48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2010, Orlando, Florida
AIAA 2010-1017
Micro Air Vehicle Flapping Wing Effectiveness, Efficiency
and Aeroelasticity Relationships
Pin Wu1 and Peter Ifju2
University of Florida, Gainesville, Florida, 32611
Abstract
By utilizing passive wing deformation, thrust can be produced with a single-degree-offreedom flapping motion. Studies have shown that wings of different flexibility produce
effective thrust at different frequency ranges. This work focuses on the efficiency of the
wings: comparing the thrust production of certain power input to wings of different
structural properties. The aeroelasticity of the wings is examined with full-field deformation
measurement techniques. Four pairs of flexible membrane wings of different reinforcement
skeletons are tested. Their bending and twisting stiffness are characterized, with
deformation plots compared and correlated with thrust production at different frequencies.
The results show that the wing compliance is crucial in thrust production: thrust is
effectively produced with some particular patterns of passive deformation. The experimental
setup consists of a flapping mechanism that enables actuation up to 45 Hz at 70º stoke
amplitude; a force and torque sensor that measures the lift and thrust; and a digital image
correlation system that consists of four cameras, capable of capturing the complete stroke
kinematics and structural deformation. This work solves several technical challenges:
measuring low magnitude of forces, monitoring power consumption rate, measuring the
aeroelastic deformation and intensive data post processing.
Nomenclature

twist

T
=
=
=
=
a
=
c
=
d
=
f
=
i
=
l
=
r
=
s
=
x,y,z =
1
2
flapping wing position angle, deg
angle of twist at 83% span location away from the root, deg
motor rotational angle, deg
triggering time interval, s
horizontal distance from the rocker base pin center to the reciprocator center, 5 mm
wing root chord length, 25 mm
length of the rocker bar, 16 mm
flapping frequency, Hz
vertical displacement of the reciprocator, mm
length of the push rod in the crank-slider mechanism, 50 mm
offset distance in the crank module, adjustable to change the flapping amplitude, 3 mm
number of samples per cycle
local coordinate system of the flapping wings, mm
Research Assistant, Department of Mechanical and Aerospace Engineering, AIAA member, [email protected].
Professor, Department of Mechanical and Aerospace Engineering, AIAA member.
1
Copyright © 2010 by Wu, Pin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
I.
Introduction
HIS work is conducted to identify the relationship between passive flapping wing deformation and the
concomitant aerodynamic force in terms of thrust magnitude and efficiency. Unlike birds and bats that have
muscles and skeletal joints to change the wing shape during flight, insects fly with wings that have no active
shape control. Seen in high-speed videos and documented by Ellington1, the key element for insect flight is the
thrust produced by the sweeping motion. The sweeping motion is mainly a back and forth fan movement with
various wing tip traces. Here, to emphasize pure flapping motion and ignore rotation (as in pronation and
supination), a test bed mechanism is designed and created to perform a single degree-of-freedom (DOF) kinematics.
This is categorized as normal mode hovering flapping flight with constant pitch angle, as illustrated by Shyy et al.2
Ho et al.3 pointed out that such kinematics are not biologically-inspired, and the flapping of a rigid wing will not
develop significant time-averaged lift/thrust. Wing flexibility then, becomes an important factor.
Recent development in micro air vehicles (MAVs) has realized a hover capable flapping wing aircraft. However,
there are still many challenges in terms of power, control, payload, etc., along with the most fundamental of all: an
effective and efficient wing with well designed structure. Therefore, understanding the structure requirements of the
wing that is actuated under certain kinematics to create effective aerodynamic forces is critical, and is the focus of
this work. Since hummingbirds behave in the transition region between insect flight (completely passive wing
deformation) and bird flight (active shape control), it is used as an example for the current flapping MAV
development. Wu et al.4 have studied wings with certain parameters comparable to hummingbirds’ as well as other
biological examples. Experimental characterization of such wings is challenging, as scaling must preserve many
parameters (such as Reynolds number, reduced frequency, etc.) relative to structure and material properties 2. Due to
these difficulties, it is desired to conduct tests on full-scale models, leading to resolution issues in loads
measurements: time-averaged lift and thrust may only be a few grams. Singh et al. 5 describe various manufacturing
issues associated with lift and thrust measurements via piezo-resistive strain gages. Kahn and Agrawal 6 use a
commercial force/torque sensor with six DOFs. A similar sensor is used in this work. Furthermore, several subsystems (flapping mechanism, load sensor, strobe, cameras, etc.) must be synchronized within the flapping cycle,
which requires a complex triggering system7.
Previous work by Wu et al.4 confirms that leading edge stiffness has a direct influence on thrust production
effectiveness: more flexible leading edge is more effective at low frequencies (10~20 Hz) and stiffer leading edge is
more effective at high frequencies (30~40 Hz). The structural deformation and airflow measurements are also
performed8 to observe the aeroelastic detail for such different behaviors. The structural deformation measured with
full-field method and extracted into two parameters (wing tip deflection and twist angle) is seen to directly relate to
the aerodynamic performance, which is shown with velocity and vorticity fields. However, the efficiency
considering power consumption is not measured: stiffer wings may require substantial more power in order to
produce more thrust at high frequencies.
Therefore, this study measures both the thrust and power to evaluate the system efficiency for four pairs of
wings. The four pairs of wings are designed with different topology and reinforcement so that each wing exhibits
unique structural properties, which are described with dynamic deformation measurements. A full-field surface
measurement technique called digital image correlation (DIC) is used to record wing kinematics and deformation.
This technique has been successfully applied to micro air vehicle flapping wing study with large rotation and out-ofplane deformation9. Previously other non-contact methods have also been applied to shape measurements: Tian et
al.10 utilized similar multiple reflective markers over a bat wing, and stereo high-speed cameras to quantify the
motion. Wallace et al.11 and Agrawal and Agrawal12 utilized a similar photogrammetry technique for insect-size
wings. A more full-field method is discussed by Zeng et al.13, who used a fringe shadow method to measure the
flapping and torsional angle of a dragonfly wing. Similar fringe-based methods are given by Wang et al.14, along
with sign points placed on the wing, to measure deformation of a free-flight dragonfly. Cheng et al.15 extended this
technique with a windowed Fourier transform to process the fringe patterns and extract phase. However, these
methods cannot provide both full-field and high-resolution measurement of a complicatedly deformed surface,
making DIC the most advanced approach.
The remainder of this paper is organized as follows. First the flapping mechanism and the four tested wings are
introduced. Then the experimental setup is described in detail, including a vacuum chamber, a four-camera digital
image correlation system, overall system trigger/synchronization and the force measurement system. The
experimental procedure and data analysis are then presented, including measurement uncertainty discussion. Finally,
results are given to reveal the intrinsic relationship between wing deformation and aerodynamic performance.
T
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II.
Flapping Mechanism and Tested Wings
A single DOF flapping mechanism is designed and created for this study, as shown in Figure 1-A. The design is
based on a Maxon motor system that includes a 15 W brushless DC motor EC16, a 57/13 reduction ratio planetary
gear box, a 256 counts-per-turn encoder and an EPOS 24 controller. This system provides precise control: the sensor
provides position and velocity feedback to the controller that actively regulates the motor. The encoder also provides
power consumption feedback so that energy efficiency can be calculated. Using a single rotational input to perform
flapping allows taking the advantage of the high precision preassembled planetary gear head rather than constructing
a custom gear transmission. The final output range of the motor shaft is of speeds from 0 to 45 revolutions per
second (RPS) and a nominal torque up to 21 N·mm. In this work, data are taken with flapping frequencies varying
from 5 to 35 Hz at ±35º amplitude. The rotation input from the motor is first transformed into a reciprocating motion
with a crank-slider mechanism; then a bar linkage mechanism realizes the flapping motion at the wing mount. A
detailed schematic description of the flapping kinematics is presented in Figure 1-B. The geometric relationship
between motor rotation (angle ) and flap angle  is expressed in these equations:
The crank-slider mechanism:
i  r sin   l 2  r 2  l 2  r 2 cos 2 
The bar linkage mechanism:
(1  cos  ) 2 a 2
i  a sin   d (1  1 
)
d2
where i is the vertical displacement from the center point defined at the horizontal wing position ( = 0). Each
value is defined in Nomenclature; the selected parameters result in a sinusoidal kinematics profile, as compared in
Figure 1-C.
Fig. 1 Flapping mechanism and its kinematics profile
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All of the four wings tested are of a Zimmerman planform, formed by two ellipses that intersect at quarter-chord.
This wing planform is selected to have comparable geometric features with real hummingbird wings (Altshuler et
al.16, 2004), with an aspect ratio of 7.65, a 75 mm wing length and a 25 mm root chord, as shown in Figure 2. For
this work, the wing design is two dimensional: no camber or airfoil profile. The wings are constructed with
unidirectional carbon fiber to form the skeleton and Capran® as the membrane. The four wings are reinforced with
and named to reflect the different structures: 1) Wing 1-BP with battens parallel to the root; 2) Wing 2-HUM with
radial diagonal battens similar to hummingbird’s feather; 3) Wing 3-LEO without any batten reinforcement; and 4)
Wing 4-PR with reinforcement around the perimeter (Table 1).
To manufacture the wing skeleton, a three-layer bidirectional carbon fiber triangular plate is first placed at the
crossing of the leading edge and wing root, allowing other structure elements to be attached. This triangle is
significantly stiffer than other structural elements; therefore it is used as a reference for later deformation calculation
and attachment location to the flapping mechanism. Unidirectional carbon fiber strips (0.8 mm wide) are used to
construct the leading edge, battens, wing root and the trailing edge (only in Wing 4-PR). The strips are laid up on a
flat plate according to each reinforcement pattern by different numbers of layer. Wing 1-BP has 2 complete leading
edge layers and an extra one covering from the root to the third batten (counting from the root). The other three
wings all have 2 layers at the leading edge. All the battens are of 1 layer and all the roots are of 2 layers. The
structural features and reasons for topology selection are summarized in Table 1.
Table 1 Tested wing structure
Reinforcement
pattern
Leading edge
Batten
Root
Trailing edge
Weight
Wing 1-BP
Battens Parallel
2.5
1
2
0
0.125 g
Wing 2-Hum
Hummingbird-like
2
1
2
0
0.150 g
Wing 3-LEO
Leading Edge Only
2
0
2
0
0.100 g
Wing 4-PR
Perimeter Reinforced
2
0
2
1
0.140 g
Fig. 2 Reinforcement layout of the tested wings
After the carbon fiber skeleton is cured, the piece is applied with spray glue and laminated to a membrane
material called Capran® (Honeywell’s Capran Matt 1200), a biaxially oriented nylon film. Unlike the low elastic
modulus and deteriorative latex rubber, Capran® is as light as Mylar® (density: 1.16 g/cm3), as tough as Tyvek®
(tensile strength at break: 193~276 MPa) and as consistent as Kapton® (thermal shrinkage coefficient: 1% ~ 2% at
160° C). This thin film is available in matt surface finish, making it amenable for DIC measurements. Its low heat
shrink coefficient also allows curing the film together with carbon fiber without building up excessive thermal
stresses. Its high elastic modulus (2.5~3.4 GPa) and tear resistant properties eliminate concerns on reinforcing the
trailing edge. Finally, random patterns of flat black speckles are sprayed onto the wings for DIC measurements.
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III.
Experimental Setup
The overall experimental setup is shown in Figure 3. The system includes a vacuum chamber, a four-camera DIC
system, a force and torque sensor and a control system that synchronizes all the instruments. Instrument
specifications and configurations are discussed in this section for anyone who wants to understand, repeat or
improve the experiments.
Fig. 3 Experimental setup
A. Vacuum Chamber
The vacuum chamber allows measurements to examine wing structural properties and inertial effect, because
both loads and deformation are only caused by inertia, isolated from aeroelastic effects. A square aluminum base
plate (30” x 30” x 1”) is used as the platform for all of the instrumentation, and is outfitted with four outlets for the
vacuum pump, vacuum gauge, release valve and electric feed-through. A half-inch thick clear acrylic bell-jar, with
24” inner diameter and 24” inner height, is placed on the base plate and encloses all equipment: digital image
correlation cameras (described below), the flapping mechanism and wings, and the force and torque sensor, as
shown in Figure 3. The bell jar is lifted up to avoid airflow obstruction during experiments that are conducted in
hover condition. Reflective material is also placed around the bell jar to diffuse and bounce the stroboscopic light
source. An Edwards VB12 vacuum pump is used for this setup, which lets the system reach -29.5 in-Hg vacuum in
five minutes.
B. Digital Image Correlation System
Digital image correlation (DIC) is a well-developed non-contact full-field stereo-image measurement technique
used in this work to capture wing kinematics and structural deformation. The system uses stereo triangulation to
digitize a random speckling pattern on measurement surface, and thus compute its three-dimensional features. This
is followed by a temporal matching process, where the system tracks a subset of the speckling pattern, and
minimizes a cross correlation function to compute the undeformed location of this subset, and thus the
displacements. The correlation system consists of four Point Grey Research Flea2 cameras. Such a setup, after finetuning the depth of field, is able to capture the rigid body displacements (wing kinematics) and structural
deformations of a single wing up to a ± 90° flapping amplitude. The upper pair camera system monitors the upper
half stroke and the lower pair the lower half stroke. The four cameras are synchronized internally with an output to
trigger a stroboscope for the lighting. Since the camera and stroboscope comprise a low speed system, the
kinematics and deformation sequences are generated by recording aliased image sequences (triggering at a
progressing moment in the repeating cycle).
The Flea2 cameras have 1/1.8” progressive scan CCDs with 1624 x 1224 pixel resolution: a high-resolution
speckle pattern can be applied for superior correlation. Their 29 x 29 x 30 mm3 dimension allows the cameras to fit
inside the vacuum chamber. The multiple Flea2 cameras networked on the same IEEE-1394 bus are automatically
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synchronized to within a maximum deviation of 125 s and equipped with triggering signal output. Computar’s 1236mm F2.8 lenses are chosen for the Flea2 cameras. This combination gives the cameras a field of view between
22°and 61°. Careful selection of each camera parameter is crucial to obtaining a satisfactory depth of field. For
example, a 95.2 mm depth of field results from a 0.25 m object distance and a 20 mm focal length, shot at F/16
aperture, with the circle of confusion defined as 20 microns for speckle recognition. The zoom lenses provide a
certain degree of flexibility in positioning the cameras, and their continuous iris aperture helps to adjust for the
desired depth of field.
The cameras are positioned and configured so that even large wing rotation and bending can be captured and
there is enough depth of field to obtain sharp enough images during the whole flapping cycle. The cameras are not
placed symmetrical to the test wing, as shown in Figure 3. The upper pair of cameras is responsible for the upper
half stroke including twist so that they are positioned symmetrical to a plane that is normal to the wing surface at an
expected twist angle (flap angle 35º, twist angle 22.5º), and in a plane that is normal to the wing surface at half the
upper flapping angle (flap angle 17.5º, twist angle 0º). The lower pair of cameras takes images of the lower half
stroke and is positioned in the same way. After positioning the cameras, camera parameters are adjusted: focal
length, focus, gain and aperture. First the aperture is maximized and the focal length is adjusted so that the wing fills
the field of view when the wing area appears to be maximal. Then the wing is moved to flap angle ±17.5º and the
foci of both pairs of cameras are adjusted. Once the focal plane is defined, the aperture is minimized (closed). Then
all camera gain values are adjusted to the mid-point of the available range (in this case, 9.96 dB). The stroboscope is
activated after this step. Then the aperture of each camera is opened so that the image has reasonable contrast
between the white mat finish and the black speckles. The aperture is kept as small as possible to obtain the sufficient
depth of field. Cameras are then calibrated with a grid pattern that fills the field of view, comparable to the wing
size. The calibration grid is placed to imitate four wing locations for each camera pair: mid-plane without rotation,
mid-plane with maximum rotation, the end of each stroke without rotation, and the end of each stroke with rotation.
This step also double checks all previous parameters. Finally, a reference image is taken when the wing is placed at
the mid-plane (in a vertical position so that no deformation is caused by gravity). This reference image is taken for
both camera pairs and is later used to unify the data in post process.
C. System Synchronization Trigger
Instrument configuration and trigger timing determination are discussed as follows. The peak continuous
sampling rate of the 4 cameras is 7.5 Hz. In order to capture flapping motion up to 35 Hz, correct triggering time is
required so that a sequence of images at all flapping angles can be captured. High-speed cameras are not necessarily
a superior alternative because of lighting requirements and difficulties of fitting into vacuum chambers. For the
current work, a linear stroboscope (Checkline LS-10-6000), triggered together with the shutter of the cameras, bursts
an 8~10 µs pulse of light onto the flapping wings. The energy of each flash is 0.72 joules with 1960 Lux
illumination. This short flash duration freezes the flapping motion with a dark background (no motion blur was
observed up to 35 Hz). Mirrors and sheets of reflective material are used to direct the emitted light onto the wings to
obtain more efficient illumination. By using the nine-pin 1394b interface to control all attributes of the cameras,
registry values that control exposure, triggering modes and strobe signal output can be modified. The cameras are set
to high gain values according to the aperture value that gives a reasonable depth of field. This high gain setting
drastically enhances the picture contrast, while also allowing additional noise that has a negligible effect upon the
image correlation analysis. To reproduce a sequence of images that simulates what could be captured with highspeed videography, it is assumed that the wing deformation at different flapping frequencies and amplitudes should
be time-periodic. Other high frequency content caused by structural vibration is out of the scope of this study;
although it is observed in some cases in vacuum. The time interval between each trigger is determine by the
following relationship: ∆T=(N+1⁄s)/f, where ΔT is the trigger time interval, s is the number of samples per cycle, f is
the flapping frequency at steady state, and N is the number of complete cycles between sequential triggers. Because
of the low speed system and data transfer rate constraints, T needs to be greater than 300 ms.
D. Nano17 Force and Torque Sensor
A force and torque sensor is used to measure the aerodynamic forces produced by the wings. The sensor needs to
be able to measure at high sampling rates and have a high resolution for small forces; therefore an industrial sensor
Nano17 from ATI Automation Inc. is selected, as shown in Figure 3, part 3). In 2007 the Nano17 was the smallest
commercially available 6-axis transducer within the budget of this project. Its resolution is 0.319 g, adequate for the
current application. The sensor’s EDM wire-cut high-yield-strength steel allows it to be overloaded 4.4 times its
rated capacity before being damaged. In this experiment the maximum possible loading condition is substantially
below its rated capacity. The built-in silicon strain gages provide a signal 75 times stronger than conventional foil
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gages. This signal is amplified, resulting in near-zero noise distortion. The system, along with the associated 16-Bit
DAQ system by National Instruments, is calibrated to SI-12-0.12, the finest calibration profile available. The F x and
Fy forces correspond to the thrust and lift directions; both have 1/320 N (0.319 g) measurement resolution. In this
study the sensor is used to measure the average thrust produced by the wings in air. There are structural vibrations
that should be taken into account, as the sensor is not directly positioned at the wings; but such vibration should not
affect the average values, which is used to assess the wings’ aerodynamic performance.
IV.
Experimental Procedure and Data Analysis
A. Experimental Procedure
A flow chart is shown in Figure 4 to illustrate the experimental procedure that includes: control/input, operation,
data acquisition and data analysis. The experiment requires three control inputs: flapping frequency (5 to 35 Hz), the
number of samples per flapping cycle (500 in this study) in load measurements and time interval between triggers
(300 to 450 ms) for the DIC cameras and stroboscope. The first two inputs are given to a virtual instrument (VI)
program created for this experiment. The T input is given to commercial software called VIC-Snap, which
generates calibration correlation files and sends out trigger signals to the cameras.
Fig. 4 Experimental Procedure
The VI graphic user interface consists of two modules: one that communicates to the EPOS serial controller of
the flapping mechanism and the other that communicates to the data acquisition (DAQ) box of the Nano17. In the
first module, the program establishes communication parameters and has the motor controller standing by. One can
command position, velocity, and acceleration to the motor. At this stage, PID gains have already been tuned for
operation. The information is stored in the EPOS controller and is called out by the VI. The PID control is
performed by the EPOS controller and does not require resources from the VI. The VI controls input values to the
EPOS controller and synchronizes with the other module. This module also records the electric current consumed by
the motor, which is later converted to average power. In the second module, the VI specifies sampling rate and
number of samples per measurement to the Nano17 DAQ box. A constant number of samples per flapping cycle is
first specified by the user (500 in this case), then the sampling frequency is calculated as the product of the flapping
frequency and samples per cycle. Both of the modules allow users store the motor feedback data and loads
measurements into text files. Only two components of the forces are recorded, corresponding to the thrust and lift.
In this study, the wings are actuated from 5 Hz to 35 Hz (the highest frequency for each of the four wings varies
because of different structure). In all cases the wings start at the same initial position. The operation sequence is as
follows. After the user has defined a flapping frequency, sample number and time interval, the VI control loop starts
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and establishes communication with the EPOS controller and Nano17. DIC cameras are then initiated, taking
pictures at the calculated frequency. The cameras control the stroboscope by a pulse signal generated with camera
shutter actuation. Immediately, a trigger button is pressed in the VI to activate the flapping mechanism and loads
sensor. From the initial position, the wings accelerate at 2000 rpm/s to reach the command flapping frequency. The
mechanism then stays at that frequency until the measurement is completed. About 40~100 cycles of load
measurement data are taken in each run and three separate runs of data are taken for calculating system errors. Three
cycles of deformation measurements are recorded and there are about 50 frames of pictures in each cycle. This is
done for each frequency and in both air and vacuum. This procedure outputs the text files for loads measurements
and TIFF files for DIC measurements. Converting these raw files into data is discussed as follows.
B. Data Acquisition and Post Processing
The loads measurement text file output by the VI contains a data array, in which each row is the measurement
for one flapping cycle. Since 500 samples are taken in each flapping cycle, there are 500 columns in the array (the
sampling rate is altered along with the flapping frequency, i.e. at 10 Hz, 5000 samples per second and at 30 Hz,
15000 samples per second). Usually 40 to 120 rows of data are taken for averaging. Due to random delays occurring
at the hardware interface (for example, time delay at reading from computer memory buffer), each cycle recording is
slightly shifted (phase delay). Therefore the data are shifted back before the averaging filter is applied. An example
for this procedure is shown in Figure 5-A. Part a) is the instantaneous data taken for one cycle at 37.5 Hz of Wing 3LEO. It can be seen that measurement noise is significant. Part b) shows the ensemble averaged data over 60
continuous cycles. High frequency vibration content (45 peaks per cycle, flapping frequency independent) is
observed in b). This vibration is diagnosed to be the impact force occurred at the contact of the teeth in the gear box.
The shape of the waveform is as expected: two peaks and two valleys are present in one flapping cycle,
corresponding to two thrust peaks occurred during both upstroke and downstroke because of the symmetric motion.
Part c) shows the maximum and minimum noise of the lift data taken from all the 60 cycles, indicating the system
noise level. A sinusoidal pattern is observed from the lift data, this is because the aerodynamic lift is combined with
the inertial force generated by the flapping mechanism (The reciprocator, part-4). Due to the symmetrical flapping
motion, the average value for the lift is always zero. Therefore in this study, because the kinematics is performed in
hovering condition, only time averaged thrust is computed for each frequency and used for the following data
analysis.
Fig. 5-A Force data post processing
The TIFF files are processed with commercial software VIC3D provided by Correlated Solution Inc. The
program correlates each pair of images and outputs the coordinates of data points on the wing surface into text files.
These coordinates are computed relative to a reference image, which is given by the mid-plane of the flapping stroke
at time zero. As discussed above, this reference image, taken of the static wing at mid-plane, is captured by both
pairs of cameras. Based upon the position/orientation of each camera, various calibration parameters, and the
orientation of the static wing with respect to each camera, the reference coordinate system established by each pair
of cameras cannot be expected to coincide. Care must be taken then to stitch the two systems together, so that the
flapping profile remains smooth as the data transitions from one camera system to the other, as shown in Figure 5,
part B-a. This is done by rotating both sets of reference data such that the static wing lies parallel to the x-y plane,
and the leading edge is tangential to the y axis at the root. A separate transformation matrix is then available for
each camera system. Next, each pair of wings is translated such that the wing root coincides with the x axis and the
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leading edge with the y axis. A separate displacement vector is then available for each camera system. Each image
of the dynamic flapping wing captured with the upper pair of cameras is then rotated with the transformation matrix,
and translated with the displacement vector corresponding to the upper pair of cameras. A similar process is
undertaken with the lower pair of cameras. Figure 5-B, part a. also shows the undeformed wing at upstroke and
downstroke ends. Having stitched the two systems together, the DIC data can be used to compute the kinematic
parameters.
VIC3D then generates the displacements of the wings at other positions during flapping. The displacements are
composed of both rigid body motions (kinematics) and structural deformations. It is desired to separate the two: the
latter is much smaller than the former, but is expected to be the sole source of lift and thrust. For the test bed
mechanism in this study, the single DOF flapping of a rigid wing does not produce time-averaged loads, but
adaptive feathering of the trailing edge will. As such, the flexible wings designed and built in this work are very
compliant to provide a large amount of bending and twisting. The rigid body motions and local surface deformations
are separated by creating a fictitious undeformed wing surface at the same flapping angle as the deformed wing
measured during flapping. Transformation of the reference wing profile is performed to match with the deformed
profile at the rigid triangle base (Figure 5-B, part b). First, three data points are selected on the rigid triangle base.
They are very close to one another, and very close to the leading edge of the wing root. As these points are located
close to the wing joint, where the rigid triangular structure locates and is assumed that their motion follows the rigid
body kinematics without elastic deformation.
Fig. 5-B Deformation data post processing
The displacement data for each flapping image can then be used to find the new coordinates of these three data
points throughout the stroke. For each flapping image, local coordinate systems are computed for the two pairs of
triplets (one set which remains stationary at the mid-plane, and one which travels with the wing), and the rotational
transformation matrix is subsequently computed. The static wing at mid-plane is then appropriately rotated, and
then translated so that the two triplets coincide. The difference between the fictitious rigid surface and the elastic
wing provides the sought-after structural deformations, indicated by  in the figure. Three parameters describing the
wing deformation are extracted from the data: the tip deflection  tip, and the angle of twist twist. The tip deflection
is the value of the aforementioned  at the wing tip, in mm. This value indicates how much the wings bend during
flapping. The angle of twist twist is measured at 2y/b = 83% of the wing. This is the angle between the cross section
of the deformed profile and the undeformed profile. This value indicates the amount of wing twist (feathering)
during flapping, in degrees. The wing camber is measured at the same span station as the twist angle. It is the
highest point of inflation of the membrane during flapping (adaptive cambering), measured in mm.
C. Data Analysis
As stated earlier, the experiment is designed to seek the relationship between the thrust production and the
related structural deformation of flapping wings, because the wing compliance is the sole source for generating
aerodynamic thrust. Three raw data types have been collected: average thrust, power consumption, and the full-field
deformation. For the first data type, it alone can indicate the aerodynamic performance of the wings; though thrust
coefficient can also be derived. The power consumption is calculated into efficiency using the metric g/W,
9
evaluating the thrust generated for each unit of power input. The full-field deformation has been represented with tip
deflection and wing twist angle: the tip deflection tells the amount of wing bending (span-wise stiffness) and the
twist angle describes the torsional compliance (or chord-wise stiffness) of the wing. These two values are functions
of flap angle, as illustrated in Figure 6. Three example wings are selected from Wu et al. [reference]; their stiffness
varies from weak to strong, all being actuated at 25 Hz. On the left, the phase loops go in counterclockwise direction;
one the right, clockwise.
Fig. 6 Structural deformation data analysis
These phase loops formed by the three wings enclose different areas and orient at different phase angles due to
their structure difference. The phase angle is defined as the angle between the line formed by the maximum and
minimum y values and the x axis, as shown on the left in Figure 6. Example 2 produces the most thrust and it
encloses large area in both tip deflection and wing twist, with an orientation following the commanded kinematics.
The other two examples are inferior in thrust production: example 1 is too compliant to follow the kinematics,
resulting in a phase angle larger than 90 deg; and example 3 is too stiff, enclosing very small loop areas. Therefore
two scalars can be used to represent the wing compliance: the loop enclosed area and phase angle.
The processed data sheet contains the following information: flapping frequency, average thrust, net energy
efficiency, total energy efficiency, tip deflection loop area in air and its phase, angle of twist area in air and its phase,
tip deflection loop area in vacuum and its phase, and angle of twist area in vacuum and its phase. Regression and
correlation analyses are then used to find statistic relationships among these values.
D. Measurement Uncertainties
The measurement uncertainties of each experiment are listed in Table 2. It should be noted that the absolute
uncertainty values changes as the experiment parameter varies. Therefore the uncertainty value is presented by
rounded percentage. The errors of DIC are induced during the calibration phase and the uncertainty will remain the
same after calibration. If a camera pair is carefully calibrated, the system uncertainty is under ±0.1 mm in the current
setup (except occasionally the speckle pattern introduces other error). However, the tip deflection and angle of twist
data involves more than just DIC measurements: flapping mechanism precision, wing response and density of data
points in a loop would also change the extracted area and angle values. Also, because it is a low speed system, the
number of samples for calculating the uncertainty is limited to using discrete data.
Table 2 Measurement uncertainties
Experimental result values
Unit
Average thrust
Efficiency
Loop area
g
g/W
deg·mm or deg2
Uncertainties of 95%
confidence
±1%
±8%
±5%
10
Number of samples used
60
20
3 cycles of data
Phase angle
deg
±10%
V.
3 cycles of data
Results
A. Wing Performance
In hovering conditions, flapping wing performance is evaluated with the effectiveness and efficiency in
producing thrust. The average thrust produced by the four wings is shown in Figure 7. The results clearly show that
different wing structures lead to different performance. At low frequency range (below 25 Hz), PR and LEO have
superior performance because of larger passive deformation: PR has significant mass distributed on the trailing edge
and LEO has no reinforcement. At higher frequency range (above 25 Hz), the more reinforced BP and Hum yielded
higher thrust values. Similar results are also observed in previous studies4 with stiffer wings producing much more
thrust at high frequencies. It should be noted that in all these four cases, a linearly increasing portion can be found in
a certain frequency range. This indicates that the unsteady aerodynamic effect in the frequency range may not be
dominant. Otherwise aerodynamic loads should not be perfectly proportional to the kinematic parameter of flapping
rate: as if the air momentum produced in each stroke cycle is a constant.
Fig. 7 Average thrust of the four differently reinforced wings
However, wing effectiveness (average thrust) alone cannot represent overall performance, because a wing that
requires higher frequency to achieve higher thrust output may be inefficient. Therefore their net efficiency and
overall efficiency are compared in Figure 8. The total efficiency is calculated from thrust divided by the total power;
and the net efficiency uses thrust divided by the difference between the total power and the power needed to flap the
wing in vacuum (therefore the power consumed by the system inertia is removed in net efficiency calculation). The
power is measured from the sensor integrated with the Maxon motor system, averaged over time.
It can be seen that Wing 3-LEO is the most efficient. Because LEO is not reinforced with extra carbon fiber
battens, it has the lightest weight (Table 1) therefore the least power consumed for wing actuation. This also allows
the wing to deform in a much excessive manner, which can be beneficial at certain frequency range. With the same
reasoning, Wing 4-PR has significant mass distributed outwards (also the heaviest), costing more energy for
actuation and therefore less efficient (net efficiency on the left). However, combined with Figure 7, PR’s excessive
deformation due to inertia allows for producing the most thrust between 17.5 and 30 Hz, rating its overall efficiency
better (such deformation is discussed later). Two sudden peaks in both net and total efficiencies are observed due to
structural resonance. At those resonance frequencies, the power required to actuate the wings in vacuum
significantly drops, yet the wing amplitude is excited larger, beneficial for thrust. However, modal analysis is to be
performed with laser Doppler vibrometry.
11
BP and Hum have more batten reinforcement therefore wing deformation is more constrained, resulted in lower
thrust efficiency. Hum performs the worst among the 4 wing types because the batten structure does not tend to
direct airflow in the thrust direction (defined parallel to the wing root). As expected, for BP at 35 Hz, although the
absolute value of thrust is very high, the net efficiency drops to about half of the one at 20 Hz. The net efficiency
data is not plotted for 5 and 10 Hz because the measurement resolution is not high enough to differentiate the input
power differences, causing overestimation. At high frequencies, some wings cannot be actuated in vacuum because
too high inertial loading would cause damage; therefore some unavailable data are plotted zero in the figure.
Fig. 8 Wing efficiency comparison
B. Structural Deformation
1. Effect of Frequency
Higher flapping frequency corresponds to higher loads for the flapping wings, therefore larger passive wing
deformation. Figure 9 shows Wing 1-BP’s structural deformation varies from 5 to 35 Hz. Part A of the figure shows
five selected frames during downstroke in each case. The color contour represents the out-of-plane deformation
normalized to the root chord length, scaled from -1 to 1. The fictitious reference plane is plotted in the solid grey
lines to indicate the rigid body kinematics. Therefore the full-field technique has well captured details of the
structural deformation: wing’s tip-snap at stroke reversal due to inertial loading and significant washout caused by
aerodynamic loading near the mid-plane. The complete cyclic deformation history is depicted with tip/c and twist in
part B. It can be seen that at 5 Hz, the wing experiences no significant deformation (also shown in part A). As the
flapping frequency increases, the area enclosed by the loops as well as the phase angles increases. Compared to
Figure 7, the increase of the passive wing deformation is well correlated to the increase of the average thrust
produced by this wing. The small structural asymmetry due to one-sided membrane lamination is reflected in the
deformation phase loops as well, especially in the bending case shown in tip/c.
Figure 10 shows Wing 3-LEO’s structural deformation varies from 15 to 22.5 Hz. This small frequency range is
selected because the corresponding thrust value increases linearly (Figure 7). Part A and B are in the same format as
Figure 9, the only difference is that the color contour scale is now -1.5 to 1.5, meaning much larger deformation is
observed, even over a lower frequency range. This is because Wing 1-BP has an extra layer of leading edge
reinforcement (refer to Table 1), therefore higher bending stiffness. Wing 3-LEO’s lack of batten reinforcement also
allows the membrane to deform excessively. In Figure 10-B, the gradual increase of the area size and the growing of
the wing twist duration (which is cause by aerodynamic loads at higher frequencies) correspond well to the linear
increase of average thrust produced. Compared to Figure 9, the maximum angle of twist is constrained around 40
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deg: Wing 1-BP reaches it at 35 Hz while Wing 3-LEO reaches it across the frequency range with different peak
locations and sustaining durations.
Fig. 9 Wing 1-BP at different frequencies in air
Referring to Figure 7, such behavior has lead to a linear increase of average thrust: it means that the output
airflow is proportional to flapping frequency. This shows that the passive deformation pattern shown in Figure 10-B
didn’t contribute to the extra thrust. Unlike in Figure 9, the deformation pattern corresponds to a parabolic increase
in thrust production. This result explains that wings with excessive flexibility may not be ideal to achieve high thrust,
albeit very efficient.
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Fig. 10 Wing 3-LEO at different frequencies in air
2. Effect of Structure
At the same flapping frequency, different wing structure would generate different thrust with unique deformation
patterns. Figure 11 shows the four wings’ deformation at 20 Hz. Part A shows the full-field deformation during the
downstroke: tip-snap magnitude indicates the wing bending stiffness as well as the mass distribution. Wing 1-BP has
the stiffest leading edge therefore deforms the least. Wing 2-Hum has radial diagonal battens that also reinforce in
the span direction, resulting in the least deformation of all the 2-layer-leading-edge wings. Wing 3-LEO has the
largest wing twist because of the absence of batten reinforcement. Wing 4-PR has the largest bending deformation
due to the mass distributed on the trailing edge.
Referring to Figure 7, LEO produces the most thrust, PR the second, BP the third and Hum the least. The
deformation history shown in part B matches with this thrust result very well: LEO encloses the largest loop area in
both plots and has the largest amount of wing twist, therefore the most thrust. However, Wing 1-BP encloses smaller
areas than Wing 2-Hum while it is producing more thrust, showing that the phase angle may be playing a more
important role: Wing 2-Hum is more flexible, reaching tip deflection peaks much later after wing reversal. Between
-15 deg and 15deg flap angle, the area difference in the angle of twist loops does not benefit additional flow in the
thrust direction, even if passive wing twist is a good indicator of fluid/structure interaction. There may be extra
airflow generated but scattered to other directions. These correlation trends will be further discusses.
14
Fig. 11 All wings’ structural deformation at 20 Hz in air
3. Effect of Aeroelastic Coupling
When the experiment is conducted in vacuum, wing deformation is purely caused by inertia, as shown in Fig. 12.
The wing stiffness and mass distribution are then reflected in the deformation phase plots, which also vary at
different frequencies. The results in vacuum can then be compared with the results in air to observe aeroelastic
effects. The deformation measured in air (Fig. 9) consists of coupled inertial and aerodynamic conditions. At 5 Hz,
the phase loop of twist angle encloses almost no area in vacuum while very small loop area can still be seen in the
air case. As the frequency increases, at 15 Hz, inertia causes the wing to deform more, but the enclosed area is still
near zero. Particularly in the tip deflection phase loop, tip-snap at wing reversal goes further but doesn’t contain any
area, unlike the air case, where the tip stays at a delayed position and forms a rectangular loop. This explains that
after inertial tip-snap at each wing reversal, the passive deformation sustained for a period of time is purely due to
aerodynamic loading. But the shape of the loops measure in air always contains both effects.
15
Fig. 12-A Wing 1-BP contour at different frequencies in vacuum
The wing stiffness, therefore, dictates how large the phase loop would form in vacuum. As flapping frequency
increases, inertial loads increases exponentially and the response time for the wing tip to recover becomes longer,
forming a loop as seen in the 25 Hz case. If the frequency goes even higher, at 35 Hz, each tip-snap becomes a
mechanism to store kinetic energy into elastic potential energy: the wing is elastically bent like a loaded spring. In
the absence of air damping, the tip trajectory overshoots its kinematic route near the mid-stroke-plane and forms a
third loop. The vacuum environment also exaggerates the asymmetry properties of the wing: bending stiffness is
smaller during upstroke, therefore the larger loop.
Fig. 12-B Wing 1-BP phase loops at different frequencies in vacuum
C. Thrust and Deformation Correlation
Given that all the four pairs of wings are actuated under exactly the same conditions (kinematics,
frequency/Reynolds number and environment), the cause for producing different thrust as shown in Fig. 7 is
completely due to the differences in wing structure. Such differences are captured with the full-field DIC
measurements and expressed in two key parameters: tip deflection for bending and twist angle for feathering. The
statistical correlation between such parameters and the average thrust value may reveal certain trends that may lead
to better wing design. Fig. 13 shows the correlation results between thrust and tip deflection, the data of which is
extracted in to the enclosed area by the phase loops (unit: deg·mm) and the loop phase angle which describes how
much the actual motion is lacking behind the actuation. Subplot A shows the relationships of all four wings between
the three variables: area, phase angle and thrust, viewed at 0º azimuth angle and 45º elevation angle.
16
Data from BP forms a linear trend line, fitting onto a plane out of page; so are the other three wings’. This means
the trend lines are bending stiffness specific: the three HUM, LEO and PR wings have the same leading edge
structure therefore the similar bending stiffness, falling into the same trend line. It is important to realize that in this
figure the trend lines are independent from flapping frequency (which is the only kinematic variable in this study).
This means the figure relates wing structure directly to aerodynamic performance. Similarly, subplots B and C show
the two trend lines that reflects how the bending stiffness affects wing deformation during flapping and the thrust
generated by such deformation. In subplot C, however, it is interesting to notice that at the last two data points, BP
reaches maximum phase angle while its enclosed area linearly increases with thrust.
Subplot D tells a story that ignores aerodynamic results: the relationship between the enclosed area and phase
angle. In previous subplots, two trend lines are formed distinctly because of the different leading edge stiffness.
Here, the two lines are very close to each other, showing a more general trend. This result suggests that a stiffer
wing would enclose smaller area while the phase angle increases at a very similar rate as more compliant wings.
Such characteristics of BP allow producing the most thrust at high frequencies.
Fig. 14 shows the relationship between wing twist and average thrust in a similar order: A shows the 3D view at
45º azimuth angle and 45º elevation angle; B plots the twist loop area versus average thrust; C the twist loop angle
versus average thrust and D the relationship between the loop area and phase. It is important to note that the phase
angle starts at 180º instead of 0º because of the opposite loop direction (clockwise, Fig. 6). The data are more
scattered in the wing twist case compared to the bending case discussed above. However, general trends still exist.
In subplot B, all of the four wings produce more thrust as the wing twist amplitude increases (shown with larger
enclosed loop area). Since these four wings are of different reinforcement, each trend line is unique, as opposed to
Fig. 13-B. where the three wings of the same leading edge would have the bending deformation relationship collapse
into one. However, subplot C in Fig. 14 shows similar relationship between loop phase and thrust as in Fig. 13-C:
phase angle of the three same-leading-edge wings shares the same trend line. This may mean that the leading edge
stiffness has contribution to the delay (or phase) of the wing twist as well (but not influencing the magnitude of wing
twist). BP again shows high thrust with restricted phase angle increase at large deformation frequencies.
17
Fig. 13 Correlation between average thrust and wing tip deformation
The data in subplot D in Fig. 14 are the most scattered at large deformations (corresponding to high frequencies).
This could be explained with different dominant factors in causing the enclosed loop areas (which is due to chordwise compliance, mass distribution and the magnitude aerodynamic loading) and the loop phase (which is a result of
bending stiffness, span-wise mass distribution and the time history of aerodynamic loading). The bending stiffness
and span-wise inertia would affect the relative time in a cycle of the maximum deformation during wing reversal,
ergo changing the time history of aerodynamic loading. Therefore, unlike Fig. 13-D, the trend lines in Fig. 14-D
cannot be represented with simple functions.
In summary, Fig. 13 and Fig. 14 have shown intrinsic relationships between wing structure and performance,
without relating to flapping frequency, under the same 1 DOF kinematics. It also shows that in hover conditions,
thrust production is closely related to both wing bending and torsion compliance: high thrust can be produced with
large loop area with phase angles that don’t increase with flexibility.
18
Fig. 14 Correlation between average thrust and wing twist
D. Efficiency and Deformation Correlation
Efficiency and deformation data are also correlated, as shown in Fig. 15. In total efficiency correlation, except
for LEO, which demonstrates a clear trend between the wing deformation and the total efficiency, all other data are
scattered randomly. The system efficiency is more difficult to measure than the thrust therefore larger errors are
presented in the efficiency measurement. However, this result indicates that wing aeroelastic properties may not be a
dominant factor in determining either total or net efficiency. The relationship of Hum and PR between net efficiency
and loop enclosed area shows two horizontal trend lines: meaning the power that is required to deform the wings
cancels with the power for thrust gain. Larger loop area indicates structural properties, but it also requires the change
of inertial loads, which require additional power.
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Fig. 15 Correlation between efficiency and wing tip deformation
VI.
Conclusion
This study has employed sophisticated experimental techniques and setup to examine the relationship between
wing structure and thrust, which is generated by passive wing deformation of four micro flexible flapping wings.
The aerodynamic performance of these wings is examined with their ability and efficiency in generating thrust; on
the other hand, the structural properties are carefully measured and some parameters are extracted for further
analysis. The effect of frequency, wing structure and aeroelastic coupling are presented with selected full-field color
contour as well as whole-cycle deformation phase loops of wing tip deflection and twist angle. Correlation is then
performed between thrust/efficiency and the features (the enclosed area and phase angle) of the deformation phase
loops.
From the thrust measurement results, it again shows wings with more bending compliance produce more thrust
at lower frequencies and stiffer wings produce more thrust at higher frequencies. Wing LEO is the most efficient of
all because of its low inertial loads and allowing for excessive passive deformation. The effect of frequency is
illustrated with BP for the large range frequency sweep from 5 to 35 Hz and LEO focusing on the thrust-productive
range. It is shown that the phase loop size, shape and orientation are correlated to thrust production. The effect of
structure is illustrated with all the four wings at the same frequency, with different thrust and deformation phase
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loops. The comparison also indicates the existence of an intrinsic trend between wing structure and performance.
The effect of aeroelastic coupling is examined by comparing structural deformation in vacuum and in air. The
deformation recorded in vacuum reveals the inertial loading and structural response: allowing for understanding the
deformation phase loop in air: deformation peaks are indeed resulted from combinative inertial and aerodynamic
loading and the wash-out/wash-in observed at mid-plane are due to aerodynamic forces and damping. These results
add up to motivate a correlation analysis: first, the deformation phase loops are converted to two scalar values:
enclosed area and phase angle; then these values are correlated with thrust and efficiency. Clear trend lines of tip
deflection and wing twist are observed while no obvious relationship is found between efficiency and deformation.
Acknowledgments
The authors would like to thank AFOSR-69726 for funding this project and Dr. Bret Stanford for his valuable
input and support.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Ellington, C., “The Aerodynamics of Hovering Insect Flight III. Kinematics,” Philosophical Transactions of
the Royal Society of London, Series B, Biological Sciences, Vol. 305, No. 1122, pp. 41-78, 1984.
Shyy, W., Lian, Y., Tang, J., Viieru, D., and Liu, H., Aerodynamics of Low Reynolds Number Flyers,
Cambridge University Press, New York, 2008.
Ho, S., Nassef, H., Pornsinsirirak, N., Tai, Y., and Ho, C., “Unsteady Aerodynamics and Flow Control for
Flapping Wing Flyers,” Progress in Aerospace Sciences, Vol. 39, No. 8, pp. 635-681, 2003.
Wu, P., Stanford, B., Love, R., LaCroix, B., Lind, R., and Ifju, P., “Thrust effective flapping wing structure
characteristics in biologically-inspired hovering flight I. Wing flexibility and aerodynamic forces,”
Bioinspiration and Biomimetics, (Under review) 2009.
Singh, B. and Chopra, I., “Insect-Based Hover-Capable Flapping Wings for Micro Air Vehicles: Experimnts
and Analysis,” AIAA Journal, Vol. 46, No. 9, pp. 2115-2124, 2008.
Khan, Z. and Agrawal, S., “Design and Optimization of a Biologically Inspired Flapping Mechanism for
Flapping Wing Micro Air Vehicles,” IEEE International Conference on Robotics and Automation, Rome,
Italy, April 10-14, 2007.
Wu, P., Stanford, B., Bowman, S., Schwartz, A. and Ifju, P., “Digital Image Correlation Techniques for FullField Displacement Measurements of Micro Air Vehicle Flapping Wings,” Experimental Techniques, Vol.33,
No.6, 2009.
Wu, P., Stanford, B., Sallstrom, E., Ukeiley, L., and Ifju, P., “Thrust Effective Flapping Wing Structure
Characteristics in Biologically-Inspired Hovering Flight II. Aeroelastic Analyses: Deformation/Airflow
Interaction,” Bioinspiration and Biomimetics, in review.
Wu, P., Stanford, B., and Ifju, P., “Insect-Inspired Flapping Wing Kinematics Measurements with Digital
Image Correlation,” SEM Annual Conference & Exposition on Experimental and Applied Mechanics,
Albuquerque, New Mexico, June 1-4, 2009.
Tian, X., Iriarte-Diaz, J., Middleton, K., Galvao, R., Israeli, E., Roemer, A., Sullivan, A., Song, A., Swartz, S.,
and Breuer, K., “Direct Measurements of the Kinematics and Dynamics of Bat Flight,” Bioinspiration and
Biomimetics, Vol. 1, No. 4, pp. S10-S18, 2006.
Wallace, I., Lawson, N., Harvey, A., Jones, J., and Moore, A., “High-Speed Photogrammetry System for
Measuring the Kinematics of Insect Wings,” Applied Optics, Vol. 45, No. 17, pp. 4165-4173, 2006.
Agrawal, A. and Agrawal, S., “Design of Bio-Inspired Flexible Wings for Flapping-Wing Micro-Sized Air
Vehicle Applications,” Advanced Robotics, Vol. 23, No. 7, pp. 979-1002, 2009.
Zeng, L., Matsumoto, H., and Kawachi, K., “A Fringe Shadow Method for Measuring Flapping Angle and
Torsional Angle of a Dragonfly Wing,” Measurement Science and Technology, Vol. 7, No. 3, pp. 776-781,
1996.
Wang, H., Zeng, L., and Yin, C., “Measuring the Body Position, Attitude and Wing Deformation of a FreeFlight Dragonfly by Combining a Comb Fringe Pattern with Sign Points on the Wing,” Measurement Sciences
and Technology, Vol. 13, No. 6, pp. 903-908, 2002.
Cheng, P., Hu, J., Zhang, G., Hou, L., Xu, B., and Wu, X., “Deformation Measurements of Dragonfly’s Wing
in Free Flight by Using Windowed Fourier Transform,” Optics and Lasers in Engineering, Vol. 46, No. 2, pp.
157-161, 2008.
Altshuler, D., Dudley, R., Ellington, C., “Aerodynamic Forces of Revolving Hummingbird Wings and Wing
Models”, The Zoological Society of London, Vol. 264, pp. 327-332, 2004.
21