Solid State Morphing Aircraft
Old Dominion University
Mechanical & Aerospace Engineering Department
Project Design & Management II – MAE 435 Final Report
April 21, 2015
Spring 2015
Team Members:
Joe Altomare
Adam Horn
Thomas Lamb
Nathan LaPuma
Aaron Rosenberg
Austin Stallworth
Advisor:
Dr. Onur Bilgen
Graduate Assistant:
Francis Hauris
Table of Contents
Table of Contents ........................................................................................................................................... i
List of Figures ................................................................................................................................................ ii
Abstract ........................................................................................................................................................ iii
Introduction .................................................................................................................................................. 1
Methods ........................................................................................................................................................ 2
First Iteration ............................................................................................................................................ 3
Second Iteration ........................................................................................................................................ 9
Results ......................................................................................................................................................... 11
Discussion.................................................................................................................................................... 16
Conclusions ................................................................................................................................................. 19
References .................................................................................................................................................. 21
Appendices................................................................................................................................................ A-1
Appendix A: MatLab Codes ................................................................................................................... A-1
Appendix B: Vacuum Bagging Process ..................................................................................................B-1
Appendix C: Second Iteration Fabrication ............................................................................................ C-1
Appendix D: Budget .............................................................................................................................. D-1
Appendix E: Gantt Chart ........................................................................................................................ E-1
i
List of Figures
Figure 1: Inventor FEA................................................................................................................................... 3
Figure 2: Inventor simple wing planform ...................................................................................................... 5
Figure 3: COMSOL substrate simulation ....................................................................................................... 6
Figure 4: COMSOL simulation with substrate ............................................................................................... 6
Figure 5: Finished wing ................................................................................................................................. 7
Figure 6: Bonded MFCs with one set of wires soldered ............................................................................... 7
Figure 7: Testing apparatus........................................................................................................................... 8
Figure 8: Example of 180 degree phase shift ................................................................................................ 9
Figure 9: Completed 2nd Iteration assembled ............................................................................................. 9
Figure 10: 4-bar linkage tests ...................................................................................................................... 11
Figure 11: Deflection of a theoretical beam under a distributed load ....................................................... 11
Figure 12: Deflection of a beam under a concentrated laod ...................................................................... 12
Figure 13: XFoil- Coefficient of lift vs Angle of Attack as a function of Camber ......................................... 12
Figure 14: Displacement as a function of Voltage ...................................................................................... 13
Figure 15: Bending displacement when the twisting actuator orientation is varied ................................. 13
Figure 16: Twist angle when the twisting actuator orientation is varied ................................................... 14
Figure 17: Effect of increased voltage on wing bending displacement ...................................................... 14
Figure 18: Effect of increase voltage on wing twist comparison ................................................................ 15
Figure 19: First Iteration phase shift results ............................................................................................... 15
Figure 20: Second Iteration phase shift results .......................................................................................... 16
ii
Abstract
The research presented studies solid-state flapping wing aircraft, or ornithopters. For the
purposes of this project, solid-state is defined as no mechanically actuated or operated parts. The
research investigated the use of Macro-Fiber Composite (MFC) actuators to generate the flapping
motion. MFCs are piezoelectric devices that use electromechanical coupling for bending,
extension, and torsion. The MFCs were modeled to determine a theoretical deflection value. A
simple wing shape was modeled and fabricated out of carbon fiber for testing. Two MFC actuators
were bonded to the wing in order to produce bending and twisting motions similar to birds. A
voltage and frequency sweep was performed on the wing-actuator composite structure to
determine the resonant frequency and deflection response of the wing. At the resonant frequency,
maximum deflection of the wings will occur, which is important for maximizing lift and forward
thrust.
iii
Introduction
An ornithopter is a machine designed to achieve flight by means of flapping wings.
Ornithopters have the advantage of maneuverability; they are more maneuverable than fixed wing
aircraft and have high performance in low speed flight conditions [1]. Current ornithopter designs
are rigid, with gear like mechanisms to create the flapping motion in the wing. Rigid mechanical
systems add weight, and require extra power [1].
An alternative to rigid mechanical designs is to utilize materials that respond to external
stimuli in a controlled, predictable fashion, or “smart materials” [2]. The implementation of smart
materials into wing morphing designs could allow for flight to be achieved with a solid-state
aircraft. Smart materials are materials that have one or more properties that can be significantly
changed in a controlled fashion by external stimuli, such as stress, temperature, moisture,
pH, electric or magnetic fields. Solid-state aircraft do not use conventional mechanical moving
parts, leaving the propulsion, energy production, and storage to be integrated within the structure
of the aircraft [3]. As a result, the aircraft relies on thrust provided from the flapping motion
produced via smart material actuation in the wings.
Macro-Fiber Composites (MFCs) are a type of piezoelectric device that converts electrical
energy to mechanical energy, which can be used for bending, extension, and torsion.
Electromechanical coupling occurs when a voltage is applied to electrodes that are attached to each
side of the piezoelectric material, producing a material strain. Because MFC actuators have short
response times and significant force output, they could function well as flapping wing actuators
for an ornithopter.
The flapping wing designs are expected to be quieter than the propellers used in traditional
small aircraft. The flapping technology may also be more fuel-efficient and offer a more
1
maneuverable aircraft [4]. This design is capable of operating at lower speeds because of the
flapping motion, therefore it will not need to rely so heavily on thrust to create lift on the aircraft
[5]. The large wingspan and the low cruising flight flap frequency of birds with high aspect ratio
make them good candidates for wing mimicry.
The purpose of this project is to continue research on the feasibility of solid-state flight in
a small ornithopter based on the work that was commenced by the 2013-2014 Solid-State Aircraft
(SSA) Undergraduate Design Team [6]. The cruising flight behavior seen in nature will be
mimicked through the use of smart materials (MFCs). Using the 2013-2014 SSA Team’s research,
which was based on the Blue Heron, essential characteristics will be analyzed including: wing
shape, chord length, camber, flapping frequency, wing deflection during flapping cycles and angle
of attack. Using a harmonic voltage output to match the flapping frequency of the Blue Heron, the
MFCs will create forces on the wing, causing deflection. The structure of the wing must be able to
endure the forces from both the MFC and aerodynamic loads. The wings must produce a positive
net lift and thrust.
Methods
The MFC actuators were tested on two wing iterations so a comparison could be done.
Baseline data was collected from testing the first iteration of the wing. The geometry of the wing
and placement of the actuators were changed on the second iteration of the wing. Data collected
from testing the second iteration was compared with the baseline data. Results were analyzed
and conclusions were made based on what the study revealed. This approach allowed for a basic
understanding of the effects MFC actuators could have on the flapping motion of a wing.
2
First Iteration
The first iteration used a basic geometry and was tested with varying voltages over a range
of frequencies in order to establish some baseline data. Both bending and twisting were analyzed
in the first iteration.
Structural:
Finite element analysis was performed in Inventor (Autodesk Inc., San Rafael, California)
to determine the deflection of a beam. To test the validity of the model, arbitrary dimensions were
chosen for the beam. The dimensions of the beam were 5 meters wide, 1 meter thick and 25 meters
long. First the beam was analyzed with a concentrated load at the end, then the beam was analyzed
with a distributed load across the entire length of the beam (
Figure 1).
Figure 1: Inventor FEA
To verify the Inventor results, classical beam theory was implemented in MATLAB (The
Mathworks, Natick, MA) to calculate the deflection of the beams modeled using end load
(equation1) and uniformly distributed load (equation 2) equations as shown below (Figures A.1
and A.2).
𝑤𝑥 2
𝑦 = 24𝐸𝐼 (𝑥 2 + 6𝑙 2 − 4𝑙𝑥)
𝑦=
𝑃𝑥 2
6𝐸𝐼
(3𝑙 − 𝑥)
(1)
(2)
3
where w is the distributed load, P is the end load, E is the modulus of elasticity, I is the moment
of Inertia and l is the length of the beam.
Aerodynamics:
The basic aerodynamic properties of any airfoil are thrust, lift, drag and weight. The
equation for lift (equation 3) and drag (equation 4) were analyzed in depth for basic wing
planforms.
𝐿=
𝐷=
𝐶𝐿 𝜌𝑉 2 𝐴
2
𝐶𝐷 𝜌𝑉 2 𝐴
2
(3)
(4)
where 𝐶𝐿 and 𝐶𝐷 are the coefficients of lift and drag respectively, 𝜌 is the density of the fluid the
aircraft is in, A is the area of the object, and V is the velocity of the aircraft relative to the air. These
parameters that dictate lifting force and drag force were carefully studied to determine how they
contribute to their respective force and how to design the ornithopter for successful flight. The
Solid-State Aircraft aerodynamics subgroup collaborated with the biomechanics subgroup to
determine what makes birds successful ornithopters and how to model our wing based on how
nature’s ornithopters generate the forces required for flight. In continuing with the 2013-14 SSA
team’s research, the Great Blue Heron’s wing was chosen as our base model to replicate.
A major parameter of ornithopter cruising flight is their wing aspect ratio (equation 5).
A.R =
𝑏2
𝑆
(5)
where b is the wingspan and S is the wing area. The higher the aspect ratio, the better the cruising
capabilities of the ornithopter. The aspect ratio was calculated based on of the measurements of a
Blue Herron’s wings and used in the design of the wing shape. For simplicity of fabrication and
to help develop a basic understanding of the effect the actuators have on the flapping motion, a
4
basic wing design was chosen. This design incorporated the Blue Herron’s aspect ratio but scaled
down chord length and wing span (Figure 2). It was modeled using Autodesk Inventor (Autodesk,
Mill Valley, CA).
Figure 2: Inventor simple wing planform
XFoil (Massachusetts Institute of Technology, Cambridge, MA) was used to analyze the
properties of airfoils. Camber, which is the rise of a curve in an airfoil, was varied during the
simulations, while airflow and airfoil thickness were held constant. This analysis was done so the
effects of camber could be considered for the wing design.
Smart Materials:
COMSOL (COMSOL, Inc., Burlington, MA), a finite element analysis software, was used
to simulate the MFC actuator’s behavior when attached to an aluminum substrate that matched the
dimensions of the actuator (14mm x 85mm) (Figure 3). Ten domain point probes were placed
along the length of the substrate so that the static deflection could be determined. Voltage was
applied starting at -500V and increased in increments of 500V until 1500V was reached. After
this simulation was performed, actuators were applied to a 3-D model of the wing design. One
actuator was applied parallel to the leading edge of the wing. Another actuator was applied at
5
varying angles to see the effect that actuator placement would have on bending and twisting
(Figure 4). Point probes were applied again to measure bend and twist.
Figure 3: COMSOL substrate simulation
Figure 4: COMSOL simulation with substrate
Fabrication:
The wing was made out of carbon fiber using the vacuum bagging process. This process
involved laying carbon fiber fabric on a mold and applying an epoxy-resin (Figure B.1). The mold
was put in an airtight bag and placed under vacuum (Figure B.2). As the air was pulled out, the
carbon fiber formed to the mold under atmospheric pressure and hardened as the resin cured. The
finished product was then cut into the desired wing shape using a Dremel (Figure 5). Carbon fiber
was used for the wing because of its desirable material properties, cost, and availability.
6
Figure 5: Finished wing
Once the wing was fabricated, MFCs actuators needed to be bonded to the wing. Two
actuators were applied to each wing (Figure 6). One was placed parallel to the leading edge to
function as the primary bending actuator. The other was placed at an angle of 15 degrees to
function as the primary twisting actuator. The actuators were bonded to the wing using a similar
vacuum bagging process. Wires were soldered to the actuators after undergoing vacuum bagging
for the second time.
Figure 6: Bonded MFCs with one set of wires soldered
7
Testing:
The fabricated wing was placed in the testing apparatus. A clamp held the wing in place
while two lasers positioned above the wing were used to measure displacement (Figure 7).
LabVIEW software (National Instruments, Austin, Texas) was used to operate the actuators and
collect the data. Low resolution frequency sweeps were conducted from 1 Hz to 10 Hz at 0.25 Hz
increments. The voltage started at 100 volts and was increased by 100 volts for each frequency
sweep through 500 volts. This testing procedure was applied to the bending actuator only, the
twisting actuator only and the bending and twisting actuator simultaneously. Data was collected
across the wing at the 25%, 50% and 75% span locations. The low resolution sweeps were done
to determine a range of frequencies where the maximum displacement of the wing was occurring.
High resolution sweeps using a step size of 0.01 Hz were conducted using the same method in
order to determine a more precise frequency where the maximum displacement was occurring.
The frequency at which maximum displacement occurs at is known as resonant frequency.
Resonant frequency is important to determine in order to maximize the performance of the wing
design.
Figure 7: Testing apparatus
8
Phase shift tests were also performed. This test supplied harmonic voltage independently
to the primary bending and primary twisting actuator at the same frequency and voltage but a phase
angle is applied to the two waves causing the two actuators to move out of sync of each other.
Figure 8 shows an example of two sine waves
shifted 180 degrees.
Phase angles were
tested from 0 to 180 degrees in 15 degree
increments. This test was done to see where
the maximum bending and twisting would
both occur simultaneously.
Figure 8: Example of 180 degree phase shift
Second Iteration
A second iteration of the wing was fabricated in order to have data for comparison. In an
attempt to design a full aircraft, a fuselage was integrated into the wing design of the second
iteration. The wing geometry of the first iteration was maintained while placement of the primary
twisting MFC actuator was changed in order see the effects on bending and twisting.
Fabrication:
A fuselage was incorporated into the design and fabrication of the second iteration. This
was done by modeling a basic symmetric shape in Inventor (Figure C.1). The model was 3-D
printed in ODU’s 3-D printing lab. Because of the size constraints of the 3-D printer the fuselage
had to be printed in 4 sections: 2
Snap Fasteners
for the top half and 2 for the
bottom half (Figure C.2).
The
wing was again made out of
carbon fiber using the vacuum
Figure 9: Completed 2nd Iteration assembled
9
bagging process but when the carbon fiber fabric was laid out it was laid on top of the fuselage
piece before the epoxy resin was applied. This method allowed for the carbon fiber to bond to the
fuselage while forming around it during the vacuum bagging (Figure C.3). The wing shape was
cut out and MFC actuators were bonded to the wing using the methods for the first iteration. The
primary bending actuator was placed in the same location but the primary twisting actuator was
placed mid-span on the wing and oriented at 45 degrees (Figure C.4). The top and bottom halves
of the fuselage were fabricated separately. When the fabrication was finished, snaps were used as
fasteners to allow for ease of assembly and disassembly of the fuselage (Figure 9).
Testing:
The fully assembled second iteration was placed in the testing apparatus and underwent
similar testing to measure bending and twisting. Low resolution frequency sweeps were conducted
from 1 Hz to 6 Hz at a step size of 0.25 Hz to determine a more narrow range to test for the resonate
frequency. The high resolution frequency sweeps were done from 3.25 Hz to 4.5 Hz. Again the
measurements were taken at the 25%, 50%, and 75% span locations while the lasers measured
displacement. Phase shift testing was also performed on this iteration.
The second iteration of the wing was also tested for lift and thrust. Aerodynamic behavior
was analyzed using a 4-bar linkage apparatus that was developed by the 2013-14 SSA design team
(Figure 10) [6]. The apparatus fixes all degrees of freedom except one. This apparatus was
arranged to only allow travel in a vertical direction. The aircraft was arranged in a horizontal
position parallel to the ground to test for lift. Next the aircraft was in a vertical position
perpendicular to the ground to test for thrust. The wings were actuated and the apparatus was
observed for any movement in the vertical direction to determine if any lift or thrust was produced
10
respectively. Movement in the horizontal configuration would be indicative of lift, movement in
the vertical configuration would be indicative of thrust.
Direction of
Movement
Direction of
Movement
Figure 10: 4-bar linkage tests
Results
A theoretical beam was loaded with a concentrated load and a distributed load in Inventor.
The same beam was also analyzed using classical beam theory. The resulting difference in
deflection is illustrated in the deflection vs. length plots shown in Figure 11 and Figure 12. The
analytical and numerical results were compared. The results from this comparison show the
validity of the numerical model. This allows for further FEA to be done using Inventor.
0
Deflection (mm)
-0.005
-0.01
Analytical
-0.015
Numerical
-0.02
-0.025
-0.03
-0.035
-0.04
0
5
10
15
20
25
30
Length (m)
Figure 11: Deflection of a theoretical beam under a distributed load
11
Deflection (mm)
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.09
-0.1
Analytical
Numerical
0
5
10
15
Length (m)
20
25
30
Figure 12: Deflection of a beam under a concentrated laod
Aerodynamics:
The results of the XFoil simulation are illustrated in Figure 13. This shows that as camber
is increased, the lift coefficient increases. The angle of attack at which stall occurs decreased with
the increase of camber. Additionally, these results show that with the addition of camber, lift
occurs at negative angles of attack.
Figure 13: XFoil- Coefficient of lift vs Angle of Attack as a function of Camber
Smart Materials:
The amount of deflection of an aluminum substrate when increasing voltages are applied
to a MFC actuator is shown in Figure 14. As voltage was increased so was deflection. It was also
observed that a negative voltage causes the actuator to deflect in the opposite direction.
12
0.2
-500V
0V
500V
1000V
1500V
Displacement (mm)
0.15
0.1
0.05
0
-0.05
-0.1
0
20
40
60
Length (mm)
80
100
Figure 14: Displacement as a function of Voltage
The effects of actuator orientation on bending and twisting of a wing design were studied
in COMSOL. As the twisting actuator orientation angle was increase this effected the bending
displacement negatively (Figure 15). The effect of twist as the twisting actuator orientation angle
is increased is shown in Figure 16. The twisting angle decreased in one direction and increased in
the other direction as the orientation angle of the twisting actuator increased.
0.002
0 degrees
0.0018
5 degrees
0.0016
10 degrees
Displacement (in)
0.0014
15 degrees
0.0012
20 degrees
0.001
25 degrees
0.0008
30 degrees
0.0006
35 degrees
0.0004
0.0002
0
0
2
4
6
Span (in)
8
10
12
14
Figure 15: Bending displacement when the twisting actuator orientation is varied
13
Twist (Deg)
0.001
0.0008
0.0006
0.0004
0.0002
0
-0.0002
-0.0004
-0.0006
-0.0008
-0.001
0
10
20
Actuator Orientation (deg)
30
40
Figure 16: Twist angle when the twisting actuator orientation is varied
Multiple tests were performed on the both iterations of the wing with MFC actuators
bonded to it. The data collected allowed for multiple studies to be done. The first study looked at
two things, identifying the resonant frequency and the effect increasing voltage had on bending
displacement (Figure 17). Because this is a vibrating beam the maximum displacement occurred
at the resonate frequency. The resonant frequencies were 5.42 Hz for 100V, 5.31 Hz for 300V,
and 5.23 Hz for 500V for the first iteration. For the second iteration the resonant frequencies were
3.96 Hz for 100V, 3.86 Hz for 300V, and 3.89 Hz for 500V. The bending displacement was tested
with voltage being supplied to the bending actuator only. As voltage was increased, displacement
increased in a linear fashion.
Figure 17: Effect of increased voltage on wing bending displacement
14
The next study looked at the effects increased voltage had on the maximum angle of twist
(Figure 18). The twisting tests were done with voltage being supplied only to the twisting actuator.
As voltage increased greater twist was produced. Additionally, there was little twist at resonant
frequency.
Figure 18: Effect of increase voltage on wing twist comparison
A third study examined the effect that phase shift had on the relationship between bending
and twisting.
Voltage was increasingly supplied harmonically while the phase angle was
increased. For the first iteration, there seems to be a direct relationship between bending and
Figure 19: First Iteration phase shift results
15
twisting. As the phase angle was increased to 180 both bending and twisting appeared to decrease
(Figure 19). For the second iteration, bending remained constant while great twisting appeared to
be greater at higher phase shift angles (Figure 20).
Figure 20: Second Iteration phase shift results
Discussion
The purpose of the 2014-2015 Solid State Aircraft project is to study the feasibility of using
Macro-Fiber Composites as actuators to produce thrust. The MFC actuators will be able to control
the deflection of the wing in order to achieve flapping motions similar to those of birds.
The FEA performed demonstrates that for a concentrated load at the end of the cantilever
beam and a distributed load over the length of the beam, the numerical solution is very close to the
analytical solution, which confirms the validity of the models. The data shows that a concentrated
load causes a larger deflection than the distributed load; however, the distributed load is a closer
approximation of the forces that will actually be affecting the wing. When a voltage is applied to
the MFC actuators, they create local distributed loads where they are placed. Undergoing the steps
16
to verify a simple model, allowed observation of the general behavior of the wing model and also
proved the accuracy of the FEA program.
The XFoil analysis showed that as camber is increased in an airfoil that the coefficient of
lift increases. It also indicated that stall occurs at lower angles of attack as camber is increased.
For an ornithopter, the angle of attack is never constant because during the flapping motion the
wing is also twisting. A high cambered airfoil would not work for this situation because it is likely
to exceed the angle at which it would stall during the twisting. Based on this data, the airfoil for
the ornithopter would need to be one with a lower camber. Because this project is trying to develop
a basic understanding of how a wing behaves when actuated by a MFC, a wing with zero camber
needs to be studied first.
In the static deflection simulations performed in COMSOL, the placement of the probes
along the length of the substrate allows visualization of the gradual slope in deflection. The data
from this test can be used for observing the effects of displacement and slope of the overall wing
at different applied voltages. Applying these tests through COMSOL eliminates some
experimental testing, saving on time and money.
The dynamic tests that were performed on both iterations provided insightful data on the
behavior of the wings when they are actuated. This data shows that as voltage increases so does
the bending displacement as well as twisting angle. At the resonant frequency, the maximum
displacement occurs with bending. The same does not happen with twisting as it was observed
that twisting goes close to zero at the resonate frequency. The reason for this dampening effect on
twisting is due to bending being maximized for this particular arrangement. The bending motion
becomes so dominant that carbon fiber cannot flex or twist in any other direction, resulting in
twisting being minimized.
17
Phase shifting was used in an attempt to uncouple the bending from the twisting. For the
first iteration, results showed that in order to have significant bending and twisting simultaneously
in the first iteration, a phase shift of approximately 75 degrees is required. As the phase angle
approached 180 degrees bending displacement was close to zero. One of the main reasons for this
is the placement of the actuators. They originate at approximately the same point with one rotated
towards the trailing edge while the other is perpendicular to the leading edge. At a phase shift
angle of 180 degrees the actuators are moving completely opposite of each other causing the wing
to become rigid in the outboard direction thus cancelling bending. For the second iteration there
were no canceling effects with bending. This was due to relocating the primary bending actuator
to a mid-span location. Bending occurred at all phase shift angles studied because it did not have
a second actuator arranged acting opposite of it to cancel out its movement. Bending and twisting
appeared to be maximized with 120 to 135 degrees of phase shift.
When comparing the first iteration to the second iteration there are a few noteworthy
differences. Bending was increased significantly in the second iteration. This is largely due to the
relocation of the primary bending actuator. Moving it further outward on the wing redistributed
the weight and relocated the center of gravity of the wing further outward as well. This created a
greater moment on the wing, increasing the displacement. This also decreased the resonant
frequency from approximately 5.5 Hz to 3.9 Hz. This could result in power savings with less
voltage being needed over time, making this configuration more efficient. Twisting did decrease
slightly, however. This could be due to the location and orientation of the primary twisting
actuator. The arrangement of the primary twisting was such that it went from leading to the trailing
edge at a 45 degree angle. Because this was a short distance, the actuator did not have as long of
a “moment arm” to allow for as much oscillation parallel to its orientation.
18
The other dynamic test performed was the 4-bar linkage test. This was done to test for any
lift or thrust forces.
When the tests were run with the second iteration in the horizontal
configuration, the aircraft did not move, indicating no lift was being produced. Since the wing is
a flat plate being actuated up and down, the net lift produced is zero. As the wing moves up
through the air, the force produced ends up being negated as the wing moves downward. There is
also no freestream velocity, which is needed for producing lift. In standard aircraft, engines usually
produce thrust, inducing the needed freestream velocity.
When the solid-state aircraft was placed in the vertical configuration to test for thrust, the
aircraft again did not move. There could be several reasons for this. Twisting is an important part
of the flapping motion of a bird. The data collected indicated a twisting angle of less than 1 degree,
this could be too small of an angle to produce significant thrust. In order to produce thrust the
wings of the solid-state aircraft need to produce enough power to propel itself forward. Power was
not measured or studied for this project and could be a contributing factor.
Conclusions
The purpose of this project was to research the feasibility of solid-state flight in a small
ornithopter using smart materials as actuators for the flapping motion. MFC actuators were
incorporated into a solid-state ornithopter wing design and shown to be capable of producing a
flapping motion. Experiments were performed to gain an understanding of how the wings behaved
when actuated. Once enough data was collected, lift and thrust tests were performed.
Although no lift or thrust was produced, insightful information was gained. The research
presented in this paper could be used going forward to contribute to the design of a functional
solid-state ornithopter. As the stated purpose of this research was to gain a basic understanding of
the effects MFC actuators could have on the flapping motion of a wing, there were a number of
19
wing features that were not incorporated or tested in our investigations as they were beyond the
scope of this design. The current design had no hinges or joints in the wing to allow for the
asymmetric flapping motion that is seen with birds. Incorporation of camber into this design could
also greatly improve lifting forces, a concept used by both birds and current fixed wing aircraft.
Finally, future study focused on determining the relationship between wing design, size of
actuators and power produced may help elucidate the reasons for why no significant thrust was
detected. Future work could benefit from the incorporation of these concepts and add to the
understanding of elements needed for a functional solid-state ornithopter.
20
References
[1]
A. Wissa, N. Guerreiro, J. Grauer, C. Altenbuchner, J. E. Hubbard Jr, Y. Tummala, et al.,
"Flight testing of novel compliant spines for passive wing morphing on ornithopters," in
54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials
Conference, April 8, 2013 - April 11, 2013, Boston, MA, United
[2]
states, 2013.
Newnham, R. E. (1992). Piezoelectric sensors and actuators: smart materials. IEEE
Frequency Control Symposium, 27-29 May 1992, New York, NY, USA, IEEE.
[3]
A. Colozza, M. Shahinpoor, P. Jenkins, C. Smith, K. Isaac, and T. DalBello, "Solid state
aircraft concept overview," in Evolvable Hardware, 2004. Proceedings. 2004 NASA/DoD
Conference on, 2004, pp. 318-324.
[4]
M. J. Schulz, M. J. Sundaresan, J. McMichael, D. Clayton, R. Sadler, and B. Nagel,
"Piezoelectric materials at elevated temperature," Journal of Intelligent Material Systems
and Structures, vol. 14, pp. 693-705, 11/ 2003.
[5]
K. Lal Kummari, D. Li, S. Guo, and Z. Huang, “Development of piezoelectric actuated
mechanism for flapping wing micro-aerial vehicle applications,” Advances in Applied
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J. Bird, R. Bounthisane, A. Cook, E. Gumapas, T. Nguyen, J. Silvis, F. Hauris, O. Bilgen,
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21
Appendices
Appendix A: MatLab Codes
%Concentrated Cantilever Load
clear;clc;
%1.)General Analysis
prompt1='Input value of Base of crossection ';
b = input(prompt1);
prompt2='Input value of Height of crossection ';
h=input(prompt2);
prompt3='Input Length of cantilever beam ';
L=input(prompt3);
%-Section Properties
Ix=(1/12)*b*h^3;
%area moment of inertia meters^4
E=133e9;
%-Carbon Fiber
%E=150e9;
N=6;
%-Concentrated Load
prompt4='Input value of load (+ is down, - is up) ';
Load=input(prompt4);
prompt5='Input location of load (0 < x <= L) ';
a=input(prompt5);
yab=@(x)(((Load*x^2)/(6*E*Ix))*(x-3*a));
ybc=@(x)(((Load*a^2)/(6*E*Ix))*(a-3*x));
ThetaAB=@(x)((Load*x^2)/(6*E*Ix) - (Load*x*(3*a - x))/(3*E*Ix));
ThetaBC=@(x)( -(Load*a^2)/(2*E*Ix));
%Deflection
CB=@(x)0;
%Cantilever Beam
figure(3)
hold on
fplot(CB,[0 L],'r')
%Plotting Cantilever Beam
fplot(yab,[0 a])
%Plotting Shear Diagram
if a<L
fplot(ybc,[a L],'g')
end
grid on
title('Deflection')
xlim([-1 L])
xlabel('x'),ylabel('Deflection (m)')
%Slope
CB=@(x)0;
%Cantilever Beam
figure(4)
hold on
xlabel('x'),ylabel('Slope (rads)')
Figure A.1: Concentrated Load, Cantilever Beam Analytical Deflection
A-1
fplot(CB,[0 L],'r')
%Plotting Cantilever Beam
fplot(ThetaAB,[0 a])
%Plotting Shear Diagram
if a<L
fplot(ThetaBC,[a L],'g')
end
grid on
title('Slope')
xlim([-1 L])
xlabel('x'),ylabel('Slope (rads)')
x=linspace(0,L,N);
for y=1:N
if x(y)<=a
Y(y)=yab(x(y));
else if x(y)>a
Y(y)=ybc(x(y));
end
end
end
format long
Displacement=[x' Y'.*1000]
x=linspace(0,L,N);
FEA=[0;-0.00472;-0.01848;-0.03901;-0.06404;-0.0913]
plot(x,FEA,'r*')
Figure A.1: Concentrated Load, Cantilever Beam Analytical Deflection (continued)
A-2
%Distributed Cantilever Load
clear;clc;
%1.)General Analysis
prompt1='Input value of Base of crossection ';
b = input(prompt1);
prompt2='Input value of Height of crossection ';
h=input(prompt2);
prompt3='Input Length of cantilever beam ';
L=input(prompt3);
%-Section Properties
Ix=(1/12)*b*h^3;
%area moment of inertia meters^4
E=133e9;
%-Carbon Fiber
N=6;
%-Distributed Load
prompt4='Input value of Distributed Load (w) (+ is down, - is up) ';
w=input(prompt4)/L;
prompt6='Input Length of distributed load ';
a=input(prompt6);
yab=@(x)((w*x^2)/(24*E*Ix))*(4*a*x-x^2-6*a^2);
ThetaAB=@(x)(w*x^2*(4*a - 2*x))/(24*E*Ix) - (w*x*(6*a^2 - 4*a*x +
x^2))/(12*E*Ix);
%Slope
CB=@(x)0;
%Cantilever Beam
figure(4)
hold on
fplot(CB,[0 L],'r')
%Plotting Cantilever Beam
fplot(ThetaAB,[0 a])
%Plotting Shear Diagram
if a<L
ThetaBC=ThetaAB(a);
j=ThetaBC*ones(1,N);
i=linspace(a,L,N);
line(i,j)
end
grid on
title('Slope')
xlim([-1 L])
xlabel('x'),ylabel('Slope (rads)')
%Deflection
CB=@(x)0;
%Cantilever Beam
figure(3)
hold on;
fplot(CB,[0 L],'r')
%Plotting Cantilever Beam
fplot(yab,[0 a])
%Plotting Shear Diagram
if a<L
ybc=@(x)yab(a)+ThetaBC*(x-a);
fplot(ybc,[a L],'g')
end
grid on
title('Deflection')
xlim([-1 L])
xlabel('x'),ylabel('Deflection (m)')
Figure B.2: Distributed Load, Cantilever Beam Analytical Deflection
A-3
for y=1:N
if x(y)<=a
Y(y)=yab(x(y));
else if x(y)>a
Y(y)=ybc(x(y));
end
end
end
format long
Displacement=[x' (Y'.*1000)]
x=linspace(0,L,N);
FEA=[0;-0.00222;-0.00811;-0.0161;-0.0249;-0.0341];
plot(x,FEA,'r*')
Figure B.2: Distributed Load, Cantilever Beam Analytical Deflection (continued)
A-4
Appendix B: Vacuum Bagging Process
Figure B.1: Composite Samples pre-Epoxy
Figure B.2: Composite Samples post-epoxy, during vacuuming process
B-1
Appendix C: Second Iteration Fabrication
Figure C.1: Fuselage Inventor model
Top Half
Bottom Half
Figure C.2: 3-D Printed Fuselage
C-1
Figure C.3: 2nd Iteration during vacuum bagging process
Primary Bending Actuators
Primary Bending Actuators
Figure C.4: Bottom half of second iteration with actuators bonded
C-2
Appendix D: Budget
Solid State Aircraft Team
Budget
Materials
Item
M 8514 P1 85mm x 14mm
?? Twill Weave Carbon Firber Frabric ??
60 Min Epoxy Hardener
120 Min Eposy Hardener
Epoxy
3M Super 77 spray
Fabrication Snaps (pack of 10)
Hand Punch
Die for Female
Die for Male
Zinc Plated Screw 10-24 thread (pack of 100)
Zinc Plated Nut 10-24 thread (pack of 100)
1" Velcro (5 foot length)
Application Brushes
High Voltage Amplifier
Nylon Bagging Film 5 yd Roll
Breather and Bleeder 5yd Roll
Strechlon Bagging Film 5 yd Roll
Low Temperature Release Film 5 yd Roll
Activities
Research
Design
Vacuum Bagging/Wing Fabrication
MFC Testing
Fuselage Design and Fabrication
Wing Assembly
Assembly of the Aircraft
Final Modifications
Qty.
20
0
1
1
2
2
2
1
1
1
1
1
1
25
2
1
1
1
1
Unit Cost ($) Unit
$
58.00
ea.
$
44.95
sq. yd.
$
44.95
qt.
$
44.95
qt.
$
104.95
Gal.
$
29.95
Can
$
9.28
ea.
$
14.85
ea.
$
11.51
ea.
$
11.51
ea.
$
3.26
ea.
$
1.72
ea.
$
8.18
ea.
$
1.25
ea.
$
279.00
ea.
$24.95
ea.
$39.95
ea.
$19.95
ea.
$29.95
ea.
Person
Work Hours
300.00
600.00
Aaron/Nathan
100.00
Adam
40.00
Joe/Austin
75.00
Thomas/Joe
50.00
Thomas/Nathan
20.00
Adam
15.00
Total Hours
1,200.00
Freight EstimateTotal Cost Range ($)
$
37.00 $ 1,197.00
$
40.00 $
$
9.95 $
54.90
$
9.95 $
54.90
$
19.95 $
229.85
$
9.95 $
69.85
$
$
18.56
$
$
14.85
$
$
11.51
$
$
11.51
$
$
3.26
$
$
1.72
$
$
8.18
$
9.95 $
41.20
$
$
558.00
$19.95 $
44.90
$
39.95
$
19.95
$
29.95
Total Material Cost:
$
2,410.04
Labor Rate Labor Cost
$
25.00 $
7,500.00
$
25.00 $ 15,000.00
$
25.00 $
2,500.00
$
25.00 $
1,000.00
$
25.00 $
1,875.00
$
25.00 $
1,250.00
$
25.00 $
500.00
$
25.00 $
375.00
Total Labor Cost
$ 30,000.00
Software Licnese Fees
AutoDesk Inventor License
MatLab License
Foilsim License
Xfoil License
Flapsim License
Qty
Unit Cost
1 $ 7,295.00
1 $
99.00
1 $
1 $
1 $
Total Software Costs
Equipment
3-D Printer Rental & Material
Wind Tunnel Lab Rental
Time (hrs)
Travel
Total Cost Range
Competition Entry Fees
Hotel Reservation
Transportation
Dining Expenses
Total Travel Expenses
Total Cost Range
$
$
$
$
$
$
7,295.00
99.00
7,394.00
Rate
Total Cost Range
8 $
20.00 $
160.00
0 $
50.00 $
Total Equipment Costs $
160.00
$ 250.00
$ 1,000.00
$ 200.00
$ 450.00
$
Total Budget: $ 32,570.04
D-1
This undergraduate research project was awarded $2,500 from the Batten College of Engineering
and Technology. The total cost of materials required for completion was $2,410.04.
Budget Analysis
(Based on budget through week 27)
Total Budgeted Cost(TBC)
From the Budget Spreadsheet - $32,570.04
Cumulative Budgeted Cost (CBC)
CBC (based off of cost curve) - $30,716.39
Cumulative Actual Cost (CAC)
Total Expenditures to date - $2,463.67
Labor Costs - $43,300.00
CAC = Labor + Expenditures = $43,300.00 + $2,463.67 = $45,763.67
Cumulative Earned Value (CEV)
In 27 weeks 100% of Overall project has been completed.
CEV=TBC*Percent Complete = $32,570.04* 1.00= $32,570.04
Cost Performance Index Calculation (CPI)
CPI = CEV / CAC =$32,570.04/ $45,763.67=0.71
Cost Variance (CV)
CV = CEV – CAC = $32,570.04-$45,763.67 = -$13,193.63
Forecasted Cost at Completion (FCAC, 3 ways)
1st method FCAC = TBC / CPI = $32,570.04/0.71 = $45,763.67
2nd method FCAC = CAC + (TBC – CEV) =
$45,763.67 + ($32,570.04- $32,570.04) = $45,763.67
3rd method FCAC = CAC + Re-estimate of remaining work =
$345,763.67+ 0 = $45,763.67
To Complete Performance Index (TCPI)
TCPI = (TBC – CEV) / (TBC-CAC) =
($32,570.04- $32,570.04) / ($32,570.04- $45,763.67) = 0
D-2
Cumulative Budgeted Cost Curve
160.00%
140.00%
Percent of Budget
120.00%
100.00%
Cumulative Budget Cost
80.00%
Cumulative Actual Cost
60.00%
Cumulative Earned Value
40.00%
20.00%
0.00%
0
5
10
15
20
25
30
Weeks
D-3
Appendix E: Gantt Chart
E-1