force, signifying the importance of LEV in augmenting force production. Our analysis also shows that forewing-hindwing interaction plays a favorable role in enhancing both lift and thrust production during takeoff.

Wing kinematics measurement and aerodynamics of a dragonfly in turning flight

This study integrates high-speed photogrammetry, 3D surface reconstruction, and computational fluid dynamics to explore a dragonfly (Erythemis Simplicicollis) in free flight. Asymmetric wing kinematics and the associated aerodynamic characteristics of a turning dragonfly are analyzed in detail. Quantitative measurements of wing kinematics show that compared to the outer wings, the inner wings sweep more slowly with a higher angle of attack during the downstroke, whereas they flap faster with a lower angle of attack during the upstroke. The inner-outer asymmetries of wing deviations result in an oval wingtip trajectory for the inner wings and a figure-eight wingtip trajectory for the outer wings. Unsteady aerodynamics calculations indicate significantly asymmetrical force production between the inner and outer wings, especially for the forewings. Specifically, the magnitude of the drag force on the inner forewing is approximately 2.8 times greater than that on the outer forewing during the downstroke. In the upstroke, the outer forewing generates approximately 1.9 times greater peak thrust than the inner forewing. To keep the body aloft, the forewings contribute approximately 64% of the total lift, whereas the hindwings provide 36%. The effect of forewing-hindwing interaction on the aerodynamic performance is also examined. It is found that the hindwings can benefit from this interaction by decreasing power consumption by 13% without sacrificing force generation.

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.

Lift enhancement by bats' dynamically changing wingspan

This paper elucidates the aerodynamic role of the dynamically changing wingspan in bat flight. Based on direct numerical simulations of the flow over a slow-flying bat, it is found that the dynamically changing wingspan can significantly enhance the lift. Further, an analysis of flow structures and lift decomposition reveal that the elevated vortex lift associated with the leading-edge vortices intensified by the dynamically changing wingspan considerably contributed to enhancement of the time-averaged lift. The nonlinear interaction between the dynamically changing wing and the vortical structures plays an important role in the lift enhancement of a flying bat in addition to the geometrical effect of changing the lifting-surface area in a flapping cycle. In addition, the dynamically changing wingspan leads to the higher efficiency in terms of generating lift for a given amount of the mechanical energy consumed in flight.

A CFD-informed quasi-steady model of flapping wing aerodynamics

Aerodynamic performance and agility during flapping flight are determined by the combination of wing shape and kinematics. The degree of morphological and kinematic optimisation is unknown and depends upon a large parameter space. Aimed at providing an accurate and computationally inexpensive modelling tool for flapping-wing aerodynamics, we propose a novel CFD (computational fluid dynamics)-informed quasi-steady model (CIQSM), which assumes that the aerodynamic forces on a flapping wing can be decomposed into the quasi-steady forces and parameterised based on CFD results. Using least-squares fitting, we determine a set of proportional coefficients for the quasi-steady model relating wing kinematics to instantaneous aerodynamic force and torque; we calculate power with the product of quasi-steady torques and angular velocity. With the quasi-steady model fully and independently parameterised on the basis of high-fidelity CFD modelling, it is capable of predicting flapping-wing aerodynamic forces and power more accurately than the conventional blade element model (BEM) does. The improvement can be attributed to, for instance, taking into account the effects of the induced downwash and the wing tip vortex on the force generation and power consumption. Our model is validated by comparing the aerodynamics of a CFD model and the present quasi-steady model using the example case of a hovering hawkmoth. It demonstrates that the CIQSM outperforms the conventional BEM while remaining computationally cheap, and hence can be an effective tool for revealing the mechanisms of optimization and control of kinematics and morphology in flapping-wing flight for both bio-flyers and unmanned air systems.