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First published online December 28, 2007
Journal of Experimental Biology 211, 224-233 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.007575
Review, Biomechanics of Flight |
When wings touch wakes: understanding locomotor force control by wake–wing interference in insect wings
Biofuture Research Group, Institute of Neurobiology, University of Ulm, 89069 Ulm, Germany
e-mail: fritz.lehmann{at}uni-ulm.de
Accepted 21 May 2007
Summary
Understanding the fluid dynamics of force control in flying insects requires the exploration of how oscillating wings interact with the surrounding fluid. The production of vorticity and the shedding of vortical structures within the stroke cycle thus depend on two factors: the temporal structure of the flow induced by the wing's own instantaneous motion and the flow components resulting from both the force production in previous wing strokes and the motion of other wings flapping in close proximity. These wake–wing interactions may change on a stroke-by-stroke basis, confronting the neuro-muscular system of the animal with a complex problem for force control. In a single oscillating wing, the flow induced by the preceding half stroke may lower the wing's effective angle of attack but permits the recycling of kinetic energy from the wake via the wake capture mechanism. In two-winged insects, the acceleration fields produced by each wing may strongly interact via the clap-and-fling mechanism during the dorsal stroke reversal. Four-winged insects must cope with the fact that the flow over their hindwings is affected by the presence of the forewings. In these animals, a phase-shift between the stroke cycles of fore- and hindwing modulates aerodynamic performance of the hindwing via leading edge vortex destruction and changes in local flow condition including wake capture. Moreover, robotic wings demonstrate that phase-lag during peak performance and the strength of force modulation depend on the vertical spacing between the two stroke planes and the size ratio between fore- and hindwing. This study broadly summarizes the most prominent mechanisms of wake–wing and wing–wing interactions found in flapping insect wings and evaluates the consequences of these processes for the control of locomotor forces in the behaving animal.
Key words: wing–wing interaction, wake capture, clap-and-fling, LEV destruction, phase-shifted stroking, dragonfly, fruit fly, Drosophila
Introduction
The extraordinary evolutionary success of flying insects is largely due to
their ability to control locomotor behavior precisely in response to sensory
stimuli. Numerous studies have emphasized the complexity of the feedback
cascade that allows insects to convert sensory information, coming from the
compound eyes, the gyroscopic halteres or the wing's campaniform sensilla,
into locomotor activity (e.g. Dickinson
and Palka, 1987
; Egelhaaf and
Borst, 1993; Kern et al.,
2006; Nalbach,
1994; Sherman and Dickinson,
2004; Taylor,
2001). Behavioral performance may be limited at each step of this
cascade, including the fluid dynamic processes with which flapping insect
wings produce aerodynamic lift and drag. Force production and flight control
in insects become most complex when fluid acceleration fields interfere with
the flapping wings (Birch and Dickinson,
2003). Consequently, in a freely flying animal, the production of
vorticity and shedding of vortical structures in each stroke cycle depend on
several factors, such as (i) the instantaneous wake structure produced by the
wing's own motion, (ii) wake components produced in a preceding half stroke or
preceding stroke cycles, (iii) flow components resulting from force generation
of wings flapping in close distance, (iv) changes in fluid velocity at the
wings due to the animal's body motion along and around the three body axes
and, finally, (v) external disturbances in the surrounding air. Taken
together, these components determine the instantaneous flow regime around a
flapping insect wing, and thus lift and drag production. To answer the
question of how the neuro-muscular system of flying insects copes with
changing fluid environments is intriguing and requires a deeper understanding
of the fluid dynamic processes occurring in flapping insect wings (for
reviews, see Lehmann, 2004;
Sane, 2003).
In the past, the majority of studies on insect flight aerodynamics focused
on the performance of single flapping wings and widely ignored the
significance of wake patterns (wake history) produced by previous stroke
cycles (e.g. Ellington, 1984).
Fluid dynamic effects due to wake history, however, may be quite distinct, as
demonstrated in a robotic Drosophila wing mimicking hovering
conditions (Birch and Dickinson,
2001). In their study, Birch and Dickinson showed that the first
stroke in a fruit fly model wing produces approximately 9% more lift than the
subsequent strokes. The initial acceleration of the induced flow is
responsible for this effect, because under the given experimental conditions
induced flow may attenuate the wing's effective angle of attack by more than
10° (approximately 40° during first stroke cycle, 28–32° in
subsequent cycles). The same kinematic pattern may also produce different
amounts of lift due to the interaction of wakes produced by two flapping
wings. The clap-and-fling mechanism that produces wake interferences between
an ipsi- and contralateral wing and kinematic phase lag effects manipulating
the flow regime between ipsilateral fore- and hindwings, are presumably the
most prominent examples of wake–wing interactions in flapping flight
(Ellington, 1975;
Maybury and Lehmann, 2004;
Saharon and Luttges, 1989;
Weis-Fogh, 1973).
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;
Srygley and Thomas, 2002).
Wake capture at the beginning of the half stroke benefits from an inter-vortex
stream produced by the leading and trailing edge vortex system that
accelerates the fluid during wing rotation at the end of each half stroke
(Birch and Dickinson, 2003)
(Fig. 1A–D). However,
this interpretation of wake capture force generation has been questioned by
computational fluid dynamics (CFD) modeling of flapping insect wings,
suggesting that the rotational-independent lift peak is due to a reaction of
accelerating an added mass of fluid and does not rely on a momentum transfer
of the fluid (Sun and Tang,
2002). In the past the effect of inertial reaction forces during
the stroke reversals has been well recognized and discussed as a cause for
wing rotation, twisting and bending
(Daniel and Combes, 2002;
Ennos, 1988a). For example, in
two species of flies, the blowfly Calliphora vicina and the hoverfly
Eristalis tenax, the high stroke frequency, ranging from 100 to 200
Hz, produces inertial forces sufficiently high to elicit passive wing pitch
(angle of attack) changes when the wing reverses its direction of motion
(Ennos, 1988b). Apart from
this controversial view on the wake capture mechanism, it remains unclear how
exactly the benefit of wake capture changes during fast forward or maneuvering
flight of an insect when the wings experience additional fluid components
produced by the animal's own body motion. This study focuses on the most recent findings related to locomotor force control via wake–wing interaction in flapping insect wings and gives a broad summary of the fluid dynamic mechanisms underlying bilateral and ipsilateral wing–wing interference during hovering flight conditions. Novel data on the potential significance of (i) stroke plane distance between fore- and hindwing and (ii) wing size, for fore- and hindwing lift production in an electromechanical dragonfly model during phase-shifted stroking are also presented. In a first set of experiments, the distance of both stroke planes was varied between 1.25 and 5 mean chord width of the hindwing in order to examine how changes in kinematic phase between the fore- and hindwing stroke cycles alter lift production. In a second set of experiments, the ratio of fore- to hindwing length was modified to explore (i) how these changes affect the phase between the two wings' beat cycles in which the wings generate maximum lift, and (ii) how the magnitude of peak-to-peak lift modulation alters with changing kinematic phase lag.
Dorsal wake–wing interference: the clap-and-fling mechanism
Wing kinematics at dorsal stroke reversal
The dorsal clap-and-fling mechanism in two- and four-winged insects was
first described by Weis-Fogh (Weis-Fogh,
1973) and since then has been found in many insects with a vast
variety of flight modes. It has been subjected to several detailed
experimental evaluations. Quite recently, new approaches in experimental
design have provided several new insights, and numerical modeling (CFD) has
contributed much to our understanding of this particular kinematic
maneuver.
The clap-and-fling is a close apposition of the ipsi- and contralateral
wing at dorsal stroke reversal preceding pronation. During the clap, the
insect brings the leading edges of the two wings together, then pronates them
until the `v-shaped' gap vanishes and the wings are parallel in close
apposition. During the fling, the wings pronate about their trailing edges,
creating a growing gap as the leading edge pulls apart
(Fig. 1E–H). In
Weis-Fog's classical reconstruction, the axis of wing rotation changes from
rotation around the leading edge (upstroke) to a rotation around the trailing
wing edge (downstroke) during pronation. This clap-and-fling kinematic pattern
has been used for several experimental and numerical approaches (see below).
Recent reconstructions of wing motion in tethered flight, however, have shown
that during fling phase, the fruit fly Drosophila virilis apparently
rotates its wings around the leading rather than the trailing wing edge. In
rigid wings the latter maneuver would require that the wings be quickly pulled
apart during rotation, whereas in the elastic wing of Drosophila,
chordwise flexion permits the wings to rotate large angles of attack even at
low gap angles (F.-O.L., manuscript in preparation). The latter kinematic
pattern has previously been described as the `peel' motion and found in
several insects such as flies (Götz,
1987), butterflies (Brodsky,
1991), bush cricket
(Brackenbury, 1990) and locust
(Cooter and Baker, 1977).
Preliminary two-dimensional digital particle image velocimetry (2D-DPIV) data
on the wake structure of flying fruit flies during fling motion imply some
fundamental fluid dynamic differences between rigid and elastic wings,
particularly when considering the sign of circulation around the wings during
pronation (F.-O.L., manuscript in preparation).
The fluid dynamic mechanisms of bilateral wake–wing interaction
The fling phase preceding the downstroke is thought to enhance circulation
due to fluid inhalation in the cleft formed by the moving wings, causing
strong vortex generation at the leading edge while the development of trailing
edge vorticity is inhibited by trailing edge wing contact. Several studies
have estimated the benefit of the fling part of wing motion, using either
numerical models or a combined approach incorporating measurements of flow
velocities and forces in robotic wings (e.g.
Bennett, 1977;
Edwards and Cheng, 1982;
Ellington, 1975;
Lighthill, 1973;
Sunada et al., 1993). More
recently, numerical simulations have been performed on the entire
clap-and-fling sequence in both three dimensions (3D)
(Sun and Yu, 2003) and two
dimensions (2D) across a wide range of Reynolds numbers
(Miller and Peskin, 2004). In
addition, a dynamically scaled mechanical model of Drosophila
melanogaster demonstrated that alteration in force production due to
clap-and-fling wing motion is not limited to the dorsal stroke reversal but
may also enhance lift approximately at mid downstroke and the beginning of the
upstroke (Lehmann et al.,
2005). Thus, clap-and-fling wing motion should be considered as a
mechanism that may distort the spatio-temporal structure of the wake during
up- and downstroke rather than affecting lift and drag production only in the
brief moment during dorsal stroke reversal.
The strength of wake–wing interaction during clap-and-fling depends
on several factors, including the thickness of the wing's boundary layer, as
well as strength and direction of the induced flow during stroke reversal
(Lighthill, 1973;
Maxworthy, 1979). Experiments
modifying the distance between the two rotating wings show that lift
enhancement requires an angular separation between the two wings of no more
than 10–12° (Reynolds number=134)
(Lehmann et al., 2005). This
value corresponds to a distance between the two rotational wing axes of
approximately one mean wing chord of the Drosophila model wing. The
relative benefit of clap-and-fling lift enhancement strongly depends on stroke
kinematics. For example, insects that flap their wings with small stroke
amplitudes should benefit relatively more from clap-and-fling force
augmentation than insects that produce elevated flight forces by flapping
their wings with stroke amplitudes close to the mechanical limit of the
thoracic exoskeleton. In Drosophila model wings (160° stroke
amplitude), maximum lift augmentation amounts to approximately 17% of the mean
lift produced by a single wing flapping free from downwash of an image
wing.
The time course of lift enhancement due to clap-and-fling is quite complex
and consists of at least six distinct positive and negative force peaks. Two
positive major force peaks are associated with wing motion during fling and a
major negative peak occurs during the clap phase, in which lift and drag are
transiently attenuated in the presence of an image wing. 2D-DPIV analysis has
revealed that at this initial moment of dorsal wing–wing interaction,
the local flow velocity at the wing's trailing edge is reduced by
approximately 20%, compared to a single wing
(Lehmann et al., 2005).
Consequently, as the wings start the clap, the presence of an image wing
diminishes the ability of each wing to accelerate fluid and thus generate
aerodynamic forces. In other words, the presence of a contralateral image wing
creates circulation of opposite sense very close to the ipsilateral wing that
diminishes the ability of the wings to maintain circulation. Interestingly,
this result is not confirmed by Sun's numerical model of the clap-and-fling
(Sun and Yu, 2003). Their
simulation suggests that, rather than an initial decrement, the wings in the
two-wing case generate consistently higher force during wing motion preceding
the clap than in the one-wing case.
During fling, force measurements yield two temporally transient positive
peaks in lift and drag enhancement: (i) a large peak immediately after the
wings start fling motion (0.08 of the stroke cycle), which accounts for most
of the benefit in lift, and (ii) a second, smaller peak (0.20 of the stroke
cycle), which enhances force at the end of the fling when the wings start to
move apart. The DPIV images in Fig.
2B–E show the two leading edge vortices (LEV) in the opening
cleft right before lift production peaks at early fling (0.05 of stroke
cycle). Although at this time, circulation in the LEVs is not yet
significantly larger than in a single wing
(Fig. 2, white box and data
traces; red, single wing; black, two wings), the translational velocity of the
inflow into the opening cleft is significantly enhanced when flapping the
ipsi- and contralateral wing (Fig.
2, length of black vectors). A possible explanation for the minor
change in circulation of the LEV at this early state of the fling is fluid
viscosity that acts against vortex induction. At low gap angles, circulation
is significantly smaller than predicted by inviscid 2D numerical models,
whereas circulation nearly matches the prediction at the late fling phase
(Lighthill, 1973;
Lehmann et al., 2005).
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Moreover, it has been suggested that the biphasic character of fling-induced lift enhancement results from a transient inhibition of lift production due to the development of trailing edge vortices (Fig. 2C–E), rather than from distinct yet unknown fluid dynamic mechanisms. In contrast to Weis-Fogh's original model, wing separation in our robotic wing model allowed trailing edge vortices to form during the fling phase. The presence of trailing edge vorticity, however, may inhibit the development of the LEV because fluid that is accelerated in the cleft from the rear potentially interferes with LEV induction (Fig. 1H, Fig. 2C–E). In elastic wings such as in Drosophila, the `peel' offers a solution to that problem, because the tight contact between the trailing wing edges functions as a barrier to prevent fluid from being sucked into the opening cleft around the trailing edges.
Wake–wing interference between ipsilateral wings: dragonfly aerodynamics
Kinematic phase relationship
The third type of wake–wing interaction so far investigated is found
in functionally four-winged insects such as dragon- and damselflies
(Maybury and Lehmann, 2004;
Reavis and Luttges, 1988;
Saharon and Luttges, 1989;
Somps and Luttges, 1985;
Wang et al., 2003). The
neuromuscular system allows these animals to actively change many aspects of
wing motion in a single wing, such as the angle of attack, stroke plane, and
more conventional parameters such as stroke amplitude and stroke frequency.
Unlike four-winged insects with indirect flight musculature such as
butterflies, bees, wasps and ants, however, dragon- and damselflies may
actively control the timing between fore- and hindwing stroke cycles [the
kinematic phase relationship (Norberg,
1975; Wakeling,
1993)]. In this respect, dragon- and damselflies even differ from
other more primitive orders of functionally four-winged insects, such as
locusts, in which phase relationship is highly consistent during flight with
only little variation during steering maneuvers
(Wortmann and Zarnack,
1993).
In general, dragonflies vary their phase relationship between ipsilateral
fore- and hindwings with different behaviors. Behavioral studies on freely and
tethered flying animals have reported three major categories of phase
relationships: parallel stroking, counterstroking and phase-shifted stroking.
During (i) straight forward and upward flight, (ii) escape behavior in which
the animal produces peak lift of approximately 20 times its body weight and
(iii) maneuvering flight, dragonflies typically use a conventional flight mode
(Reavis and Luttges, 1988;
Somps and Luttges, 1985;
Wakeling and Ellington, 1997;
Wang et al., 2003). A highly
consistent characteristic for this flight mode is a 54–100° phase
shift, during which the hindwing leads forewing motion. Larger phase
differences of up to 180° (counterstroking) have been found in hovering
dragonflies and maneuvering animals flying freely in a wind tunnel
(Alexander, 1986).
Besides the changes in phase relationship between the two ipsilateral
wings, dragonflies may employ two different gross types of wing motion:
vertical and horizontal wing stroking. During vertical stroking, the animal's
body is orientated approximately horizontally and both wing pairs beat in a
vertical plane with high angle of attack during the downstroke and small
angles of attack during the upstroke. During horizontal stroking, in contrast,
the body is tilted upwards, as found in many other hovering insects and the
wings beat approximately in a horizontal stroke plane
(Fig. 1I)
(Wakeling and Ellington,
1997). In this flight mode, the wing hinges of the fore- and
hindwing are aligned approximately vertically and the wake produced by the
forewings passes over the beating hindwings. Azuma et al. predicted that under
those conditions, lift production of the hindwing should critically depend on
the complex wake pattern produced by the beating wings, and thus on the fluid
dynamic effects occurring during wing–wake interactions
(Azuma et al., 1985). During
maneuvering flight those complex interactions change, especially with
transient changes in kinematic phase relationship, in which the relative
timing of vortex shedding and fluid acceleration produced by the forewing
changes with respect to hindwing aerodynamics.
Previous assumptions on wake–wing interaction in tandem wings
In previous studies on the aerodynamics of flying dragonflies
(Alexander, 1986;
Rüppell, 1989), it was
suggested that in-phase, or parallel stroking, might produce higher
aerodynamic forces than phase-shifted stroking or counterstroking. This
conclusion was drawn from kinematic reconstructions of wing motion during the
energetically most demanding flight modes such as hovering, take-off and
load-lifting flight. Under these conditions, peak lift may increase by up to
approximately 2.3–6.3 the times body weight when the animal decreases
the phase angle between ipsilateral fore- and hindwing. However, the latter
result apparently runs counter to previous numerical modelling
(Lan, 1979). Lan's study
predicts that the hindwing extracts maximum energy from the forewing downwash
when the hindwing leads wing motion by a quarter stroke cycle. According to
bi-plane theory, total lift production in tandem wings depends on the
proximity and strength of forewing downwash that interferes with the hindwing
(Milne-Thomson, 1966). Under
such conditions, the hindwing must cope with a potential reduction in
effective angle of attack and the interference between shed vorticity such as
the forewing's start vortex and the hindwing's LEV. Since wake–wing
interaction depends on forewing wake structure and the timing with which the
hindwing interacts with the forewing wake, two long and narrow wings working
independently should have higher lift-to-drag coefficients than a combined
wing with the same area but different aspect ratio. In contrast to his later
experimental findings, Alexander
(Alexander, 1984) thus
predicted that tandem wings flapping in-phase should produce less lift,
because the two wings are always closer together than two wings flapping
out-of-phase.
The impact of phase relationship on lift production in tandem wings
Dragonfly kinematics are very diverse, and various authors have modeled
different types of dragonfly aerodynamics, employing both numerical and
physical models (Kliss et al.,
1989; Saharon and Luttges,
1988; Wang et al.,
2004). More recently, Maybury and Lehmann
(Maybury and Lehmann, 2004)
used a fully computer-controlled robotic wing (electromechanical flapper) and
performed direct force measurements on the wing hinge, including measurements
on the wake structure, using 2D-DPIV, Fig.
3A,D). While varying the phase relationship between the two
horizontally beating wings, the authors showed how the performance of the
fore- and hindwing varies in response to kinematic phase-shifting
(Fig. 4A,B). The most
unexpected result in this research was that the hindwing regains aerodynamic
performance close to that of a wing without forewing interference, when the
motion of the hindwing leads the forewing by approximately a quarter stroke
cycle. When the forewing leads wing motion by a quarter stroke cycle, hindwing
lift production decreases by approximately 40% compared to a single wing. The
approximately twofold change in aerodynamic performance of the hindwing
follows a sinusoidal curve when phase relationship linearly changes from
–50% (forewing leads wing motion) to 50% stroke cycle (hindwing leads
wing motion, counterstroking, Fig.
4B). This relationship implies that small changes in phase lag
around –25% and 25% stroke cycle only produce moderate changes in
hindwing lift production, whereas in parallel stroking, the same phase
alterations produce considerable larger modulations in hindwing lift.
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The modulation effects in aerodynamic performance due to kinematic phase
relationship are not restricted to the hindwing but also produce considerable
changes in lift production of the forewing. Although those changes are smaller
and only occur in phase-shift cases where fore- and hindwings were moving
close to each other (blue line, Fig.
4A), combined lift of both wings varies accordingly. It seems
likely that some of the modulations in forewing lift are caused by the wall
effect due to the physical distortion of the forewing downwash by the
hindwing. Previous work predicted maximum increase in forewing lift when the
forewing downwash is directed completely onto the dorsal surface of the
hindwing throughout the stroke cycle
(Rayner, 1991). At a vertical
distance of 1.25 wing chord between both stroke planes, this situation occurs
when the forewing leads wing motion by approximately 2.5–5%, whereas
forewing lift is significantly diminished when the hindwing leads wing motion
(Fig. 4A).
Vortex travel time
Although the above findings may enable functionally four-winged insects to
control ipsilateral flight force without further changes in wing beat
kinematics, phase lag at peak performance should critically depend on (i) the
animal's flight speed and thus reduced frequency, (ii) the vertical distance
between the two wing hinges and (iii) shape and size of the fore- and
hindwing. While wing size determines downwash strength and spatial shape of
the wake (cf. below), flight speed and vertical wing separation affect travel
time of vortical structures shed from the forewing, until they interfere with
hindwing motion. To understand the fluid dynamic consequences of vertical wing
spacing in more detail, we reconstructed the vertical position of start
vortices shed by the two wings from our DPIV data
(Fig. 3E,F) and calculated the
travel velocity from vortex positions in 12 subsequent, temporally equally
spaced images (0.08 s spacing; Fig.
3H,I). The analysis reveals that the travel velocity of the
hindwing start vortices reaches peak values of approximately 25 cm
s–1 and appears to be broadly independent on the phase lag
between fore- and hindwing stroke cycle. The forewing's start vortices, in
contrast, transiently achieve much higher travel velocities of up to 60 cm
s–1, close to the hindwing stroke plane. A most likely
explanation of this phenomenon is that the two wings produce an elevated
pressure gradient in the space between both stroke planes. Thus, a vortex
passing through that space might experience higher accelerations compared to a
vortex shed by a single flapping wing. It must remain open, however, whether
the pronounced acceleration of the forewing start vortices is limited to
flapping conditions in which the hindwing leads wing motion by 25% stroke
cycle (Fig. 3I), because it was
almost impossible to detect the forewing's start vortices in the hindwing wake
when the forewing leads wing motion by 25% stroke cycle
(Fig. 3H).
The consequences of increasing the vertical spacing between the two wing hinges of the dragonfly model are twofold. First, an increasing vertical spacing should attenuate the amplitude of modulation in fore- and hindwing lift, because fluid viscosity smoothes out temporal fluctuations in the wake. The required distance between fore- and hindwing to avoid lift fluctuations in response to phase-shifting depends on both the strength of induced flow and fluid viscosity, and thus on Reynolds number. At an intermediate Reynolds number of our model wings (Re=105–125), the data show that force modulation of the hindwing ceases when both wing hinges are separated by at least five mean chord widths, i.e. approximately 20 cm. Since wall effects on the forewing are absent at this spacing, the forewing, in this case, produces lift similar to the performance of a single wing (Fig. 4A, red). However, the hindwing is still affected by the uniform forewing downwash and thus generates approximately 15% less lift than a single wing flapping free of forewing downwash (Fig. 4B, red). Second, the quarter-stroke cycle phase lag (25%), at which the hindwing achieves maximum mean lift when stroke planes are closest, should decrease with increasing distance between the stroke planes because of an increase in vortex travel time. This relationship may be demonstrated by plotting kinematic phase lag at peak lift production as a function of the vertical distance between both wing hinges (Fig. 4C). As expected from the significance of forewing start vortices for wake–wing interaction of the hindwing, the data show that kinematic phase lag for maximum hindwing lift (Fig. 4C, red) linearly decreases from 25% to –50% stroke cycle with increasing wing separation (linear regression fit, y=55.3–26.1x, N=6, R2=0.99, P<0.0001), whereas phase lag for forewing lift (Fig. 4C, black) tends to increase with increasing distance (linear regression fit, P=0.09). Within the limits of our experimental approach, this finding eventually means that in-phase, or parallel, stroking produces maximum hindwing lift only when the two stroke planes are separated by approximately two mean wing chords – a value that is well above the value typically found in dragon- and damselflies.
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). The measurements show that the amplitude of modulation in hindwing lift strongly depends on the size ratio between fore- and hindwing. At maximum hindwing length (aspect ratio=3.1), modulation in hindwing lift decreases with decreasing forewing length while maximum lift at 25% phase-shift remains approximately unchanged (Fig. 5A). In contrast, at maximum forewing length (aspect ratio=3.1), maximum hindwing lift decreases with decreasing hindwing length due to the decreasing wing area (Fig. 5D). Compared to the hindwing, the changes in peak-to-peak amplitude of modulation in forewing lift are less pronounced and limited to a small window of approximately ±15% phase lag (Fig. 5B). Consequently, the combined lift of both wings shows two characteristic positive peaks: a smaller peak during parallel stroking (0% phase lag) due to the wall effect on the forewing and a larger lift peak during phase-shifted stroking (25% phase lag) due to beneficial wake capture of the hindwing (Fig. 5C). Most notably, kinematic phase at mean peak lift slightly increases with increasing hindwing/forewing size ratio in the forewing (linear regression fit, y=–9.13+4.97x, N=16, R2=0.54, P=0.0013; Fig. 5E, black) and the hindwing (linear regression fit, y=15.1+6.66x, N=16, R2=0.46, P=0.004; Fig. 5E, red).
In contrast to the comparatively small changes in peak phase, the modulation of lift varies considerably at different wing size ratios (Fig. 5F). Although vertical distance between both wings was identical in all experiments (1.25 mean wing chord), the data expose a complex dependency of peak-to-peak modulation from size ratio that can be broadly summarized as follows: At length ratios of between 0.7 and 1.0, hindwing lift modulation (Fig. 5F, red) changes only little, whereas forewing modulation (Fig. 4F, black) tends to increase with increasing size ratio. At length ratios of between 1.0 and 1.5, in contrast, forewing lift modulation changes only little, but hindwing lift modulation sharply decreases with increasing wing length ratio. Thus, when insects change the phase lag between fore- and hindwing to modulate the total amount of generated lift, this modulation might be affected by the ratio of fore- and hindwing length. Consequently, in dragon- and damselflies with long fore- and short hindwings (length ratios 0.6–1.0) changes in phase lag mainly modulate how much lift is generated by the hindwings, while in insects with short fore- and long hindwings (length ratio 1.0–1.5), both wings might experience significant modulations of their mean lift.
Concluding remarks
Wing–wing and wake–wing interactions in flapping insect wings
permit flying animals to modulate their flight forces due to comparatively
complex fluid dynamic processes. Bilateral wing–wing interaction
(clap-and-fling), for example in Drosophila, requires only small
changes in dorsal wing stroke angle of no more than 12° in order to
modulate total lift of up to approximately 17%, compared to a single wing.
Changes in kinematic phase lag between ipsilateral fore- and hindwings might
enable dragonflies and other functionally four-winged insect to modulate lift
by a factor of two without further changes in stroke kinematics. In this
context, it has been suggested that wake–wing induced changes in
instantaneous lift and drag might also favor the control of moments around the
animal's roll, pitch and yaw body axes. Since the clap-and-fling in
Drosophila mainly causes lift at the dorsal stroke reversal, it
produces nose-down pitching moments that conveniently counterbalance nose-up
pitching moments due to an increase in ventral stroke amplitude
(Lehmann et al., 2005).
Although this mechanism might help an animal to stabilize its body posture
during flight, the situation is more complex because kinematic patterns that
produce similar fling-induced mean lift and drag augmentation may produce
different amounts of pitching moments
(Lehmann and Pick, 2007).
Moreover, even if we assume that lift and drag modulations due to
wing–wake interaction may be high enough to sufficiently serve the
insect as a tool to control its flight performance, it still remains an
unproven hypothesis whether the insect's neuromuscular system can control
these complex interactions to use them for flight control. An alternative
concept would thus be to consider wake–wing interactions simply as an
unavoidable effect that insects have to deal with during flight. In this case,
the contribution of wake–wing interactions to forces and moments renders
mute the issue of any possible irrelevance for insect flight control.
Eventually, even though robotic experiments would find some inherently
uncontrollable fluid dynamic interactions between two beating wings, then
those studies might teach us which kinematic patterns insects should avoid at
all costs, or have yet to exploit to make their flight behavior erratic.
Acknowledgments
I would like to thank Ursula Seifert for critically reading an early version of this manuscript. The presented work was funded by a German Federal Ministry for Education and Research (BMBF) grant Biofuture 0311885 and a German Science Foundation grant Le905/8-1.
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in the leading edge vortex
(LEV), measured in a region of interest (ROI, white box). LEV circulation when
flapping one and two wings are plotted in red and black, respectively. Gray
bars in the graphs indicate wing clap and time at which the DPIV analysis was
performed, respectively. White lines in panels indicate wing sections. The
leading edge of the dorsal wing surface is indicated by a white triangle. The
magnitude of vorticity is plotted in color code and arrows correspond to the
magnitude of the velocity vector at each point in the fluid, longer arrows
signify larger velocities. t=stroke cycle (0–1),
R=wing length. See Lehmann et al.
(Lehmann et al., 2005
s) between
fore- and hindwing stroke plane changes kinematic phase relationship between
both wings (
).
(C) Phase-shift between the stroke cycles of both wings during mean peak lift
changes with changing vertical distance between the two wing hinges. Black,
forewing; red, hindwing; aspect ratio of the wings=2.7; flapping frequency=666
mHz; wing rotation symmetrical, starting 10% prior to and ending 10% after
stroke reversal; Reynolds number=137;
