51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR>18th
12 - 15 April 2010, Orlando, Florida
AIAA 2010-2789
Advanced Flapping Wing Structure Fabrication for
Biologically-Inspired Hovering Flight
Lunxu Xie1, Pin Wu2 and Peter Ifju.3
University of Florida, Gainesville, FL, 32611, USA
Insect wings have complicated vein structures that are strong enough to support large
acceleration, light enough to endure high flapping frequency and flexible enough to passively
deform to enhance aerodynamic performance. As hover-capable artificial flapping flight has
been realized in micro/nano air vehicles (by Aerovironment Inc.), the technical challenge for
creating an efficient flapping wing has attracted more research attention. This work presents
the current flapping wing structure development at University of Florida, in tailoring the
flexibility and mass distribution of membrane-laminated and carbon-fiber-skeletonized
anisotropic flexible wings: the wing skeletal topology has been designed for enhancing
passive deformation for a one-degree-of-freedom kinematics; the cross-section of each
skeletal member is controlled with modern manufacturing techniques to produce the
designed structure; and the final wing is carefully examined for its thrust generation
efficiency and aeroelastic properties (wing deformation). Several challenging aspects are
overcome: realizing a varying skeletal cross-section to achieve a controlled stiffness to weight
ratio, determining the skeletal topology and mass distribution, developing a reliable and
consistent manufacturing technique and examining the wings with different methods. The
results show that a more energy efficient design can be achieved with the developed
manufacturing techniques that allow for complicated structures.
Nomenclature
w
k
L
b
h0
h1
v
E
Fx,y
=
=
=
=
=
=
=
=
=
line load acting on the batten, (N/mm)
line load coefficient, (N/mm3)
length of the wing batten, (mm)
width of the wing batten, (mm)
root height of the wing batten, (mm)
tip height of the wing batten, (mm)
tip deflection of the wing batten, (mm)
elastic modulus of unidirectional carbon fiber in axial direction, (MPa)
thrust and lift component of the aerodynamic forces generated by wing flapping, (N)
I. Introduction
T
HE complicated structure of insect wings has been challenging biologists for a complete answer: is the vein
pattern evolved for better aerodynamic performance, more robust under loading, more efficient in growth or
other reasons? Combes and Daniel1 have conducted point-loaded static experiments to understand the functional
significance of phylogenetic trend in wing venation, finding that wing spanwise flexural stiffness is 1-2 orders of
magnitude higher than the chordwise value. This means that during flight, under the assumption of uniform mass
distribution, passive deformation of wing twisting will be more significant than wing bending. As a design by
natural selection, such wing property should be closely related to and beneficial for generating aerodynamic forces.
1
Research assistant, MAE-B #237, Gainesville, FL, 32611, AIAA member, lunxu@ufl.edu
Research assistant, MAE-A #231, Gainesville, FL, 32611, AIAA member, diccidwp@ufl.edu
3
Professor, Dept. Mechanical and Aerospace Engineering, MAE-A #231, Gainesville, FL, 32611, AIAA member.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2010 by Lunxu Xie. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
In recent research and development in aerospace engineering, micro or nano air vehicles (MAVs and NAVs)
have attracted attention from researchers in different disciplines. Flapping wing MAVs in particular, requires
understandings of aerodynamics, wing structure, kinematics, electronics, control and examples from nature for
design and development. If designing a flapping wing MAV is a multidisciplinary engineering problem, then
understanding flapping wing flight is an interdisciplinary scientific question: aeroelastic behavior of the wing is
coupled of wing kinematics, structural dynamics and aerodynamics. In other words, the kinematics of the wing
affects the inertial loading to the structure, causing deformation that is also affected by aerodynamic loading; while
both the kinematics and wing deformation acts upon air to generate lift and thrust. As seen in nature, wing structural
properties (flexibility and mass distribution) are crucial to flapping flight (aerodynamics). The goal of this paper is
to develop an advanced wing structure for biologically inspired flapping flight.
Natural wing study has revealed that wing flexibility is crucial to insect flight. Combes and Daniel2 have studied
hawkmoth (Manduca Sexta) wings by comparing a fresh compliant wing with a dry one (the lost mass is made up
from additional spray paint) and found that the more flexible one generates much more directed flow than the other
(measured with particle image velocimetry). Of the same species, Combes and Daniel3 have conducted similar
experiments in helium to seek the deformation contributed by inertial loads in comparison to aerodynamic loads and
found that the deformation is mainly caused by wing inertia. This result may be species specific and it means that
the wing deformation may either be just a by-product of kinematics (acceleration) or another factor assisting
kinematics in regulating airflow. Contradictory cases, however, are found by Sun and Tang4, who concludes that
passive wing deformation in insect fly is strongly coupled between both aerodynamic and inertial forces.
Figure 1 shows the detail features of a dragonfly wing: 1) varying structure cross section accentuated at the
leading edge; 2) complicated vein structure supporting the wing integrity; 3) thin membrane material resulting in
light weight; 4) reinforcement topology evolved for aeroelasticity; and 5) the sophisticated airfoil profile affecting
both aerodynamic performance and reinforcing the wing bending stiffness. This work will not compete with the
complexity with such highly evolved natural wing, but will focus on the capability in manufacturing a wing that
emulates these features.
Figure 1. Detail features of a dragonfly wing.
In flapping wing MAV development, significant attention has been paid to the design of the flapping mechanism
and onboard electronics. Successful prototypes such as the two degree of freedom flapping study by Singh and
Chopra5 have allowed measurements of aerodynamic forces in hovering mode. However, the wings utilized are
constructed in a simplified manner: machined aluminum perimeter reinforcing a thin membrane. Other actual
airborne micro air vehicles such as the DelFly6 use carbon fiber rods taped to thin membranes (such as Mylar) to
form the flapping wing. Although such wings have been proven to enable flight, additional structure optimization
could be applied to achieve a more efficient design.
Therefore a manufacturing method is called for to realize different designs that aim for better performance.
Pornsinsirirak et al.7 have successfully applied MEMS technology with titanium alloy to manufacture biologicallyshaped wings: photo-etched titanium (Ti-6Al-4V) skeleton laminated with thin membrane (parylene-C). This opens
up opportunities for very small scale flapping wing designs that have complicated features and require high
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precision. However, such technology is limited to materials that subjects to etching and the high performance
representative titanium has about 2.5 times the density (4.5 g/cm3 vs. 1.75 g/cm3) of carbon fiber but only 1/2 of the
stiffness (unidirectional Young’s modulus 110 GPa vs. 230 GPa). This means if the wing design can be realized
with composite material, it can be lighter without compromising strength.
Previous studies about flapping wings have probed into different disciplines: Galinski and Zbikowski8 have
designed and built an excellent flapping mechanism that is capable of rapid wing rotation at the end of each flapping
stroke; Raney and Slominsky9 have reviewed numerous possible control methods; and Ho et al.10 have summarized
about flapping wing flight in both physics stand point and engineering perspectives. However, these studies, like
many others, focus strongly on the interaction between kinematics and aerodynamics, ignoring wing structural
properties and the structure/fluid interaction. Heathcote11 has conducted experiments of flapping airfoil in still air to
evaluate thrust production with wing flexibility, finding that only certain flexibility under a particular excitation may
benefit thrust. Lin et al.12 created preliminary carbon fiber skeletonized membrane wings that are comparable to
avian dimensions to study aerodynamic performance of different structures. Recently, a circumspect,
multidisciplinary study by Wu et al.13 has examined hummingbird-size wings (75 mm long) at 5~40 Hz for both
flapping wing aerodynamic performance and aeroelastic behavior. The results present very good correlation among
wing flexibility, thrust production, structural deformation and the airflow: moderate passive deformation can
enhance net thrust in one cycle and propel more airflow.
Therefore the results from studying both natural and artificial wing properties indicate that an ideal wing for
flapping flight at insect/hummingbird scale should behave a particular flexibility and mass distribution that allow
passive deformation to improve aerodynamic performance. Also, previous studies have been constrained by limited
design, manufacturing and experimental techniques to explore the vast design space for flapping wings. This work
combines the latest test facilities with design and manufacture techniques of composite materials to develop
advanced flapping wings. The paper is organized as follows. First, the design of flapping wing structure is explained
in detail from three aspects: topology definition, cross section selection and design variables. Then, the
manufacturing techniques used to produce the design are discussed, including mold manufacture and wing
fabrication. Finally, the wings are tested for thrust production and structural deformation and compared with
previous results. The paper will conclude after the results are presented and discussed.
II. Material and Methods
A. Design Parameters
1) Wing topology
The wing planform is chosen to be a 7.65 aspect ratio Zimmerman shape, formed by two ellipses which intersect
at the quarter-chord point. The length of the wing is chosen to be 75 mm. Because the focus of this research is on the
structural properties, the wing is flat (no camber, though the skeletal structure has depth variation). The skeleton
profile is shown in Figure 2. Three quarter-elliptical-shaped battens equally divide the trailing edge into four parts.
This allows each member to control the chordwise flexibility through the torsional properties (dictated by the crosssection). In addition, this pattern can be used for showing that the wing fabrication method presented in this work
can handle curved structure very well.
Figure2. Wing skeleton topology.
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2) Cross-section selection
Each batten is assumed to be a cantilever beam for selecting the cross section shape that has the highest stiffness
to weight ratio. This would allow to control the stiffness with minimum material use, therefore reducing the
structure inertia. A simplified study about cross-section shape selection has been conducted: different shapes are
compared with the same unit area and their area moments of inertia are compared. The area moment of inertia with
respect to the horizontal axis through the centroid of the given shape is shown in Table 1.
Table 1. The area moment of inertia of cross-section shape
Cross-section shape
Area (normalized)
Area moment of inertia
Circle
1
0.0796
Equilateral triangle
1
0.0962
Square
1
0.0833
Regular hexagon
1
0.0802
Semi-circle
1
0.0445
Manufacture feasibility is another factor to be considered in this study. Other shapes may have higher area
moment of inertia (for the same unit area), such as an annulus shape or an I shape. But because of manufacturing
cost with composite materials, these complex shapes are not considered. Based on Table 1, equilateral triangle has
the highest area moment of inertia value. However, considering manufacturing precision, triangular cross section is
not ideal for milling machining, which is the primary method for manufacturing here. This is because a triangular
shape requires an end mill of a cone shape. During machining, the center of the end mill is theoretically not cutting
due to the zero tangential speed. For this reason the equilateral triangle is not the best choice. This makes a square
cross section be considered. The square cross section has the 2nd highest area moment of inertia and can easily be
produced with a cylindrical cutter, with high accuracy. So, a square shape is selected for the cross section. But as
explained in the following, this work will use a varying depth to control the stiffness variation, making the final
cross section rectangular.
3) Design variable
The initial attempt is to achieve a uniform curvature radius during bending by varying the cross section, so that
the material use can be minimized. Therefore each batten is designed as a linearly tapered structure: thicker at the
root and thinner at the tip. The tip height of each batten is chosen to be the same (0.2 mm). Preliminary tests show
that a thinner tip height will cause tip damage during fabrication. Therefore the only design variable is the root
height of the tapered beam (or the gradient in the change of thickness). As shown in Figure 2, a rectangular crosssection shape with 0.5 mm width is selected. The root height is determined based on the comparison between the
tapered cantilever beam and a reference uniform-cross-section cantilever beam under the same load condition and
constraint with the same volume. The reference beam uses parameters based on a leading edge used in previous
research13. The leading edge was made with 3 layers of unidirectional carbon fiber strip (0.8 mm width). The overall
thickness of the cured structure is 0.3 mm. Therefore the reference beam has a rectangular cross section of 0.3×0.8
mm2 and a length of 75 mm. The aerodynamic load acting on the beam is assumed to be a parabolic loading that is
defined as follows:
w  x   kx 2 N/mm
where the coefficient k = 5.575×10-7 N/mm3 is calculated based on an arbitrary 8 gram average load13. The
analytical solution of tip deflection of the reference beam under this line load is 28.849 mm.
Figure 3. Tapered beam under parabolic line load.
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The tip deflection of tapered beam under the same loading condition is governed by the following equation:
1 4 1 3
1
L - L x  x4
12kL3 4
3
12
v " x  
g
3
Eb
 Lh - h - h x 
0 1 
 0


where  is the deflection, b is the width of the tapered beam, h0 and h1 are the root and tip height, and E is the
elastic modulus of the carbon fiber in the axial direction (138~233 GPa).
Because the equation above cannot be integrated directly, a 10th degree polynomial is used as an approximation.
Integrate this polynomial, the approximate analytical solution of tip deflection of the tapered beam is 25.58 mm
when the root height h0=0.45 mm, which presents a reasonable comparison to the reference case.
In order to verify this approximate solution, two finite element models are created in ABAQUS. Because this
program limits the direct modeling of a tapered structure, the tapered beam is modeled as a stepped beam of 25 parts
of equal length and uniform cross section. An illustration is shown in Figure 3, explaining two different
configurations: Model 1 has higher bending stiffness than the actual tapered beam; Model 2 has lower bending
stiffness than the actual tapered beam, so the exact solution of tip deflection should be between the result of Model 1
and Model 2. Both models use quadratic beam element, the length of which is 0.5 mm. There are 150 elements in
total for each Model.
The calculation result shows that the tip deflection calculated with Model 1 is 24.34 mm, and 27.05 mm with
Model 2. The approximated analytical solution is indeed between these two values. Therefore the polynomial
approximation of Equation 2 is valid. This means that a root height of h0 = 0.45 mm can result in similar tip
deflection as the reference beam while using the same amount of material. The final dimensions are shown in Figure
2.
Figure 4. Finite element model - stepped beam .
B. Wing Fabrication
1) Wing mold manufacture
The wing mold is made of a common aluminum alloy 6061. A high speed and high precision Mikron UCP 600
Vario CNC machine is used to create the mold. The CNC machine has a 5 micron machining resolution and is able
to reach 20 thousand rpm maximum spindle speed. A two-flute square head end mill with 0.5 mm (0.02”) diameter
and a maximum 0.75 mm (0.03”) cutting length is used. The wing mold dimension and the machining tool paths are
shown in Figure 5.
Each wing has 5 independent structures which correspond to five tool paths, in which the depth varies linearly
from root to tip. A reinforcement region (shown in pink) machined with 0.3 mm depth is created to connect all other
structure members together. A wing release region (shown in orange) machined with 0.7 mm depth is designed for
placing an extra aluminum insertion plate(0.4 mm thick, shaped as the release region). This plate will help releasing
the cured carbon fiber wing skeleton from the mold. Both the pink and orange regions are milled by a 1 mm square
head end mill. The actual wing mold is shown in Figure 6. In the picture, noticeable scratches are found on the mold
surface. These are formed during the sanding process which will be explained later.
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Figure 5. Wing mold dimension and tool path layout.
After the mold is completed, a deburring process is required. No.1000 sandpaper is used to carefully clean the
burrs in the mold. Before the carbon fiber skeleton fabrication, several layers of release coat (FREKOTE®
No.88428) are applied onto the mold surface. This release material can stop the curing epoxy bonding with the mold
so that the carbon fiber skeleton can be better preserved during separation.
Figure 6. Actual wing mold after several sanding processes
2) Skeleton fabrication
During wing fabrication, the aluminum wing mold is first placed on a heated surface (40 C°) to raise the initial
temperature so that the pre-impregnated carbon fiber material can be placed into the wing mold conveniently. The
releasing insertion plate is first placed into the orange region to fill up the depth difference. Then a layer of
bidirectional carbon fiber is placed at the pink region. An excessive amount of unidirectional carbon fiber is then
filled into the slots. More bidirectional carbon fiber material is then used to fill up any concave regions in the pink or
orange areas. A piece of porous Teflon is then used to cover all the material to allow excessive resin to flow out
during the curing process. Finally, everything is packaged in a vacuum bag and placed into an oven. The whole
curing process takes 7 hours, as shown in Figure 8.
Figure 7. Temperature profile for the curing process.
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Once the carbon fiber was cured, the wing mold is ready to be sanded. The goal is to remove all the extra carbon
fiber above the mold surface so that the final skeleton is exactly the same as the designed shape. Based on previous
sanding test, large friction force can pull out (like in shear) the carbon fiber near the tip of each member. Therefore
small friction force is preferred. But this will extend the sanding time substantially.
Again, No.1000 sandpaper is used. Another aluminum piece with the same dimension as the mold is placed on
top of the mold to apply uniform gravitational pressure. The sandpaper is stick on a flat glass surface with spray
adhesive. The mold is sanded in parallel motion on contact with the sandpaper by hand without applying additional
vertical force (otherwise the mold wear may be uneven).
After sanding, remove the aluminum insertion plate on the bottom of the root corner. The carbon fiber skeleton
can then be gradually separated from the wing mold by lifting the structure up. This step is illustrated in Figure 8.
Figure 8. Final wing skeleton
3) Membrane attachment
The carbon fiber skeleton is applied with spray paint and glue before attaching to the wing membrane. The
membrane material, called Capran® (Honeywell’s Capran Matt 1200), is a biaxially oriented nylon film used in food
packaging. 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 (diffusive to light),
making it amenable to digital image correlation. It also has an extremely low heat shrink coefficient (<2% at 160° C),
making it possible to cure the film with carbon fiber without building up excessive thermal stresses. Its high elastic
modulus and tear resistant properties eliminate concerns on reinforcing the trailing edge. These characteristics make
it a better choice over Mylar® or latex. For DIC experiment, the membrane is painted with random black speckles, as
shown in Figure 9.
To compare between the new fabrication method and the original method14, another pair of wings of the exact
same planform and batten topology is manufactured, as shown in Figure 9. The unidirectional carbon fiber strip has
a uniform 0.8×0.15 mm rectangular cross section. Both the leading edge and the wing root are reinforced with two
layers of such strip and all other battens are reinforced with one layer.
Figure 9. Completed wings.
4) Structure mass comparison between the two wings
It is important for this work to identify how material use in creating the wing structure would affect the bending
stiffness. The reinforcement portion in both wings has used large amount of material comparing to other slender
structures, therefore including this portion in the comparison would induce large error. Measuring the weight of
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whole wing cannot represent the differences between the structure created with the two different methods. A
calculation with measured dimensions is then preferred to compare the mass of each wing structure. It is assumed
that the material density in both wings are the same, and the volume can be calculated with cross sectional area
integrated along the length dimension. The Length of a quarter elliptical batten can be calculated as follows:


  a  b 
L
1 
4
 10 




2 
 a b  
4  3

 a  b  
 a b 
3

 ab
2
For the original wing, both the leading edge and the wing root is reinforced with two layers of unidirectional
carbon fiber strip with 0.8 mm width, all other battens are built with one layer. A single layer of unidirectional
carbon fiber strip is 0.15 mm thick, so the leading edge batten of original wing can be treated as a beam which has
uniform 0.8×0.3 mm2 rectangular cross section, and other battens have 0.8×0.15 mm2 uniform cross section.
Therefore, the volume of all structural members of Wing 1 is 38.4 mm3. Wing 2 has rectangular cross section
changing linearly from 0.5×0.45 mm2 to 0.15×0.2 mm2, resulting in a volume of 39.7 mm3. This shows that both
Wing 1 and Wing 2 have used almost the same amount of material. It would be very interesting to see their
differences in stiffness in the experiments.
C. Experimental Setup
1) Flapping mechanism
The flapping mechanism is shown in Figure 10. The design is created around a Maxon motor system that
includes a 15 W brushless DC motor (EC16), a 57/13 reduction ratio planetary gear head, a 256 counts-per-turn
encoder and an EPOS 24 controller. This system provides precise control of the motor: the sensor provides position
and velocity feedback to the controller that actively regulates the motor. In combination with the Maxon serial
controller, the motor system can output any velocity, position or current profile within the specification range.
Two mechanisms are used to realize the flapping motion: the reciprocating motion created by a slider-crank
mechanism and the flapping motion realized with a linkage mechanism. Such a design emphasizes the use of a
single rotational source to reduce asymmetry of motion. It also avoids slots that may lead to excessive frictional
wear and potential excitation vibration problems. The crank module is connected to the gear head shaft, which
outputs up to 124 revolutions per second. This corresponds to a possible flapping frequency up to 124 Hz. The offset
distance of the pin joint from the shaft axis on the crank module defines the flapping amplitudes. Several holes are
tapped into the module: by screwing the pin to these holes, different flapping amplitudes can be realized. Several
crank modules have been manufactured to allow a wide range of selection: from ±10° to ±60° flapping amplitude.
The main structure is made of aluminum alloy with some carbon fiber parts and two stainless steel slider guides. All
reciprocating parts are made as light weight as possible. The reciprocator on the slider is the most important
component of the mechanism: eight 3 mm outer-diameter ball bearings are used to construct this linear bearing that
allows well-constrained reciprocating motion. The linkage of the wing mount and the rocker applies geometric
constraints so that the wings will rotate around the upper pin joint of the rockers during flapping. All joints are well
lubricated and installed with either brass sleeve bearings or steel ball bearings, though minor part wearing after long
duration flapping is observed. Therefore, the flapping mechanism has been designed so that all parts can be quickly
replaced to restore worn components. As can be seen in the front view of , a plate on the left of the motor mount is
attached to the force and torque sensor described below.
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Figure 10. Flapping mechanism FL2D3.
2) Full-field wing kinematics and deformation measurement
The kinematics and deformation of flapping wings are measured with digital image correlation (DIC). DIC is a
well-developed non-contact stereo-image measurement technique used in this work to capture full-field
displacement and local deformation. The system uses stereo triangulation to digitize a random speckling pattern
placed on an object, 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 un-deformed location of this subset, and thus the displacements. The correlation system consists of
four Point Grey Research Flea2 cameras divided into two pairs. Such a setup should be able to capture the rigid
displacements (wing kinematics) and concomitant structural deformations of a single wing up to a 180° flapping
amplitude. Each pair of Flea2s can capture stereo pictures of a wing moving through a 90° angle after fine-tuning
the depth of field. The cameras are positioned symmetrically about the plane of flapping motion. They are tilted
towards the same wing and zoomed in so that the wing fills the picture frame. The upper pair captures the stroke
above the flapping mid-plane; the lower pair captures the stroke below the mid-plane. The digital image correlation
setup is shown in Figure 11, along with the loads measurement sensor (below) and overall experimental setup on the
right. Details of the hardware connection, control and trigger timing are described in the previous work15.
Figure 11. DIC and force measurement system experimental setup.
3) Aerodynamic performance measurement
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Time-averaged aerodynamic forces produced by the flapping wings are measured with a force and torque sensor
(ATI Industrial Automation’s Nano17, http://www.ati-ia.com/), which is mounted underneath the flapping
mechanism, as shown in Figure 2, A-8). The sensor has 0.319 g of force resolution, which is adequate for the current
application. The forces in the x and y directions correspond to the thrust and lift directions; both have the stated
measurement resolution. Both the flapping mechanism and the sensor are controlled with a virtual instrument
program in LabVIEW. The sampling rate is set to change along with the flapping frequency so that a constant
sampling resolution of 500 samples per flapping cycle can be achieved (i.e. at 10 Hz, 5000 samples per second and
at 30 Hz, 15000 samples per second). The data structure contains a number of rows of 500 data points, saved in a
text file. Each row represents the force history of one flapping cycle. Usually 40 to 150 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 shift is corrected
before an averaging filter is applied.
In this particular 1-DOF case, however, if both the kinematics and structural properties are symmetrical to the
wing’s leading edge, the average lift measurement should be zero. This leaves only the averaged thrust to evaluate
the aerodynamic performance. There are three points that needs to be made clear in this force measurement step: 1)
why the inertial forces of the wing and the mechanism would not affect the averaged measurement in both lift and
thrust directions; 2) why the aerodynamic lift generated with a symmetrical 1 DOF motion should be zero and why
with a non-deforming wing such kinematics would not produce significant thrust; and 3) why the average thrust
value can be used as a metric to evaluate flexible flapping wing performance. Details pertaining the related
discussion can be found in parallel work by Wu and Ifju16.
4) Data post processing
A reference image, taken of the static wing at mid-plane, is captured by each pair 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. 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 parallel to the y axis. 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 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.
Having stitched the two systems together, the DIC data can be used to compute the kinematic parameters. As
discussed by Wu et al.14, the u, v, and w displacements of each flapping wing image (referenced from the static wing
at mid-plane) are available in a full-field manner over the wing. This data can be interpolated onto a small triangle
located towards the root of the leading edge. The three points can be used to form two coordinate systems: the
undeformed triangle (of the static wing at mid-plane) merely corresponds to the unit vectors of the x-y-z coordinate
system. The coordinate system associated with the new position of the triangle corresponds to a system that travels
and rotates with the flapping wing: a body-attached frame. Three Euler angles make up to the transformation matrix
that rotates the static coordinate system into the body-attached frame: one of these angles is the flapping angle,
another is the rotation angle. The third angle should be close to zero, as no yawing motion is expected with the
current flapping mechanism.
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.
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III. Results
The results presented here discuss on two aspects: the performance of the wings and the aeroelastic behavior of
the structure. The main objective is to compare Wing 1 and Wing 2 in these two aspects. As explained in the wing
design portion, the new manufacturing method controls the wing cross section, therefore can produce a structure
with much higher bending stiffness. This will cause much less passive deformation in Wing 2, while Wing 1 should
perform similarly to previous work13, generating significant thrust due to the passive deformation.
B. Thrust Production
The time-averaged thrust produced by the two wings is shown in Figure 12. The effect of wing bending
stiffness on thrust production is clearly illustrated, the more flexible Wing 1 generates much higher thrust than the
stiffer Wing 2 at all frequencies. The thrust produced by Wing 1 has an linear crease, similar to observation in
previous studies in flexible wings13. Wing 2 has a trend of parabolic increase, which has also been observed in stiffer
wings. As the flapping frequency increases, the average thrust increase generated by original wing is growing faster
than the new wing. These trends show that at a certain flapping frequency and flapping amplitude, wing flexibility in
bending affects aerodynamic performance significantly.
Figure 12. Average thrust comparison between Wing 1 and Wing 2.
On the other hand, when the flapping frequency is above 25 Hz, the thrust produced by Wing 2 increases faster
than the one by Wing 1, as shown in Figure 13. This is because for the very stiff Wing 2, passive wing deformation
can only be achieved at higher flapping frequency when inertial loading increase quadratically. For the flexible
Wing 1, large deformation has been realized at low frequencies, therefore deformation at high frequency is limited
by the inelastic membrane. In order to observe this wing behavior, the structural deformation needs to be measured.
Figure 13. Average thrust increment as a function of flapping frequency.
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American Institute of Aeronautics and Astronautics
C. Structural Deformation
In this study, all results are measured at flapping amplitude ±35° and at flapping frequency 20 Hz. In Figure 14.
the structural deformation color contours during downstroke for both Wing 1 (the Original Wing) and Wing 2 (the
New Wing) are shown. All x, y and z dimensions are normalized to the chord length 25 mm. The grey line shows
the undeformed reference rotated to the same flapping position, representing the rigid body kinematics. It can be
seen that indeed Wing 2 has a much stiffer structure and experience much less wing deformation, especially if the
comparison is made in the mid-plane where large washout (0.8 of 25 mm deflection) exists in Wing 1. This explains
well why there is almost no time averaged thrust produced by Wing 2 at 20 Hz.
Figure 14. Deformation comparison of the original and the new wing at 20 Hz in air, downstroke.
Figure 15 shows the complete deformation history in one flapping cycle, normalized tip deflection on the left and
wing twist rotation angle on the right. Wing 1's flexibility is described by the two phase loops while the randomness
of the Wing 2 data indicates its rigidity and high frequency vibration due to actuation.
Figure 15. Phase plot for wing deformation showing the complete flapping cycle.
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American Institute of Aeronautics and Astronautics
The results show that the flexibility is the key in creating thrust by passive deformation. This, however, does not
render the new manufacturing method non-beneficial, but rather points out that the design philosophy behind
flapping wing structure design should focus on both stiffness tailoring and mass distribution so that beneficial
passive wing deformation can be achieved.
IV. Conclusions
This work has used high precision manufacturing techniques in creating micro air vehicle flexible flapping wings
with desired flexibility and mass distribution to improve thrust generation. The wing topology is selected so that
torsional and bending flexibility can be controlled through the change of depth variation of the cross-section in each
batten. Combining composite manufacturing techniques and computational numerical controlled milling,
complicated wing skeletal structure is realized according to the design.
The final composite wing is proven to have very different aerodynamic performance measured by thrust
produced in hovering conditions comparing to flexible wings made under previous techniques. This is because the
weight distribution of the wing has be dramatically reduced (focused near the root. but this makes potential higher
flapping frequency feasible) and the stiffness of each structure has increased because of the controlled cross section.
These two factors makes Wing 2 deform much less than Wing 1, therefore producing much less time averaged
thrust.
The deformation of the wings is also examined with a full field technique. The measurement result is confirming
the results found in previous studies: a rigid wing structure undergoing no passive deformation cannot generate time
averaged thrust with one degree of freedom flapping motion. Therefore the new manufacturing method would be
perfect for creating stiff wing structure for complicated kinematics at very high frequencies. Furthermore, the
amplitude and phase of the passive deformation (as shown in Figure 15) is the cause for thrust generation with 1
DOF flapping kinematics. In other words, designing the wing structure has become the design for passive
deformation that dictates thrust production efficiency.
The new fabrication technique presented in this work also shows promise in other aspects: consistent and rapid
manufacturing is now feasible with machining tools ready; the process can even be automated in future. Future work
will include tailoring the stiffness and mass distribution for both one and two degree-of-freedom flapping flight and
searching for the optimum topology for certain parameters.
Acknowledgment
This work is supported by the Air Forced Office of Scientific Research under MURI program 69726. The
authors whole heartedly thank Professor Tony Schmitz and his research group for their help during the
manufacturing process.
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