SIMULATION, DESIGN AND VALIDATION OF A SOLID OXIDE FUEL CELL
POWERED PROPULSION SYSTEM FOR AN UNMANNED AERIAL VEHICLE
by
Peter Allan Lindahl
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Electrical Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
April, 2009
© Copyright
by
Peter Allan Lindahl
and portions by
The Institute of Electrical and Electronics Engineers
2009
All Rights Reserved
Unless otherwise indicated, this information has been authored by Peter Lindahl,
under US Government Contract no. FA8650-08-D-2806. The U.S. Government has
unlimited rights to use, reproduce, and distribute this information.
ii
APPROVAL
of a thesis submitted by
Peter Allan Lindahl
This thesis has been read by each member of the thesis committee and has been
found to be satisfactory regarding content, English usage, format, citations, biblio-
graphic style, and consistency, and is ready for submission to the Division of Graduate
Education.
Dr. Steven R. Shaw
Approved for the Department of Electrical and Computer Engineering
Dr. Robert C. Maher
Approved for the Division of Graduate Education
Dr. Carl A. Fox
iii
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfullment of the requirements for a master’s
degree at Montana State University, I agree that the Library shall make it available
to borrowers under rules of the Library.
If I have indicated my intention to copyright this thesis by including a copyright
notice page, copying is allowable only for scholarly purposes, consistent with “fair
use” as prescribed in the U.S. Copyright Law. Requests for permission for extended
quotation from or reproduction of this thesis in whole or in parts may be granted
only by the copyright holder.
Peter Allan Lindahl
April, 2009
iv
ACKNOWLEDGEMENTS
I would like to thank Dr. Steven Shaw for allowing me to take part in this
project and for his advice and support through out its duration. His willingness
to share his technical knowledge and professional experiences as well as answer
questions and concerns is greatly appreciated.
I would also like to thank: Eric Moog for his help in all facets of component
testing; particularly for his alacrity and precision in the modification of motor
controllers, Chris Colson for his general support and ideas, and the other faculty
and students at Montana State University who have helped me along the way.
Finally, I want to express my appreciation to my family and friends for their
unrelenting support through the ups and downs of graduate school.
Portions of this thesis were previously published and presented at the 2009
Institute of Electrical and Electronics Engineers (IEEE) Aerospace Conference
under the title, ƒSimulation, Design and Validation of a UAV SOFC Propulsion
System‚, ©2009, Institute of Electrical and Electronics Engineers.
Funding Acknowledgment
Finally, I would also like to thank the United States Air Force Research Lab-
oratory and the National Science Foundation grant 0547616 for their respective
roles in supporting my research.
vTABLE OF CONTENTS
1. INTRODUCTION ........................................................................................1
Current State of Fuel Cell Powered UAVs.......................................................1
Steady-state Optimization Approach ..............................................................3
Thesis Organization ......................................................................................4
2. SYSTEM MODEL ........................................................................................6
Solid Oxide Fuel Cell ....................................................................................7
SOFC Emulation..................................................................................... 11
Brushless DC Motor System ........................................................................ 12
BLDC Motor .......................................................................................... 12
Motor Controller ..................................................................................... 15
Propeller .................................................................................................... 18
3. SIMULATION PROGRAM ......................................................................... 21
4. EXPERIMENTAL SETUP.......................................................................... 27
Instruments ................................................................................................ 29
Fuel Cell Emulator Voltage and Current ................................................... 31
Duty Cycle ............................................................................................. 31
Motor Torque and Propeller Thrust.......................................................... 31
Propeller Rotational Speed ...................................................................... 31
Wind Tunnel Velocity and Air Density ..................................................... 32
Test Schedule.............................................................................................. 33
Test Procedure ........................................................................................... 33
5. EXPERIMENTAL RESULTS...................................................................... 35
Fuel Cell Modeling Results .......................................................................... 35
BLDC Motor Modeling Results.................................................................... 42
Propeller Modeling Results .......................................................................... 52
Measurement Uncertainty............................................................................ 58
6. CONCLUSION........................................................................................... 61
Future Work ............................................................................................... 61
REFERENCES CITED.................................................................................... 63
vi
TABLE OF CONTENTS – CONTINUED
APPENDICES ................................................................................................ 66
APPENDIX A: Simulation Results ............................................................ 67
APPENDIX B: Wind Tunnel Test Results ................................................. 93
vii
LIST OF TABLES
Table Page
2.1 Solution Vector Elements .......................................................................7
2.2 Fuel Cell Models ................................................................................. 11
2.3 Motors................................................................................................ 15
2.4 Propellers ........................................................................................... 19
4.1 Propulsion System Test Schedule.......................................................... 34
5.1 Measurement Confidence Intervals ........................................................ 58
B.1 SOFC Model 08, AXI Double 5330/20 Motor, APC 22 x 12 Prop Wind
Tunnel Data........................................................................................ 95
B.2 SOFC Model 08, AXI 5345/14 Motor, APC 27 x 13 Prop Wind Tunnel
Data................................................................................................... 96
B.3 SOFC Model 08, AXI Double 5345/18 Motor, APC 24 x 12 Prop Wind
Tunnel Data........................................................................................ 97
B.4 SOFC Model 08, AXI Double 5360/20 Motor, APC 26 x 15 Prop Wind
Tunnel Data........................................................................................ 98
B.5 SOFC Model 09, AXI Double 5330/20 Motor, APC 27 x 13 Prop Wind
Tunnel Data........................................................................................ 99
B.6 SOFC Model 09, AXI 5345/14 Motor, APC 26 x 15 Prop Wind Tunnel
Data................................................................................................. 100
B.7 SOFC Model 09, AXI Double 5345/18 Motor, APC 22 x 12 Prop Wind
Tunnel Data...................................................................................... 101
B.8 SOFC Model 09, AXI Double 5360/20 Motor, APC 24 x 12 Prop Wind
Tunnel Data...................................................................................... 102
B.9 SOFC Model 10, AXI Double 5330/20 Motor, APC 22 x 12 Prop Wind
Tunnel Data...................................................................................... 103
B.10 SOFC Model 10, AXI 5345/14 Motor, APC 27 x 13 Prop Wind Tunnel
Data................................................................................................. 104
B.11 SOFC Model 10, AXI Double 5345/18 Motor, APC 24 x 12 Prop Wind
Tunnel Data...................................................................................... 105
viii
LIST OF TABLES – CONTINUED
Table Page
B.12 SOFC Model 10, AXI Double 5360/20 Motor, APC 26 x 15 Prop Wind
Tunnel Data...................................................................................... 106
B.13 SOFC Model 11, AXI Double 5330/20 Motor, APC 24 x 12 Prop Wind
Tunnel Data...................................................................................... 107
B.14 SOFC Model 11, AXI 5345/14 Motor, APC 22 x 12 Prop Wind Tunnel
Data................................................................................................. 108
B.15 SOFC Model 11, AXI Double 5345/18 Motor, APC 26 x 15 Prop Wind
Tunnel Data...................................................................................... 109
B.16 SOFC Model 11, AXI Double 5360/20 Motor, APC 27 x 13 Prop Wind
Tunnel Data...................................................................................... 110
B.17 SOFC Model 12, AXI Double 5330/20 Motor, APC 26 x 15 Prop Wind
Tunnel Data...................................................................................... 111
B.18 SOFC Model 12, AXI 5345/14 Motor, APC 24 x 12 Prop Wind Tunnel
Data................................................................................................. 112
B.19 SOFC Model 12, AXI Double 5345/18 Motor, APC 27 x 13 Prop Wind
Tunnel Data...................................................................................... 113
B.20 SOFC Model 12, AXI Double 5360/20 Motor, APC 22 x 12 Prop Wind
Tunnel Data...................................................................................... 114
B.21 SOFC Model 13, AXI Double 5330/20 Motor, APC 27 x 13 Prop Wind
Tunnel Data...................................................................................... 115
B.22 SOFC Model 13, AXI 5345/14 Motor, APC 26 x 15 Prop Wind Tunnel
Data................................................................................................. 116
B.23 SOFC Model 13, AXI Double 5345/18 Motor, APC 22 x 12 Prop Wind
Tunnel Data...................................................................................... 117
B.24 SOFC Model 13, AXI Double 5360/20 Motor, APC 24 x 12 Prop Wind
Tunnel Data...................................................................................... 118
ix
LIST OF FIGURES
Figure Page
1.1 Fuel Cell Propulsion System Operation...................................................4
2.1 Fuel Cell Propulsion System Overview ....................................................6
2.2 Solid Oxide Fuel Cell .............................................................................9
2.3 SOFC Polarization Curve..................................................................... 10
2.4 Brushless DC (BLDC) motor system topology 2.4(a) and required con-
troller operation 2.4(b) ........................................................................ 13
2.5 AXI 5345/14 BLDC Motor .................................................................. 15
2.6 Modified Jeti Spin99 Motor Controller.................................................. 17
2.7 APC 22 x 12 in. Propeller Coefficients of Power & Thrust ..................... 20
3.1 Simulation Program Output of Well Designed Propulsion System........... 22
3.2 Simulation Program Output of Poorly Designed Propulsion System........ 24
3.3 Simulation Program Output with Second Source ................................... 26
4.1 Wind Tunnel and Test Stand Setup...................................................... 28
4.2 Wind Tunnel Calibration ..................................................................... 30
4.3 Mock Fuselage..................................................................................... 32
5.1 Polarization Curve for SOFC PNNL Model 08 ...................................... 36
5.2 Polarization Curve for SOFC PNNL Model 09 ...................................... 37
5.3 Polarization Curve for SOFC PNNL Model 10 ...................................... 38
5.4 Polarization Curve for SOFC PNNL Model 11 ...................................... 39
5.5 Polarization Curve for SOFC PNNL Model 12 ...................................... 40
5.6 Polarization Curve for SOFC PNNL Model 13 ...................................... 41
5.7 AXI DBL 5330/20 Voltage vs Speed ..................................................... 44
5.8 AXI DBL 5330/20 Torque vs Current ................................................... 45
5.9 AXI 5345/14 Voltage vs Speed ............................................................. 46
5.10 AXI 5345/14 Torque vs Current ........................................................... 47
xLIST OF FIGURES – CONTINUED
Figure Page
5.11 AXI 5345/18 Voltage vs Speed ............................................................. 48
5.12 AXI 5345/18 Torque vs Current ........................................................... 49
5.13 AXI 5360/20 Voltage vs Speed ............................................................. 50
5.14 AXI 5360/20 Torque vs Current ........................................................... 51
5.15 APC 22 in. x 12 in. Propeller Measured Performance ............................ 54
5.16 APC 24 in. x 12 in. Propeller Measured Performance ............................ 55
5.17 APC 26 in. x 15 in. Propeller Measured Performance ............................ 56
5.18 APC 27 in. x 13 in. Propeller Measured Performance ............................ 57
A.1 SOFC Model 8, AXI 5330 DBL Motor Simulation Results ..................... 69
A.2 SOFC Model 8, AXI 5345-14 Motor Simulation Results ......................... 70
A.3 SOFC Model 8, AXI 5345-18 Motor Simulation Results ......................... 71
A.4 SOFC Model 8, AXI 5360 Motor Simulation Results ............................. 72
A.5 SOFC Model 9, AXI 5330 DBL Motor Simulation Results ..................... 73
A.6 SOFC Model 9, AXI 5345-14 Motor Simulation Results ......................... 74
A.7 SOFC Model 9, AXI 5345-18 Motor Simulation Results ......................... 75
A.8 SOFC Model 9, AXI 5360 Motor Simulation Results ............................. 76
A.9 SOFC Model 10, AXI 5330 DBL Motor Simulation Results.................... 77
A.10 SOFC Model 10, AXI 5345-14 Motor Simulation Results ....................... 78
A.11 SOFC Model 10, AXI 5345-18 Motor Simulation Results ....................... 79
A.12 SOFC Model 10, AXI 5360 Motor Simulation Results............................ 80
A.13 SOFC Model 11, AXI 5330 DBL Motor Simulation Results.................... 81
A.14 SOFC Model 11, AXI 5345-14 Motor Simulation Results ....................... 82
A.15 SOFC Model 11, AXI 5345-18 Motor Simulation Results ....................... 83
A.16 SOFC Model 11, AXI 5360 Motor Simulation Results............................ 84
A.17 SOFC Model 12, AXI 5330 DBL Motor Simulation Results.................... 85
xi
LIST OF FIGURES – CONTINUED
Figure Page
A.18 SOFC Model 12, AXI 5345-14 Motor Simulation Results ....................... 86
A.19 SOFC Model 12, AXI 5345-18 Motor Simulation Results ....................... 87
A.20 SOFC Model 12, AXI 5360 Motor Simulation Results............................ 88
A.21 SOFC Model 13, AXI 5330 DBL Motor Simulation Results.................... 89
A.22 SOFC Model 13, AXI 5345-14 Motor Simulation Results ....................... 90
A.23 SOFC Model 13, AXI 5345-18 Motor Simulation Results ....................... 91
A.24 SOFC Model 13, AXI 5360 Motor Simulation Results............................ 92
xii
LIST OF SYMBOLS
Symbol Description Units
a Motor phase a -
b Motor phase b -
c Motor phase c -
CP Propeller coefficient of power -
CT Propeller coefficient of thrust -
D Motor controller duty cycle -
Ecell Ideal individual fuel cell voltage V
en motor phase n back emf V
Ic Current at fuel cell stack terminals A
Icell Individual fuel cell current
Im Effective motor current A
in Motor phase n current A
I0 Motor no-load current A
J Advance ratio -
K Motor speed constant V s/rad
L Propeller diameter m
Lm Motor inductance per winding H
Nc Number of series connected fuel cells -
np Propeller speed rev/s
Rm Motor resistance per winding Ω
Rth Thevenin equivalent approximated
fuel cell ohmic resistance Ω
S Air craft speed / Measured wind tunnel velocity m/s
T Propeller thrust N
Vc Voltage at fuel cell stack terminals V
Vcell Individual fuel cell voltage V
Vcell,act Individual fuel cell activation
voltage loss V
xiii
LIST OF SYMBOLS – CONTINUED
Symbol Description Units
Vcell,con Individual fuel cell concentration
voltage loss V
Vcell,ohm Individual fuel cell ohmic
voltage loss V
Vm Effective motor voltage V
vn Motor phase n voltage V
Voc Linear approximated open circuit
fuel cell stack voltage V
V0 Motor no-load voltage V
Greek Symbols
αn Coefficients of quadratic approximation
of propeller coefficient of power CP -
α′n Coefficients of quadratic approximation
of motor torque τ -
β Motor drag coefficient N-m s/rad
ρ Air density kg/m3
τ Motor torque rad/s
τe Motor torque of electric origin rad/s
ω Motor speed N-m
xiv
ABSTRACT
This thesis presents a physically-based model for design and optimization of a
fuel cell powered electric propulsion system for an Unmanned Aerial Vehicle (UAV).
Components of the system include a Solid Oxide Fuel Cell (SOFC) providing power,
motor controller, Brushless DC (BLDC) motor, and a propeller. Steady-state models
for these components are integrated into a simulation program and solved numerically.
This allows an operator to select constraints and explore design trade-offs between
components, including fuel cell, controller, motor and propeller options. We also
presents a graphical procedure using the model that allows rapid assessment and
selection of design choices, including fuel cell characteristics and hybridization with
multiple sources. To validate this simulation program, a series of experiments con-
ducted on an instrumented propulsion system in a low-speed wind tunnel is provided
for comparison. These experimental results are consistent with model predictions.
1INTRODUCTION
In recent years, fuel cells have received increased interest for their ability to effect
efficient, quiet, and clean conversion of chemical to electrical energy. These attributes
also make fuel cells an attractive power source for electric propulsion and a possible
alternative to gasoline powered internal combustion (IC) engines in Unmanned Aerial
Vehicles (UAVs). Potential advantages of fuel cell / electric UAV propulsion include
decreased emissions, increased efficiency, increased range and loiter time, and quieter,
lower profile flight. Additionally, because fuel cells are chemical to electrical energy
conversion devices, while IC engines are chemical to mechanical, an added advantage
is the readily available electricity for UAV payloads such as surveillance equipment.
Current State of Fuel Cell Powered UAVs
To date, several fuel cell powered UAVs have been built and successfully flown
[1, 2, 3]. However, documented design and optimization processes have been limited.
In 2004, Ofoma and Wu [4] presented a design methodology for developing a fuel cell
powered UAV used as a remote sensing tool, finding that fuel cell selection was a
major driver in aircraft design. While this study investigated many important facets
of propulsion system and aircraft design, the study was not integrated and often
only qualitative in nature. The study did compare simulated propeller thrust values
and air foil lift values generated with the web-based software code, Javaprop and
Javafoil to experimental results, but the thrust experiments utilized batteries which
have significantly different current/voltage characteristics from fuel cells. Further,
the criteria used for fuel cell selection was limited to power ratings, weight and cost
2with no investigation into the current and voltage coupling requirements between the
fuel cell and motor.
In 2005, Soban and Upton [5] described a completely integrated qualitative map-
ping scheme designed to narrow the classes of UAVs best suited for fuel cell propulsion.
In this study, propulsion architectures were broken down into classes of components,
i.e. fuel cell type, fuel type, and fuel storage systems, and their associated measures
of effectiveness such as fuel consumption rates, emissions, and power density. Aircraft
architecture was split into classes of UAVs represented by current UAV systems such
as Pioneer and Predator, with each class assigned common vehicle performance ratings
for performance requirements such as range, altitude, and rate of climb. Through a
combination of several commonly used qualitative assessment tools, optimal propul-
sion designs were assigned to different UAV classes. The findings of the study sug-
gested that while current fuel cell technology was inferior to conventional propulsion
systems, the anticipated advances in fuel cell technology, particularly that of solid
oxide fuel cells (SOFCs), hold significant advantages in UAVs designed for long range
and long endurance flights.
Between 2005 and 2007, members of the Aerospace Systems Design Laboratory at
the Georgia Institute of Technology designed and built a proton exchange membrane
(PEM) fuel cell demonstration UAV [1, 6, 7]. In [6], the authors describe the two
level approach used in design and construction of the aircraft. The top level of this
approach is a conceptual task used to explore the design space for optimal UAV
designs. The design space is comprised of five contributing analyses (CAs): aero-
dynamic simulation, propulsion system analysis, weights tabulation and calculation,
performance analysis and hydrogen storage. These CAs are assembled into a design
structure matrix allowing assessment of millions of combinations of UAV designs and
components. The optimal conceptual design is selected based on thrust margin, the
3thrust available divided by thrust required for a given air speed, and overall propulsion
efficiency. Using this conceptual design, the low level task provides a more in depth
analysis focusing on design and integration of the fuel cell system and improvements
upon the aerodynamic design of the aircraft. From this study, a demonstrator fuel
cell UAV was constructed utilizing a 32 cell, 500 W PEM fuel cell power plant [7].
The results of this project suggest that the proper matching of motor and propeller
to the characteristics of a given fuel cell is the most important aspect of a successful
design.
While these studies point to fuel cell technology as a promising alternative to
conventional IC engine propulsion systems, they also emphasize the importance of fuel
cell selection and propulsion system component matching to fuel cell characteristics in
the design of the aircraft. This thesis presents a steady-state optimization approach
and a graphical procedure for investigating the performance implications of various
propulsion system components and fuel cell models.
Steady-state Optimization Approach
For long endurance UAVs, the aircraft spends the majority of its flight time in
steady flight mode, i.e. constant velocity. Thus, the propulsion system should be
optimized at its required operation point for steady flight. Figure 1.1 shows fuel cell
data for a typical flight test of the Georgia Institute of Technology demonstrator UAV
described in [6, 7].
The figure shows three regions of operation. Region one is idle operation with
the propeller static. The low level current draw seen here is the result of powering
auxiliary equipment and the balance of plant of the fuel cell. Region two starts
around the 6 second mark and is the high powered condition corresponding to take
4Figure 1.1: Sample data for a straight line flight test of the 500 W Proton Exchange
Membrane (PEM) fuel cell powered demonstrator UAV detailed in [7]. Figure used
with permission of author. ©American Institute of Aeronautics and Astronautics.
off and climbing. Around the 48 second mark, region three begins. Current draw is
reduced and the aircraft assumes steady flight for about 8 seconds before descending
and landing. The steady flight region is very short in this test flight. However, for
a long endurance UAV deployed in a real world application, this is the region of
primary operation. This is the region of propulsion system operation that should be
optimized. It should be noted however that final propulsion system design must be
able to provide adequate power for all three regions of operation. From Figure 1.1
we see that for UAV steady flight, the operation of the propulsion system remains
relatively constant and thus can be accurately described using steady-state models of
its components.
Thesis Organization
This thesis considers the steady-state modeling, design, and component selection
for a fuel cell powered electric propulsion system. Chapter two discusses in depth
5the major components of the propulsion system along with first-order mathematical
models used to describe their operation. In addition, information is provided for
the corresponding components used in the experimental validation part of the thesis.
In chapter three, the simulation program comprised of these models is explained,
and a graphical solution approach that allows easy assessment of design choices, e.g.
changing stack specifications, is presented. Chapters four and five describe the wind
tunnel testing procedure aimed at verifying the individual component models and the
results of the tests, respectively. The thesis concludes in chapter six with discussion
of the project’s successes, necessary improvements, and recommendations for further
work.
6SYSTEM MODEL
Figure 2.1 depicts the propulsion system investigated in this thesis. The system is
comprised of an SOFC fuel cell providing electrical power to a Brushless DC (BLDC)
motor system that converts the electricity to mechanical power for turning a propeller.
The input to the system is the duty cycle, D, which controls the voltage and current
applied to the motor, while the output is the thrust, T produced by the propeller. Of
particular concern is the optimization of power delivery from the fuel cell terminals
to the propeller.
Figure 2.1: The propulsion system considered is comprised of four major components:
the SOFC fuel cell stack, the BLDC motor and controller and the propeller. The input
to the system is the duty cycle, D and the output is thrust, T [8], ©2009, Institute
of Electrical and Electronics Engineers.
The primary purpose of the simulation program, described in further detail in
chapter three, is to explore the performance implications of different fuel cell per-
formance characteristics, operating points, and component choices for motor and
propeller in the block diagram in Figure 2.1. To accommodate various component
models, explicit modularity is maintained in the program codes which is mirrored
in the descriptions of components in the following paragraphs. These models are
7numerically combined to find an overall solution vector
(
Ic Vc D Im Vm ω τ T
)
(2.1)
the components of which are detailed in the descriptions of each subsystem, below.
The elements of this solution vector can be constrained in the simulation, and the
program solved to find the non-constrained elements. Table 2.1 defines these elements.
Table 2.1: Elements contained in the solution vector of equation 2.1
Symbol Quantity Units
Ic Current at fuel cell terminals A
Vc Voltage at fuel cell terminals V
D Motor controller duty cycle -
Im Effective motor current A
Vm Effective motor voltage V
ω Motor speed rad/s
τ Motor torque N-m
T Propeller thrust N
The following sections describe the operation of the individual components of the
propulsion system in Figure 2.1, their first-order steady-state mathematical models,
and the corresponding physical components used in the test stand.
Solid Oxide Fuel Cell
Fuel cells are electrochemical devices that convert chemical energy, stored in
hydro-carbon fuel, into electrical energy. The basic structure of a fuel cell consists of
three layers: the anode (negative electrode), the cathode (positive electrode), and a
thin electrolyte layer separating the two. Fuel is supplied to the anode while an oxi-
dant is fed to the cathode. The electrochemical reaction occurring at the boundaries
8between the electrodes and the electrolyte produces an electric current through the
electrolyte that is returned through a complimentary external load [9].
Fuel cell types are typically distinguished by their electrolyte technology, which
dictates the type of ionic conduction through the electrolyte [9, 10, 11]. For example,
PEM fuel cells employ a proton conducting polymeric ion exchange membrane, while
the electrolyte in an alkaline fuel cell (AFC) is an hydroxide ion (OH−) conducting
aqueous alkaline solution. SOFCs have a solid metal oxide electrolyte and operate at
high temperatures, usually between 600 ◦C and 1000 ◦C, where the ionic conduction
of oxygen ions (O2−) occur. The high temperature operation and ionic conduction
of oxygen in SOFCs hold several advantages over other fuel cells. Most notably for
military applications, this combination allows the possibility for internal reformation
of heavy hydrocarbon fuels such as JP-8 jet fuel and diesel fuel. Additionally, SOFCs
are potentially less susceptible than other fuel cell technologies to poisoning from low
level sulfur content in hydrocarbon fuels, and carbon-monoxide (CO), a potential
byproduct of fuel reformation and poisonous to PEM fuel cells, acts as a fuel in
SOFCs [9, 10].
Figure 2.2 shows conceptual and actual images of an SOFC. Oxygen acquires
electrons from the external circuit in the porous, electrically conductive cathode. The
resulting oxygen ions diffuse readily toward the reducing atmosphere at the anode by
means of oxygen vacancies in the lattice of the electrolyte. The electrolyte has a
low electronic conductivity. Oxygen ions arriving at the anode combine readily with
reformed fuel constituents, (H2 and CO), and give up electrons to the external circuit.
The result of this energetically favorable process is direct conversion of chemical to
electrical energy, without the efficiency implications of a heat engine.
The Scanning Electron Micrograph (SEM) image in Figure 2.2(b) of an anode
supported cell provides some indication of the actual scale of a fuel cell structure.
9(a) Solid Oxide Fuel Cell Diagram (b) SEM Image of SOFC
Figure 2.2: (a) Cross-sectional conceptual diagram and (b) scanning electron micro-
graph of a solid oxide fuel cell [8], ©2009, Institute of Electrical and Electronics
Engineers.
The anode appears on the left of the SEM image. The thickness of the anode provides
structural support. The electrolyte and cathode appear on the right margin above
the scale bar.
Fig. 2.3 shows measured data representing the current voltage relationship of a
typical anode supported fuel cell. The data in Fig. 2.3 is for an InDEC anode-
supported cell with an active area of 18 cm2, at 750 ◦C, operating on oxygen and
hydrogen. The output voltage of an SOFC can be characterized as
Vcell = Ecell − Vcell,act − Vcell,ohm − Vcell,con (2.2)
Ecell, represents the ideal performance of the fuel cell and is dependent on the operat-
ing temperature of the cell and the reactants involved. Vcell,act, Vcell,ohm, and Vcell,con
are voltage losses due to an electrochemical activation process, ohmic resistances in
the cell components, and finite mass transport rates, respectively [9, 12]. In equation
2.2, contributions of the anode and cathode are lumped. These losses dominate dif-
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Current Density (A/cm2)
Fu
el 
Ce
ll V
olta
ge
 (V)
Activation
Region
Ohmic Region Concentration
Region
Figure 2.3: Measured current-voltage relationship of a typical InDEC anode sup-
ported SOFC [8], ©2009, Institute of Electrical and Electronics Engineers.
ferent regions of the polarization curve as depicted in Figure 2.3. Individual cells are
typically “stacked”, or connected in series, to form a power source with convenient
output voltages. Fuel cell stack operation is derived from the individual cell operation
by
Vc = NcVcell (2.3)
where Nc is the number of series connected cells [12]. In the UAV application, it is
reasonable to assume that the stack will be designed under a weight constraint so
that the nominal operating point is near the peak power point in the ohmic region
of the fuel cell curve. In the ohmic region, the fuel cell can be approximated by a
Thevenin circuit equivalent, i.e.
Vc = Voc − IcRth, (2.4)
where Voc is the zero-current voltage intercept of the linear approximation of the
ohmic part of the response, and Rth is the slope.
11
Table 2.2 lists the characteristics for the six fuel stacks involved in this study.
Research and design of the fuel cell stacks took place at the Pacific Northwest National
Laboratory (PNNL) in Richland, Washington. The specified operating voltages, Vc
correspond to optimal voltage levels for producing around 2 kW of electric power as
dictated by PNNL.
Table 2.2: Physical and modeling parameters of the SOFC stacks investigated
Fuel Cell Nc Vcell (V) Voc (V) Rth (Ω) Vc (V)
Model 8 67 0.7 70.1 0.55 46.9
Model 9 60 0.7 67.3 0.55 42
Model 10 60 0.625 66.4 0.55 37.6
Model 11 67 0.625 67.8 0.55 41.9
Model 12 73 0.625 57.8 0.28 45.6
Model 13 73 0.7 62.0 0.28 51.1
SOFC Emulation
Because operating a multi-kW SOFC stack is expensive and requires significant
infrastructure, an SOFC emulator was built to mimic steady-state stack operation for
testing purposes. A 10 kW Sorenson DCR 160-62T power supply in combination with
a resistor built from a variable-length of 6.4 mm diameter 316 stainless steel tube was
used to recreate fuel cell Ohmic Region polarization characteristics at power levels in
the laboratory. A Miller Coolmate 4 welding torch cooling system rated for 4.4 kW
was used to stabilize the temperature (and therefore the resistance) of the stainless
steel by circulating a low-conductivity coolant through the tubing.
12
Brushless DC Motor System
Brushless DC (BLDC) motors feature high efficiency, ease of control, and aston-
ishingly high power density at reasonable shaft speeds [13]. In general, BLDC motors
outperform conventional permanent DC motors with better speed and torque char-
acteristics, efficiency, longer operating lives, and increased reliability [14, 15]. These
features make BLDC motors a natural choice for electric propulsion of small craft.
BLDC motors are permanent magnet synchronous motors, which from a modeling
standpoint are similar to conventional permanent magnet DC motors [16]. The salient
difference is that the BLDC motor is commutated externally by power electronic
switches rather than by the brushes and commutator built into a standard DC motor.
This introduces some electronic complexity, as an external controller is required to
switch three phases of windings according to a real-time estimate of the rotor position.
Figure 2.4(a) shows the topology of a typical sensorless three-phase BLDC motor
system. The inverter used in the motor controller is the same as a conventional three-
phase inverter, however because the permanent magnet motor used has trapezoidal
shaped back emfs, rectangular stator currents are required to produce constant torque
[13, 17]. This operation is illustrated in Figure 2.4(b).
BLDC Motor
For steady-state modeling purposes, the modeling complexity of the BLDC con-
troller is ignored so that the motor and controller is treated “as commutated”, i.e. the
controller estimates the rotor position and commutates the motor efficiently in the
steady-state. Under this assumption, the system can now be treated as an ideal DC
machine with current Im, voltage Vm, and resistance 2Rm. The equations describing
13
(a) BLDC Motor Topology
 ia
 ea
pi/6 5pi/6
7pi/6
 ib
 eb
pi/2
5pi/6 3pi/2
 ic
 ec
pi/6
pi/2 7pi/6
(b) BLDC Drive Signals and Back Emf Relationship
Figure 2.4: Brushless DC (BLDC) motor system topology 2.4(a) and required con-
troller operation 2.4(b)
14
the motor are then
Vm = Kω + 2RmIm (2.5)
τe = KIm, (2.6)
where K is the motor speed constant, ω is the shaft speed, τe is the torque of electric
origin, and Rm is the winding resistance. Values for K and Rm are typically supplied
by the manufacturer. Note that Rm appears with a factor of two in this equation
because resistance is specified per winding and two windings are in series for each
commutating sequence.
Motor manufacturers also typically provide current I0 and voltage V0 data under
“no-load” conditions to indicate the amount of core, friction and windage losses during
steady-state motor operation [9]. These losses are lumped together as a windage loss
by calculating a drag coefficient
β =
K2I0
V0 − 2I0Rm
, (2.7)
which modifies the output torque τ to ensure that the motor model passes through
the specified no-load operating point, i.e.
τ = τe − βω. (2.8)
The net mechanical output is torque τ at speed ω.
Several motors made by AXI Model Motors were selected for evaluation in the
test stand. These motors advertise efficiencies in excess of 90% at the power levels
required and have speed constants in a range which does not require a gear box
between motor and propeller. Parameters for the motors are listed in Table 2.3. The
values for I0 correspond to V0 = 30V. For an indication of motor size, the first two
numbers in the motor name give the rotor diameter (mm), and the second two give
15
Table 2.3: Modeling parameters of the AXI motors investigated [8],©2009, Institute
of Electrical and Electronics Engineers.
Motor K (Vs rad−1) Rm (Ω) I0 (A)
AXI Double 5330/20 0.041 0.012 4.8
AXI 5345/14 0.042 0.014 2.6
AXI 5345/18 0.056 0.021 1.6
AXI 5360/20 0.080 0.034 1.8
Figure 2.5: AXI 5345/14 BLDC Motor
the stator length (mm). The AXI 5345/14 motor is shown in Figure 2.5. The AXI
Double 5330/20 motor is two 5330/20 motors sharing a common rotor.
Motor Controller
In addition to switching the output transistors with rotor position, which is
lumped with the model motor, the motor controller can introduce a duty cycle D
in the pulses applied to the motor windings. The duty cycle is the input to the
propulsion system allowing flight control to change power delivered to the prop. From
the power electronics perspective, the average motor voltage over a commutating se-
16
quence is modulated by D, so the duty cycle effectively introduces an integrated buck
converter. Assuming the converter is lossless, the equivalent voltage Vm and current
Im at the motor terminals are given by
Vm = DVc (2.9)
Im =
1
D
Ic, (2.10)
where D is the duty cycle and Vc, Ic are the fuel cell voltage and current. Losses in
the motor controller are neglected because they are estimated to be on the order of
10 W while the motor is drawing in excess of 1 kW.
For all laboratory tests, Jeti Spin99 motor controllers were used. These controllers
are designed for the appropriate power levels, but are intended for use with NiMH
or Li based batteries that have low series resistance compared to the fuel cell. As
a result, the no-load voltages in the fuel cell systems exceed the voltage rating of
the parts used in these controllers. The Spin99 controllers were disassembled and
the power MOSFETS and capacitors were replaced with higher voltage rated parts.
Figure 2.6 depicts the process. An Agilent 33220A function generator replaced the
radio controlled transmitter and receiver associated with the motor controller allowing
precise control of duty cycle.
17
(a) Disassembled Motor Controller
(b) Modified Motor Controller
Figure 2.6: Components of the Jeti Spin99 motor controller were replaced with compo-
nents that matched the voltage requirements of the fuel cell systems studied. 2.6(a)
shows the completely disassembled controller, and 2.6(b) shows the modified con-
troller
18
Propeller
The propeller determines the relationship between motor speed and load torque,
and therefore ultimately determines the operating point of the propulsion system.
Typically, propeller performance is expressed using dimensionless thrust coefficient
CT and power coefficient CP . The coefficients are functions of the relative speed of
the craft and the prop, or the advance ratio
J =
S
npL
, (2.11)
where S is the air speed, np = ω2pi is the rotational speed of the prop in revolutions
per second, and L is the prop diameter [18]. Given CP at a particular advance ratio,
the shaft power required is
P = CPρL
5n3p, (2.12)
where ρ is the local air density. Setting the propeller power requirement equal to the
mechanical power at the shaft, i.e. τω = P , yields the desired relationship between
motor speed and torque
τ = CPρL
5 ω
2
(2pi)3
(2.13)
Similarly, given CT , the thrust produced by the propeller is
T = CTρL
4n2p (2.14)
For steady flight, the thrust and lift produced by the propulsion system and wings,
respectively, must be sufficient to overcome the aircraft’s drag and weight. The
relationship between these forces acting on an aircraft and the craft’s air speed is
complex, and requires an understanding of the aerodynamic properties of the vehicle
and the flight profile. The simulation program simply calculates the available thrust
19
Table 2.4: APC brand propellers used in wind tunnel testing and the 2nd order models
used to describe their operation [8], ©2009, Institute of Electrical and Electronics
Engineers
Propeller Coefficients
APC 22x12 CT = −0.039J2 − 0.055J + 0.062
CP = −0.049J2 − 0.001J + 0.031
APC 24x12 CT = −0.038J2 − 0.055J + 0.057
CP = −0.045J2 − 0.005J + 0.028
APC 26x15 CT = −0.040J2 − 0.053J + 0.067
CP = −0.053J2 − 0.002J + 0.042
APC 27x13 CT = −0.037J2 − 0.055J + 0.054
CP = −0.044J2 − 0.005J + 0.026
at a target airspeed. If this number is in excess of the thrust requirement anticipated
by the airframe designer, the craft is predicted to fly.
Four lightweight APC composite propellers were selected for testing in the wind
tunnel. For each propeller, APC provided estimated values of CP and CT for discrete
values of J . Figure 2.7 shows an example of these relationships along with second
order polynomial trendlines fit to the data using the least-squares method. These
polynomials capture CT and CP as continuous functions of J for use in the simulation
program. Table 2.4 show these functions for the four propellers selected. The first
number in the propeller specification is the diameter in inches, while the second
number is the pitch in inches. The pitch of a propeller defines the distance the
propeller would travel in one revolution if there were no slip.
20
(a) Coefficient of Power
(b) Coefficient of Thrust
Figure 2.7: Power and Thrust coefficient plots for the APC 22 x 12 in. propeller.
21
SIMULATION PROGRAM
The simulation program is comprised of four analysis functions corresponding to
the mathematical models presented in chapter two. Parameters of the individual
component models (Tables 2.2, 2.3 and 2.4) are stored in global variables and serve
as inputs to the analysis functions. With a user-specified controller duty cycle, D,
aircraft flight speed, S and local air density, ρ, the combined analysis functions can
be solved with standard techniques to find the system operation point, defined in
equation 2.1. While this solution is valuable information, it does not provide design
insight needed to understand trade-offs in fuel cell output characteristics, control
opportunities, or the relative merit of different propeller and motor combinations.
Rather than solving for a single operating point found from a single input variable, it
is more useful to solve for a collection of operating points that can be presented in a
graphical format. The most intuitive independent variable for this purpose appears to
be the fuel cell stack terminal current Ic. Numerically, Ic is constrained to a succession
of values from a vector, and the matlab command fsolve() is used to determine every
other variable as a function of current. The outputs are then reflected to the fuel cell
terminals where they can be interpreted on one plot in conjunction with the fuel cell
response.
Figure 3.1 shows a sample output. This two dimensional voltage/current space
represents the design space of the fuel cell stack. The line labeled “linearized FC
curve” is simply a plot of the output characteristic of one specific fuel cell stack. In
this example, SOFC PNNL Model 12 with an open circuit voltage of 57.8 V and a
Thevenin equivalent resistance of 0.28 Ω is used. The red box, labeled “propeller and
motor operation region”, represents a family of voltage/current curves for the motor
and propeller combination at the specified airspeed. The lower margin of this box
22
10 20 30 40 50 60 70 80
0
20
40
60
80
100
Current at fuel cell terminals (A)
Vo
lta
ge
 a
t f
ue
l c
el
l t
er
m
in
al
s 
(V
)
39.5 N
20 N
35 N
50 N
D = 0.5
D = 1
Lines of
Constant Thrust
Linearized FC Curve
Propeller and Motor Operation Region
Figure 3.1: Predicted performance of the PNNL Model 12 SOFC, AXI 5345/18 motor,
Jeti Spin 99 controller and APC 27x13 in. propeller. The simulation was performed
assuming a cruising velocity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.
23
shows the relationship between current and voltage for the motor and propeller with
duty cycle D = 1. The upper margin of the box is the curve corresponding to D = 0.5.
The operating point of the propulsion system is determined by the intersection of the
motor/propeller curve at a specified duty ratio and the fuel cell curve. Thus, the
interpretation of the graph is that any point on the fuel cell curve within the box
is an achievable operating point at a reasonable steady-state duty ratio between 0.5
and 1.
The other variables of equation 2.1 can also be constrained to provide interpre-
tation of the achievable operating points. Contours of constant thrust are added
to the plot by constraining thrust, T , to specific values and repeating the solution
process. These are the dashed lines labeled with thrust values. These curves provide
current/voltage relationships required for the motor and propeller to produce the
thrusts specified.
The operating point as specified by the PNNL defined optimal fuel cell output
voltage is found by constraining Vc to the Vop value of 45.6 V. This is indicated by a
large point in Figure 3.1 and shows the estimated thrust to be 39.5 N at a duty ratio
of roughly 0.75. With relatively high estimated thrust and an operation point well
within the duty cycle limits of the propeller and motor operation region, Figure 3.1
represents a good propulsion system design.
In contrast, Figure 3.2 shows a poor combination of components, the AXI 5360/20
motor and APC 22 x 12 propeller, for the same fuel cell parameters. In this case,
it is not possible to select a duty ratio where the motor and propeller are even able
to use the power that the fuel cell is capable of delivering. The nominal fuel cell
operating point is outside of the propeller curve box, demonstrating that this system
is also incapable of producing the thrust achieved by the system in Figure 3.1. At
the maximum duty ratio of 1.0, this system would only produce slightly more than
24
10 20 30 40 50 60 70
0
20
40
60
80
100
120
140
160
180
200
Current at fuel cell terminals (A)
Vo
lta
ge
 a
t f
ue
l c
el
l t
er
m
in
al
s 
(V
)
37.1 N
20 N
35 N
50 N
D = 0.5
D = 1
Lines of
Constant Thrust
Linearized FC Curve
Propeller and Motor
Operation Region
Figure 3.2: Predicted performance of the PNNL Model 12 SOFC, AXI 5360 motor,
Jeti Spin 99 controller and APC 22x12 in. propeller. The simulation was performed
assuming a cruising velocity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.
25
20 N of thrust. Furthermore, even if it were possible to command the necessary duty
cycle, Figure 3.2 is predicted to produce less thrust at the same power level.
Graphs of these kind immediately connect the quantities of interest to the fuel
cell stack designer, i.e. current and voltage at the stack terminals, to the ability
to command thrust, which is of interest to the airframe designer. Additionally, the
graphs lend themselves to understanding how the current/voltage characteristics of
a fuel cell might be modified with an auxiliary source, e.g. photovoltaics or bat-
tery, and the effect that the new current/voltage characteristic might have on flight
performance. As a specific example, the inherently sloping fuel cell curves tend to
become parallel to lines of constant thrust at higher currents. Even if the fuel cell is
subjected to severe high-current loading, very little additional thrust is possible. On
the other hand, an alternate source with a flat current voltage characteristic could be
used to temporarily cross several thrust curves and substantially increase the flight
envelope. This idea is illustrated in Figure 3.3 with the dotted line indicating the
polarization curve of an second power source with a flat current voltage relationship.
The 3 kW operating point shown would still draw only 2 kW from the fuel cell with
the remaining 1 kW of power being provided by the secondary source.
Appendix A contains the full set of simulation results for all combinations of
propulsion system components.
26
10 20 30 40 50 60 70 80
0
20
40
60
80
100
Current at fuel cell terminals (A)
Vo
lta
ge
 a
t f
ue
l c
el
l t
er
m
in
al
s 
(V
)
39.5 N
3 kW
56.8 N
20 N
35 N
50 N
D = 0.5
D = 1
Lines of
Constant Thrust
Linearized FC Curve
Propeller and Motor Operation Region
Figure 3.3: Predicted performance of the propulsion system of Figure 3.1 with an
added second power source. The simulation was performed assuming a cruising ve-
locity of 31.3 m/s (70 mph) and air density of 1.2 kg/m3.
27
EXPERIMENTAL SETUP
As indicated in chapter two, the propeller models relate thrust, T , and torque,
τ , to the advance ratio, J (equations 2.11, 2.13 and 2.14). These models assume a
non-zero free-stream velocity, S, up stream of the propeller. Thus, static propeller
tests are inadequate for verifying propeller models. An open circuit wind tunnel,
Figure 4.1(a), was constructed for the purpose of testing propulsion systems under
flight conditions. The working section of the wind tunnel is 91 cm x 91 cm and 3 m in
length. Ideally, the wind tunnel would be capable of an air flow velocity equivalent to
the 30 m/s desired aircraft velocity. However, this would require a significantly large
and expensive excitation fan that would exceed our available lab space and budget.
Instead, the wind tunnel is excited by a 3.7kW, 91cm diameter Dayton tube-axial duct
fan upstream of the propeller capable of wind tunnel velocities around 40% aircraft
velocities. Data achieved at these lower wind tunnel velocities can be extrapolated
to predict performance at actual flight speeds.
A test stand was mounted in the working section of the wind tunnel 4.1(b). The
test stand consists of an interchangeable motor mounting plate fixed to a steel rod.
The rod is supported at its center of gravity on a pillow block, so that it is free to
translate and rotate. The rod is constrained by only a torque/force load cell which
provides direct measurement of motor torque and developed thrust. In addition to
torque and thrust, we measure atmospheric conditions, air speed, propeller speed, fuel
cell current and voltage, and duty cycle on the controller. This allows a comparison
of simulation variables with lab measurements. The propeller is mounted in a pusher
configuration.
As recommended in [19], both a screen and a honeycomb section were installed
in an effort to normalize the air flow through the wind tunnel. Screens have the
28
(a) Wind Tunnel
(b) Test Stand
Figure 4.1: The open circuit wind tunnel 4.1(a) and test stand 4.1(b) constructed
for testing propulsion system components [8], ©2009, Institute of Electrical and
Electronics Engineers.
29
benefit of creating a more uniform flow velocity through the wind tunnel as well
as reducing turbulence intensity. Honeycombs reduce swirl and also have a minor
turbulence reduction effect. The screen was made of heavy duty nylon construction.
The honeycomb was constructed of 396 pieces of 1.5 inch PVC pipe 6 inch in length,
18 pieces to a row and 22 rows. To measure the effectiveness of these components, the
test stand was removed from the wind tunnel and a grid was constructed from kite
string along the cross section of the tunnel corresponding to the propeller location.
The grid consisted of 25 measurement locations as indicated by Figure 4.2. Velocity
measurements were taken using a Kestrel 3500 Weather Meter at each location with
the screen installed, the honeycomb installed and with neither installed. The instal-
lation point for both the screen and the honeycomb was 3 feet downstream of the
axial fan and 5 feet upstream of the propeller location.
With no normalizing device installed, the wind tunnel had an average wind speed
of 13.7 m/s and a maximum deviation from the average of 29%. Unexpectedly,
both screen and honeycomb had adverse affects on air flow. The screen caused a
reduction in average velocity to 9.7 m/s, and an increase in flow variation to 61%.
The honeycomb reduced the average velocity to 12.2 m/s and increased the maximum
variation in velocity to 43% from the average. Thus, it was determined that wind
tunnel testing should procede without either component installed. The effects of the
screen and the honeycomb on wind tunnel swirl were not measured.
Instruments
The instruments used to measure system operation for comparison with simulated
variables are described below.
30
(a) Honeycomb (b) Screen
(c) Nothing
Figure 4.2: Both a honeycomb and a screen were installed in the wind tunnel in an
attempt to normalize air flow. The velocities measured are shown in m/s.
31
Fuel Cell Emulator Voltage and Current
As described in chapter two, a Sorenson DCR 160-62T in series with a stainless
steel resistor was used to simulate the steady-state performance of the fuel cell stacks.
The current delivered from the power supply, Ic was recorded off the power supply
ammeter which has an accuracy of 0.1%. Voltage at the emulated fuel cell terminals,
Vc was measured using a B&K Test Bench 389A digital multimeter. The 389A has
an accuracy of 0.25% for DC voltage readings.
Duty Cycle
Duty cycle D was recorded using a Tektronix P5205 high voltage probe in conjunc-
tion with a DPO 4054 Tektronix Oscilloscope. The P5205 has a maximum voltage
rating of 1300 V and bandwidth of 100 MHz.
Motor Torque and Propeller Thrust
Propeller torque τ and thrust T were measured using a Cooper LXT-920 force /
torque load transducer. The linearity, hysteresis and repeatability ratings for thrust
are ±1.8 N, ±0.9 N and ±0.4 N, respectively. These ratings for torque are ±0.045
N-m, ±0.023 N-m and ±0.011 N-m.
Propeller Rotational Speed
A CheckLine DT-205L non-contact tachometer was used to access the propeller’s
rotational speed ω. The DT-205L has a maximum measurement rating of 10,470
rad/s and an accuracy of 0.1 rad/s for the range of speeds observed.
32
Wind Tunnel Velocity and Air Density
The simulated craft velocity S and the atmospheric conditions used to calculate
air density ρ were measured using a Kestrel 3500 Weather Meter. For velocity, the
Kestrel has an operating range of 0.4 to 60 m/s, and 3% accuracy. Atmospheric
pressure, temperature and dew point are required for estimating air density. The
Kestrel’s accuracy for these measurements are ±1.5 hPa (hectopascals), ±1 ◦C and
±2 ◦C respectively.
Figure 4.3: A mock fuselage, 6 in. x 6.5 in. and 3 feet in length was constructed
for installation on the test stand. This allowed testing of propeller performance with
partial occlusion by the aircraft fuselage.
33
Test Schedule
With six fuel cell models, four BLDC motors and four propellers considered, a
complete study would involve 96 combinations of components. Additionally, a mock
aircraft fuselage was constructed for installation on the test stand (figure 4.3). With
the mock fuselage installed, tests could be repeated to determine if the UAV fuse-
lage would occlude the propeller enough to invalidate the propeller models used in
the simulation. To limit the number of tests required, an experiment schedule was
constructed so that each motor/propeller combination was tested at least once, and
that each fuel cell model was tested with each motor and each propeller at least once.
This allowed a comprehensive study of the possible components while reducing the
required testing to 25% of the total combinations. This schedule is displayed in Table
4.1. The results of these experiments are discussed in the next chapter, and presented
in full in Appendix B.
Test Procedure
Each experiment consists of two runs through the test procedure; the first with the
mock fuselage installed and the second without. First, the resistor is calibrated to the
desired fuel cell output resistance using a precise meter. The resistor cooling system
and wind tunnel excitation fan are then turned on. Atmospheric conditions and any
instrumentation offsets are then recorded. The power supply simulating the fuel cell
is then adjusted to the required open circuit Thevenin equivalent voltage. Then the
duty cycle command is adjusted until the desired operating point is achieved. All
variables are recorded, and the process is repeated for several duty cycle controlled
operating points.
34
Table 4.1: 24 of the 96 possible combinations of components were tested in the wind
tunnel. Each motor/propeller combination was tested at least once and each fuel cell
model was tested with each motor and each propeller at least once. Results of these
tests are described in chapter five and listed in Appendix B.
Test FC Model Motor Prop
Test 1 PNNL Model 08 AXI DBL 5330/20 APC 22 x 12
Test 2 PNNL Model 08 AXI 5345/14 APC 27 x 13
Test 3 PNNL Model 08 AXI 5345/18 APC 24 x 12
Test 4 PNNL Model 08 AXI 5360/20 APC 26 x 15
Test 5 PNNL Model 09 AXI DBL 5330/20 APC 27 x 13
Test 6 PNNL Model 09 AXI5345/14 APC 26 x 15
Test 7 PNNL Model 09 AXI5345/18 APC 22 x 12
Test 8 PNNL Model 09 AXI5360/20 APC 24 x 12
Test 9 PNNL Model 10 AXI DBL 5330/20 APC 22 x 12
Test 10 PNNL Model 10 AXI5345/14 APC 27 x 13
Test 11 PNNL Model 10 AXI5345/18 APC 24 x 12
Test 12 PNNL Model 10 AXI5360/20 APC 26 x 15
Test 13 PNNL Model 11 AXI DBL 5330/20 APC 24 x 12
Test 14 PNNL Model 11 AXI5345/14 APC 22 x 12
Test 15 PNNL Model 11 AXI5345/18 APC 26 x 15
Test 16 PNNL Model 11 AXI5360/20 APC 27 x 13
Test 17 PNNL Model 12 AXI DBL 5330/20 APC 26 x 15
Test 18 PNNL Model 12 AXI5345/14 APC 24 x 12
Test 19 PNNL Model 12 AXI5345/18 APC 27 x 13
Test 20 PNNL Model 12 AXI5360/20 APC 22 x 12
Test 21 PNNL Model 13 AXI DBL 5330/20 APC 27 x 13
Test 22 PNNL Model 13 AXI5345/14 APC 26 x 15
Test 23 PNNL Model 13 AXI5345/18 APC 22 x 12
Test 24 PNNL Model 13 AXI5360/20 APC 24 x 12
35
EXPERIMENTAL RESULTS
As outlined in chapter four, each test listed in Table 4.1 was conducted twice;
once with the mock fuselage installed and once without. These combinations of
components were assembled on the test stand in our wind tunnel and tested at a
variety of operating points. Using these operating points as inputs along with the
measured air density and wind tunnel velocity, the simulation program was run to
solve for individual component models.
Fuel Cell Modeling Results
Figures 5.1 - 5.6 show the experimental results for the six fuel cell models. Each
fuel cell model was tested with four different motor/propeller loads which are indi-
cated in the accompanying figure legend. The blue line in each figure is the simulated
ohmic region of the fuel cell. While this is somewhat of a trivial result since the fuel
cell emulator is simply a voltage source with a resistor in series, an accurately sloping
voltage/current power source is required for characterizing motor performance with a
fuel cell power source. Additionally, with an emulator current of 60 A, and resistance
set to 0.55 Ω, the variable resistor dissipates around 2 kW of power. These tests prove
the cooling systems effectiveness in regulating resistor temperature and maintaining
constant resistance values for a wide range of emulated fuel cell currents.
36
0 10 20 30 40 50 60 7030
35
40
45
50
55
60
65
70
75
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 22 x 12, no fuselage
AXI5330DBL, APC 22 x 12, fuselage
AXI5345−14, APC 27 x 13, no fuselage
AXI5345−14, APC 27 x 13, fuselage
AXI5345−18, APC 24 x 12, no fuselage
AXI5345−18, APC 24 x 12, fuselage
AXI5360−20, APC 26 x 15, no fuselage
AXI5360−20, APC 26 x 15, fuselage
Simulation
Figure 5.1: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 08 emulator assuming operation in the ohmic
region
37
0 10 20 30 40 50 60 7030
35
40
45
50
55
60
65
70
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 27 x 13, no fuselage
AXI5330DBL, APC 27 x 13, fuselage
AXI5345−14, APC 26 x 15, no fuselage
AXI5345−14, APC 26 x 15, fuselage
AXI5345−18, APC 22 x 12, no fuselage
AXI5345−18, APC 22 x 12, fuselage
AXI5360−20, APC 24 x 12, no fuselage
AXI5360−20, APC 24 x 12, fuselage
Simulation
Figure 5.2: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 09 emulator assuming operation in the ohmic
region
38
0 10 20 30 40 50 60 7030
35
40
45
50
55
60
65
70
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 22 x 12, no fuselage
AXI5330DBL, APC 22 x 12, fuselage
AXI5345−14, APC 27 x 13, no fuselage
AXI5345−14, APC 27 x 13, fuselage
AXI5345−18, APC 24 x 12, no fuselage
AXI5345−18, APC 24 x 12, fuselage
AXI5360−20, APC 26 x 15, no fuselage
AXI5360−20, APC 26 x 15, fuselage
Simulation
Figure 5.3: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 10 emulator assuming operation in the ohmic
region
39
0 10 20 30 40 50 60 7030
35
40
45
50
55
60
65
70
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 24 x 12, no fuselage
AXI5330DBL, APC 24 x 12, fuselage
AXI5345−14, APC 22 x 12, no fuselage
AXI5345−14, APC 22 x 12, fuselage
AXI5345−18, APC 26 x 15, no fuselage
AXI5345−18, APC 26 x 15, fuselage
AXI5360−20, APC 27 x 13, no fuselage
AXI5360−20, APC 27 x 13, fuselage
Simulation
Figure 5.4: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 11 emulator assuming operation in the ohmic
region
40
0 10 20 30 40 50 60 7035
40
45
50
55
60
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 26 x 15, no fuselage
AXI5330DBL, APC 26 x 15, fuselage
AXI5345−14, APC 24 x 12, no fuselage
AXI5345−14, APC 24 x 12, fuselage
AXI5345−18, APC 27 x 13, no fuselage
AXI5345−18, APC 27 x 13, fuselage
AXI5360−20, APC 22 x 12, no fuselage
AXI5360−20, APC 22 x 12, fuselage
Simulation
Figure 5.5: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 12 emulator assuming operation in the ohmic
region
41
0 10 20 30 40 50 60 7040
45
50
55
60
65
Current at fuel cell terminals (A)
Vo
lta
ge
 at
 fu
el 
ce
ll t
er
mi
na
ls 
(V)
 
 
AXI5330DBL, APC 27 x 13, no fuselage
AXI5330DBL, APC 27 x 13, fuselage
AXI5345−14, APC 26 x 15, no fuselage
AXI5345−14, APC 26 x 15, fuselage
AXI5345−18, APC 22 x 12, no fuselage
AXI5345−18, APC 22 x 12, fuselage
AXI5360−20, APC 24 x 12, no fuselage
AXI5360−20, APC 24 x 12, fuselage
Simulation
Figure 5.6: Comparison of simulated polarization curve to experimental values for
the steady-state SOFC PNNL Model 13 emulator assuming operation in the ohmic
region
42
BLDC Motor Modeling Results
The propeller determines the relationship between motor speed and load torque.
If the propeller models used in the simulation program do not accurately describe
the propeller performance in the wind tunnel, comparison between simulated mo-
tor performance and wind tunnel motor performance is not effective. To eliminate
discrepancies between simulated and wind tunnel motor performance caused by in-
accuracies in the propeller models, a second order polynomial was fit to the recorded
torque and propeller speed values for each test. As indicated in equation 2.13, torque
is a function of air density, the propeller’s coefficient of power, propeller diameter and
propeller speed. Table 2.4 and Figure 2.7(a) show that this coefficient is accurately
described as a second order function of the advance ratio, the ratio of velocity and
propeller speed (equation 2.11). Assuming constant velocity, CP becomes a function
of propeller speed with the form
CP =
α2
n2p
+
α1
np
+ α0 (5.1)
Combining this with equation 2.13, and assuming constant ρ, the relationship
between τ and ω takes the form
τ = α′0ω
2 + α′1ω + α
′
2 (5.2)
Thus, fitting simulated models to measured results simply shifts the 2nd order
propeller model to match experimental data. Similarly, a 1st order polynomial is fit
to the emulator’s voltage and current data. This removes any differences in emulator
open circuit voltage and resistance from simulated models. For all polynomial fits,
the coefficient of determination, R2, values were greater than 0.99.
43
Figures 5.7 through 5.14 show experimental results for each BLDC motor system.
Each motor was tested with six combinations of fuel cell models and propellers. The
solid lines indicate the simulated relationships between fuel cell voltage and propeller
speed, and fuel cell current and motor torque using the method described above.
Since simulation variables Vm and Im are not directly measurable, performance of the
controller and motor are lumped together.
Wind tunnel tests show very good correlation to motor models. These tests en-
compass a variety of power source characteristics and load profiles with the simulation
program predicting motor performance in every test reasonably well.
The AXI double 5330/20, AXI 5345/14 and AXI 5345/18 motor models slightly
over-predict motor performance. That is, for a given fuel cell current, the simulation
program predicts a higher motor torque than is measured. Similarly, for a given motor
speed, the fuel cell emulator voltage is lower than the simulated fuel cell voltage. This
indicates a lower motor operating efficiency than predicted in simulation and tends
to be more predominant for low power operation and with the larger APC propellers.
The reduced efficiencies for low power operation is expected as all motors advertise
maximum efficiencies when current is in excess of 20 A. Additionally, the low power
levels correspond to low duty cycle numbers where switching losses in the motor
controller represent a higher percentage of total system losses. The simulation model
assumes a lossless controller.
The higher operating efficiencies with the APC 22 x 12 and 24 x 12 propellers was
also expected for the AXI 5345/14 and 5345/18 motors. These motors are smaller
than the 5360/20 and only rated for use with 22 in. and 24 in. propellers. However,
both the AXI double 5330/20 and the AXI 5360/20 are rated for large propellers so
higher operating efficiencies with the smaller props is somewhat surprising.
44
250
300
350
400
450
500
550
600
650
700
750
30354045505560657075
Sha
ft ro
tati
ona
l ve
loc
ity 
(Ra
dian
s/se
c)
Voltage at fuel cell terminals (V)
 
 
PN
NL
 Mo
del
 08
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
7:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
vo
lt
ag
e-
sp
ee
d
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
D
B
L
53
30
/2
0
m
ot
or
to
ex
p
er
im
en
ta
lr
es
ul
ts
45
0
10
20
30
40
50
60
70
80
00.511.522.533.544.55
Cu
rren
t at
 fue
l ce
ll te
rmi
nal
s (A
)
Torque on shaft (N−m)
 
 
PN
NL
 Mo
del
 08
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
8:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
to
rq
ue
-c
ur
re
nt
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
D
B
L
53
30
/2
0
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
46
250
300
350
400
450
500
550
600
650
700
750
303540455055606570
Sha
ft ro
tati
ona
l ve
loc
ity 
(Ra
dian
s/se
c)
Voltage at fuel cell terminals (V)
 
 
PN
NL
 Mo
del
 08
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
9:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
vo
lt
ag
e-
sp
ee
d
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
45
/1
4
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
47
0
10
20
30
40
50
60
00.511.522.533.544.5
Cu
rren
t at
 fue
l ce
ll te
rmi
nal
s (A
)
Torque on shaft (N−m)
 
 
PN
NL
 Mo
del
 08
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
10
:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
to
rq
ue
-c
ur
re
nt
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
45
/1
4
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
48
250
300
350
400
450
500
550
600
650
700
354045505560657075
Sha
ft ro
tati
ona
l ve
loc
ity 
(Ra
dian
s/se
c)
Voltage at fuel cell terminals (V)
 
 
PN
NL
 Mo
del
 08
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
11
:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
vo
lt
ag
e-
sp
ee
d
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
45
/1
8
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
49
0
10
20
30
40
50
60
00.511.522.533.544.5
Cu
rren
t at
 fue
l ce
ll te
rmi
nal
s (A
)
Torque on shaft (N−m)
 
 
PN
NL
 Mo
del
 08
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
12
:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
to
rq
ue
-c
ur
re
nt
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
45
/1
8
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
50
300
350
400
450
500
550
600
40455055606570
Sha
ft ro
tati
ona
l ve
loc
ity 
(Ra
dian
s/se
c)
Voltage at fuel cell terminals (V)
 
 
PN
NL
 Mo
del
 08
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
13
:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
vo
lt
ag
e-
sp
ee
d
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
60
/2
0
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
51
0
5
10
15
20
25
30
35
40
45
50
00.511.522.533.544.5
Cu
rren
t at
 fue
l ce
ll te
rmi
nal
s (A
)
Torque on shaft (N−m)
 
 
PN
NL
 Mo
del
 08
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 08
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 09
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 09
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 10
, A
PC
 26
 x 1
5, n
o fu
sel
age
PN
NL
 Mo
del
 10
, A
PC
 26
 x 1
5, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 11
, A
PC
 27
 x 1
3, n
o fu
sel
age
PN
NL
 Mo
del
 11
, A
PC
 27
 x 1
3, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 12
, A
PC
 22
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 12
, A
PC
 22
 x 1
2, f
use
lag
e
Sim
ula
tion
PN
NL
 Mo
del
 13
, A
PC
 24
 x 1
2, n
o fu
sel
age
PN
NL
 Mo
del
 13
, A
PC
 24
 x 1
2, f
use
lag
e
Sim
ula
tion
F
ig
ur
e
5.
14
:
C
om
pa
ri
so
n
of
si
m
ul
at
ed
to
rq
ue
-c
ur
re
nt
re
la
ti
on
sh
ip
s
fo
r
th
e
A
X
I
53
60
/2
0
m
ot
or
to
ex
p
er
im
en
ta
l
re
su
lt
s
52
The AXI 5360/20 model under predicts motor operation, though only slightly. It
is important to note however, that even with a maximum duty ratio of 1.0, this motor
cannot reach the PNNL dictated operation points when operating with any of the
studied propellers. Thus, the motor cannot turn the propeller at speeds required for
adequate thrust. This is reflected in comparing propeller speeds of the farthest most
right measured operating points of Figure 5.13 to those of Figures 5.7, 5.9 and 5.11.
Propeller Modeling Results
Equations, 2.12, 2.13 and 2.14 show that propeller torque and thrust are functions
of air density ρ, their respective dimensionless coefficients (CP and CT ), propeller
diameter L and propeller rotational speed np. Coefficients CP and CT are functions
of advance ratio, J , which itself is a function of simulated craft velocity, S, L and
np as explained in Table 2.4 and equation 2.11. Both ρ and S can vary between and
during propeller tests. Therefore, the most effective method for comparing measured
data to propeller models is to calculate J , CP and CT for all measured operating
points. Figures, 5.15 through 5.18 show these results.
The calculated CP for the APC 22 x 12, 24 x 12 and 27 x 13 propellers show fairly
good correlation to APC provided propeller models. These values tend to be slightly
higher than model values, but follow the same trend as a function of J . The calculated
CP values for the APC 26 x 15 propeller differ significantly from the model. CP can
be thought of as a measure of power required to turn a propeller at a specific advance
ratio. Compared to measured results, the simulation model grossly over predicts the
amount of power required for the APC 26 x 15 to spin. This is why the simulation
program predicts much lower thrust values for propulsion systems operating with this
propeller (see Appendix A for the full set of simulation results). Because measured CP
53
values for the other propellers correlate well with propeller models and the observed
CP values for the 26 x 15 prop are comparable to those of the other propellers, the
disparity between measured CP and the model is thought to be due to model error.
In all cases, the observed values of CT exceed model values for low J where pro-
peller speeds are high. This is largely due to a wind tunnel blockage effect discussed
in [20, 21]. In a limited air space environment such as a wind tunnel, higher static
pressures build aft of the propeller than upstream of the propeller. This exaggerates
thrust measurements with the effect more prominent at high propeller speeds.
54
0.25 0.3 0.35 0.40.02
0.022
0.024
0.026
0.028
0.03
0.032
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Powe
r (C P)
 
 
PNNL Model 08, AXI5330DBL, no fuselagePNNL Model 08, AXI5330DBL, fuselagePNNL Model 09, AXI5345−18, no fuselagePNNL Model 09, AXI5345−18, fuselagePNNL Model 10, AXI5330DBL, no fuselagePNNL Model 10, AXI5330DBL, fuselagePNNL Model 11, AXI5345−14, no fuselagePNNL Model 11, AXI5345−14, fuselagePNNL Model 12, AXI5360−20, no fuselagePNNL Model 12, AXI5360−20, fuselagePNNL Model 13, AXI5345−18, no fuselagePNNL Model 13, AXI5345−18, fuselageSimulation
(a) Coefficient of Power (CP )
0.25 0.3 0.35 0.4
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Thru
st (C T
)
 
 
PNNL Model 08, AXI5330DBL, no fuselagePNNL Model 08, AXI5330DBL, fuselagePNNL Model 09, AXI5345−18, no fuselagePNNL Model 09, AXI5345−18, fuselagePNNL Model 10, AXI5330DBL, no fuselagePNNL Model 10, AXI5330DBL, fuselagePNNL Model 11, AXI5345−14, no fuselagePNNL Model 11, AXI5345−14, fuselagePNNL Model 12, AXI5360−20, no fuselagePNNL Model 12, AXI5360−20, fuselagePNNL Model 13, AXI5345−18, no fuselagePNNL Model 13, AXI5345−18, fuselageSimulation
(b) Coefficient of Power (CT )
Figure 5.15: Comparison of simulated CP and CT values with experimental results
for the APC 22 in. x 12 in. propeller
55
0.25 0.3 0.35 0.4 0.450.014
0.016
0.018
0.02
0.022
0.024
0.026
0.028
0.03
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Powe
r (C P)
 
 
PNNL Model 08, AXI5345−18, no fuselagePNNL Model 08, AXI5345−18, fuselagePNNL Model 09, AXI5360−20, no fuselagePNNL Model 09, AXI5360−20, fuselagePNNL Model 10, AXI5345−18, no fuselagePNNL Model 10, AXI5345−18, fuselagePNNL Model 11, AXI5330DBL, no fuselagePNNL Model 11, AXI5330DBL, fuselagePNNL Model 12, AXI5345−14, no fuselagePNNL Model 12, AXI5345−14, fuselagePNNL Model 13, AXI5360−20, no fuselagePNNL Model 13, AXI5360−20, fuselageSimulation
(a) Coefficient of Power (CP )
0.25 0.3 0.35 0.4 0.45
0.025
0.03
0.035
0.04
0.045
0.05
0.055
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Thru
st (C T
)
 
 
PNNL Model 08, AXI5345−18, no fuselagePNNL Model 08, AXI5345−18, fuselagePNNL Model 09, AXI5360−20, no fuselagePNNL Model 09, AXI5360−20, fuselagePNNL Model 10, AXI5345−18, no fuselagePNNL Model 10, AXI5345−18, fuselagePNNL Model 11, AXI5330DBL, no fuselagePNNL Model 11, AXI5330DBL, fuselagePNNL Model 12, AXI5345−14, no fuselagePNNL Model 12, AXI5345−14, fuselagePNNL Model 13, AXI5360−20, no fuselagePNNL Model 13, AXI5360−20, fuselageSimulation
(b) Coefficient of Power (CT )
Figure 5.16: Comparison of simulated CP and CT values with experimental results
for the APC 24 in. x 12 in. propeller
56
0.25 0.3 0.35 0.4 0.45
0.025
0.03
0.035
0.04
0.045
Advance Ratio J = S/(nD)
Calc
ulate
d Co
effici
ent o
f Pow
er (C P
)
 
 
PNNL Model 08, AXI5360−20, no fuselagePNNL Model 08, AXI5360−20, fuselagePNNL Model 09, AXI5345−14, no fuselagePNNL Model 09, AXI5345−14, fuselagePNNL Model 10, AXI5360−20, no fuselagePNNL Model 10, AXI5360−20, fuselagePNNL Model 11, AXI5345−18, no fuselagePNNL Model 11, AXI5345−18, fuselagePNNL Model 12, AXI5330DBL, no fuselagePNNL Model 12, AXI5330DBL, fuselagePNNL Model 13, AXI5345−14, no fuselagePNNL Model 13, AXI5345−14, fuselageSimulation
(a) Coefficient of Power (CP )
0.25 0.3 0.35 0.4 0.450.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Thru
st (C T
)
 
 
PNNL Model 08, AXI5360−20, no fuselagePNNL Model 08, AXI5360−20, fuselagePNNL Model 09, AXI5345−14, no fuselagePNNL Model 09, AXI5345−14, fuselagePNNL Model 10, AXI5360−20, no fuselagePNNL Model 10, AXI5360−20, fuselagePNNL Model 11, AXI5345−18, no fuselagePNNL Model 11, AXI5345−18, fuselagePNNL Model 12, AXI5330DBL, no fuselagePNNL Model 12, AXI5330DBL, fuselagePNNL Model 13, AXI5345−14, no fuselagePNNL Model 13, AXI5345−14, fuselageSimulation
(b) Coefficient of Power (CT )
Figure 5.17: Comparison of simulated CP and CT values with experimental results
for the APC 26 in. x 15 in. propeller
57
0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42
0.016
0.018
0.02
0.022
0.024
0.026
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Powe
r (C P)
 
 PNNL Model 08, AXI5345−14, no fuselagePNNL Model 08, AXI5345−14, fuselagePNNL Model 09, AXI5330DBL, no fuselagePNNL Model 09, AXI5330DBL, fuselagePNNL Model 10, AXI5345−14, no fuselagePNNL Model 10, AXI5345−14, fuselagePNNL Model 11, AXI5360−20, no fuselagePNNL Model 11, AXI5360−20, fuselagePNNL Model 12, AXI5345−18, no fuselagePNNL Model 12, AXI5345−18, fuselagePNNL Model 13, AXI5330DBL, no fuselagePNNL Model 13, AXI5330DBL, fuselageSimulation
(a) Coefficient of Power (CP )
0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Advance Ratio J = S/(nD)
Calcu
lated
 Coe
fficie
nt of 
Thru
st (C T
)
 
 
PNNL Model 08, AXI5345−14, no fuselagePNNL Model 08, AXI5345−14, fuselagePNNL Model 09, AXI5330DBL, no fuselagePNNL Model 09, AXI5330DBL, fuselagePNNL Model 10, AXI5345−14, no fuselagePNNL Model 10, AXI5345−14, fuselagePNNL Model 11, AXI5360−20, no fuselagePNNL Model 11, AXI5360−20, fuselagePNNL Model 12, AXI5345−18, no fuselagePNNL Model 12, AXI5345−18, fuselagePNNL Model 13, AXI5330DBL, no fuselagePNNL Model 13, AXI5330DBL, fuselageSimulation
(b) Coefficient of Power (CT )
Figure 5.18: Comparison of simulated CP and CT values with experimental results
for the APC 27 in. x 13 in. propeller
58
Measurement Uncertainty
In the wind tunnel experiments, there are two primary mechanisms for measure-
ment uncertainty. First, as was mentioned in the Instruments section of the previous
chapter, each instrument has an associated amount of measurement uncertainty. Sec-
ond, the turbulent air flow in the wind tunnel causes stochastic fluctuations in air
velocity, which causes stochastic fluctuations in all data measurements. Table 5.1
below gives confidence intervals (i.e. 95% of measurements within the interval) for
the directly measurable quantities.
Table 5.1: The uncertainty in measurements is due to a combination of instrument
limitations and system noise primarily caused by turbulent air flow through the wind
tunnel. This table lists the 95% confidence intervals for each measured quantity.
Measurement Confidence Interval
Wind Tunnel Air Velocity (S) ±2 m/s
Fuel Cell Emulator Current (Ic) ±0.2 A
Fuel Cell Emulator Voltage (Vc) ±0.3 V
Duty Cycle (D) ±0.005
Motor/Propeller Speed (ω) ±1 rad/s
Motor Torque (τ) ±0.1 N-m
Propeller Thrust (T ) ±3 N
For the fuel cell emulator and BLDC system results, error analyses of collected
data are determined directly from the confidence intervals of table 5.1. This is be-
cause the data presented in their analyses are all directly measurable quantities. The
propeller analysis is more complicated as results are expressed in calculations of CT
and CP as functions of J . These calculations require two or more measurements each
with an associated amount of uncertainty. To determine the total uncertainty in the
calculated values of CT , CP and J , the uncertainty analysis method presented in [22]
is used. In this method, the uncertainty in the calculated result F where F is a
59
function of independent variables, x1, x2, ..., xn, each with an associated measure of
uncertainty, w1, w2, ..., wn, is determined by the formula
wF =
((
∂F
∂x1
w1
)2
+
(
∂F
∂x2
w2
)2
+ ...+
(
∂F
∂xn
wn
)2
)1/2
(5.3)
Using the confidence intervals of table 5.1 as the measures of uncertainty, confi-
dence intervals for each calculated value of J , CP and CT are found. These results are
included in Appendix B along with the calculated values of J , CP and CT . Noting
these results, we see that the variability in the operation points seen in the propeller
results, i.e. figures 5.15 through 5.18 is easily explained. First, primarily due to tur-
bulent air flow, J is found to have confidence intervals ranging from ±0.04 to ±0.07
with the larger intervals corresponding to larger J . This indicates that data points
shown in figures 5.15 through 5.18 could vary fairly significantly along the horizontal
axis, especially for higher values of J . Similarly, CT and CP have relatively large
confidence intervals also corresponding to higher values of J . This is primarily due
to inherent uncertainty in instrument measurements. High values of J correspond
to low propeller speeds, and thus, small measurements of thrust and torque. The
inherent inaccuracies of the Cooper LXT-920 load cell are significant in magnitude
compared to the thrust and torque values recorded for these operation points. Thus,
as is reflected in the figures, calculated values of CT and CP show large variances
especially for high values of J .
Despite these variations, the general trends of CP and CT as functions of J match
model expectations. Additionally, little appreciable difference in propeller perfor-
mance is seen between tests with and without the mock fuselage installed. These
results give some confidence that component models (with the exception of the CP
values for the APC 26 x 15 propeller) are accurate.
60
It is important to note that this error analysis only serves to quantify error present
in data measurements caused by measurement uncertainty. Other mechanisms of
error such as the wind tunnel blockage effect mentioned earlier cause offset deviations
in measured quantities from model predictions. Further, this error analysis assumes
variable uncertainties to be independent, which is obviously not the case for the
stochastic fluctuations in all data measurements caused by turbulent air flow. Still,
the results of the error analysis are consistent with the number of significant digits
presented in data tables of Appendix B and provides further insight into the variability
seen in wind tunnel testing.
61
CONCLUSION
In this thesis, a physically-based model for design and optimization of a fuel cell
powered UAV electric propulsion system comprised of a solid oxide fuel cell providing
power, a brushless DC motor and controller, and a propeller was presented. The
individual component models were integrated into a simulation program which used
the MATLAB command fsolve() to numerically find specific propulsion operating
points. A graphical procedure using this simulation program was introduced that
allows rapid assessment and selection of design choices, including fuel cell character-
istics and hybridization with multiple sources. Experimental results from wind tunnel
tests provided validation of the component models.
In addition to providing insight into design choices, the graphical presentation
of simulation results such as Figure 3.1 proved to be very effective for coordinating
the efforts of multiple groups involved in building a fuel cell / electric propulsion
system. Stack designers could immediately appreciate the implications of increasing
the height of the stack or changing cell thickness, simply by sketching a new fuel cell
curve on the plot. Further, the effect of power source hybridization or alternate power
electronic topologies can be displayed on the same graph by adding the associated
curves to the plot as in Figure 3.3. Finally, the implications of design changes in the
fuel cell / electric propulsion are immediately apparent to the air frame design team.
Future Work
There are a couple remaining concerns and important goals for future work in
this project. Though wind tunnel test results give some confidence that a UAV uti-
lizing a propulsion system designed with the simulation program will fly, variations
62
in measured propeller performance from model values exist. Further, wind tunnel
air flow velocities measure only around 40% of specified UAV velocity so propulsion
system performance at higher velocities must be extrapolated from these experimen-
tal results. To alleviate remaining concerns, it is recommended that propeller tests
take place in a fully calibrated wind tunnel such as the Kirsten Wind Tunnel at the
University of Washington. The working section of this wind tunnel is 2.4 m x 3.7 m in
cross-sectional area which should significantly reduce the wind tunnel blockage effect
described in chapter five. Additionally, the wind tunnel’s low turbulence intensity
factor would reduce measurement fluctuations and with maximum velocities of 90
m/s, the wind tunnel easily meets UAV velocity specifications.
For future studies, further design investigations should center around dynamic
models, which can be combined with aircraft dynamic models for a fully integrated
UAV simulation program. Also, investigation into a hybrid power source is required
to increase the operation range of the propulsion system as illustrated in Figure 3.3.
In addition to increasing maximum propulsion system thrust, a second power source
could also be utilized to protect the fuel cell from exposure to severe high-current
loading and load transients.
63
REFERENCES CITED
64
[1] T.J. Becker. Flying on Hydrogen: Georgia Tech Researchers Use Fuel Cells to
Power Unmanned Aerial Vehicle. Research News & Publication Office, Georgia
Institute of Technology, August 2006.
[2] E. Lafey. U-M Students Set Fuel-Cell Airplane Flight Record. Chicago Tribune,
November 2008.
[3] S. Kearns, M. Yu. Cal State L.A.’s Fuel-Cell Plane Passes Key Flight Test. CSU
Newsline California State University-L.A., September 2006.
[4] U. C. Ofoma, C. C. Wu. Design of a Fuel Cell Powered UAV for Environmental
Research. AIAA 3rd Unmanned Unlimited Technical Conference, Workshop and
Exhibit, 2004.
[5] D. S. Soban, E. Upton. Design of a UAV to Optimize Use of Fuel Cell Propulsion
Technology. Infotech@aerospace, 2005.
[6] B. A. Moffitt, T. H. Bradley, D. E.Parekh, D. Mavris. Design and Performance
Validation of a Fuel Cell Unmanned Aerial Vehicle. 44th AIAA Aerospace Sci-
ences Meeting and Exhibit, 2006.
[7] T. H. Bradley, B. A. Moffitt, D. E.Parekh, D. Mavris. Flight Test Results for a
Fuel Cell Unmanned Aerial Vehicle. 45th AIAA Aerospace Sciences Meeting and
Exhibit, 2007.
[8] P. Lindahl, E. Moog, S. Shaw. Simulation, Design, and Validation of a UAV
SOFC Propulsion System. IEEE Aerospace Conference, 2009.
[9] EG&G Technical Services, Inc. Fuel Cell Handbook Seventh Edition. U.S. De-
partment of Energy, 2004.
[10] B. Viswanathan, M. Aulice Scibioh. Fuel Cells Principles and Applications. CRC
Press, Taylor & Francis Group, 2007.
[11] S. Pasricha, S. R. Shaw. A Dynamic PEM Fuel Cell Model. IEEE Transactions
on Energy Conversion, 21:484–490, June 2006.
[12] Caisheng Wang, M. Hashem Nehrir. A Physically Based Dynamic Model for
Solid Oxide Fuel Cells. IEEE Transactions on Energy Conversion, 22(4):887–
897, December 2007.
[13] S. Ogasawara, H. Akagi. An Approach to Position Sensorless Drive for Brushless
DC Motors. IEEE Transactions on Industry Applications, 27:928–933, Sept.-Oct.
1991.
65
[14] C. G. Kim, J. H. Lee, H. W. Kim, M. J. Youn. Study on Maximum Torque
Generation For Sensorless Controlled Brushless DC Motor With Trapezoidal
Back EMF. Electric Power Applications, IEEE Proceedings, 152:277–291, March
2005.
[15] P. Yedamale. Brushless DC (BLDC) Motor Fundamentals. Technical Report,
Microchip Technologies, 2003.
[16] H. A. Toliyat, G. B. Kliman, editors. Handbook of Electric Motors. Taylor &
Francis Group, 2004.
[17] Pragasen Pillay, Ramu Krishnan. Modeling, Simulation, and Analysis of
Permanent-Magnet Motor Drives, PartII: The Brushless DC Motor Drive. IEEE
Transactions on Industry Applications, 25(2):274–279, March/April 1989.
[18] B. W. McCormick. Aerodynamics, Aeronautics, and Flight Mechanics. John
Wiley & Sons, 1979.
[19] R. D. Mehta, P. Bradshaw. Design Rules for Small Low Speed Wind Tunnels.
Aeronautical Journal of the Royal Aeronautical Society, pages 443–449, Novem-
ber 1979.
[20] R. E. Fitzgerald. Wind Tunnel Blockage Corrections for Propellers. Master’s
Thesis, University of Maryland, 2007.
[21] E. K. Corrigan IV. Survey of Small Unmanned Aerial Vehicle Electric Propulsion
System. Master’s Thesis, University of Dayton, 2007.
[22] J. P. Holmes. Experimental Methods for Engineers. McGraw-Hill, Inc., 1994.
66
APPENDICES
67
APPENDIX A
SIMULATION RESULTS
68
Appendix A contains the full set of simulation results for all combinations of
propulsion system components used in this study as indicated by Figure 2.1. The
SOFC stack models and their associated parameters are listed in Table 2.2, the BLDC
motors in Table 2.3, and the propellers in Table 2.4. The blue line in the figures below
represent the linearized fuel cell stack, the dashed black lines indicate constant thrust
values, and the red box defines a family of voltage/current curves for the motor and
propeller combination. The physically based models used in the simulation program
and the simulation program itself are described in chapters two and three, respectively.
In all cases, the motor controller was treated as a lossless component. Air density
was assumed to be 1.2 kg/m3 and cruising velocity, 31.3 m/s.
69
Solid Oxide Fuel Cell Model 8
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.1 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.8 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 38.8 N20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.1: Simulation results for the propulsion system with components: SOFC
Model 8, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
70
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.9 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 29 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.3 N20 N
35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.2: Simulation results for the propulsion system with components: SOFC
Model 8, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
71
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.9 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
40 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
29.3 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.6 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.3: Simulation results for the propulsion system with components: SOFC
Model 8, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
72
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.2 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.9 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.6 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.4: Simulation results for the propulsion system with components: SOFC
Model 8, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
73
Solid Oxide Fuel Cell Model 9
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.2 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.3 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.1 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.5: Simulation results for the propulsion system with components: SOFC
Model 9, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
74
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.1 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.1 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.3 N20 N
35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.6: Simulation results for the propulsion system with components: SOFC
Model 9, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
75
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.1 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.2 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.5 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.7: Simulation results for the propulsion system with components: SOFC
Model 9, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
76
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
36.4 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.7 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.2 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.7 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.8: Simulation results for the propulsion system with components: SOFC
Model 9, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
77
Solid Oxide Fuel Cell Model 10
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.8 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.9 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.6 N
20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.6 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.9: Simulation results for the propulsion system with components: SOFC
Model 10, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is
indicated below each figure.
78
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.7 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.8 N
20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.2 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.10: Simulation results for the propulsion system with components: SOFC
Model 10, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
79
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.8 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
29.1 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.4 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.11: Simulation results for the propulsion system with components: SOFC
Model 10, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
80
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.4 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.7 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.4 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.12: Simulation results for the propulsion system with components: SOFC
Model 10, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
81
Solid Oxide Fuel Cell Model 11
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.9 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.7 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.13: Simulation results for the propulsion system with components: SOFC
Model 11, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is
indicated below each figure.
82
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.8 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.9 N20 N
35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.2 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.14: Simulation results for the propulsion system with components: SOFC
Model 11, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
83
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.9 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
29.2 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.4 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.15: Simulation results for the propulsion system with components: SOFC
Model 11, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
84
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.1 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.4 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.8 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.16: Simulation results for the propulsion system with components: SOFC
Model 11, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
85
Solid Oxide Fuel Cell Model 12
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.9 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.7 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.7 N20 N
35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.17: Simulation results for the propulsion system with components: SOFC
Model 12, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is
indicated below each figure.
86
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.8 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.9 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.2 N
20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.18: Simulation results for the propulsion system with components: SOFC
Model 12, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
87
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.9 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
29.2 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.5 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.19: Simulation results for the propulsion system with components: SOFC
Model 12, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
88
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.1 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.4 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.8 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.20: Simulation results for the propulsion system with components: SOFC
Model 12, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
89
Solid Oxide Fuel Cell Model 13
AXI 5330 DBL BLDC Motor
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.9 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39 N20 N
35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.7 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 38.8 N20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.21: Simulation results for the propulsion system with components: SOFC
Model 13, AXI 5330 DBL Motor, and Jeti Spin 99 Controller. The propeller is
indicated below each figure.
90
AXI Motor 5345-14 BLDC Motor
10 20 30 40 50 600
20
40
60
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N
50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.8 N
20 N 35 N
50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 28.9 N20 N 35 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V) 39.3 N20 N 35 N
50 N
(d) APC 27 in. x 13 in.
Figure A.22: Simulation results for the propulsion system with components: SOFC
Model 13, AXI 5345-14 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
91
AXI Motor 5345-18 BLDC Motor
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.8 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.9 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
10
20
30
40
50
60
70
80
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
29.2 N
20 N 35 N
50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
20
40
60
80
100
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
39.5 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.23: Simulation results for the propulsion system with components: SOFC
Model 13, AXI 5345-18 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
92
AXI Motor 5360 BLDC Motor
10 20 30 40 50 600
50
100
150
200
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
37.1 N
20 N 35 N 50 N
(a) APC 22 in. x 12 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N 50 N
(b) APC 22 in. x 12 in.
10 20 30 40 50 600
20
40
60
80
100
120
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
28.8 N
20 N 35 N 50 N
(c) APC 26 in. x 15 in.
10 20 30 40 50 600
50
100
150
Current at fuel cell terminals (A)
Volta
ge a
t fue
l cell
 term
inals
 (V)
38.5 N
20 N 35 N 50 N
(d) APC 27 in. x 13 in.
Figure A.24: Simulation results for the propulsion system with components: SOFC
Model 13, AXI 5360 Motor, and Jeti Spin 99 Controller. The propeller is indicated
below each figure.
93
APPENDIX B
WIND TUNNEL TEST RESULTS
94
Appendix B lists the data gathered in the wind tunnel tests along with calcu-
lated values of J , CT and CP . These calculations assume data measurements with a
minimum of 2 significant digits.
95
T
ab
le
B
.1
:
W
in
d
T
un
ne
l
D
at
a
fo
r
SO
F
C
M
od
el
08
,
A
X
I
D
ou
bl
e
53
30
/2
0
M
ot
or
,
A
P
C
22
x
12
P
ro
p
W
in
d
T
un
ne
l.
A
ir
de
ns
it
y,
ρ
w
as
m
ea
su
re
d
to
b
e
1.
20
kg
/m
3
(a
)
W
it
ho
ut
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
21
66
.0
7.
6
0.
9
12
37
8
12
0.
35
±
0.
06
0.
02
9±
0.
00
7
0.
02
5±
0.
00
3
0.
31
62
.3
14
.7
1.
6
26
46
2
12
0.
30
±
0.
05
0.
04
2±
0.
00
5
0.
02
8±
0.
00
2
0.
43
56
.0
26
.3
2.
3
44
54
0
13
0.
27
±
0.
04
0.
05
1±
0.
00
4
0.
03
0±
0.
00
1
0.
55
49
.7
38
.0
2.
7
54
58
4
13
0.
25
±
0.
04
0.
05
4±
0.
00
3
0.
03
0±
0.
00
1
0.
66
44
.0
48
.4
3.
0
62
61
1
13
0.
24
±
0.
04
0.
05
6±
0.
00
3
0.
03
1±
0.
00
1
0.
80
38
.0
59
.1
3.
2
67
62
2
13
0.
23
±
0.
04
0.
05
8±
0.
00
3
0.
03
1±
0.
00
1
(b
)
W
it
h
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
20
66
.5
6.
9
0.
9
12
37
5
12
0.
35
±
0.
06
0.
02
9±
0.
00
7
0.
02
4±
0.
00
3
0.
31
62
.3
14
.6
1.
6
28
46
1
12
0.
29
±
0.
05
0.
04
4±
0.
00
5
0.
02
8±
0.
00
2
0.
45
55
.9
26
.4
2.
3
45
54
0
12
0.
25
±
0.
04
0.
05
2±
0.
00
4
0.
03
0±
0.
00
1
0.
55
49
.6
37
.6
2.
8
56
58
4
13
0.
24
±
0.
04
0.
05
5±
0.
00
3
0.
03
1±
0.
00
1
0.
67
43
.9
48
.4
3.
0
63
60
8
13
0.
23
±
0.
04
0.
05
8±
0.
00
3
0.
03
1±
0.
00
1
0.
80
37
.8
59
.4
3.
2
68
62
2
13
0.
23
±
0.
04
0.
05
9±
0.
00
3
0.
03
1±
0.
00
1
96
T
ab
le
B
.2
:
W
in
d
T
un
ne
l
D
at
a
fo
r
SO
F
C
M
od
el
08
,
A
X
I
D
ou
bl
e
53
45
/1
4
M
ot
or
,
A
P
C
27
x
13
P
ro
p
W
in
d
T
un
ne
l.
A
ir
de
ns
it
y,
ρ
w
as
m
ea
su
re
d
to
b
e
1.
18
kg
/m
3
(a
)
W
it
ho
ut
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
23
66
.1
7.
5
1.
2
16
30
8
13
0.
38
±
0.
06
0.
02
6±
0.
00
5
0.
01
8±
0.
00
2
0.
31
61
.7
15
.7
2.
1
34
37
0
13
0.
31
±
0.
05
0.
03
8±
0.
00
3
0.
02
1±
0.
00
1
0.
38
58
.5
21
.6
2.
6
44
40
0
12
0.
28
±
0.
05
0.
04
2±
0.
00
3
0.
02
2±
0.
00
1
0.
45
54
.0
30
.0
3.
0
55
42
9
14
0.
30
±
0.
04
0.
04
5±
0.
00
2
0.
02
3±
0.
00
1
0.
53
48
.3
40
.4
3.
5
65
45
0
14
0.
28
±
0.
04
0.
04
9±
0.
00
2
0.
02
4±
0.
00
1
0.
61
43
.4
49
.5
3.
7
70
46
3
14
0.
27
±
0.
04
0.
05
0±
0.
00
2
0.
02
4±
0.
00
1
(b
)
W
it
h
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
24
66
.1
7.
5
1.
2
19
30
7
13
0.
38
±
0.
06
0.
03
0±
0.
00
5
0.
01
8±
0.
00
2
0.
31
61
.6
15
.7
2.
1
36
37
1
12
0.
30
±
0.
05
0.
03
9±
0.
00
3
0.
02
1±
0.
00
1
0.
38
58
.5
21
.5
2.
6
45
40
0
13
0.
30
±
0.
05
0.
04
2±
0.
00
3
0.
02
2±
0.
00
1
0.
43
54
.0
30
.0
3.
1
56
42
9
13
0.
27
±
0.
04
0.
04
6±
0.
00
2
0.
02
3±
0.
00
1
0.
53
48
.4
40
.2
3.
4
64
45
1
14
0.
29
±
0.
04
0.
04
7±
0.
00
2
0.
02
3±
0.
00
1
0.
63
42
.4
51
.0
3.
7
70
46
4
14
0.
27
±
0.
04
0.
05
0±
0.
00
2
0.
02
4±
0.
00
1
97
T
ab
le
B
.3
:
W
in
d
T
un
ne
l
D
at
a
fo
r
SO
F
C
M
od
el
08
,
A
X
I
D
ou
bl
e
53
45
/1
8
M
ot
or
,
A
P
C
24
x
12
P
ro
p
W
in
d
T
un
ne
l.
A
ir
de
ns
it
y,
ρ
w
as
m
ea
su
re
d
to
b
e
1.
18
kg
/m
3
(a
)
W
it
ho
ut
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
31
66
.4
6.
9
1.
1
18
34
8
13
0.
38
±
0.
06
0.
03
7±
0.
00
6
0.
02
2±
0.
00
2
0.
43
62
.7
14
.0
1.
8
35
42
1
13
0.
31
±
0.
05
0.
04
8±
0.
00
4
0.
02
5±
0.
00
1
0.
56
56
.6
25
.3
2.
4
53
48
6
13
0.
27
±
0.
04
0.
05
4±
0.
00
3
0.
02
6±
0.
00
1
0.
67
51
.7
34
.1
2.
8
59
51
8
13
0.
25
±
0.
04
0.
05
3±
0.
00
3
0.
02
6±
0.
00
1
0.
79
46
.7
43
.5
3.
1
60
54
1
13
0.
25
±
0.
04
0.
04
9±
0.
00
3
0.
02
6±
0.
00
1
0.
91
42
.5
51
.2
3.
3
63
55
2
13
0.
24
±
0.
04
0.
05
0±
0.
00
2
0.
02
7±
0.
00
1
(b
)
W
it
h
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
32
66
.4
6.
9
1.
0
19
34
8
13
0.
38
±
0.
06
0.
03
9±
0.
00
6
0.
02
2±
0.
00
2
0.
43
62
.1
15
.0
1.
8
36
42
6
12
0.
29
±
0.
05
0.
04
8±
0.
00
4
0.
02
5±
0.
00
1
0.
55
56
.6
25
.1
2.
5
53
48
6
12
0.
26
±
0.
04
0.
05
4±
0.
00
3
0.
02
6±
0.
00
1
0.
67
51
.7
34
.1
2.
8
58
52
0
13
0.
25
±
0.
04
0.
05
2±
0.
00
3
0.
02
6±
0.
00
1
0.
80
46
.7
43
.4
3.
2
63
54
0
12
0.
23
±
0.
04
0.
05
2±
0.
00
2
0.
02
7±
0.
00
1
0.
91
42
.5
51
.0
3.
3
66
55
3
13
0.
24
±
0.
04
0.
05
2±
0.
00
2
0.
02
7±
0.
00
1
98
T
ab
le
B
.4
:
W
in
d
T
un
ne
l
D
at
a
fo
r
SO
F
C
M
od
el
08
,
A
X
I
D
ou
bl
e
53
60
/2
0
M
ot
or
,
A
P
C
26
x
15
P
ro
p
W
in
d
T
un
ne
l.
A
ir
de
ns
it
y,
ρ
w
as
m
ea
su
re
d
to
b
e
1.
20
kg
/m
3
(a
)
W
it
ho
ut
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
43
65
.4
8.
8
1.
6
19
31
0
14
0.
42
±
0.
06
0.
03
4±
0.
00
5
0.
02
8±
0.
00
2
0.
56
61
.5
16
.3
2.
4
35
36
5
12
0.
32
±
0.
05
0.
04
5±
0.
00
4
0.
03
0±
0.
00
1
0.
68
57
.5
23
.5
3.
0
47
40
1
13
0.
31
±
0.
05
0.
05
0±
0.
00
3
0.
03
1±
0.
00
1
0.
80
53
.0
31
.7
3.
5
58
42
8
14
0.
30
±
0.
04
0.
05
4±
0.
00
3
0.
03
1±
0.
00
1
0.
90
49
.3
38
.8
3.
8
64
44
5
13
0.
28
±
0.
04
0.
05
6±
0.
00
3
0.
03
2±
0.
00
1
1.
00
45
.8
45
.0
4.
0
69
45
6
14
0.
29
±
0.
04
0.
05
7±
0.
00
2
0.
03
2±
0.
00
1
(b
)
W
it
h
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
43
65
.4
8.
6
1.
6
21
30
8
11
0.
35
±
0.
06
0.
03
8±
0.
00
6
0.
02
8±
0.
00
2
0.
55
61
.5
15
.8
2.
4
35
36
2
13
0.
35
±
0.
05
0.
04
6±
0.
00
4
0.
03
0±
0.
00
1
0.
67
57
.6
23
.2
3.
0
48
39
9
13
0.
30
±
0.
05
0.
05
2±
0.
00
3
0.
03
1±
0.
00
1
0.
78
53
.5
30
.7
3.
4
57
42
5
13
0.
30
±
0.
04
0.
05
4±
0.
00
3
0.
03
1±
0.
00
1
0.
91
49
.3
38
.5
3.
8
64
44
3
14
0.
31
±
0.
04
0.
05
7±
0.
00
3
0.
03
2±
0.
00
1
1.
00
45
.7
45
.1
4.
0
69
45
4
14
0.
29
±
0.
04
0.
05
8±
0.
00
2
0.
03
2±
0.
00
1
99
T
ab
le
B
.5
:
W
in
d
T
un
ne
l
D
at
a
fo
r
SO
F
C
M
od
el
09
,
A
X
I
D
ou
bl
e
53
30
/2
0
M
ot
or
,
A
P
C
27
x
13
P
ro
p
W
in
d
T
un
ne
l.
A
ir
de
ns
it
y,
ρ
w
as
m
ea
su
re
d
to
b
e
1.
20
kg
/m
3
(a
)
W
it
ho
ut
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
20
63
.4
7.
7
1.
3
13
31
0
12
0.
36
±
0.
06
0.
02
0±
0.
00
5
0.
01
8±
0.
00
1
0.
31
56
.3
20
.6
2.
4
37
38
9
12
0.
29
±
0.
05
0.
03
6±
0.
00
3
0.
02
2±
0.
00
1
0.
44
48
.6
34
.8
3.
2
54
43
6
13
0.
28
±
0.
04
0.
04
2±
0.
00
2
0.
02
3±
0.
00
1
0.
56
40
.4
49
.8
3.
6
62
45
9
14
0.
27
±
0.
04
0.
04
4±
0.
00
2
0.
02
4±
0.
00
1
0.
67
34
.5
60
.5
3.
8
65
46
6
13
0.
26
±
0.
04
0.
04
5±
0.
00
2
0.
02
4±
0.
00
1
(b
)
W
it
h
F
us
el
ag
e
D
V
c
(V
)
I c
(A
)
τ
(N
-m
)
T
(N
)
ω
(r
ad
/s
)
S
(m
/s
)
J
C
T
C
P
0.
20
63
.6
7.
6
1.
3
15
31
0
12
0.
35
±
0.
06
0.
02
4±
0.
00
5
0.
01
9±
0.
00
1
0.
31
56
.4
20
.8
2.
4
38
39
0
13
0.
31
±
0.
05
0.
03
8±
0.
00
3
0.
02
2±
0.
00
1
0.
44
48
.6
34
.8
3.
2
55
43
6
13
0.
27
±
0.
04
0.
04
3±
0.
00
2
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T
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B
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106
T
ab
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B
.1
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107
T
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B
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108
T
ab
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B
.1
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109
T
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B
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T
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