Two-Dimensional Aerodynamic Models of Insect Flight for Robotic Flapping Wing Mechanisms of Maximum Efficiency

In the ＂modified quasi-steady＂ approach, two-dimensional （2D） aerodynamic models of flapping wing motions are analyzed with focus on different types of wing rotation and different positions of rotation axis to explain the force peak at the end of each half stroke. In this model, an additional velocity of the mid chord position due to rotation is superimposed on the translational relative velocity of air with respect to the wing. This modification produces augmented forces around the end of each stroke. For each case of the flapping wing motions with various combination of controlled translational and rotational velocities of the wing along inclined stroke planes with thin figure-of-eight trajectory, discussions focus on lift-drag evolution during one stroke cycle and efficiency of types of wing rotation. This ＂modified quasi-steady＂ approach provides a systematic analysis of various parameters and their effects on efficiency of flapping wing mechanism. Flapping mechanism with delayed rotation around quarter-chord axis is an efficient one and can be made simple by a passive rotation mechanism so that it can be useful for robotic application.

NUMERICAL SIMULATION OF INSECT FLIGHT

In the non-inertial coordinates attached to the model wing, the two-dimensional unsteady flow field triggered by the motion of the model wing, similar to the flapping of the insect wings, was numerically simulated. One of the advantages of our method is that it has avoided the difficulty related to the moving-boundary problem. Another advantage is that the model has three degrees of freedom and can be used to simulate arbitrary motions of a two-dimensional wing in plane only if the motion is known. Such flexibility allows us to study how insects control their flying. Our results show that there are two parameters that are possibly utilized by insects to control their flight： the phase difference between the wing translation and rotation, and the lateral amplitude of flapping along the direction perpendicular to the average flapping plane.

Analysis of Maneuvering Flight of an Insect

Wing motion of a dragonfly in the maneuvering flight, which was measured by Wang et al. [1]was investigated. Equations of motion for a maneuvering flight of an insect were derived. These equations were applied for analyzing the maneuvering flight. Inertial forces and moments acting on a body and wings were estimated by using these equations and the measured motions of the body and the wings. The results indicated the following characteristics of this flight: (1)The phase difference in flapping motion between the two fore wings and two hind wings, and the phase difference between the flapping motion and the feathering motion of the four wings are equal to those in a steady forward flight with the maximum efficiency. (2)The camber change and the feathering motion were mainly controlled by muscles at the wing bases.

A flow control mechanism in wing flapping with stroke asymmetry during insect forward flight

A theoretical modeling approach as well as an unsteady analytical method is used to study aerodynamic characteristics of wing flapping with asymmetric stroke-cycles in connection with an oblique stroke plane during insect forward flight. It is revealed that the aerodynamic asymmetry between the downstroke and the upstroke due to stroke-asymmetrical flapping is a key to understand the flow physics of generation and modulation of the lift and the thrust. Predicted results for examples of given kinematics validate more specifically some viewpoints that the wing lift is more easily produced when the forward speed is higher and the thrust is harder, and the lift and the thrust are generated mainly during downstroke and upstroke, respectively. The effects of three controlling parameters, i.e. the angles of tilted stroke plane, the different downstroke duration ratios, and the different angles of attack in both down- and up-stroke, are further discussed. It is found that larger oblique angles of stroke planes generate larger thrust but smaller lift; larger downstroke duration ratios lead to larger thrust, while making little change in lift and input aerodynamic power; and again, a small increase of the angle of attack in downstroke or upstroke may cause remarkable changes in aerodynamic performance in the relevant stroke.

Control for going from hovering to small speed flight of a model insect

The longitudinal steady-state control for going from hovering to small speed flight of a model insect is studied, using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques based on the linear theories of stability and control for determining the non-zero equilibrium points. Morphological and certain kinematical data of droneflies are used for the model insect. A change in the mean stroke angle （δФ） results in a horizontal forward or backward flight; a change in the stroke amplitude （δФ） or a equal change in the down- and upstroke angles of attack （δα1） results in a vertical climb or decent; a proper combination of δФ and δФ controls （or δФ and δα1 controls） can give a flight of any （small） speed in any desired direction.

Dynamic flight stability of a hovering model insect:lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.

Aerodynamic Effects of Corrugation in Flapping Insect Wings in Forward Flight

We have examined the aerodynamic effects of corrugation in model wings that closely mimic the wing movements of a forward flight bumblebee using the method of computational fluid dynamics. Various corrugated wing models were tested （care was taken to ensure that the corrugation introduced zero camber）. Advance ratio ranging from 0 to 0.57 was considered. The results shown that at all flight speeds considered, the time courses of aerodynamic force of the corrugated wing are very close to those of the flat-plate wing. The cornlgation decreases aerodynamic force slightly. The changes in the mean location of center of pressure in the spanwise and chordwise directions resulting from the corrugation are no more than 3% of the wing chord length. The possible reason for the small aerodynamic effects of wing corrugation is that the wing operates at a large angle of attack and the flow is separated： the large angle of incidence dominates the corrugation in determining the flow around the wing, and for separated flow, the flow is much less sensitive to wing shape variation.

Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Lateral dynamic flight stability of hovering insects: theory vs. numerical simulation

In the present paper, the lateral dynamic flight stability properties of two hovering model insects are predicted by an approximate theory based on the averaged model, and computed by numerical simulation that solves the complete equations of motion coupled with the Naviertokes equations. Comparison between the theoretical and simulational results provides a test to the validity of the assumptions made in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The following conclusion has been drawn. The theory based on the averaged model works well for the lateral motion of the dronefly. For the hawkmoth, relatively large quantitative differences exist between theory and simulation. This is because the lateral non-dimensional eigenvalues of the hawkmoth are not very small compared with the non-dimensional flapping frequency （the largest lateral non-dimensional eigenvalue is only about 10% smaller than the non-dimensional flapping frequency）. Nevertheless, the theory can still correctly predict variational trends of the dynamic properties of the hawkmoth＇s lateral motion.

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.

Effects of wing deformation on aerodynamic performance of a revolving insect wing

Flexible wings of insects and bio-inspired micro air vehicles generally deform remarkably during flapping flight owing to aerodynamic and inertial forces,which is of highly nonlinear fluid-structure interaction（FSI）problems.To elucidate the novel mechanisms associated with flexible wing aerodynamics in the low Reynolds number regime,we have built up a FSI model of a hawkmoth wing undergoing revolving and made an investigation on the effects of flexible wing deformation on aerodynamic performance of the revolving wing model.To take into account the characteristics of flapping wing kinematics we designed a kinematic model for the revolving wing in two-fold：acceleration and steady rotation,which are based on hovering wing kinematics of hawkmoth,Manduca sexta.Our results show that both aerodynamic and inertial forces demonstrate a pronounced increase during acceleration phase,which results in a significant wing deformation.While the aerodynamic force turns to reduce after the wing acceleration terminates due to the burst and detachment of leading-edge vortices（LEVs）,the dynamic wing deformation seem to delay the burst of LEVs and hence to augment the aerodynamic force during and even after the acceleration.During the phase of steady rotation,the flexible wing model generates more ver-tical force at higher angles of attack（40°–60°）but less horizontal force than those of a rigid wing model.This is because the wing twist in spanwise owing to aerodynamic forces results in a reduction in the effective angle of attack at wing tip,which leads to enhancing the aerodynamics performance by increasing the vertical force while reducing the horizontal force.Moreover,our results point out the importance of the fluid-structure interaction in evaluating flexible wing aerodynamics：the wing deformation does play a significant role in enhancing the aerodynamic performances but works differently during acceleration and steady rotation,which is mainly induced by inertial force in acceleration but by aerodynamic forces in steady rotation.

Added Mass Effect and an Extended Unsteady Blade Element Model of Insect Hovering

During the insect flight, the force peak at the start of each stroke contributes a lot to the total aerodynamic force. Yet how this force is generated is still controversial. Two current explanations to this are wake capture and Added Mass Effect （AME） mechanisms. To study the AME, we present an extended unsteady blade element model which takes both the added mass of fluid and rotational effect of the wing into account. Simulation results show a high force peak at the start of each stroke and are quite similar to the measured forces on the physical wing model. We found that although the Added Mass Force （AMF） of the medium contributes a lot to this force peak, the wake capture effect further augments this force and may play a more important role in delayed mode. Furthermore, we also found that there might be an unknown mechanism which may augment the AME during acceleration period at the start of each stroke, and diminish the AME during deceleration at the end of each stroke.

Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee （Bombus terrestris） were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study （the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0-0.66）. The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed （advance ratio 0.66）, i.e. the power curve is Jshaped. Except at the highest flight speed, storing energy elastically can save power up to 20%-30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque （due to the smaller stroke amplitude and stroke frequency used）, the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.

Dynamic flight stability of a model dronefly in vertical flight

The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.

Stabilization control of a bumblebee in hovering and forward flight

Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability （passive stability）. But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle （which can be measured by the sensory system of the insect）, to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.

天气雷达空中生态监测系统建设和应用

为深度挖掘天气雷达数据应用价值,设计并建设了天气雷达空中生态监测系统。分析天气雷达晴空回波数据特征和空中生物散射特性,利用模糊逻辑算法识别天气雷达网数据中的生物回波,实现对生物密度、迁飞路径、时空分布等昆虫生态活动的实时动态监测。2022年5月天气雷达空中生态监测系统投入试运行,在实时监测期间发现昆虫活动具有明显的时空分布特征、昼夜活动和迁飞活动规律,8—9月全国昆虫活动呈现数量大、活动范围广的特点,是虫灾防治的重点关注时段,监测结果符合昆虫活动特征。该系统可有效服务空中生态实时监测,为虫灾精准防治提供监测技术与数据支持。

Control of flight forces and moments by flapping wings of model bumblebee

The control of flight forces and moments by flapping wings of a model bumblebee is studied using the method of computational fluid dynamics. Hovering flight is taken as the reference flight： Wing kinematic parameters are varied with respect to their values at hovering flight. Moments about （and forces along） x, y, z axes that pass the center of mass are computed. Changing stroke amplitude （or wingbeat frequency） mainly produces a vertical force. Changing mean stroke angle mainly produces a pitch moment. Changing wing angle of attack, when down- and upstrokes have equal change, mainly produces a vertical force, while when down- and upstrokes have opposite changes, mainly produces a horizontal force and a pitch moment. Changing wing rotation timing, when dorsal and ventral rotations have the same timing, mainly produces a vertical force, while when dorsal and ventral rotations have opposite timings, mainly produces a pitch moment and a horizontal force. Changing rotation duration has very small effect on forces and moments. Anti-symmetrically changing stroke amplitude （or wingbeat frequency） of the contralateral wings mainly produces a roll moment. Anti-symmetrically changing angles of attack of the contralateral wings, when down- and upstrokes have equal change, mainly produces a roll moment, while when down- and upstrokes have opposite changes, mainly produces a yaw moment. Anti-symmetrically changing wing rotation timing of the contralateral wings, when dorsal and ventral rotations have the same timing, mainly produces a roll moment and a side force, while when dorsal and ventral rotations have opposite timings, mainly produces a yaw moment. Vertical force and moments about the three axes can be separately controlled by separate kinematic variables. A very fast rotation can be achieved with moderate changes in wing kinematics.

Characterization of the Intracellular Distribution of Adenine Nucleotide Translocase (ANT) in Drosophila Indirect Flight Muscles

Background: The high power output necessary for insect flight has driven the evolution of muscles with large myofibrils (primary energy consumers) and abundant mitochondria (primary energy suppliers). The intricate functional interrelationship between these two organelles remains largely unknown despite its fundamental importance in understanding insect flight bioenergetics. Unlike vertebrate muscle that relies on a phosphagen (creatine phosphate/creatine kinase) system to regulate high energy phosphate flux, insect flight muscle has been reported to lack mitochondrial arginine kinase (analogous to creatine kinase), a key enzyme that enables intracellular energy transport. Creatine kinase is known to interact with mitochondrial adenine nucleotide translocase (ANT) in the transfer of ADP and ATP into and out of the mitochondria. Results: Here, we use quantitative immunogold transmission electron microscopy to show that in Drosophila melanogaster indirect flight muscles (IFM), ANT is present in the mitochondria as well as throughout the myofibril. To confirm this unexpected result, we created a transgenic line that expresses a chimeric GFP-ANT protein and used an anti-GFP antibody to determine the intracellular distribution of the fusion protein in the IFM. Similar to results obtained with anti-ANT, the fusion GFP-ANT protein is detected in myofibrils and mitochondria. We confirmed the absence of arginine kinase from IFM mitochondria and show that its sarcomeric (i.e., intramyofibrillar) distribution is similar to that of ANT. Conclusions: These results raise the possibility that direct channeling of nucleotides between mitochondria and myofibrils is assisted by an ANT protein thereby circumventing the need for a phosphagen shuttle in the IFM. The myofibrillar ANT may represent a unique adaptation in the muscles that require efficient exchange of nucleotides between mitochondria and myofibrils.

LATERAL DISPERSAL OF ADULT AQUATIC INSECTS FOLLOWING EMERGENCE FROM THE MIDDLE REACHES OF THE CHIKUMA RIVER(HONSHU ISLAND,JAPAN)IN RELATION TO WATERFRONT VEGETATION

To clarify the role of waterfront vegetation of floodplains for adult aquatic insects, Trichoptera and Diptera (Tipulidae and Chironomidae), in the middle reaches of the Chikuma River from May to July, an investigation of the number of these insects was conducted by trapping in each type of vegetation using board traps.A total of 2608.5 adults/m 2 were collected, and we identified a total of 26 species belonging to three taxa,i.e., seven species of Trichoptera, four species of Tipulidae and 15 species of Chironomidae. The most abundant species was Psychomyia acutipennis in Trichoptera (95.7%). There was a significant difference between the number of P.acutipennis in the all vegetation area (especially, Salix subfragilis) and the control area (no vegetation) during the investigation periods (P<0.05, Mann-Whitney U-test). Other taxa did not show a significant difference between the all vegetation area and the control. Moreover, the numbers of adult P. acutipennis showed a significant difference in height on each vegetation. In the case of Vicia villosa varia and V. villosa varia plus dead Phragmites australis, the highest number was caught in the traps set in the boundary between one plant and the plant above (P<0.05, Steel-Dwass Test) in May.On the other hand, in the case of almost all vegetation during the investigation periods (except of S.subfragilis in May, Melilotus officinalis plus dead P.australis in June), the highest number was caught in the traps set up within the vegetation (P<0.05, Steel-Dwass Test).As a result, a significant difference was observed in the number of trapped P.acutipennis according to the vegetation and its height.It is suggested that the existence of multiple types of vegetation in the floodplain plays an important role for maintaining the diversity of the fauna there.

Intraspecific scaling and early life history determine the cost of free-flight in a large beetle(Batocera rufomaculata)

The scaling of the energetic cost of locomotion with body mass is well documented at the interspecific level.However,methodological restrictions limit our understanding of the scaling of flight metabolic rate(MR)in free-flying insects.This is particularly true at the intraspecific level,where variation in body mass and flight energetics may have direct consequences for the fitness of an individual.We applied a 13C stable isotope method to investigate the scaling of MR with body mass during free-flight in the beetle Batocera rufomaculata.This species exhibits large intraspecific variation in adult body mass as a consequence of the environmental conditions during larval growth.We show that the flight-MR scales with body mass to the power of 0.57,with smaller conspecifics possessing up to 2.3 fold higher mass-specific flight MR than larger ones.Whereas the scaling exponent of free-flight MR was found to be like that determined for tethered-flight,the energy expenditure during free-flight was more than 2.7 fold higher than for tethered-flight.The metabolic cost of flight should therefore be studied under free-flight conditions,a requirement now enabled by the 13C technique described herein for insect flight.