Measuring wing kinematics, flight trajectory and body attitude during forward flight and turning maneuvers in dragonflies
1 State Key Laboratory of Precision Measurement Technology and Instruments,
Department of Precision Instruments, Tsinghua University, Beijing 100084,
China
2 Computer and Information Division, The Institute of Physical and Chemical
Research (RIKEN), Japan
* Author for correspondence (e-mail: whao98{at}mails.tsinghua.edu.cn)
Accepted 29 November 2002
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Summary |
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Key words: free flight, dragonfly, Polycanthagyna melanictera, insect wing, wing deformation, kinematics, fringe pattern projection, attitude
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Introduction |
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A number of recent studies have focused on the kinematics of hovering and
forward flight, using a variety of techniques. Azuma and Watanabe
(1988) changed the velocity of
the wind tunnel in their measurements. Dudley and Ellington
(1990
) calculated angles of
attack in the free forward flight of bumblebees. Willmott and Ellington
(1997
) employed a
variable-speed wind tunnel associated with the optomotor response to
investigate wing and body kinematics during free forward flight of a hawkmoth
over a range of speeds from hovering to 5 m s-1. Wakeling and
Ellington (1997
) filmed the
free flights of dragonflies and damselflies flying over the pond in the
greenhouse at the University of Cambridge. The individuals were not restrained
by either tethers or wind tunnels, but were free to vary the velocity and
acceleration and could perform any flight action. In their analyses of forward
flight, the stroke plane was constructed based on the assumption of bilateral
wing symmetry, and variations in roll, yaw and pitch angles of the body
through each flapping cycle were neglected. To date no detailed information on
wing orientation or shape during free flight has been acquired.
All kinds of flight behaviors are important for studying the aerodynamics and the control of flight. In turning maneuvers, the wings move asymmetrically, and the change in attitude is obvious even during one flapping cycle. We have also found that dragonflies exhibit substantial chordwise deformation and changes in camber during free flight, which might be important for aerodynamic models of flight performance.
To study turning maneuvers involving obvious changing of the insect attitude, the description of wing kinematics should be based on a local body-centered coordinate system, together with the body attitude and flight trajectory. We have developed a method utilizing a Projected, Comb-Fringe technique combined with the Landmarks procedure (PCFL), in which a comb-fringe pattern with high intensity and sharpness was projected onto the transparent wing of a dragonfly in free flight. Images of the wings with distorted fringes were then recorded by a high-speed camera. Based on the distorted fringe pattern and the natural landmarks on the dragonfly wings, we reconstructed wing shape and established the body-centered coordinate system. This method allowed us to derive kinematic parameters without assumptions of rigid chords or kinematic symmetry, except for the assumption of rigid leading edges. The instantaneous attitude of the body was also measured simultaneously. We measured dragonflies in two flight behaviors: forward flight and turning maneuvers, and compared the kinematics results obtained for each of them.
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Materials and methods |
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Global coordinate system and PCFL system
Fig. 1 shows the PCFL system
based on the global coordinate system (OXYZ). A dragonfly was induced
by a fluorescent lamp (pilot light) to fly across the experimental region. The
flight was captured by a high-speed camera HCCD (Dalsa D256). Frame capture
speed was 955 frames s-1 at a resolution of 256x256 pixels;
exposure time was 1/4000 s. The experimental background was illuminated by an
incandescent lamp with an output spectrum close to the response peak of the
camera, thereby allowing the outline of the wing to be easily identified.
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A fringe pattern projector (FPP) with an interbeam fringe angle of
0.77° was used to project a fringe pattern onto the wing. Wing deformation
was calculated by using the resulting distorted fringe pattern observed from
the camera view. Given the camera position, the location of the FPP, and the
angle of the measurement fringe, the three-dimensional position of any point
on the distorted fringe could be calculated by using spatial analytic geometry
(Zeng et al., 1996,
2000
;
Song et al., 2001
). The angle
of the measurement fringe was determined using a reference fringe, which was
thicker and brighter than the measurement fringes. The reference fringe was
generated by using a semiconductor laser together with a cylindrical lens. The
rank order of measurement fringes was counted from the reference fringe,
allowing determination of the angle of each measurement fringe. Although the
reference fringe was not visible during some frames while the dragonfly was
flying through the experimental region, the fringe order was maintained, as
the fringe shift caused by wing flapping was much smaller than the distance
between fringes. Constancy of fringe order could therefore be used to identify
individual fringes by consecutive counting.
Three-dimensional (3-D) coordinates of points on the distorted fringes were
calculated by spatial analytic geometry
(Song et al., 2001).
Interpolation was used to calculate the spatial position of points of interest
not on the fringes. We reconstructed 3-D wing shape throughout the flapping
cycle by digitizing the fringe coordinates frame-by-frame from the recorded
fringe sequence. The body position, attitude and kinematic parameters of wing
were based on the 3-D reconstruction.
Local body-centered coordinate, flight trajectory and attitude
The body position and attitude of an insect in free flight should be
described on the basis of a global coordinate system in order to obtain the
flight trajectory. By contrast, the kinematic parameters should be described
on the basis of the local body-centered coordinate system. Uncertainties in
body position and attitude bring errors in local body-centered coordinate
system construction, and therefore uncertainties in the wing kinematics
description.
We defined the local body-centered coordinate relative to the body position and attitude in the global coordinate system using the four wingbases. Because the wingbases cannot be identified in captured images, the wingbase coordinates were constructed using identifiable landmarks on the wings. Fig. 2A shows the natural landmarks near the wing tip (Q). Because the leading edge of the wing bends little during flapping motion, it can be considered a rigid bar. Given the 3-D coordinates of two arbitrary points on leading edge projected by fringes, the equation of the leading edge (the line joining wingbase E and landmark Q) can be obtained. Then, the coordinate of Q can be calculated based on the image of Q and the leading edge equation. According to the distance S between E and Q, which is constant for a given dragonfly wing and can be measured in advance, the coordinate of each wingbase can be calculated based on spatial analytic geometry. Then the local body-centered coordinate system is constructed based on the four wingbases, its origin KF being the midpoint of the two fore-wingbases (see Fig. 2B).
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A dragonfly in flight has six degrees of freedom (d.f.) for its movement.
It can translate in three dimensions in space and rotate around its center of
mass, which is approximated by the origin of the body-centered coordinate
system. The flight trajectory (or the variation in body position of a free
flight dragonfly) is defined by the movement of the origin of the local
body-centered coordinate system, and measured in the global coordinates. Body
attitude is defined by the orientation of a body (or vectors of three axes of
the body-centered coordinate) with respect to a reference orientation, and
described by three angles: yaw angle , pitch angle
and roll angle
(Schilstra, 1999). The reference orientation is defined when the body
axis of a dragonfly is along the X-axis and the symmetry plane of its
body is in XOZ plane in the global coordinate system. The three
angles can be deduced from the local body-centered coordinate system
O'X'Y'Z' and the reference orientation. For
the reference orientation, the body-centered coordinate system was rotated in
the following sequence: first, around its Z'-axis with angle
; second, around its X'-axis with angle
; and
finally, around its Y'-axis with angle
. To describe the
attitude change of free flight visually, we used the common aeronautical
descriptions where the angles
,
and
are positive as they are
turning clockwise, respectively. The arrows in
Fig. 2B show the direction
definitions.
Because insects can fly within the same trajectory but with different body attitudes, it is important to describe flight behavior by combining the flight trajectory together with the aeronautical descriptions of roll, pitch and yaw angles.
Stroke plane and kinematic parameters
The kinematic parameters, including wingbeat frequency, flapping angles,
angles of attack, torsional angle and camber deformation of the fore- and
hindwings are relevant to the aerodynamic analysis of insect flight. We
assumed that the wing's leading edge did not bend during its stroke in
calculating the kinematic parameters. The assumption is robust for almost all
flight behaviors. The leading edge equation, the arch and the chord
vector MN of each wing at any flapping angle can be calculated based on
the 3-D reconstruction of the wings.
The plane in which the wings oscillate relative to the dragonfly's body is
called the stroke plane, which is defined by three points: the wing base, and
the wingtip at the maximum and minimum angular positions in a flapping cycle.
The kinematic parameters, including the flapping angle , angle of attack
, torsional angle
and camber deformation
, are described
based on the stroke plane. Fig.
3 shows the parameters of the left forewing; those of other three
wings are defined by the same way.
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After calculating flapping angle and torsional angle
from the
distorted fringe, we described the wing kinematics by fitting the angles
and
using a Fourier series:
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Uncertainty in measurement
To estimate the uncertainty of the measurement system, we measured a
half-round surface with a radius of 19.00 mm, which was placed on a horizontal
plane normal to the optical axis of the high speed camera. The profile of the
object was measured from the distorted fringe. Using this real curve as a
reference, the fitted curve from the measured results had a standard deviation
of 0.10 mm. The accuracy is mainly limited by the pixel resolution of the
image. If the error of any point on the distorted fringe is 0.1 mm, the error
in wingbase is 0.14 mm, according to the equation of leading edge.
Because the 3-D coordinate of wingbase E can be deduced according to only
two arbitrary fringes on one wing, the number of the calculated coordinate of
E is (N is the total number of
fringes on the wing). The final coordinate of wingbase is the optimization of
these coordinates according to a least-squares method. The relationship of the
four wingbases is nearly invariable, and is used to estimate the effectivity
of the local body-centered coordinate system.
Applicability of the PCFL method
The PCFL method is based on the assumption of rigid leading edges, which is
applicable for most insects. We can measure the kinematic parameters for a
wide range of insect wing size, from a small Drosophila wing to a
large magpie wing, by adjusting the magnification of optical system and the
interbeam angle of fringes. For the system with only one camera and one FPP,
the flight measurement is limited, because the fringes may not project on a
certain wing or leading and trailing edges may be confluent in the camera view
field when the insect is at a particular place, especially for the insect
wings that oscillate through large angles. Moreover, the FPP or camera view of
a wing may be obstructed by the body or other wings when the insect turns. On
such occasions, two cameras and two FPPs, mounted in the measurement system
with different angles, should be used.
On the other hand, in order to ensure the measurement accuracy of the method, the insect should be sufficiently large in the camera view field, that it only needs to be kept in view for a short time. In our experiment, the proportion of dragonfly in the view field was selected carefully to ensure that the dragonfly was monitored for at least for one stroke period. We are now designing a tracking measurement system, including video tracking and fringe pattern tracking, to allow us to record the image of dragonfly continuously over more stroke cycles.
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Results |
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Flight trajectory and attitude
The 3-D flight trajectories of the two flight behaviors, forward flight and
turning maneuvers, are described by each trajectory of the origin of the
body-centered coordinate system (see Fig.
5). Note that the forward flight is not a proper rectilinear
forward flight, for it contains alternating pitching turns and large pitch
velocities and accelerations (see Figs
5,
6). Because the body pitch of a
dragonfly is nearly a constant during hovering
(Azuma et al., 1985), we assume
that it should also be a constant during proper rectilinear forward
flight.
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The detailed differences between the two flight behaviors are difficult to distinguish from the flight trajectories alone. However, the difference between the two flight behaviors becomes obvious on considering the velocities, accelerations and attitude of the dragonfly (see Fig. 6). When the dragonfly is in forward flight, its acceleration at each position is nearly normal to the horizontal plane, so that the body moves in the vertical plane containing the body axis; in contrast when it performs turning maneuvers, its acceleration at each position is nearly parallel to the horizontal plane, which must induce the body axis to deviate from the vertical plane, resulting in a turn.
The difference between forward and turning maneuvers can also be found from the variations in the roll, pitch and yaw angles. During forward flight, only the pitch angle has a distinct fluctuation, while the roll and yaw angles are almost constant, implying flight in a vertical plane. During turning maneuvers, the roll, pitch and yaw angles are increasing by almost the same slope, implying that the dragonfly turns right with the body inclined to the right and the head elevated. Within the limits of the camera view field, the turning was not completed before the dragonfly flew out of the fringe pattern.
Kinematics of flight
Based on the 3-D reconstruction of the dragonfly wings and the
interpolation algorithm, the time-dependent variation in flapping angle
, torsional angle
and the camber deformation | for each
wing were obtained (see Fig.
7). The wingbeat frequency was 33.4 Hz and 35.0 Hz with respect to
forward flight and turning maneuvers, respectively.
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In forward flight, time-dependent variation in wing flapping angles indicated remarkable rightleft symmetry of the flapping angles, though the flight had up-and-down fluctuation. The phase difference between the fore and hind pairs of wings, by which the fore pair followed the hind pair, was approximately 100°. And for both forewings and hindwings, the flapping amplitudes were approximately ±30°. In turning maneuvers, the wingbeat motion was not rightleft symmetrical for the forewing pair, but was nearly symmetrical for the hindwing pair. The flapping amplitude of the inner wing (the right forewing) was not as distinct as that of the outboard wing (the left forewing). A similar phenomenon was also seen with the hind pair.
The rightleft symmetry of the torsional angles in both fore and hind pairs showed little differences between two flight behaviors. Note that the variation in torsional angles of forewing in turning maneuvers was larger than that in forward flight, while that of hindwing in turning maneuvers was smaller than that in forward flight.
In forward flight, the negative camber deformation in both fore and hind pairs during their upstrokes was of short duration, while in turning maneuvers, the negative camber deformation only occurred in the hind pair, but the duration was longer than that in forward flight.
Unsteady aerodynamics of forward flight
Unsteady aerodynamics of forward flight was further studied numerically by
solving the unsteady flow about a single airfoil as a two-dimensional model of
the right forewing in the forward flight mode. The computation was conducted
using an in-house NavierStokes solver developed by Liu (see
Liu and Kawachi, 1998). As
illustrated in Fig. 8A, the
geometric model is a 10 mm long, flat-plate airfoil of the same length as the
mid-span chord length (defined as c) and thickness approximately 2%
of the chord length. The kinematic model consists of two motions, a
translational component (plunging), defined as the movement of the mid-span
chord corresponding to the flapping angles
(Fig. 7A), and a rotational one
(pitching) described by the torsional angles
(Fig. 7C). The camber
deformation is described by a time-varying mean line of the airfoil, with the
maximum ordinate occurring constantly at the one-quarter chordwise position
throughout a complete beating cycle (Fig.
8A). The shape of the mean line is analytically expressed as two
parabolic arcs tangent at the position of maximum mean-line ordinate. The
mid-span chord length (c=10 mm) is defined as the reference length
and the maximum flight speed (U0=1.71 m s-1) as
the reference speed. Hence, the Reynolds number was calculated to be
approximately 1140 and the reduced frequency,
K=2
fc/2U0 is 0.6136. Computed lift
and drag forces are nondimensionalized, as in the study by Liu and Kawachi
(1998
).
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The airfoil is placed in a body-centered inertial frame of reference that
undergoes the plunging motion, and pitches about a fixed axis at the
one-quarter chordwise position. Inflow conditions of the forward flight are
realized by defining a velocity vector at upstream, U0, in
which two velocity components form an angle identical to the stroke plane
inclination of approximately 15°, namely =15°, constantly
during a complete beating cycle. Simulations were undertaken till the
periodicity of force coefficients was clearly captured with a constant
fluctuation, typically more than three cycles for the given reduced frequency;
the results at the fourth cycle were used in the evaluation of the
force-related quantities and in the flow visualization.
Fig. 8B illustrates
comparison of the time variations of the force coefficients,
Cy (drag) and Cz (lift), with and
without the camber deformation. Their relationship with the vertical force and
the thrust force can be given as:
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Discussion |
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The camber deformation may play an important role in lift and drag
coefficients. Positive camber deformation of the hindwing during the
downstroke generates the vertical force, whereas negative camber deformation
of the wing during upstroke generates thrust force. In contrast to some
previous reports that the camber deformation has a rather minor effect on
aerodynamic forces at high angles of attack (see Dickinson and Gutz, 1993;
Sunada et al., 1993), we
notice that it may be important for aerodynamic models of flight performance.
Our present computational fluid dynamics study of the unsteady aerodynamics of
the right forewing undergoing forward flight indicates that the airfoil with
time-varying camber deformation very likely plays a role in delaying the
development and shedding of the leading-edge vortex (see
Fig. 8C,D), and hence enhances
the delay of the dynamic stall. At the same moment with a zero flapping angle,
the vortex over the upper surface of the airfoil with the camber deformation
clearly is smaller and closely attached, leading to a much lower negative
pressure region on the upper surface (Fig.
8C,D). Hence, at downstroke the airfoil with the camber
deformation obviously generates greater forces in both thrust and lift than
the rigid airfoil (Fig. 8B). At
upstroke, however, it is very interesting to notice that this discrepancy is
remarkably reduced (Fig. 8B).
On the other hand, the value of wing camber deformation under steady state
conditions is clear. In the range of Reynolds' number within which insects
operate (Re<4x104) an arched plate gives higher lift
coefficient values than a flat plate
(Hertel, 1966
). Though any
non-steady benefits are less apparent, active alteration of camber deformation
by the raising and lowering of flaps may be important in maneuvering and in
the maintenance of stability. Wootton
(1981
) mentioned that
Agrion (Odonata) asymmetrically lowers the cubitoanal region of fore
and hindwings during the downstroke when turning; and Pringle
(1961
) described how the
hindwing of bees might similarly be depressed in the control of rolling
movements. During insect flapping, it was reported that the wings themselves
deform semi-automatically, optimizing aerodynamic forces
(Wootton, 2000
). Alexander
(2000
) remarked,
`Previously, we thought of insect wings as stiff, flat plates now
we know that some bend and twist in flight in ways that must have large
aerodynamic effects.' However, the effect of the wing camber deformation
on unsteady aerodynamic forces is still not clear, particularly in the case of
large angles of attack; more extensive studies need to be done.
The flight characteristics of the forewings reveal many differences between forward flight and turning maneuvers, while differences in the hindwings are rare. All show that the freely flying dragonfly's hindwings play an important role in providing a stable lift force, and the forewings are very important for controlling flight behavior, such as turning, climbing and so on.
Further understanding of wingbeat kinematics and flight attitude would
require a detailed analysis of simultaneous aerodynamic and inertial forces on
the wing. Using a PCFL method, flapping angles, angles of attack and camber
deformation of insect wings can be determined for unrestrained free flight. No
assumptions concerning wing geometry or deformability are necessary, and wing
contours can be determined with high accuracy. Moreover, the body attitude at
any instant can be determined simultaneously, which is important for analyzing
flight control in the insect. These experimental results show that there is
considerable camber deformation during free flight of dragonflies. The
wingbeat kinematic parameters of the dragonfly studied here are broadly
similar to those reported by previous works for similar-sized dragonflies (see
Azuma and Watanabe, 1988;
Wakeling and Ellington, 1997
),
but to date no detailed information on wing profile and flight attitude during
free flight has been acquired. This study thus demonstrates the feasibility of
obtaining detailed information on wing geometry during the flight of
insects.
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Acknowledgments |
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References |
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