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First published online December 3, 2004
Journal of Experimental Biology 207, 4707-4726 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01319

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The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings

Will J. Maybury and Fritz-Olaf Lehmann^*

Department of Neurobiology, University of Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany

^* Address for correspondence (e-mail: fritz.lehmann{at}biologie.uni-ulm.de)

Accepted 30 September 2004

	Summary

TOP Summary Introduction Materials and methods Results Discussion References

 
Insects flying with two pairs of wings must contend with the forewing wake passing over the beating hindwing. Some four-winged insects, such as dragonflies, move each wing independently and therefore may alter the relative timing between the fore- and hindwing stroke cycles. The significance of modifying the phase relationship between fore- and hindwing stroke kinematics on total lift production is difficult to assess in the flying animal because the effect of wing-wake interference critically depends on the complex wake pattern produced by the two beating wings. Here we investigate the effect of changing the fore- and hindwing stroke-phase relationship during hovering flight conditions on the aerodynamic performance of each flapping wing by using a dynamically scaled electromechanical insect model. By varying the relative phase difference between fore- and hindwing stroke cycles we found that the performance of the forewing remains approximately constant, while hindwing lift production may vary by a factor of two. Hindwing lift modulation appears to be due to two different fluid dynamic phenomenons: leading edge vortex destruction and changes in strength and orientation of the local flow vector. Unexpectedly, the hindwing regains aerodynamic performance near to that of the wing free from forewing wake interference, when the motion of the hindwing leads the forewing by around a quarter of the stroke cycle. This kinematic relationship between hind- and forewing closely matches the phase-shift commonly used by locusts and some dragonflies in climbing and forward flight. The experiments support previous assumptions that active neuromuscular control of fore- and hindwing stroke phase might enable dragonflies and other functionally four-winged insects to manipulate ipsilateral flight force production without further changes in wing beat kinematics.

Key words: insect flight, aerodynamics, DPIV, leading edge vortex, wake, dragonfly

	Introduction

TOP Summary Introduction Materials and methods Results Discussion References

 
Functionally four-winged insects such as dragon- and damselflies use a large variety of wingbeat kinematics to produce and control aerodynamic forces for flight (Alexander, 1984; Azuma et al., 1985; Azuma and Watanabe, 1988; Chadwick, 1940; Grodnitsky and Morozov, 1992; Reavis and Luttges, 1988; Rüppell, 1989; Rüppell and Hilfert, 1993; Sato and Azuma, 1997; Somps and Luttges, 1985; Wakeling, 1993; Wakeling and Ellington, 1997; Wang et al., 2003; Weis-Fogh, 1967). The neuromuscular system allows these animals to actively manipulate many aspects of wing motion such as stroke amplitude, stroke frequency, the angle of attack and stroke plane (Norberg, 1975; Rüppell, 1989), but also to actively control the timing between the fore- and hindwing stroke cycles (kinematic phase relationship, Alexander, 1984; Azuma and Watanabe, 1988; Clark, 1940; Grodnitsky and Morozov, 1992; May, 1995; Sato and Azuma, 1997; Simmons, 1977a,b; Wakeling and Ellington, 1997; Wang et al., 2003). Thus dragonflies and damselflies differ significantly from other four-winged insect species such as butterflies, bees, wasps and ants, whose fore- and hindwings always beat in phase, due to a sophisticated joint that mechanically couples the motion of both wings throughout the entire stroke cycle (Gorb, 2001). Other insects of more primitive orders, such as locusts, lie somewhere between both extremes; in locust, the stroke-phase relationship seems to be highly consistent, with little variation during flight control (Chadwick, 1953; Weis-Fogh, 1956; Wilson, 1968; Wortmann and Zarnack, 1993). Cooter and Baker (1977) reconstructed wing motion of freely flying locust Locusta migratoria and found a fixed phase relationship between their fore- and hindwings in which the forewing slightly leads by approximately 61°.

In contrast, dragonflies vary the phase relationship between ipsilateral fore- and hindwings with different behaviors (Norberg, 1975; Reavis and Luttges, 1988; Wakeling and Ellington, 1997; Wang et al., 2003). Three categories of phase relationship between fore- and hindwing have been established: phase-shifted stroking, counterstroking and parallel stroking. A highly consistent characteristic for the conventional flight modes is a 54-100° phase shift (the hindwing leads forewing motion) common for dragonflies during (i) straight forward and upward flight, (ii) the escape mode, in which a tethered animal produces peak lift in each stroke cycle of up to approximately 20 times their body weight, and (iii) during maneuvering flight (Somps and Luttges, 1985; Wakeling and Ellington, 1997; Wang et al., 2003). The kinematic phase shift persists even when the animals are changing forward flight speed (Wakeling and Ellington, 1997). In contrast, hovering flight seems to be supported by larger phase differences of up to 180°, in which the wings beat out of phase (counterstroking; Alexander, 1986; Norberg, 1975; Wakeling and Ellington, 1997). Counterstroking was also found in a study on maneuvering flight in dragonflies flying freely in a wind tunnel (Alexander, 1986). Detailed analysis of wing kinematics during various flight behaviours suggests that in-phase, or parallel stroking, might produce higher aerodynamic forces and should be favored during the energetically most demanding flight such as hovering, take-off or load-lifting flight (Alexander, 1984, 1986; Rüppell, 1989).

Direct force measurements on tethered dragonflies flying in a wind tunnel show that peak lift increases from approximately 2.3 to 6.3 times body weight when the animal decreases the phase angle between both flapping wings (Reavis and Luttges, 1988). Although this finding supports the assumption that parallel stroking might maximize lift production, it has been questioned by analytical modeling in which flight efficiency and mean thrust coefficient was estimated as a function of kinematic phase relationship (Lan, 1979). This study predicts that the hindwing extracts maximum energy from the forewing downwash when the hindwing leads by a quarter stroke cyle (90°), while the thrust coefficient is largest when the phase relationship is 45°. As a consequence, dragonflies exhibiting parallel stroking will increase thrust, but at the expense of a relative increase in energetic costs.

According to biplane theory, total lift production in tandem wings depends on the proximity and the strength of forewing downwash that interferes with the hindwing (Milne-Thomson, 1966). In dragonflies, the hindwing flaps in close proximity to the forewing and thus must cope with a potential reduction in the effective angle of attack (the angle between the wing chord line and the oncoming fluid) due to forewing downwash. The attenuation in aerodynamic performance of the hindwing in turn critically depends on forewing wake structure and the timing with which the hindwing interacts with the forewing downwash (Azuma et al., 1985). Assuming two-dimensional (2D) flapping conditions, two long and narrow wings working independently should have higher lift-to-drag ratios than a combined wing with the same wing area, due to the differences in aspect ratio (Bertin and Smith, 1979; Mises, 1959). Thus tandem wings flapping in phase should produce less total lift because the two wings are always closer throughout the entire stroke cycle than wings flapping out of phase (Alexander, 1984).

It is difficult to assess the significance of phase relationship to modulate lift production in a flying insect because kinematic phase shifts are mostly accompanied by other changes in wing kinematics, such as stroke amplitude or angle of attack (Reavis and Luttges, 1988; Wakeling and Ellington, 1997). For this reason various investigations on the aerodynamics of static and flapping dragonfly and damselfly wings have been conducted under various conditions, either experimentally (Kesel, 2000; Kliss et al., 1989; Newman et al., 1977; Okamoto et al., 1996; Saharon and Luttges, 1987; Somps and Luttges, 1985) or analytically (e.g. Azuma et al., 1985; Wang et al., 2003). Savage et al. (1979) modeled dragonfly aerodynamics experimentally under 2D conditions by pulling a single model wing on a carriage through the air, and derived forces from the resulting wake using inviscid flow theory. Kliss et al. (1989) used an oscillating flat plate with 90° angle of attack to study vortex shedding, and found that stroke length is critical to minimize complete flow separation during wing translation. In several elaborate studies, Saharon and Luttges (1987, 1988, 1989) demonstrated vortex generation in a mechanical-driven dragonfly under three-dimensional (3D) flapping conditions and described eight major vortices that are generated throughout each wing beat cycle. They found that in most of the tested cases, much of the interference between hindwing and forewing wake was detrimental to maximized wing-wake interaction. Different stroke-phase relationships (90, 180 and 270°) produced different flow wing-wake patterns, and vortices appeared to fuse under certain flapping conditions. A quantitative analysis of vortex displacement in the wake revealed that the travelling velocity of some vortices shed in the wake varied when phase relationship was altered (Saharon and Luttges, 1989). However, none of the studies mentioned above have directly measured aerodynamic forces produced by the flapping fore- and hindwing, nor quantified alterations in leading edge vorticity and local flow conditions in response to changing kinematic phase angles.

To investigate experimentally the complex wing-wake interaction in four-winged insects and to evaluate in more detail the functional significance of stroke-phase modulation on wake structure, aerodynamic force production and lift-to-drag ratio, we employed a 3D robotic dragonfly model mimicking hovering conditions at intermediate Reynolds number, in which stroke-phase relationships between fore- and hindwing could be altered systematically. While varying kinematic phase shift we measured aerodynamic forces using a miniaturized force transducer, and mapped the velocity field around the flapping wings using Digital Particle Imaging Velocimetry (DPIV) in order to quantify vorticity and vortical flow structures at the wings, including the structures shed into the wake.

	Materials and methods

TOP Summary Introduction Materials and methods Results Discussion References

 
To experimentally assess the gross effects on wing lift force due to modulation of fore- and hindwing stroke phase in four-winged flight, we modeled the wing-wake interaction during hovering flight of a dragonfly using a dynamically scaled electromechanical model of the right side of a four-winged insect and employing a generic kinematic pattern described below (Fig. 1B,D). The model wings were each equipped with a 6-DoF force transducer to measure instantaneous aerodynamic force production, while we systematically varied the kinematic phase relationship between the wings in steps of 2.5% of the stroke cycle. In addition to the force measurements we quantified the flow characteristics around the hindwing using 2D-DPIV for the two kinematics phase shifts that produce the maximum and minimum modulation in hindwing lift at two key times within the stroke cycle.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Wing beat kinematics of a dragonfly, set-up of the robotic wing hinge, and mechanical properties of the model wings as used in this study. (A) Diagram showing wing tip path of fore- (green) and hindwing (purple) and orientation of a freely flying dragonfly with near vertical thrust vector. Body orientation, location of the wing hinges and wing tip path were plotted after data published by Wakeling and Ellington (1997). In this kinematic study advance ratio, defined as the ratio between forward and wing flapping speed, was 0.44. Due to the steep body angle with respect to the horizontal, the wing hinges are aligned almost vertically and thus similar to the alignment of the robotic wing hinges shown in (B). (B) Schematic diagram of the robotic dragonfly setup, modeling aerodynamic characteristics on one side of the functionally four-winged insect with the forewing and hindwing wingtip trajectories of our generic dragonfly kinematics superimposed (see Materials and methods for details). The kinematics used during fore- and hindwing motion is identical in all experiments, yielding 100° stroke amplitude and symmetrical wing rotation at dorsal and ventral stroke reversal. Kinematic phase shift is the temporal offset between fore- and hindwing motion. (C) The shape of the robotic forewing and hindwing used. The wings are driven by servo motors mounted in a gear box that controls back/forth, up/down and rotational wing motion. Forces and moments acting on the wing during motion are measured on the surface mid point of the force sensor (blue circle). The center of gravity of the wing including the mass of the wing's holder is indicated by a red circle, respectively. lx, length of the horizontal moment arm for the wing's center of gravitiy; ly, length of the vertical moment arm between the wing's center of gravitiy and the wing's rotational axis. (D) Wing deflection due to bending moments under static load of the plexiglas model forewing (orange, red, black) and hindwing (cyan, green, blue). Deflection during load was measured at two distinct positions on the wing at two-third wing length (orange, cyan) and the wing tip (red, black, green, blue). To load the wing, small metal weights were placed on the upper wing surface either at two-third distance from the wing base (**, red, green, cyan, orange) or on the wing tip (*, black, blue). The vertical gray line indicates approximately mean force (0.3 N) measured throughout one complete stroke cycle on the wings during flapping motion. Horizontal gray area shows the range of deflections for fore- and hindwing, assuming the wing is loaded with mean force. The pictogram illustrates the measurement procedure showing wing holder and the wing seen parallel to the wing's surface.

Development of a generic kinematics and wing control
Owing to the range of stroke patterns used by dragonflies to balance their weight and allow maneuvering, it appears to be difficult to describe a typical dragonfly kinematics (Norberg, 1975; Rüppell, 1989). Kinematic studies on different species of dragonfly demonstrate that during forward and climbing flight some animals beat their wings with a near horizontal stroke plane (Wakeling and Ellington, 1997; Fig. 1A) and others with highly inclined stroke planes (Azuma and Watanabe, 1988; Wang et al., 2003). Moreover, dragonflies produce flight forces using various combinations of stroke amplitude and stroke frequency that range from 50 to 150° and from 27 to 73 Hz, respectively (Azuma and Watanabe, 1988; Rüppell, 1989).

Due to this diversity of dragonfly kinematics, various authors have modeled physically and analytically different types of dragonfly kinematics. In the oscillating flat plate case (Kliss et al., 1989), the authors varied stroke amplitude, frequency and aspect ratio, but did not model other characteristic features of dragonfly wing motion, including wing-wake interaction. The study, moreover, compared aerodynamic flow patterns produced over a vast range of Reynolds numbers (Re) ranging from 10 to 4300. Savage's physical model (Savage et al., 1979) of a hovering dragonfly used Norberg's kinematic data of freely flying dragonfly Aeschna (Norberg, 1975). This model wing did not flap its wing around a root, however, but rather translated during up- and downstroke. The more elaborate `pitching-plunging' dragonfly model employed by Saharon and Luttges (1988, 1989) flapped two ipsilateral wings in a tilted stroke plane and at 90° stroke amplitude. In this model the authors varied reduced frequency, which was accompanied by changes in Re, and three distinct phase angles between fore- and hindwing, but no other kinematic parameters (Saharon and Luttges, 1989). Aerodynamic characteristics of static dragonfly wings and body were conducted under 2D conditions in a wind tunnel (Kesel, 2000; Okamoto et al., 1996). In the latter study the authors mounted wings of a dragonfly and flat plates on a glider and evaluated the effect of angle of attack (dragonfly wing), camber, thickness sharpness of the leading wing edge and surface roughness (model wing) on force production at Re=1000-10 000.

To avoid too many kinematic parameters confounding the results in the present study, we developed a generic kinematic pattern that allowed us to model kinematic phase shifts similar to those reported for dragonflies (Fig. 1B). The horizontal wing trajectories were derived from a simple sinusoidal function, which was chosen because of a finding in previous studies that the first harmonic of a Fourier series gives a good representation of the stroke cycle of freely flying dragonflies (Azuma and Watanabe, 1988; Wakeling and Ellington, 1997; Wang et al., 2003). We used a constant angle of attack during wing translation with a feathering angle of 45° at mid stroke, which is similar to values reported previously (Azuma and Watanabe, 1988; Fig. 2B). This angle is the optimum lift angle of a translating wing free from wake interference and is within the range of data published for dragonflies (Dickinson et al., 1993; Rüppell, 1989). The stroke amplitude of 100° that we used is near the average measured for both the fore- and hindwing motion in dragonflies flying at various flight speeds (Wakeling and Ellington, 1997). The flapping frequency of the robotic wings was 533 mHz.

View larger version (28K): [in this window] [in a new window]   Fig. 2. Inertial forces during wing flapping due to wing mass (A) and added mass (virtual mass) of the wing (B). For kinematic details, see traces in B (bottom) and explanations given in the text. (A) Top: unfiltered raw force trace of lift (black) and drag (red) measured during a single stroke of the dragonfly model hindwing. Bottom: wing inertia in the horizontal (drag, red) and vertical (lift, black) calculated from the acceleration profile during translational and rotational wing motion of a complete stroke cycle. Total wing mass is equal to the mass of the wing and the holder attached to it. Note the different force scales. (B) Top: unfiltered total forces measured during wing motion of the model hindwing (red) within one flapping cycle with superimposed added mass inertia (black) calculated according to the equation given in the text. The blue trace shows the measured forces after subtracting added mass inertia. Bottom: kinematic pattern used for calculations of inertia. Traces show the angular position of the wing within the horizontal stroke plane (red) and the wing's angle of attack (black) throughout the entire stroke cycle.

We chose to stack the wings vertically, which seems to be sufficiently close to the orientation of wing hinges presented by a freely flying dragonfly with a near vertical mean thrust vector (Fig. 1A,B). In this respect our tandem model with vertical aligned wings differs from other dragonfly models in which the wing hinges are aligned horizontally, yielding a `front' and a `rear' wing rather than an `upper' and a `lower' wing (Saharon and Luttges, 1987, 1988). For this reason, our model only covers a limited aspect of four-winged insect flight. It is not intended to explain per se the various types of wing-wake interaction assumed during the various forward and hovering flight conditions found in freely flying dragonflies. If not stated otherwise, fore- and hindwing hinges in our robotic model were separated vertically by 1.3 mean forewing chord lengths, i.e. the closest distance between the wings at which the wings did not touch physically during flapping at the various kinematic phase relationships (Fig. 1C).

In accordance with the stroke kinematics used for an analytical dragonfly model, we chose a symmetrical wing rotation during the ventral and dorsal stroke reversal, in which the midpoint of rotational duration occurs when the wing reverses its translational direction (Wang, 2000a). A wing rotating symmetrically starts rotating before and finishes after it has reversed its flapping direction, which may minimize rotational lift because at that time translational wing velocity is smallest. To minimize inertial load produced by rotational moments in our generic kinematic pattern, wing rotation followed a sinusoidal velocity profile. The onset of wing rotation relative to stroke reversal, expressed as a fraction of the total wing cycle time, ₀, was -0.1, indicating that wing rotation begins 10% of the stroke period prior a stroke reversal. Flip duration, , was 0.2, indicating that wing rotation ends 10% after the stroke reversal (for nomenclature, see Sane and Dickinson, 2001a). The kinematic pattern we used in this study produces lift due to wing rotation equivalent to 3.2% of total lift production by the hindwing free from forewing wake interference. We estimated rotational lift contribution from total lift by subtracting the `quasi-steady' lift estimate during wing translation that was calculated using a conventional `quasi-steady' analytical model, as suggested by Dickinson et al. (1999). In sum, considering the small amount of rotational lift, it seems unlikely that the pronounced modulation in measured hindwing lift production as shown in the present study results from alterations in rotational circulation during the stroke reversals, but rather reflects aerodynamic mechanisms during wing translation.

The motion of the two model wings was driven by six servo motors that are controlled by self-written software developed under Visual C++.NET (Microsoft) for a conventional computer. To record force data and to control wing motion simultaneously, the computer was equipped with a 16-channel analog-to-digital data acquisition board (6036E, National Instruments, Austin, TX, USA) and a 24-bit digital interface card (6503, National Instruments) for controlling the motion of the servo motors via a micro-controller (Fig. 1C). We updated the angular position of the entire motor assembly with a maximum rate of 67 Hz (0.015 ms period), whereas the force sampling frequency was approximately 12-times higher, yielding 800 Hz. A potential problem during wing motion of robotic wings is that the actual wing kinematics may differ from the programmed kinematic pattern, whenever the actual power requirements for wing motion exceed the power supplied by the driving motors. This happens especially when the wings accelerate from rest under high inertial load. To avoid a confounding effect on our force measurements due to power constraints of the motor assembly, we modified the servo motors in order to monitor electrically their internal angular position, which is mechanically determined by the angle of the motor main shaft driving the wing. In a control procedure preceding each experimental series, we compared the actual angular position of each servo motor with the programmed wing angles and adjusted either the motor's power supply or the wing's flapping frequency until actual and programmed kinematics were indistinguishable. Besides other constraints, the high power requirement for wing flapping was a major factor that limited maximum flapping speed, and thus Re, of our model wings.

In addition to kinematic modifications of wing motion due to power constraints, wing kinematics may also change due to wing flexing and bending. Moreover, wing flexing can potentially produce inertial peaks that might complicate the measured force traces. Although inertial forces produced during the acceleration and deceleration periods of the wing are relatively small (see below and Fig. 2A), strong flexing of the wing might add brief periods of acceleration/deceleration components to the overall wing acceleration/deceleration profile that is produced by the translational and rotational wing motion. Fig. 2B shows that the hindwing flapping free of the forewing downwash experiences a maximum combined aerodynamic and inertial load between 0.4 and 0.6 N for each mid-halfstroke. To derive a rough estimate of the magnitude of wing flexing during the various times of the stroke cycle, we statically loaded the wing in air with small weights that we placed either at a distance of two-thirds wing length on the upper wing surface or at the wing tip, and measured the deflection of the wing at both locations (Fig. 1D). Loading the wing at the wing tip is thought to produce a rather conservative estimate because the main force vector during wing translation is thought to act close to the two-thirds wing position. The results show that with an average load of 0.3 N, which is equal to the average force measured throughout the entire stroke cycle, fore- and hindwing solely flex approximately 1.0 mm at two-thirds distance from the wing holder, and up to 1.7 mm under the maximum load of 0.5 N that occurs approximately at mid-halfstroke. Due to the sinusoidal velocity profile during wing translation, however, we assume that the wing builds up and releases its deflection more gradually at the beginning and the end of each halfstroke, respectively, which should in turn minimize sudden accelerations and thus high inertial peaks. In sum, we feel rather confident that the measured alteration in force development due to the various kinematic phase shifts between fore- and hindwing are not primarily caused by extensive wing flexion but are likely to represent aerodynamic alterations due to wing-wake interaction.

Force measurements
Fore- and hindwing planforms were based on the wings of the dragonfly Polycanthagyna melanictera Selys and were made from 2 mm Plexiglas. Since wing velocity of each wing blade element depends on its distance to the rotational axis of the robotic hinge, we calculated total wing length as the distance between the vertical rotational axis of the gear box and wing tip. Thus total forewing length was 190 mm with an aspect ratio of 6.8, and total hindwing length was 185 mm with an aspect ratio of 7.4, assuming that gear box, force sensor and wing holder add to wing length but not to wing area (Fig. 1C). However, the length of the wings sensu strictu (without wing holder, force sensor and gear box) was only 135 mm for the upper forewing (aspect ratio=3.6) and 140 mm for the lower hindwing (aspect ratio=4.2; Fig. 1C). Each wing was mounted on a robotic hinge with three-degrees of freedom, with all axes crossing a single origin.

In this study we modeled hovering flight conditions of a four-winged insect, which are thought to differ from flow conditions produced during steady forward flight. Advanced ratio as well as reduced frequency are ratios of the `steady motion' caused by the body of an insect flying through the air at constant speed, whereas `unsteady motion' is due to motion of a wing oscillating back and forth about its root. Advanced ratio and reduced frequency are thus measures that indicate which velocity component (free stream due to body motion or wing flapping) dominates the incident flow on the wing. Both quantities are important for `quasi-steady' analytical modeling and the development of dynamically scaled robotic hinges. Since we modeled hovering flight conditions, however, all flow components acting on the two wings are generated by the wing's own motion and thus advance ratio is zero and reduced frequency is infinity.

The two scaled wings were immersed in a 0.6 mx0.6 mx1.2 m glass tank filled with pharmaceutical white oil (density, 0.88x10³ kg m^-3; kinematic viscosity, 120 cSt). The size of the tank was chosen to minimize wall and ground effects that were calculated based on a set of equations derived from a robotic wing flapping in oil at similar speed (Dickinson et al., 1999). A modified force/torque sensor (Nano17, ATI, Apex, NC, USA) was alternately attached to the base of each wing, and the experiments were repeated to obtain measurement on both wings. The sensor recorded shear forces and moments along and around all three wing axes. We converted forces measured normal and parallel to the wing surface into lift and drag using commercial Active-X controls (ATI) and software written in Visual C++.NET. We typically recorded six successive stroke cycles. It has been shown that the first stroke cycle produces slightly higher forces because the downwash velocity is minimal under these conditions (Birch and Dickinson, 2001). For further data analysis we thus averaged only four stroke cycles (cycles 2-5) in order to avoid confounding effects from the initial downwash acceleration or any transient forces when the wing was started or halted at the end of the experiment. Mean total force, lift and drag were averaged subsequently throughout the entire stroke cycle. The force traces showing the maximum modulation in lift performance were filtered using a 5 Hz FFT smoothing filter in Origin 7.0 (Microcal, Northampton, MA, USA).

To derive mean lift coefficient _L, for wing motion from mean lift and drag averaged throughout the entire stroke cycle, we used the equation:

(1)

which is a modified expression of equation 12 in Ellington (1984c) developed for hovering flying insects exhibiting a horizontal stroke plane (Lehmann and Dickinson, 1998). In this equation is lift of single wing averaged throughout the stroke cycle, is the density of the mineral oil, is stroke amplitude, defined as the angle that the wings cover during wing translation, n is stroke frequency, R is wing length, S is total wing area, mean square of dimensionless wing velocity and is the non-dimensional radius of the second moment of wing area that characterizes wing shape (for nomenclature, see Ellington, 1984d). For a sinusoidal velocity pattern for wing translation, mean square of dimensionless wing velocity is 19.7 (Lehmann and Dickinson, 1998) and the non-dimensional radius of the second moment of wing area is 0.36 for the forewing and 0.38 for the hindwing in our dragonfly model. The force coefficients represent means in which all circulatory mechanisms such as Kutta-lift, leading edge vorticity and rotational circulation, including a possible wake-capture momentum transfer, are lumped into a single coefficient (Dickinson et al., 1999).

Wing inertia and added mass effects
In real and model wings the forces at the wing base consist of at least three different components: (i) aerodynamic forces due to both the pressure distribution around the wing and viscous forces in the fluid, (ii) inertial forces due to wing and added mass acceleration, and (iii) gravitational forces. The gravitational component on the force sensor is due to the mass of the wing and was subtracted from the measured forces by recording the lift component acting on the resting wing at each point of the stroke cycle. We estimated the contribution of inertial forces due to wing mass analytically, assuming that all mass of the wing, m_w, including the mass of the wing holder, is concentrated in the center of wing mass. The center of wing mass we have indicated by a red dot for each wing shown in Fig. 1C. Although the mass of the wing holder is in close distance to the mounting surface of the force sensor, to which all forces and moments refer, its total mass of approximately 7.0 g is about 54% of the mass of the larger forewing and 62% of the smaller hindwing, and should thus be considered for inertial effects. According to Ellington (1984a), inertial forces during flapping flight in the horizontal plane are proportional to the first moment of wing mass m₁ that is equal to:

(2)

In this equation ' is normalized wing mass per unit wing length and is the normalized radial position along the wing. Since the wing holder is a complex 3D piece that was difficult to model analytically, we derived the first moment of total wing mass experimentally by balancing the model wing, including the wing holder, on a small pin with an approximately 1 mm² support area. The results of these measurements show that the moment arm, l_x, between the force sensor and the wing's center of mass is 48.3 mm for the forewing and 50.8 mm for the hindwing (Fig. 1C). Inertial forces associated to accelerations in the horizontal stroke plane are then:

(3)

in which is the angular position of the wing during the stroke and t is time. However, during wing acceleration the force sensor does not solely experience inertial forces produced by the acceleration in angular wing position but also inertial forces due to changes in the angle of attack, because the center of wing mass is not located exactly on the wing's rotational axis. Thus when the wing starts to rotate, the center of wing mass may experience additional accelerations in the horizontal and vertical direction. We experimentally determined the length of the moment arm normal to the wing's rotational axis, l_y, to be 8.6 mm for the forewing and 3.8 mm of the hindwing (Fig. 1C). The horizontal inertial component modifies drag whereas as the vertical acceleration produces inertial forces acting on the lift vector. The relative contributions of rotational acceleration during stroke reversals to horizontal and vertical inertial forces thereby depend on the angle of attack. A wing that starts rotating at a low angle of attack produces more vertical than horizontal inertial force compared to a wing starting at angles near 90°. Rotational inertia adds positive lift when the wing increases angle of attack and adds negative lift when the angle of attack is decreasing. We approximated instantaneous vertical inertial force F_v similar to Equation 3, but also took into consideration the wing's angle of attack , which yields:

(4)

Changes in wing acceleration in the horizontal due to changes in angle of attack are pronounced, particularly at the stroke reversals when the wing accelerates and decelerates during translational motion. Combining Equation 3 and the inertial forces produced during wing rotation thus yields for wing inertia in the horizontal (drag) stroke plane:

(5)

We calculated the contribution of wing inertia to total lift and drag forces separately (Fig. 2A). The data indicate that wing inertia appears to be small and may account solely for a small fraction of the measured force at the beginning of the stroke cycle.

When a wing accelerates within the fluid it sets the surrounding air in motion, resulting in inertial forces by the fluid (added mass effect). Although added mass effects appear to be small during wing motion of a slightly larger Drosophila model wing that moves at similar speed and Reynolds number (Sane and Dickinson, 2001a), we calculated the potential contribution of added mass inertia using an analytical model for an infinitesimally thin 2D plate moving in an inviscid fluid modified towards 3D conditions using a blade-element approach (Sane and Dickinson, 2001a; Sedov, 1965). Similar to the wings of a fruit fly, the model wings used in this study rotate approximately at one quarter chord length from the leading edge. Total force normal to the wing surface due to the added mass acceleration of the fluid may be then expressed as (cf. erratum on equation 1 in Sane and Dickinson, 2001b, but additional corrections also apply; S. Sane, personal communication):

(6)

in which () is the non-dimensional wing chord. The left integral we approximated to be 0.41 for the fore- and 0.45 for the hindwing, whereas the right integral is 1.29 and 1.13 for the two wings, respectively. We calculated added mass forces for each of the model wings using our generic kinematic pattern (Fig. 2B). Similar to wing inertia, added mass inertia seems to be relatively small and accounts for only small changes in the measured force trace. In our analysis on the significance of kinematic phase relationship we therefore made no attempt to correct the recorded data for inertial effects.

Reynolds number
In aerodynamics the fluid flow around a wing depends on Re, which is the ratio of inertial forces to viscous forces within the fluid. In flapping flight of insects this measure is conventionally defined by the product of mean wing chord and time-averaged wing tip velocity divided by the fluid's kinematic viscosity (Ellington, 1984c). Reynolds number for wing motion in our experiments was 105 for the forewing and 125 for the hindwing, which is thought to be at the lower end of Re observed for dragonflies (Rüppell, 1989). For example, the smallest dragonfly (Nannophya pygmaea), with a hindwing length of 10.5 mm, will fly at Re=250-500, assuming a stroke amplitude of 50-100° and a wingbeat frequency of 80 Hz. Reynolds number for wing motion of Polycanthagyna melanictera as shown in Fig. 1A is higher and amounts to approximately 2000 (Wakeling and Ellington, 1997). However, Kliss et al. (1989) modeled hovering dragonfly aerodynamic using a flat plate at Re=10-4300, as mentioned above. The difference in Re between our model wing of 100 and an averaged sized dragonfly flying at Re>1000 appears to be important in this study and might be troublesome for interpreting the data. However, there are several reasons that the flow conditions at Re=100 are sufficiently similar to the flow conditions we expect at Re>1000. First, empirical data on static plates in uniform flow show that the force coefficients vary only little between Re=100 and 1000. Although this variation is slightly higher than the stable coefficients above Re=1000, it is much less than between Re=10 and 100 (Hoerner, 1965). Most of the transition from attached flow conditions to flow separation at which flow is shed at reasonable intervals seems to happen within the range Re=10-100.

Second, the shedding frequency in static plates is a function of Re and changes in Re domain between 100 and 1000 that would be relevant for our experimental approach. The force coefficients of our model fore- and hindwing depend critically on the time of vortex shedding relative to the stroke reversals. However, the strong dependency of vortex shedding on Re is questionable in root-flapping wings at which the spanwise wing blade elements face different flow velocities and thus different Re during translatory motion. Previous studies using mechanical flappers have shown that root-flapping wings may stabilize a leading edge vortex (LEV), and vortex shedding at the stroke reversals at which the wing changes the sign of the angle of attack may occur before the vortex grows too large to be shed during wing translation (Birch and Dickinson, 2001). Moreover, a recent paper on LEV stability reported that even in a continuous rotating propeller mimicking wing translation of the hawkmoth Manduca sexta, the LEV remains stable and no vortex shedding occurs, similar to those expected in a flat plate translating through the fluid at similar Re (Usherwood and Ellington, 2002a). Usherwood and Ellington (2002b) concluded that the shifts from early to steady flow conditions are relatively constant throughout a large range of Re. Thus it appears possible that the wings of a fruit fly Drosophila (Re=100-200) exhibit a similar force coefficient to the flapping wings of a quail (Re=26,000) because the high force coefficients in both animals are supposedly due to leading edge vorticity (Usherwood and Ellington, 2002b). This view is supported by an analytical model on flow separation (Miller and Peskin, 2004) suggesting that shedding behaviour in wings is only affected at Re<50, which is consistent with the experimental data on flat plate in uniform flow obtained by Hoerner (1965). In sum, all the above results suggest that investigating dragonfly wing-wake interaction at Re=100 seems to be less troublesome than would be expected from flat plate data. Moreover, the low Re used in this study was helpful for conducting DPIV because the high viscosity of the fluid (mineral oil, see below) minimized the buoyancy of the seeding particles (air bubbles) that we tested experimentally using different mineral oils. Thus, the Re selected in this experiment was the best compromise between matching the flow conditions to dragonfly hover flight between 1000 and 2000 and the experimental constraints on visualizing reliably the flow around the wings using DPIV.

Particle image velocimetry
To visualize wake structure, the oil was seeded with bubbles by pumping air through a ceramic water-purifier filter. The seeding consisted of evenly sized small bubbles with low upward velocity (<0.5 mm s^-1) and high concentration. We used a 50 mJ per pulse dual mini-Nd:YAG laser (Insight v. 5.1, TSI, Shoreview, MN, USA) to create two identical positioned light sheets approximately 5 mm thick separated in time by 2500 µs. Paired images of a 250 mm² flow field were captured using a PowerView 2M (TSI) camera. A two-frame cross-correlation of pixel intensity using the Hart Correlator engine (TSI) for a final interrogation area of 32x32 pixels, resulted in more than 10 000 vectors. Each DPIV experiment consisted of a seven-stroke wingbeat cycle, and the flow fields from the last five strokes were recorded, averaged and analyzed. No further smoothing was applied to the flow field vectors. The light sheet intersected the hindwing at 50% wing length, perpendicular to the long axis of the wing. DPIV analysis, including calculation of vorticity, was done using Insight v 5.1 and TSI macros in Tecplot v 9.0.

	Results

TOP Summary Introduction Materials and methods Results Discussion References

 
Kinematic phase modulation
The combined lift forces on the fore- and hindwing show a strong sinusoidal relationship, with modulation of kinematic phase shift between both flapping wings (Fig. 3). Higher lift forces are produced when the hindwing leads and lower lift forces are produced when the forewing leads the stroke cycle. The 24% peak-to-peak modulation in total lift production {sine fit, y=0.38+0.04sin[(x+6.2)/50], ²=0.17x10^-3; Fig. 3D, closed red circles} was accompanied by a modulation in lift-to-drag ratio of less than 10% {sine fit, y=0.81+0.03sin[(x+1.2)/50], ²=0.17x10^-3; Fig. 3D, closed blue circles}. Unexpectedly, the combined fore- and hindwing peak lift is similar (within 4.6% accuracy) to the combined fore- and hindwing lift of the wings flapping separately (0.44 N; Fig. 3D, red line). Lift and drag modulation in fore- and hindwing vanished completely when the wings were separated vertically by more than 5 forewing chord widths (Figs 1C, 3B-D, open circles). At 5-chord-width distance to the forewing stroke plane, the temporal fluctuations in the fluid due to vortex shedding had ceased superficially and the downwash exhibited a temporal constant and homogenous velocity characteristics. Compared to a single wing, the vertical flow component at 5-chord distance reduced both the lift coefficient of the hindwing on average by 22% (_L=1.43±0.007, mean ± S.D., N=20 vs single wing _L=1.84; Fig. 3C) and the lift to drag ratio (L/D) of the hindwing by 8.3% (L/D=0.78±0.02, mean ± S.D., N=20 vs single wing L/D=0.84; Fig. 3C). In contrast, the forewing performance at 5-chord wing separation (_L=1.76±0.03, mean ± S.D., N=20, L/D=0.87; Fig. 3B) was approximately similar to the performance of a single flapping forewing (_L=1.75, L/D=0.86; Fig. 3B). All measured lift coefficients are well above the maximum 2D steady-state coefficients of artifical and real dragonfly wings (typically _L=0.9-1.1) measured under various conditions, indicating that a LEV has enhanced aerodynamic force production (Okamoto et al., 1996). Although stroke kinematics was similar in the fore- and hindwing, we did not calculate an averaged lift coefficient for the combined wing performance because both wings have different shape and size.

View larger version (29K): [in this window] [in a new window]   Fig. 3. Alterations in total lift and lift-to-drag ratio of the model fore- and hindwing in response to changes in kinematic phase shift between both wings. (A) Negative phase-shift values indicate that the forewing leads wing motion (red) throughout the entire stroke cycle whereas positive phase-shift values indicate that the hindwing leads wing motion (blue). Kinematic pattern of both wings is the same (cf. Fig. 4C). (B-D) Lift averaged over an entire stroke cycle (closed red circles) and lift-to-drag ratio (closed blue circles) are shown for the forewing flapping on top of the hindwing (B), the hindwing (C) and the combined performance of both fore- and hindwing (D) during various kinematic phase relationships. Performances of single wings flapping without wake-wing interaction are shown as solid lines in the respective color. Data are presented for the robotic wings vertically separated by 1.3 (closed circles) and 5.0 (open circles) mean forewing chord lengths, measured as the distance between the rotational axis of the two wings (cf. Fig. 1C). For an explanation of L, see text.

View larger version (46K): [in this window] [in a new window]   Fig. 4. Maximum modulation in lift performance throughout a stroke cycle occurs during the second quarter of each half stroke. (A) Time history of lift forces in the robotic dragonfly hindwing during the stroke cycle are shown for stroke conditions in which the hindwing (red) or the forewing (blue) leads by a quarter stroke cycle. Lift of the hindwing free from forewing wake interference is plotted in black. (B) Lift enhancement on the hindwing calculated from the difference in performance between the hindwing with and without forewing wake interference (difference between colored and black line shown in A). Red (blue) line indicates lift enhancement when the hindwing (forewing) leads by a quarter stroke cycle. Asterisks *1 (15% stroke cycle) and *2 (35% stroke cycle) indicate the position in the stroke cycle when DPIV analysis was performed in Figs 7 and 8. (C) Translational (purple) and rotational (green) velocities of the wing (measured at the wing's second moment of area). The three translational plots represent the velocity profiles for the best (hindwing leads by 25% stroke cycle), zero (both wings move in-phase) and worst (forewing leads by 25% stroke cycle) kinematic patterns. T, stroke cycle.

Time traces of lift production
To uncover the aerodynamic mechanisms behind the phase modulation effects, we mapped the wing lift forces throughout a stroke cycle and identified positions where the interaction between the hindwing and the forewing wake has the largest effect on hindwing lift (Fig. 4). Due to stroke symmetry in both halfstrokes, the time course of force production is similar during the up- and downstroke and thus differs from the aerodynamic forces produced by a tethered dragonfly, flying with a steeply inclined stroke plane (Reavis and Luttges, 1988). Fig. 4A shows time traces of lift production for three different flapping conditions of the hindwing: hindwing lift free from forewing wake interference (black line), hindwing lift when the forewing leads by 25% stroke cycle (blue line) and hindwing lift when the hindwing leads by 25% stroke cycle (red line). The data show that positive lift is produced throughout the stroke with a small negative lift peak (lift force for all three cases = -0.013±0.003 N, mean ± S.D.) during wing rotation. Maximum lift forces of 0.37, 0.41 and 0.23 N were obtained just after the mid halfstroke (28% stroke cycle) for the three conditions: (i) single wing flapping, (ii) hindwing leads and (iii) forewing leads wing motion by 25% stroke cycle, respectively. The difference between hindwing lift produced during the two different phase-shift relationships and the single wing performance is shown in Fig. 4B. In the best phase, when the hindwing leads by a quarter stroke, hindwing lift force is attenuated at the start of the stroke by approximately 0.10 N, but then develops a larger peak force (0.10 N) at a later position in the stroke cycle than a single hindwing free from forewing downwash (Fig. 4B, red trace). For the worst phase, when the forewing leads by a quarter stroke, lift throughout the stroke is considerably reduced, producing 0.14 N less lift at peak attenuation (Fig. 4B, blue trace). The worst phase peak attenuation, and the best phase peak enhancement both occur at approximately 35% and 85% of stroke cycle. The high magnitude of lift alteration and its dynamic change within the stroke cycle is thought to reflect major changes in the complex wake structure formed by the flapping wings.

View larger version (86K): [in this window] [in a new window]   Fig. 7. Analysis of flow field velocities around the hindwing using DPIV techniques reveals the elaborate flow structures. The wing sections (white lines) are viewed at 50% distance between the wing base and tip, and have a geometric angle of attack of 45°. The direction of wing translation is from left to right in the hindwing (lower wing in panels) and, where present in the images, from right to left for the forewing (upper wing). The rotational axis for the fore- and hindwing is 0.33 and 0.22 chord widths, respectively. The DPIV images show wake velocity fields at two different times within the stroke cycle (A-C, 15% of stroke cycle; D-F, 35% of stroke cycle) when the hindwing flaps free from forewing downwash (A,D), when both wings flap but the forewing (B,E) or the hindwing (C,F) leads wing motion by a quarter stroke cycle. White open boxes in A-F indicate the region, located between the lower surface of the wing and the free stream, from which downwash flow velocities and angles were measured (see text for details). T, stroke cycle.

View larger version (52K): [in this window] [in a new window]   Fig. 8. Vorticity contours near the hindwing with superimposed velocity vectors at 35% of stroke cycle when hindwing lift is enhanced or attenuated maximally (*2 in Fig. 4). Vorticity and velocity vectors for the kinematic condition in which (A) hindwing lift is attenuated maximally (worst condition; forewing leads by a quarter stroke cycle), and (B) hindwing lift exceeds lift production of a single hindwing flapping free of forewing downwash interference (best kinematic pattern; hindwing leads by a quarter stroke cycle). Square white boxes indicate the regions from which circulation of the leading edge vortex was measured. The wing sections (white lines) are viewed at 50% distance between the wing base and tip, and have a geometric angle of attack of 45°. The direction of wing translation is from left to right. T, stroke cycle.

View larger version (138K): [in this window] [in a new window]   Fig. 5. (A-L) Time sequence of the wake produced by a tandem dragonfly model wing moving in a horizontal plane and highlighted by air bubbles in the mineral oil. The bubbles are illuminated by conventional fiber optics that intersect the wake at approximately 50% distance from the wing base and normal to the wing surface at mid half stroke. The red lines in each graph indicate inclination of the visible chordwise wing element as it appears on the video images; the upper and lower lines show wing motion of the forewing and hindwing, respectively. Leading wing edge is indicated by a red dot. (A-F) Complete half stroke (upstroke) of the forewing moving from left to right. (G-L) Complete half stroke (downstroke) of the forewing moving from right to left. The time sequence shows the wake while the forewing leads hindwing motion by a quarter stroke cycle. In all images yellow pictograms indicate the location and spin of vortices either shed in the wake (vortex core is marked by a cross) or attached to the wing (leading edge vortex). Only when clearly visible in the fluid, the vortices' spin and location were reconstructed from the video by eye and within the illuminated plane of the wake. Note: vortices that were masked by other flow structures or moving outside the imaging plane are not shown in this reconstruction. The stroke period for flapping motion is 0.96 s and stroke amplitude is 100°. See text for more details on stroke kinematics. Images were taken using a conventional 50 Hz video camera (Sony, TRV120E, Cologne, Germany).

View larger version (137K): [in this window] [in a new window]   Fig. 6 (A-L) Time sequence of the wake produced by a tandem dragonfly wing moving in a horizontal plane. In contrast to Fig. 5, the time sequence shows the wake while the hindwing leads wing motion by a quarter stroke cycle. Wing kinematics and experimental techniques are similar to those mentioned in the legend for Fig. 5. The vortex that is indicated by the broken yellow line in I appeared to break down in the video image or moved outside the image plane.

Particle image velocimetry
To gain more insights into the relationship between lift modulation and wake structure during wing-wake interaction, we characterized the flow conditions around the wings during both lift attenuation at the beginning of the stroke cycle (Figs 4B, 7, ^*1) and for the peak effects on lift later in the stroke (^*2). As a first step, we mapped the potential alterations in the strength of the leading edge vortex on the hindwing in a defined region around the wing's leading edge using DPIV (Fig. 8, white box), because it has been shown previously that leading edge vorticity may contribute significantly to total lift production (Ellington et al., 1996; Polhamus, 1971; van den Berg and Ellington, 1997). As a second step, we derived the local flow conditions, including the effective angle of attack and the velocities of the wing relative to the surrounding oil, from DPIV analysis in a region between the free stream and the lower surface of the wing (Fig. 7, white box). The local flow conditions are of great importance since they determine the magnitude of lift production due to circulation bound to the wing during wing translation and circulation produced by the LEV, because total lift is proportional to the product of local flow velocity and circulation (Ellington, 1984b).

When the forewing leads by a quarter stroke cycle, the strength of the hindwing LEV is attenuated by 23% compared to a single wing flapping free of forewing wake interference, as measured at the beginning of the stroke cycle (Figs 4B, 7A,B, ^*1). The difference in vortex strength is even higher (31%) later in the stroke cycle (Figs 4B, 7D,E, 8, ^*2) after the wing segment has travelled approximately 1.2 chord widths after stroke reversal and the LEV has gained size. The smaller leading edge vorticity in the hindwing, when the forewing leads, coincides with the attenuation of lift in the stroke cycle, as shown in Fig. 4B. In contrast, the hindwing's LEV develops differently when the hindwing leads by a quarter stroke cycle. At both the early (15% of stroke cycle) and the late time (35% of stroke cycle) within each half stroke the hindwing's LEV achieves a strength similar to that of a flapping wing free of wake interference (Fig. 7A,C,D,F). This result suggests that, at least when the hindwing leads the stroke, the local flow conditions must have changed in order to explain both the lift attenuation at the beginning of the stroke (15% of stroke cycle) and the increases in instantaneous lift forces above the lift that can be achieved by single wing flapping at 35% of the stroke cycle (Fig. 4B).

To assess the effect of local flow conditions in order to explain the changes in lift production of the hindwing, we calculated the mean orientation of the flow towards the wing (effective angle of attack) and its mean velocities from the combined orientation and velocities of the downwash, and the motion and geometric angle of the wing, similar to a procedure suggested previously (Birch and Dickinson, 2001). At 15% of hindwing stroke cycle, the fluid vector reconstruction reveals that the effective angle of attack _eff and flow velocities for the hindwing flapping in the forewing downwash, are favorable for the forewing leading phase (_eff=12.6°; Fig. 9). In contrast, when the hindwing leads, the effective angle of attack decreases close to zero (_eff=1.6°; Fig. 9). Local flow velocities remain approximately constant in all three cases (0.25-0.28 m s^-1; Fig. 9). Later in the hindwing stroke cycle (35% of stroke cycle) the local fluid vector is only favorable for the hindwing leading case and not for the forewing leading phase, which matches the respective enhancement and attenuation of lift production in our direct force measurements.

View larger version (25K): [in this window] [in a new window]   Fig. 9. Schematic reconstruction of vortices and local flow conditions at two different kinematic phase relationships between fore- and hindwing and at two different times within the stroke cycle. Hindwing lift depends on LEV strength and the velocity and angle of the oncoming fluid (local flow). Local flow conditions (black vector) on the wing segment (grey oval) are calculated from the velocity and angle of the combined fore-hindwing downwash determined in a region below the wing's surface in a single PIV image plane (green vector, see white box in Fig. 7), and the translational velocity of the hindwing section (grey vector). Blue arrows, lift attenuation; red arrow (F), lift enhancement of the hindwing compared to a wing flapping free of forewing downwash. Vortical circulation (cm2 s-1) in the hindwing's leading edge vortex is shown in square brackets close to the LEV icon. The different strengths of starting and leading edge vorticies are indicated approximately by the size of the plotted `vortex' icons. Effective angle of attack for the hindwing section (degrees, left value) and local flow velocity (m s-1, right value) are shown respectively in parentheses under the vector diagram. (A-F) The flow characteristics for a flapping hindwing free from forewing downwash (single wing flapping) at (A) 15% and (B) 35% of stroke cycle; when the forewing (upper wing) leads wing motion by a quarter stroke cycle (C) at 15% and (D) 35% of stroke cycle; when the hindwing (lower wing) leads by a quarter stroke cycle (E) at 15% and (F) 35% of stroke cycle. A detailed description of vortex development and local flow is given in the text. In all diagrams, the motion of the hindwing (lower wing) is from left to right. White arrows indicate the direction of motion of the forewing. T, stroke cycle.

	Discussion

TOP Summary Introduction Materials and methods Results Discussion References

 
The experiments using the physical model of a dragonfly have provided several new insights into how functionally four-winged insects might control lift production by varying the kinematic phase relationship between the fore and hindwing. Our results on a generic dragonfly stroke pattern show a marked modulation in hindwing lift and a small modulation in forewing lift on varying the phase-shift relationship between the fore- and hindwing stroke cycles (Fig. 3B-D). The maximum hindwing lift force is produced when the hindwing leads by around a quarter stroke cycle, corresponding to the phase-shift commonly used by locusts and dragonflies in climbing and forward flight (Alexander, 1984; Azuma and Watanabe, 1988; Baker and Cooter, 1979; Wakeling and Ellington, 1997; Wang et al., 2003; Weis-Fogh, 1956; Wortmann and Zarnack, 1993). Moreover, we have shown that the phase modulation effect on hindwing lift coincides with changes in the structure of the wake produced by the two beating wings. These changes cover alteration in leading edge vorticity (LEV destruction) on the hindwing and marked changes in the effective angle of attack and the magnitude of local flow velocities (Figs 7, 8, 9).

Wake structure in physical dragonfly models
The force measurements in our dragonfly model show that in a horizontal stroke, both half strokes contribute to aerodynamic lift production (Fig. 4). The major flow structures we visualized in the wake are thus similar to the two major vortical structures found in other physical insect models, mimicking a 3D complete stroke cycle in the horizontal: a large starting vortex shed at the beginning of each half stroke and a leading edge vortex during wing translation (Figs 5 and 6; Birch and Dickinson, 2001; Dickinson et al., 1999; Ellington et al., 1996). Due to the complex flow pattern, we could not clearly identify stop vortices at the end of each half stroke. In contrast, Saharon and Luttges (1988) described eight vortices that are shed into the wake of flapping dragonfly model wings: four vortices by each wing throughout the stroke cycle. The authors found that each simple element of wing motion, such as the transition from pitching to plunging motion, initiated its own vortex structure. Similar patterns are described for vortex shedding patterns in a 2D model wing (Savage et al., 1979). Savage et al. found that a LEV (first vortex) is initiated during wing translation, which is common in most insect model wings moving at high angle of attack and similar to the present study (Birch and Dickinson, 2001; Ellington et al., 1996). During wing rotation (supination) for the subsequent half stroke, a second vortex is shed from the trailing wing edge in conjunction with trailing edge vorticity (third vortex) left in the wake in order to satisfy the Kutta condition when the wing starts to translate (Savage et al., 1979). In most cases, these vortex structures are displaced in the 3D model in the horizontal direction or move downstream when reduced frequency (based on wing beat/plunging cycle) is increasing from 0.18 to 5.0 (Saharon and Luttges, 1988). In many instances, however, the changes in vortex travel velocity were small, suggesting that there might be only minor alteration in overall wake pattern when the animal is changing forward speed (or reduced frequency; Saharon and Luttges, 1988