Download Smoke visualization of free-flying bumblebees indicates

Exp Fluids
DOI 10.1007/s00348-009-0631-8
RESEARCH ARTICLE
Smoke visualization of free-flying bumblebees indicates
independent leading-edge vortices on each wing pair
Richard James Bomphrey Æ Graham K. Taylor Æ
Adrian L. R. Thomas
Received: 2 June 2008 / Revised: 16 January 2009 / Accepted: 5 February 2009
Ó Springer-Verlag 2009
Abstract It has been known for a century that quasisteady attached flows are insufficient to explain aerodynamic force production in bumblebees and many other
insects. Most recent studies of the unsteady, separated-flow
aerodynamics of insect flight have used physical, analytical
or numerical modeling based upon simplified kinematic
data treating the wing as a flat plate. However, despite the
importance of validating such models against living subjects, few good data are available on what real insects
actually do aerodynamically in free flight. Here we apply
classical smoke line visualization techniques to analyze the
aerodynamic mechanisms of free-flying bumblebees hovering, maneuvering and flying slowly along a windtunnel
(advance ratio: -0.2 to 0.2). We find that bumblebees, in
common with most other insects, exploit a leading-edge
vortex. However, in contrast to most other insects studied
to date, bumblebees shed both tip and root vortices, with no
evidence for any flow structures linking left and right
wings or their near-wakes. These flow topologies will be
less efficient than those in which left and right wings are
aerodynamically linked and shed only tip vortices. While
these topologies might simply result from biological constraint, it is also possible that they might have been
Electronic supplementary material The online version of this
article (doi:10.1007/s00348-009-0631-8) contains supplementary
material, which is available to authorized users.
R. J. Bomphrey G. K. Taylor A. L. R. Thomas (&)
Department of Zoology, Oxford University, South Parks Road,
Oxford OX1 3PS, UK
e-mail: [email protected]
R. J. Bomphrey
e-mail: [email protected]
specifically evolved to enhance control by allowing left and
right wings to operate substantially independently.
1 Introduction
The urban myth that aerodynamicists have proven that
bumblebees cannot fly can be traced back to at least 1919,
when an engineer, Hoff (1919), used data from an entomologist, Demoll (1918), to suggest that animals flew using
the same attached flow aerodynamics as fixed-wing aircraft. Demoll (1919) responded, using Hoff’s equations
(Hoff 1919), to show that this could not be true because a
bee would require a lift coefficient over twice that of any
aircraft, once the speed of the beating wings was taken into
account. Studies with real and model insects have since
shown that they use unsteady separated flows to enhance
aerodynamic force production, so in its most general sense,
the ‘‘bumblebee paradox’’ may now be said to be solved
(Bomphrey et al. 2005; Dickinson et al. 1999; Ellington
et al. 1996; Maxworthy 1979; Srygley and Thomas 2002;
Thomas et al. 2004) (for reviews, see Bomphrey 2006;
Lehmann 2004; Sane 2003). Nevertheless, fundamental
details of these aerodynamic mechanisms remain unresolved, and it is those which we address here.
The separated flows used by insects usually involve the
formation of a coherent vortical structure over the suction
surface of the wing. This vortex is typically generated
through separation at the leading edge, and for this reason
is commonly known as a leading-edge vortex (LEV). One
fundamental question for aerodynamicists is whether and
how LEV topology varies with wing morphology, advance
ratio, and stage of stroke. This is significant, because the
topology of the LEV potentially governs such key issues as
123
Exp Fluids
aerodynamic efficiency, vortex stability and control
authority (Bomphrey 2006; Thomas et al. 2004). Considering only the primary vortex, the three most basic types of
flow topology are as follows, each differing fundamentally
in the flow at the wing root and midline of the animal: (1) a
single continuous LEV spanning from left wingtip to right
wingtip, with a free-slip focus over the thorax and a tip
vortex trailing from each wing (Fig. 1a); (2) separate LEVs
on the left and right wings, each arising from a focus at the
wing root with a tip vortex trailing from each wing
(Fig. 1b); (3) separate LEVs on the left and right wings,
each leading into their own root and tip vortex system
(Fig. 1c). Whereas the first category is likely to come
closest to developing an even downwash distribution,
thereby maximizing aerodynamic efficiency, the second
and third categories may offer greater potential for independent operation of the left and right wings, and hence
greater control authority. Stability of the LEV in each case
will depend upon the rate of transport of vorticity along the
vortex core, which might be promoted by the second category of LEV flow topology, resembling as it does the
stable LEV of a swept-wing aircraft. Much attention has
been paid to this transport of vorticity in real insects (e.g.
Bomphrey et al. 2005; Bomphrey et al. 2006a, b; Ellington
et al. 1996), scale models (e.g. Birch and Dickinson 2001;
Ellington et al. 1996) and computational simulations (Shyy
and Liu 2007), although with varying conclusions as to its
importance.
The first category of LEV flow topology (Fig. 1a) has
been observed in a number of real insects, including freeflying butterflies (Srygley and Thomas 2002) and dragonflies (Thomas et al. 2004). The second category of LEV
flow topology (Fig. 1b) has been observed in studies with
mechanical models (Birch and Dickinson 2001; Ellington
et al. 1996), and is likely also to occur in real insects—
especially in the early stages of LEV formation (Bomphrey
et al. 2005). The third category of LEV flow topology
(Fig. 1c) is suggested by flow visualizations on mechanical
models (Ramasamy and Leishman 2006). It is important to
emphasize that while these topologies are strict alternatives
at any given instant, there is no reason why insects should
not transition between these topologies when moving
between hovering and forward flight, or even at different
stages of the wing stroke. Indeed, we have observed the
LEV topology of free-flying insects to change from one to
stroke to the next (butterflies: Srygley and Thomas 2002)
and even within a stroke (dragonflies: Thomas et al. 2004).
This ability to rapidly change kinematics, and thereby to
control flow topology, may well be important in flight
control. In this paper, we describe the flow topologies
observed around bumblebees at different stages of the
stroke and in a range of different free-flight conditions. No
single image shows the entire wake topology at any stage
123
A
B
C
Fig. 1 Three hypotheses for separated flows over insect wings. a
Continuous bound LEV spanning from wing tip to wing tip with free
slip focus over the body. Wing tip vortices present but no root
vortices. b A conical spiral LEV structure on each wing with a focus
on each wing surface close to the root. Wing tip vortices present but
no root vortices, and attached flow over the body. c A separate LEV
on each wing with no foci on the surfaces of the wings: instead, the
LEV structures inflect into the wing tip and wing root vortices
of the stroke. Rather, multiple examples are presented for
each of the flow elements we describe and each are
grouped according to the stage of the wing stroke cycle in
which they are observed. With this technique, we can
conclude for different times throughout the cycle which is
the most likely gross topological structure from a number
of simple hypotheses using what are in fact quite coarse
features of the flow.
We choose to work with real bumblebees, rather than
models, because we are interested in understanding the
aerodynamics of real insects, and existing models are not
yet able to approach the complexity revealed in studies of
insect wingbeat kinematics (Walker et al. 2008, 2009).
Although modelling approaches have many advantages, the
paucity of high-resolution data on insect wing kinematics
has meant that modelling studies to date have necessarily
used highly simplified wing kinematics. In most cases, the
Exp Fluids
wing is treated as a rigid flat plate, which necessarily
neglects the effects of varying camber and twist. In contrast, our high-speed digital video of real bumblebees
shows that their wings not only twist but also fold through
up to 90° along the hinge-like row of hooks joining the
leading edge of the hindwings to the trailing edge of the
forewings. In consequence, rigid flat plate models cannot
necessarily be assumed to replicate the flows generated by
real insects.
Simplified models of insect aerodynamics ought ideally
to be tested against data from real insects. In recent years,
we have successfully applied the quantitative flow visualization technique of Digital Particle Image Velocimetry
(DPIV) to real insects (Bomphrey 2006; Bomphrey et al.
2005, 2006a, b). Nevertheless, we choose to use the qualitative technique of smoke visualization for this study,
because it is better suited to describing the flow topologies
of real, free-flying insects than DPIV or any available
quantitative visualization technique. In particular, smoke
visualization overcomes the practical difficulty of encouraging an insect to fly freely under the conditions of dim
ambient lighting, bright laser illumination and volume
seeding of the flow which DPIV requires. Moreover,
although DPIV can yield precise measurements of the flow
field, the difficulty of deriving forces from time-varying
velocity vector fields has meant that the technique has
rarely been used to its full quantitative potential in studying
animal locomotion (Dabiri 2005; Noca et al. 1999). In
consequence, we find that the classical technique of smoke
visualization is well suited to our purpose of describing the
flow topologies of insects. It is also worth noting in this
context that all of the fundamental fluid dynamics work on
the topology of 3D unsteady separated flows is based upon
qualitative visualization techniques (Délery 2001; Perry
and Chong 1987).
2 Experimental details
A colony of approximately 100 bumblebees Bombus terrestris was trained to forage from a nest in the laboratory to
a pollen and nectar source in the working section of a lowspeed wind tunnel operating at 1.2 ms-1. This pollen and
nectar source was removed during experiments to avoid
interfering with the flow. We used a high-resolution
smokewire technique (Thomas et al. 2004) to generate a
vertical plane of smoke lines with approximately 1 mm
spacing (one tenth of the wing length). The primary evidence provided in this paper is smoke visualizations, and
while we base our conclusions on the most comprehensive
set of flow visualizations of any animal to date, it must be
borne in mind that smoke visualization is an inherently
qualitative technique, with restricted spatial resolution.
Quantitative confirmation of the results presented here are
required, for example through 3D PIV with free-flying
insects. A limitation with smoke-in-air visualization is that
the residence time of the smoke particles can be longer
than the persistence of vorticity in the wake. This effect is
known to be problematic in the far wake, where smoke
streaks appear to be delineating vortices long after the
vorticity has diffused (Cimbala et al. 1988). Here, however,
we refer only to wake structures younger than one wing
beat period (1/180 s) at a Reynolds number of Re = 2,500
(based on mean wing tip speed).
Image sequences were recorded using high-speed digital
video cameras aligned normal to the smoke plane acquiring
data at either 1,000 fps (Hi-DCamII: NAC Image Technology, CA, USA; 1,280 9 512 px; field of view
width = 85 mm; 1 px = 0.066 mm; exposure time =
1/1,000 s) or 2,100 fps (Phantom v7: Vision Research Inc,
NJ, USA; 1,024 9 512 px; field of view width = 90 mm;
1 px = 0.088 mm; exposure time = 1/2,100 s).
In total, we were able to visualize 511 aerodynamically
informative wingbeats from 32 separate flight sequences, in
which the bees performed a variety of maneuvers. In 413 of
these wingbeats, the bees were travelling approximately
parallel to the long-axis of the tunnel, facing either into or
away from the flow. Of the remaining 98 wingbeats we
observed, 78 involved quartering flight in which the bee
moved diagonal to the freestream, and a further 20 in
which the bee translated sideways with respect to the
freestream, at airspeeds as high as 1.4 ms-1.
We were able to determine the bees’ airspeed (V) while
they were flying in the plane of the smoke by reference to
the convection of smoke structures in the freestream of
1.2 ms-1. The bees flew at a range of airspeeds from
-1.5 ms-1 (slow backwards flight) to 1.8 ms-1 (slow
forwards flight). Although we did not measure stroke
amplitude (U) directly, bumblebees typically operate with
a stroke amplitude of approximately 2 rad (Dudley and
Ellington 1990). The mean wingbeat frequency (f) across
flight sequences was 180 Hz (s.d. = 13.6 Hz, n = 32 flight
sequences), so the range of airspeeds we observed corresponds approximately to advance ratios in the range
-0.2 \ J \ 0.2, where J = V/2UfR (Ellington 1984) and
wing length (R) is approximately 10 mm. Flight with an
advance ratio |J| \ 0.1 is conventionally classed as hovering, so the range of flight conditions we observed
brackets hovering flight (Ellington 1984). These advance
ratios are easily interpretable for forwards and backwards
flight, but are of little use for the many other orientations
our free-flying bumblebees adopted. For example, how
should J be calculated when the bumblebee is holding
station in the wind tunnel, but oriented roughly perpendicular to the incident flow? In this case, forwards–
backwards velocity in the bee’s frame of reference is
123
Exp Fluids
Fig. 2 Bumblebee stroke sequence in forwards flight, with arrowed c
smokelines visualizing points of attachment (yellow) and reattachment (red). The smokeline which reattaches delineates the extent of a
LEV formed at supination. We begin the cycle with pronation
occurring immediately prior to (a): pronation occurs again in (f).
Overall image brightness and contrast have been increased to best
visualize the smokelines—this inevitably incurs a loss of detail on the
wing surface when it is angled such that the illumination reflects back
into the camera lens. Frames separated by 1 ms
0 ms-1, but the oncoming flow (from the side) is 1.2 ms-1
so a value of J = 0 would be misleading since it does not
tell the full story about the flow physics.
3 Results
The flow topology we observed changed through the
wingbeat, but did so in a rather stereotyped manner,
despite the range of flight conditions. Figure 2 presents a
typical wingbeat. We found no evidence of flow separation during the first part of the downstroke (Fig. 2a) in
any of our recorded sequences (further evidence in
Fig. 3). However, by the time of supination at the end of
the downstroke, the flow over the wings had separated to
form a LEV, and that LEV persisted well into the
upstroke. During supination (Fig. 2c), a point along the
forward line of attachment can clearly be seen on
the underside of the wing, where a smokeline impacts
the wing approximately halfway along its length (yellow
arrow). The smokeline directly above this one bifurcates:
one branch flows into the wake behind the bumblebee;
the other branch flows upstream and reattaches on the
wing upper surface (red arrow), delineating a LEV over
half a chord in diameter. At the beginning of the
upstroke (Fig. 2d), the lines of attachment (yellow arrow)
and reattachment (red arrow) remain on the underside
and upperside of the wings, respectively, indicating that
the circulation continues to be of the same sense following stroke reversal. However, by mid-upstroke
(Fig. 2e), the LEV has been shed. The timing of LEV
formation is presented for a further 10 wingbeats in
Fig. 3. The first frame capturing supination is highlighted
in yellow and this is always concurrent with the first
unambiguous appearance of the LEV (white arrows),
which indicates that the LEV is formed in the latter part
of the downstroke. As we now show, the topology of the
LEV matches that hypothesized in Fig. 1c at this stage in
the stroke cycle.
During a typical downstroke, trailing vortices are shed
from both the wing tips and the wing roots. This demonstrates that the LEV is not of the form hypothesized in
Fig. 1a or b. Figure 4 presents an example of quartering
flight, in which the attitude of the bee makes it possible to
123
Exp Fluids
Fig. 3 Three bumblebees in
quartering (green background),
sideways (red background) and
slow forwards (blue
background) flight, each
oriented so the formation of the
LEV (white arrow) is visualized
by smoke lines. Consecutive
frames read down the columns.
Individual wingbeats (different
columns) have been arranged so
that the frames showing the first
evidence for supination are
aligned horizontally (yellow
background). The LEV first
appears in these frames (i.e. at
stroke reversal) in each
wingbeat where it was
visualized. The third column is
the same wingbeat as shown
magnified in Fig. 2
123
Exp Fluids
Fig. 5 Bumblebee in sideways flight, showing smokelines becoming
entrained in counter-rotating wing tip vortices (red arrow) and wing
root vortices (yellow arrow). Frames separated by 1 ms
Fig. 4 Bumblebee in upwind quartering flight, showing wing tip
vortices (red arrows, a–f) and root vortices (yellow arrows, b–f),
which are shed into the wake as a vortex loop by the stage of the
upstroke shown in panel (e). Wake elements shed on preceding
wingbeats are arrowed in white (a). See main text for detailed
description. Frames separated by 1 ms. Overall image brightness and
contrast have been increased linearly
123
visualize the structure of the vortex system along the length
of the wing. A helical wing tip vortex can be seen in
Fig. 4a where the right wing tip has impinged on the
smokelines (red arrow); the white diagonal arrows point to
vortex loop elements shed by previous wingbeats. By
Fig. 4b the wing has passed further into the vertical
smokeline plane and a root vortex is now visible (yellow
arrow). Wing tip vortices (red arrows) and root vortices
(yellow arrows) continue to trail the wing one-third of the
way into the upstroke (Fig. 4c), confirming again that the
circulation is of the same sense as on the downstroke.
However, 1 ms later (Fig. 4d), the root and tip vortices are
shed as a vortex loop in the wake behind the bumblebee,
indicating a change in the circulation around the wing. The
shed vortex loop distorts and rotates as it convects backwards and downwards into the wake (Fig. 4d–f). Figure 5
is another example showing a bee generating a counterrotating pair of tip (red arrow) and root (yellow arrow)
vortices while oriented sideways to the freestream.
Although the orientation of the bees in Figs. 4 and 5 make
it especially easy to see the 3D structure of the vortex
system, root vortices were observed in the full range of
flight modes we recorded (Movie S1). The stereotyped
Exp Fluids
Fig. 6 Bumblebee in forward
flight with smoke incident near
the midline, showing the
aerodynamic independence of
contralateral wing pairs. See
text for commentary on arrowed
structure. Frames separated by
1 ms. Overall image brightness
and contrast have been
increased linearly. Advance
ratio, J \ 0.2
sequence of flow topologies we have described is therefore
robust to large-scale changes in the direction of flow relative to the insect’s body.
Further confirmation that the LEV is not of the form
hypothesized in Fig. 1a is provided by the observation that
smokelines running along the midline of the body pass
123
Exp Fluids
Fig. 7 Cartoon to show the qualitatively different flow topologies
hypothesized for insects on the basis of mechanical models (a),
observed in live insects (b, c2, d1, d2), and or both (c1). (a) Shows
the topology described by Maxworthy (1979) for his mechanical
flapper based on the clap and fling mechanism of the Chalcid wasp.
(b) Shows the topology found over the fore and hind wings of a
dragonfly for 75% of the wingbeats analysed in Thomas et al.
(2004)—they found several variations, but this was considered to be
the ‘normal’ counter-stroking topology and was not significantly
different from the in-phase wingbeat topology. (c1) and (c2) shows
two topologies described for hawkmoths by Ellington et al. (1996)
and Bomphrey et al. (2005), the latter suggesting that (c1) was a
transient state and (c2) was the topology toward the end of the
downstroke once the flow over the thorax had separated too. The
bumblebee flow pattern presented in (d1—early downstroke) and
(d2—late downstroke) represents a novel topology with left and right
wings acting independently and a LEV forming at supination (d2).
The LEV structures are therefore clearly variable and can change
throughout the course of a single wing stroke in hawkmoths,
dragonflies, and bumblebees. Adapted from Bomphrey et al. 2005
smoothly into the wake, rising in the upwash between the
root vortices without becoming entrained by any coherent
transverse vortex structure. This is the case in Fig. 6,
which shows a bee flying upwind with the smoke incident
near the midline. In Fig. 6a the wings are parallel with one
another at the top of the upstroke. The green arrow
highlights a pair of smokelines passing to the far side of
the right wing pair, which is the brighter of the visible
wings; the blue arrow shows a second pair of smokelines
passing nearside of the body. This distortion in the vertical
alignment of the smoke plane is due to flow induced by
the previous wingbeat. In Fig. 6b the right wing pair cuts
the upper pair of smokelines (white arrow), which quickly
roll up into a well-defined root vortex (Fig. 6c–d, yellow
arrow). Crucially, the lower smokeline pair (Fig. 6d, blue
arrows) passing nearside close to the tip of the abdomen remains relatively unaffected as it passes the root
vortex. In Fig. 6e the same pair of smokelines rises in the
upwash (red arrow) between the pair of contralateral
vortex loops. Only when they are several chord lengths
behind the wings do these same smokelines (red arrows)
become visibly disrupted by the root vortices (Fig. 6g).
Smokelines passing along the midline of the body are
therefore accelerated upwards slightly at the end of the
downstroke under the influence of the pair of vortex loops
shed by the left and right wings, but in all other respects
they pass unperturbed into the wake.
123
4 Conclusions
The use of a LEV has been observed in free-flying dragonflies (Thomas et al. 2004) and butterflies (Srygley and
Thomas 2002), and also in tethered hawkmoths (Bomphrey
et al. 2005; Ellington et al. 1996). It has been inferred in
free-flying swifts (Videler et al. 2004) and hummingbirds
(Warrick et al. 2005), and has been suggested by analogy
with mechanical flappers of Chalcid wasps (Maxworthy
1979) and fruit flies (Birch and Dickinson 2001). A catalogue of the variation in LEV topologies observed between
and within different species of insect is given in Fig. 7
(adapted from Bomphrey et al. 2005). Bumblebees’ small
wings are at the limit of what can be resolved with smoke
visualizations. As a result, while the near wake flows were
Exp Fluids
A
B
Fig. 8 Cartoon of the flow expected mid downstroke behind a
bumblebee (left) and measured behind a desert locust (right). At the
top the insects are depicted flying into the page. Red boxes (a)
represent a plane aligned vertically behind the trailing edges of the
insects’ wings and show a 2D slice through the flow with
instantaneous streamlines. Yellow boxes (b) show the predicted
downwash distribution in the same plane behind the two insects—the
locust distribution being an idealized profile based on DPIV
measurement (Bomphrey et al. 2006b). Grey dashed lines represent
the edge of the trailing vortex cores
clear, the resolution of the LEV in our flow visualizations
is lower than has been achieved, for example, with dragonflies (Thomas et al. 2004). Nevertheless, the density of
smoke streams was sufficient to identify the critical features of the flow topology such as bifurcations and
attachment points. The bumblebee topologies we have
described are shown in Fig. 7d1, d2, where d1 represents
the majority of the downstroke and d2 is the topology at the
end of the downstroke and beginning of the upstroke. It is
apparent that bumblebees are unusual in comparison with
other insects which utilize LEVs to generate lift, in that the
flow appears to remain attached for the majority of the
downstroke, first separating around the time of stroke
reversal. This might suggest a role for wing rotation in the
formation of the LEV, although we have no information as
to whether this separation is the result of the angular
velocity of the wing at supination or the concomitant
increase in angle of attack (Walker 2002).
The ultimate structure of the bumblebee LEV (Fig. 7d2)
bears some resemblance to that of Maxworthy’s (1979)
flapping machine (Fig. 7a) in that a LEV is present which
does not terminate on the wing surface. Nevertheless, the
two are distinct in that the root vortices are not linked in the
bumblebee as they are in Maxworthy’s (1979) flapping
machine. Although our data have insufficient temporal
resolution to observe transient stages in LEV development,
it is quite possible that the LEV topology we have observed
in bumblebees (Fig. 7d2) develops from an attached flow
topology (Fig. 7d1) via a transient state like that proposed
by Ellington et al. (1996) for hawkmoths (Fig. 7c1, and
hypothesized in Fig. 1b).
In most other flow visualizations on birds, bats and insects
to date, the left and right wing pairs are aerodynamically
linked by transverse vortical structures (birds: (Kokshaysky
1979; Spedding 1986; Spedding 1987; Spedding et al. 2003;
Videler et al. 2004; Warrick, Tobalske and Powers 2005);
bats: (Hedenstrom et al. 2007; Norberg 1976; Swartz et al.
2005); insects: (Bomphrey 2006; Bomphrey et al. 2005,
2006b; Dickinson and Götz 1996; Grodnitsky and Morozov
1993; Lehmann et al. 2005; Maxworthy 1979; Srygley and
Thomas 2002; Thomas et al. 2004; Van den Berg and
Ellington 1997; Willmott et al. 1997)). In contrast, our
bumblebee flow visualizations provide no evidence for
such structures linking the left and right wings. The same
may be true of other insect species, including crane
flies, which have also been shown to generate wing root
vortices in addition to the usual wing tip vortices (Brodsky
1994). This must result in a loss of efficiency, because
unlike many other insects, bumblebees and crane flies are not
using the full span between their wing tips to generate lift,
and indeed wastefully accelerate air upwards in the vicinity
of the body.
Figure 8 depicts the consequences of root vortices for
the downwash distribution. Figure 8a is a cartoon depicting
instantaneous streamlines in a vertical plane behind the
trailing edges of a bumblebee and a locust. Figure 8b is a
cartoon of the corresponding downwash distributions. In
the case of the locust, we have made use of quantitative
DPIV measurements of the wake to inform the figure
(Bomphrey et al. 2006b); in the case of the bumblebee, we
have based the expected downwash distribution on a typical velocity profile through two vortex rings. While the
diagrams are idealized representations of the true flows, the
root vortices which are present in the bumblebee must
necessarily make the downwash distribution less even than
that behind the locust. Any deviation from the ideal even
123
Exp Fluids
downwash distribution is a source of aerodynamic inefficiency, reinforcing our conclusion that the flow topology of
bumblebees is aerodynamically inefficient at all stages of
the stroke. The general conclusion over the bumblebee’s
inefficiency is consistent with the conclusions Altshuler
et al. (2005) drew for honeybees (Apis mellifera). While
they did not observe the aerodynamics directly and attributed enhanced lift to wake capture and rapid rotation of the
wings, honeybees fill a similar ecological niche and also
‘underperform’ in terms of efficiency during normal flight
by operating with a shallow stroke amplitude.
Why has natural selection tolerated such inefficiency?
The aerodynamic independence of left and right wing-pairs
in bumblebees might simply result from the biological
constraint of having a wide thorax to house the massive
flight motor required for their load-carrying foraging style.
As a result the wing roots are widely separated in relation
to the wing length, and as this ratio increases, this is bound
at some point to lead to their independent operation.
Alternatively, the aerodynamic independence of the wing
pairs might reflect the low and negative advance ratios at
which the bees flew in the sequences we have visualized.
At such low airspeeds, there may simply be an insufficient
flow velocity near the wing base to generate a significant
circulation in comparison with that generated further out
along the wing. Finally, it is also possible that the independence of left and right wing pairs might enhance control
authority and could therefore represent an adaptation for
manoeuvring between flowers.
Acknowledgments Research sponsored by BBSRC Studentship
00A1S06405. RJB is a PD Research Fellow at St Anne’s College,
Oxford. GKT is a Royal Society University Research Fellow and
RCUK Academic Fellow. The authors are grateful to the BBC for
loaning the Phantom high-speed digital video camera.
References
Altshuler DL, Dickson WB, Vance JT, Roberts SP, Dickinson MH
(2005) Short-amplitude high-frequency wing strokes determine
the aerodynamics of honeybee flight. PNAS 102:18213–18218
Birch JM, Dickinson MH (2001) Spanwise flow and the attachment of
the leading-edge vortex on insect wings. Nature 412:729–733
Bomphrey RJ (2006) Insects in flight: direct visualization and flow
measurements. J Bioinsp Biomim 1:S1–S9
Bomphrey RJ, Lawson NJ, Harding NJ, Taylor GK, Thomas ALR
(2005) The aerodynamics of Manduca sexta: digital particle
image velocimetry analysis of the leading-edge vortex. J Exp
Biol 208:1079–1094
Bomphrey RJ, Lawson NJ, Taylor GK, Thomas ALR (2006a)
Application of digital particle image velocimetry to insect
aerodynamics: measurement of the leading-edge vortex and near
wake of a Hawkmoth. Exp Fluids 40:546–554
Bomphrey RJ, Taylor GK, Lawson NJ, Thomas ALR (2006b) Digital
particle image velocimetry measurements of the downwash
123
distribution of a desert locust Schistocerca gregaria. J Roy Soc
Interface 3:311–317
Brodsky AK (1994) The evolution of insect flight. Oxford University
Press, Oxford
Cimbala JM, Nagib HM, Roshko A (1988) Large structure in the far
wakes of two-dimensional bluff bodies. J Fluid Mech 190:265–298
Dabiri JO (2005) On the estimation of swimming and flying forces
from wake measurements. J Exp Biol 208:3519–3532
Délery JM (2001) Robert Legendre and Henri Werlé: toward the
elucidation of three-dimensional separation. Annu Rev Fluid
Mech 33:129–154
Demoll R (1918) Der Flug der Insekten und Vögel, vol. 69. Jena, G
Fischer
Demoll R (1919) Zuschriften an die Herausgeber. Der Flug der
Insekten und der Vögel. Die Naturwissenschaften 27:480–482
Dickinson MH, Götz KG (1996) The wake dynamics and flight forces
of the fruit fly Drosophila melanogaster. J Exp Biol 199:2085–
2104
Dickinson MH, Lehmann F-O, Sane SP (1999) Wing rotation and the
aerodynamic basis of insect flight. Science 284:1954–1960
Dudley R, Ellington CP (1990) Mechanics of forward flight in
bumblebees: I. Kinematics and morphology. J Exp Biol 148:19–52
Ellington CP (1984) The aerodynamics of hovering insect flight. III.
Kinematics. Phil Trans R Soc Lond B 305:41–78
Ellington CP, van den Berg C, Willmott AP, Thomas ALR (1996)
Leading-edge vortices in insect flight. Nature 384:626–630
Grodnitsky DL, Morozov PP (1993) Vortex formation during tethered
flight of functionally and morphologically two-winged insects,
including evolutionary considerations on insect flight. J Exp Biol
182:11–40
Hedenstrom A, Johansson LC, Wolf M, von Busse R, Winter Y,
Spedding GR (2007) Bat flight generates complex aerodynamic
tracks. Science 316:894–897
Hoff W (1919) Der Flug der Insekten und der Vögel. Die Naturwissenschaften 10:162–169
Kokshaysky NV (1979) Tracing the wake of a flying bird. Nature
279:146–148
Lehmann FO (2004) The mechanisms of lift enhancement in insect
flight. Naturwissenschaften 91:101–122
Lehmann FO, Sane SP, Dickinson M (2005) The aerodynamic effects
of wing-wing interaction in flapping insect wings. J Exp Biol
208:3075–3092
Maxworthy T (1979) Experiments on the Weis-Fogh mechanism of
lift generation by insects in hovering flight. Part 1. Dynamics of
the ‘fling’. J Fluid Mech 93:47–63
Noca F, Shiels D, Jeon D (1999) A comparison of methods for
evaluating time-dependent fluid dynamic forces on bodies, using
only velocity fields and their derivatives. J Fluids Struct 13:551–
578
Norberg UM (1976) Aerodynamics, kinematics, and energetics of
horizontal flapping flight in the long-eared bat Plecotus auritus.
J Exp Biol 65:179–212
Perry AE, Chong MS (1987) A description of eddying motions and
flow patterns using critical-point concepts. Annu Rev Fluid
Mech 19:125–155
Ramasamy M, Leishman JG (2006) Phase-locked particle image
velocimetry measurements of a flapping wing. J Aircraft
43:1867–1875
Sane SP (2003) The aerodynamics of insect flight. J Exp Biol
206:4191–4208
Shyy W, Liu H (2007) Flapping wings and aerodynamic lift: the role
of leading-edge vortices. AIAA J 45:2817–2819
Spedding GR (1986) The wake of a jackdaw (Corvus-Monedula) in
slow flight. J Exp Biol 125:287–307
Spedding GR (1987) The wake of a kestrel (Falco tinnunculus) in
flapping flight. J Exp Biol 127:59–78
Exp Fluids
Spedding GR, Rosen M, Hedenstrom A (2003) A family of vortex
wakes generated by a thrush nightingale in free flight in a wind
tunnel over its entire natural range of flight speeds. J Exp Biol
206:2313–2344
Srygley RB, Thomas ALR (2002) Unconventional lift-generating
mechanisms in free-flying butterflies. Nature 420:660–664
Swartz S, Galvao R, Iriarte-Diaz J, Israeli E, Middleton K, Roemer R,
Tian X, Breuer K (2005) Unique characteristics of aerodynamics
of bat flight evidence from direct visualization of patterns of
airflow in the wakes of naturally flying bats. Int Comp Biol
45:1080
Thomas ALR, Taylor GK, Srygley RB, Nudds RL, Bomphrey RJ
(2004) Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating
mechanisms, controlled primarily via angle of attack. J Exp
Biol 207:4299–4323
Van den Berg C, Ellington CP (1997) The vortex wake of a ‘hovering’
model hawkmoth. Phil Trans R Soc Lond B 352:317–328
Videler JJ, Stamhuis EJ, Povel GDE (2004) Leading-edge vortex lifts
swifts. Science 306:1960–1962
Walker JA (2002) Rotational lift: something different or more of the
same? J Exp Biol 205:3783–3792
Walker SM, Thomas ALR, Taylor GK (2008) Photogrammetric
reconstruction of high-resolution surface topographies and
deformable wing kinematics of tethered locusts and free-flying
hoverflies. J Roy Soc Interface. doi:10.1098/rsif.2008.0245
Walker SM, Thomas ALR, Taylor GK (2009) Deformable wing
kinematics in the desert locust: how and why do camber, twist
and topography vary through the stroke? J Roy Soc Interface.
doi:10.1098/rsif.2008.0435
Warrick DR, Tobalske BW, Powers DR (2005) Aerodynamics of the
hovering hummingbird. Nature 435:1094–1097
Willmott AP, Ellington CP, Thomas ALR (1997) Flow visualization
and unsteady aerodynamics in the flight of the hawkmoth,
Manduca sexta. Phil Trans R Soc Lond B 352:303–316
123