ON THE DESIGN OF A SMALL SOLAR POWERED UNMANNED AERIAL
VEHICLE
Brian Parker Miracle
B.S., California Polytechnic State University San Luis Obispo, 2006
THESIS
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2011
ON THE DESIGN OF A SMALL SOLAR POWERED UNMANNED AERIAL
VEHICLE
A Thesis
by
Brian Parker Miracle
Approved by:
__________________________________, Committee Chair
Ilhan Tuzcu, Ph.D.
__________________________________, Second Reader
Dongmei Zhou, Ph.D.
____________________________
Date
ii
Student: Brian Parker Miracle
I certify that this student has met the requirements for format contained in the University
format manual, and that this thesis is suitable for shelving in the Library and credit is to
be awarded for the thesis.
__________________________, Graduate Coordinator
Aki Kumagai, Ph.D.
Department of Mechanical Engineering
iii
___________________
Date
Abstract
of
ON THE DESIGN OF A SMALL SOLAR POWERED UNMANNED AERIAL
VEHICLE
by
Brian Parker Miracle
Unmanned aerial vehicles are seeing increasing use in a variety of applications
including warfare, imaging, communication, search and rescue, meteorology, agriculture,
and more. For most applications, flight endurance on the order of days, weeks, or even
years is desirable. Photovoltaic cells represent an emerging and viable method of
powering unmanned aerial vehicles on such long endurance flights. This study
investigates the design optimization of a small solar powered unmanned aerial vehicle.
The aircraft is intended to weigh less than twenty pounds and to fly for 24 hours at low
altitude over Sacramento, California during the summer months of May through
September. Photovoltaic technology and the characterization of a thin-film photovoltaic
cell are reviewed. The majority of the paper describes the methods used to implement a
continuous design approach in which the battery pack power, photovoltaic efficiency, and
aircraft weight were determined for a given aspect ratio and wing loading. The optimum
aspect ratio and wing loading to minimize both battery pack power and photovoltaic
efficiency are identified and the final design is discussed. The results indicate that aspect
ratio exhibits a strong inverse relationship with aircraft weight, wing loading is directly
related to minimum required photovoltaic efficiency, and that minimum aircraft weight
does not translate to minimum power required.
_______________________, Committee Chair
Ilhan Tuzcu, Ph.D.
_______________________
Date
iv
DEDICATION
To Melissa for her patience…
To Professor Tuzcu for always being willing to help…
To Pandora for keeping me sane…
v
TABLE OF CONTENTS
Page
Dedication ........................................................................................................................... v
List of Tables ................................................................................................................... viii
List of Figures .................................................................................................................... ix
Chapter
1. INTRODUCTION ........................................................................................................ 1
2. MISSION REQUIREMENTS AND SYSTEMS ......................................................... 3
2.1 Design Constraints ............................................................................................ 3
2.2 Systems ............................................................................................................. 3
2.3 Payload .............................................................................................................. 3
3. CONFIGURATION, AERODYNAMICS, AND PERFORMANCE .......................... 6
3.1 Configuration .................................................................................................... 6
3.2 Wing.................................................................................................................. 6
3.3 Fuselage .......................................................................................................... 10
3.4 Tail .................................................................................................................. 10
3.5 Payload Pod .................................................................................................... 10
3.6 Performance: Drag, Thrust, and Power........................................................... 11
4. PHOTOVOLTAIC ARRAY ....................................................................................... 15
4.1 I-V Cell Characterization ................................................................................ 15
4.2 Solar Insolation ............................................................................................... 23
5. PROPULSION ............................................................................................................ 25
5.1 Charge Controller............................................................................................ 25
5.2 Battery Pack .................................................................................................... 25
5.3 Electric Motor, Motor Controller, and Propeller ............................................ 26
6. STRUCTURE ............................................................................................................. 28
6.1 Wing Spanwise Bending ................................................................................. 28
6.2 Wing Torsion .................................................................................................. 32
vi
6.3 Fuselage Bending ............................................................................................ 34
7. WEIGHT AND STABILITY ..................................................................................... 35
7.1 Weight ............................................................................................................. 35
7.2 Stability ........................................................................................................... 42
8. DESIGN SPREADSHEET ......................................................................................... 46
9. RESULTS ................................................................................................................... 49
10. SUMMARY ............................................................................................................... 55
Works Cited ...................................................................................................................... 57
vii
LIST OF TABLES
Page
1.
Table 1 Component Drag Build-Up Method ........................................................ 13
2.
Table 2 PowerFilm Photovoltaic Cell Comparison .............................................. 16
3.
Table 3 Photovoltaic Cell Characterization – Environmental Variables .............. 19
4.
Table 4 Photovoltaic Cell Characterization – Voltage and Current ..................... 20
5.
Table 5 Lithium-Ion Polymer Battery Cell Characteristics .................................. 26
6.
Table 6 Wing Bending Analysis Results .............................................................. 29
7.
Table 7 Wing Torsion Analysis Results ............................................................... 33
8.
Table 8 Fuselage Bending Analysis Results ......................................................... 34
9.
Table 9 Motor Weight Manufacturer Recommendations ..................................... 36
10.
Table 10 Table of Weights .................................................................................... 38
11.
Table 11 Lowest Permitted Wing Loading for a Given Aspect Ratio .................. 49
12.
Table 12 Design Point Summary .......................................................................... 54
viii
LIST OF FIGURES
Page
1.
Figure 1. Systems Diagram ..................................................................................... 4
2.
Figure 2. Aircraft Configuration ............................................................................. 6
3.
Figure 3. Lift and Pitching Moment Coefficients Versus Angle of Attack ............ 8
4.
Figure 4. Drag Polar ................................................................................................ 9
5.
Figure 5. Pod Shape .............................................................................................. 11
6.
Figure 6. Photovoltaic Cell Characterization Test Setup ...................................... 18
7.
Figure 7. Photovoltaic Cell Characterization – I-V Curve ................................... 21
8.
Figure 8. Photovoltaic Cell Characterization – P-V Curve................................... 22
9.
Figure 9. Sacramento Executive Airport Hourly Insolation ................................. 24
10.
Figure 10. Wing Half-Span Lift Distribution ....................................................... 30
11.
Figure 11. Wing Bending Moment and Shear Force ............................................ 31
12.
Figure 12. Alpha and Beta .................................................................................... 33
13.
Figure 13. Motor Weight Trendline ...................................................................... 37
14.
Figure 14. Overall Weight .................................................................................... 39
15.
Figure 15. System Weights ................................................................................... 40
16.
Figure 16. Propulsion Weights ............................................................................. 41
17.
Figure 17. Structure Weights ................................................................................ 42
18.
Figure 18. Longitudinal Forces ............................................................................. 43
19.
Figure 19. Balanced Longitudinal Moment - Zero Tail Lift ................................. 43
20.
Figure 20. Daily Power Cycle ............................................................................... 47
ix
21.
Figure 21. Weight Versus Wing Loading ............................................................. 50
22.
Figure 22. Power-to-Weight Ratio Versus Wing Loading ................................... 51
23.
Figure 23. Minimum Photovoltaic Efficiency Versus Wing Loading .................. 52
24.
Figure 24. Carpet Plot – Aspect Ratio 20 ............................................................. 53
x
1
Chapter 1
INTRODUCTION
Advances in microprocessors have allowed the development of robotic systems
capable of intelligent interaction with their environment. What have been termed
unmanned vehicles, and specifically unmanned aerial vehicles (UAVs), have seen rapid
proliferation within the last three decades. While most unmanned aerial vehicles are
designed, built, and flown, for military purposes, there are often civilian versions or
counterparts.
The Department of Defense defines an unmanned aerial vehicle as:
A powered, aerial vehicle that does not carry a human operator, uses
aerodynamic forces to provide vehicle lift, can fly autonomously or be
piloted remotely, can be expendable or recoverable, and can carry a lethal
or non-lethal payload. Ballistic or semi ballistic vehicles, cruise missiles,
and artillery projectiles are not considered unmanned aerial vehicles.
(United States 1)
Unmanned aerial vehicles excel in applications where long endurance is required
because there is no human pilot onboard the aircraft. Missions that require long
endurance are diverse and include: imaging / mapping / photogrammetry,
telecommunications, search and rescue, resupply/delivery, surveillance, battlefield
targeting/attack, disaster relief, advertising, wildfire detection/monitoring, meteorological
research/observation, agricultural management, and wildlife tracking. While satellites
currently perform many of these missions, they are at a disadvantage because unmanned
2
aerial vehicles can be re-tasked more rapidly and can be fielded and supported at far
lower cost.
Photovoltaic cells are currently the only viable means of keeping an aircraft aloft
for extended periods of time (i.e. more than one month) because they allow energy for
propulsion to be harvested directly from the environment. However, solar powered
aircraft are a relatively new phenomenon because photovoltaic cell technology has only
recently reached a suitable level of maturity. As a result, methods for the design and
sizing of solar powered aircraft are relatively underdeveloped.
Historically, an iterative approach has been used in aircraft design. With an
iterative approach, design constants are used to produce a design, the design is evaluated,
new design constants are selected, and the process is repeated until all requirements are
met. Recently, computers have allowed a continuous approach to be used in aircraft
design. In a continuous approach, the aircraft is modeled using a computer program in
which design constants are replaced by design variables. The program automatically
iterates until all requirements are met.
This study utilizes the continuous approach by means of a design spreadsheet.
Chapters 2 through 7 describe how different elements of the design were analyzed,
including the pertinent equations that were used in the design spreadsheet. The
identification and discussion of the constraints, methods, and underlying assumptions of
the design spreadsheet constitute the bulk of this paper, after which the design
spreadsheet and the final design are reviewed and presented. Whenever possible, real
world data has been used to improve the accuracy of the method.
3
Chapter 2
MISSION REQUIREMENTS AND SYSTEMS
2.1 Design Constraints
The basis of any design is a set of requirements or constraints that define the
problem to be solved. For the purposes of this study, the final aircraft was to be
unmanned, autonomous, small (i.e. less than 20 pounds), solar powered, and be capable
of flying at low altitude for 24 hours at the latitude and longitude of Sacramento,
California. Low altitude was considered to be 400 feet and below. The aircraft was
modeled in a condition of steady level flight at a pressure altitude of 300 feet in
atmospheric conditions determined from the US 1976 Standard Atmosphere model.
Based on these design constraints, a final design will be created that is optimized for
minimum battery pack capacity and minimum photovoltaic array efficiency.
2.2 Systems
Without a pilot, an autonomous unmanned aerial vehicle requires a system
capable of providing control and navigation functions. The system chosen for this design
study is shown in Figure 1.
2.3 Payload
Early in the design process, a generic payload was modeled using an assumed
weight of one pound. As work progressed, it was found that such a payload weight
severely constrained the design space and so the payload was eliminated. Further analysis
is required regarding how payload weight affects the design.
4
Figure 1. Systems Diagram
5
External sensors, including a Global Positioning System (GPS) and a pitot-static
airspeed sensor, feed information into an autopilot that controls four actuators (servos)
and a motor controller. The photovoltaic array charges a battery pack through a charge
controller. The battery pack powers the entire system through the motor controller. The
data transceiver transmits and receives flight data to and from a ground station. It was
postulated that the transceiver would transmit for two seconds every minute. The ground
station (a laptop computer or similar device) is used to monitor the status of the aircraft as
well as to upload commands to control the aircraft while in flight. The radio receiver is
used to directly control the aircraft if the situation warrants immediate human
intervention. With a firm idea of the systems required, attention was turned to design of
the aircraft itself.
For modeling purposes, commercial off-the-shelf components were selected and
their characteristics were used. The autopilot, GPS, pitot-static airspeed sensor, and data
transceiver, were modeled on the ArduPilot Mega system available from diydrones.com.
Power consumption of the ArduPilot Mega system was taken to be 1.05 watts. Power
consumption of the data transceiver was assumed to be 0.032 watts. The servos and radio
receiver were modeled on those available from Futaba Corporation of America. Total
power consumption of the servos and radio receiver were taken to be 0.23 watts and 0.38
watts, respectively. The charge controller was based on those available from Genasun
Advanced Energy Systems. Characteristics of the electric motor/propeller, battery pack,
and photovoltaic array were left as variables to allow for optimization and will be
discussed in the following sections.
6
Chapter 3
CONFIGURATION, AERODYNAMICS, AND PERFORMANCE
3.1 Configuration
The configuration shown in Figure 2 was chosen for its high efficiency and ease
of design/modeling.
Figure 2. Aircraft Configuration
3.2 Wing
The single wing is positioned on top of the fuselage. Photovoltaic cells, which
have been joined into an array, are placed on the upper surface of the wing. In general,
solar powered aircraft locate their photovoltaic cells on the upper surface of the wing
because it offers the most exposure to the sun.
7
The wing was conceptualized as a fiberglass covered foam core of trapezoidal
planform reinforced by a carbon fiber spar of rectangular cross-section running from
wingtip to wingtip. For simplicity, wing dihedral angle was set at zero. The ratio of the
wingtip chord to the wing root chord, or the “tip-to-chord ratio”, was assumed to be 0.5.
A tip-to-chord ratio of 0.5 leads to a nearly elliptical spanwise lift distribution, which
reduces induced drag. Wing variables included wing loading and aspect ratio. Wing
loading is the weight of the aircraft divided by the planform area of the wing. Aspect
ratio is the square of the wingspan divided by the planform area of the wing.
After examination of airfoil data available on the University of Illinois at UrbanaChampaign Department of Aerospace Engineering Applied Aerodynamics Group website
(UIUC Airfoil Data Site), the SD7080 airfoil was chosen for its low parasite drag and low
pitching moment. The SD7080 airfoil was used to determine the internal volume of the
wing, as well as the lift-curve slope, pitching moment, and parasite drag of the wing (see
Figure 3 and Figure 4).
8
Figure 3. Lift and Pitching Moment Coefficients Versus Angle of Attack
9
Figure 4. Drag Polar
The wing lift-curve slope, “CLα”, is the slope of the linear portion of the lift versus
angle of attack curve. The wing lift-curve slope for steady level flight was determined
using equation found below (Raymer 324).
𝐶𝐿𝛼 =
2𝜋(𝐴𝑅)
(𝐴𝑅)2 𝛽2
𝑡𝑎𝑛2 (Λ𝑚𝑎𝑥 )
(1+
)
2+√4+
𝜂2
𝛽2
𝐶
; 𝛽 2 = (1 − 𝑀2 ) 𝑎𝑛𝑑 𝜂 = 2𝜋𝑙𝛼
⁄𝛽
(1)
Where “AR” represents the aspect ratio, “M” the Mach number, “Λmax” the sweep
angle of the wing, and “Clα” the airfoil section lift-curve slope. Wing angle of attack, or
rather wing incidence angle (the angle of attack of the aircraft was assumed to be zero
while wing angle of attack was non-zero), was determined from the wing coefficient of
lift and the lift-curve slope.
10
3.3 Fuselage
The fuselage consists of a simple carbon fiber tube of a diameter sufficient to
support the single electric motor at the front of the aircraft. For the purposes of this study,
the outside diameter of the fuselage was assumed to be 3.0 inches and the length of the
fuselage was assumed to be 50% of the wingspan.
3.4 Tail
An inverted “V-tail” was selected because it seemed to offer the lowest
interference drag with the added benefit of proverse roll-yaw coupling. Proverse roll-yaw
coupling means that a rolling moment is produced in the direction of a turn when the Vtail control surfaces, or “ruddervators”, are deflected. The total span of the tail was
assumed to be 28% of the wingspan; this percentage was chosen to approximate the size
of a normal horizontal and vertical stabilizer. The tail was assumed to have a symmetrical
airfoil, be made from balsa wood, and to have a thickness of 0.25 inches. The tip to chord
ratio of the tail was set at 0.5 and the aspect ratio was set at 6. In contrast to the wing, the
lift-curve slope of the tail (CLαh) was assumed to be the theoretical maximum of 2π.
3.5 Payload Pod
A payload “pod” suspended beneath the fuselage by a pylon was thought to offer
the most versatility due to the undetermined size and shape of any potential payload. An
added benefit of a pod is that it would protect the propeller upon landing. The pod was
assumed to have the shape of a low-drag body as detailed in Simons and shown in Figure
5; such a shape can obtain as much as 60% laminar flow along its surface under ideal
conditions (266).
11
Figure 5. Pod Shape
3.6 Performance: Drag, Thrust, and Power
The knowledge of the aircraft configuration and component geometry allowed the
overall drag to be calculated. Since thrust must equal drag during steady level flight, the
required thrust “T” was determined using the following thrust equation.
𝐶𝐷 =
𝐷
1
( 𝜌𝑉 2 )𝑆
2
1
1
≅ 𝐶𝐷0 + 𝐾𝐶𝐿 2 → 𝑇 = 𝐷 ≅ (2 𝜌𝑉 2 ) 𝑆(𝐶𝐷0 + 𝐾𝐶𝐿 2 ); 𝐾 = 𝜋(𝐴𝑅)𝑒
(2)
Where “D” represents the aircraft drag, “ρ” the atmospheric density, “V” the
flight velocity, and “S” the wing planform area. According to Raymer, the coefficient of
drag is approximately equal to the parasite drag “CD0” plus the square of the wing
coefficient of lift “CL” multiplied by a drag-due-to-lift factor “K” (321). “AR” represents
12
the wing aspect ratio and “e” is the Oswald span efficiency factor, which was assumed to
be 0.8.
All elements of the thrust equation were known except for the parasite drag.
Accordingly, the parasite drag was calculated using the “component build-up method”
outlined in Raymer (340). This method estimates the subsonic parasite drag of each
component using a calculated flat-plate skin-friction drag coefficient, “Cf”, and a
component form factor “FF” that estimates the pressure drag due to viscous separation.
The interference effects of the various components are estimated using a factor “Q”. The
component drags are then determined by multiplying all of the factors with the
component wetted surface area “Sc”. The sum of the component drags is equal to the total
parasite drag as shown below.
𝐶𝐷0 =
(𝐶𝑓 )
𝐹𝐹𝑤𝑖𝑛𝑔,
𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 𝑓𝑙𝑜𝑤
𝑡𝑎𝑖𝑙, 𝑎𝑛𝑑 𝑝𝑦𝑙𝑜𝑛
= [1 + (
(3)
𝑆
= (𝑙𝑜𝑔
0.6
𝑥
𝑐
∑(𝐶𝑓 (𝐹𝐹)𝑄𝑆𝑐 )
0.455
2.58 (1+0.144𝑀2 )0.65
10 𝑅)
𝑡
; 𝑅=
𝜌𝑉𝑙
𝜇
𝑡 4
) (𝑐) + 100 (𝑐) ] [1.34𝑀0.18 cos(Λ)0.28 ]
60
𝑓
𝑙
𝐹𝐹𝑓𝑢𝑠𝑒𝑙𝑎𝑔𝑒 𝑎𝑛𝑑 𝑝𝑜𝑑 = 1 + 𝑓3 + 400 ; 𝑓 = 𝑑
(4)
(5)
(6)
Where “S” represents the wing planform area, “R” the Reynolds number, “ρ” the
atmospheric density, “V” the flight velocity, “l” the component characteristic length, “μ”
the dynamic viscosity, “x/c” the chordwise location of the airfoil maximum thickness,
“t/c” the component thickness-to-chord ratio, “M” the Mach number, “Λ” the wing sweep
angle, and “d” the component maximum diameter.
13
Table 1 shows the results of the component build-up method for the final design.
Table 1
Component Drag Build-Up Method
Component
Cf (Flat
Plate Skin
Friction
Coefficient,
Turbulent)
FF
(Component
Form Factor)
Q
(Interference
Drag Factor)
Swet [in2]
CfFFQSwet
CDo
Wing
0.0069
0.84
1.00
1895.77
11.02
0.0118
Tail
0.0071
0.82
1.03
489.95
2.94
0.0031
Fuselage
0.0044
1.06
1.00
644.75
3.01
0.0032
Pod
0.0056
1.49
1.00
264.41
2.20
0.0023
Pylon
0.0084
0.73
1.03
25.29
0.16
0.0002
The following lift and velocity equations hold true during steady level flight.
1
𝐿 = 𝑊 = (2 𝜌𝑉 2 ) 𝑆𝐶𝐿
2
(7)
𝑊
𝑉 = √𝜌𝐶 ( 𝑆 )
(8)
𝐿
Where “L” represents lift, “W” the weight, “ρ” the atmospheric density, “V” the
flight velocity, “S” the wing planform area, and “CL” the wing coefficient of lift. The
thrust equation and the velocity equation were combined to determine the thrust-toweight ratio in level flight as shown in the equation below.
𝑇
𝑊
=
𝐷
𝐿
1
2
( 𝜌𝑉 2 )𝐶𝐷0
=[
𝑊
( )
𝑆
𝑊
] + [( 𝑆 )
𝐾
1
( 𝜌𝑉 2 )
2
]
(9)
If one examines the thrust-to-weight equation, it becomes evident that the
condition for minimum thrust is also the condition for maximum lift-to-drag ratio, or the
most efficient operating point. The velocity for maximum lift-to-drag can be found by
14
taking the derivative of equation thrust-to-weight equation with respect to velocity and
setting the result equal to zero, this was done using the following equations.
𝑇
𝑊
𝜕( )
𝜕𝑉
𝜌𝑉𝐶𝐷0
=[
𝑊
𝑆
( )
𝑊
] − [( 𝑆 )
2𝐾
1
2
( 𝜌𝑉 3 )
]=0
2 𝑊
𝐾
𝑉max 𝐿/𝐷 = √𝜌 ( 𝑆 ) √𝐶
(10)
(11)
𝐷0
The above velocity equation was substituted into the lift equation to determine the
lift coefficient for maximum lift-to-drag shown in the equation below.
𝐶𝐷0
𝐶𝐿max 𝐿/𝐷 = √
(12)
𝐾
For a given weight, the motor power required for steady level flight can be
determined by using the thrust-to-weight equation, the velocity equation for maximum
L/D, and the following equation.
𝜂𝑝 = 𝑃
𝑇𝑉
𝑚𝑜𝑡𝑜𝑟
→ 𝑃𝑚𝑜𝑡𝑜𝑟 =
𝑇
𝑊
( 𝑊)𝑉max 𝐿/𝐷
𝜂𝑝
For this study, a propulsive efficiency “ηp” of 80% was chosen, which is
representative of most propeller-driven aircraft (Raymer 22).
(13)
15
Chapter 4
PHOTOVOLTAIC ARRAY
4.1 I-V Cell Characterization
In the beginning of this study, an attempt was made to characterize the
performance of a thin-film photovoltaic cell (ASTM E1036). At that time, it was thought
that both the low weight and the aerodynamic advantage offered by thin-film’s ability to
conform to the curve of the wing would outweigh the relatively low efficiency of such
cells. Unfortunately, it was later determined that the efficiency of the photovoltaic cell
chosen for characterization was too low to satisfy the power requirements of the aircraft.
One way to characterize a photovoltaic cell is to connect the cell in series with a
variable resistor and to measure the current and voltage through the circuit as the
resistance is varied from zero to infinity. Corresponding current and voltage
measurements can be plotted to form what called an I-V curve. Short circuit current is
measured when the resistance is at a minimum. Open circuit voltage is measured when
the resistance is at a maximum. Somewhere in between lies a point where the product of
current and voltage (power) is maximized. This point is known as the maximum power
point and is the most efficient operating point of the photovoltaic cell. A pyranometer,
measures the amount of insolation, i.e. solar radiation, hitting the earth’s surface in power
per unit area. Efficiency of the solar cell can be determined by comparing the
pyranometer measurement with the dimensions and power output of the photovoltaic cell.
16
Such a characterization was undertaken, but the results were poor due to a number of
issues with the equipment used. The results of the experiment are detailed in the
following paragraphs.
Currently, photovoltaic cells manufactured by PowerFilm Incorporated are the
only thin-film solar cells readily available to the average consumer. Table 2 shows a
ranking matrix that was created in order to determine the best model in terms of power
per area and per weight. Overall rank was defined from the product of the power/area and
power/weight rankings.
Table 2
PowerFilm Photovoltaic Cell Comparison
Overall
Rank
7
13
16
20
27
28
45
50
64
84
96
102
117
120
170
198
209
252
266
360
420
Power/
Area
Rank
7
1
8
5
9
2
3
10
4
12
16
6
13
15
17
11
19
21
14
18
20
Power/
Weight
Rank
1
13
2
4
3
14
15
5
16
7
6
17
9
8
10
18
11
12
19
20
21
Model
MPT6-75
MPT15-150
MPT6-150
MP3-37
MPT4.8-75
MPT15-75
MP7.2-75
MPT4.8-150
MP7.2-150
MPT3.6-150
RC7.2-75
PT15-300
MPT3.6-75
SP4.2-37
RC7.2-75
PT15-150
SP3-37
MP3-25
P7.2-150
PT15-75
P7.2-75
Power
[watts]
0.300
1.540
0.600
0.150
0.240
0.770
0.720
0.480
1.440
0.360
0.720
3.080
0.180
0.092
0.720
1.540
0.066
0.075
1.440
0.770
0.720
Power/ Area
[watt/m2]
35.09
40.58
35.09
35.56
34.04
40.58
37.94
34.04
37.94
32.43
29.63
35.10
32.43
29.73
29.63
32.59
27.87
26.32
30.48
28.52
26.67
Specific
Power
[watt/kg]
130.43
59.23
130.43
125.00
126.32
59.23
55.81
123.08
55.60
116.13
122.03
32.59
112.50
115.50
94.74
27.30
94.29
93.75
26.23
24.21
23.00
17
Even though the MPT6-75 model was ranked the highest, the MPT15-150 model
was purchased because it was believed that the system voltage would be around 12 volts
and the MPT15-150 generates 15.4 volts. 12 volts is the standard voltage used in the
automotive industry and many charge controller manufacturers produce products
intended to charge 12 volt batteries, a fact that would simplify procurement of a charge
controller. It was also believed that having the solar cell voltage close to the battery
voltage would reduce the amount of electrical connections required and would thus
reduce weight, cost, and complexity.
A current and voltage sensor, that is designed for use with the ArduPilot Mega
autopilot, and is manufactured by AttoPilotInternational, was purchased. A hobby
oscilloscope meant to be connected to a laptop computer and a simple pyranometer were
also purchased. The hope was to vary the circuit resistance and to record the resulting
currents and voltages with the oscilloscope. The oscilloscope traces could then be
exported to the design spreadsheet. A tripod-mounted test fixture was created and the
solar cell and pyranometer were attached, refer to Figure 6.
18
Figure 6. Photovoltaic Cell Characterization Test Setup
After multiple attempts, the characterization was ultimately unsuccessful due to
difficulties with the current sensor (possibly caused by poor soldering technique on the
part of the author) and erratic resistance produced by the variable resistor. As a last resort,
the current sensor and oscilloscope were replaced with a handheld multimeter. The
results of this final survey are shown in Table 3,
19
Table 4, Figure 7, and Figure 8. Note that the solar cell was oriented horizontal to
the earth’s surface, which was assumed to approximate the upper surface of the wing.
20
Table 3
Photovoltaic Cell Characterization – Environmental Variables
Orientation:
Environmental
Variable
Horizontal
Start
End
Average
Units
Time
1310
1350
1330
PST
Elevation
29
26
27.5
feet
Latitude
38.56126
38.56139
38.561325
Longitude
-121.78657
-121.78656
-121.786565
Temperature
75.2
77
76.1
ºF
Wind Direction
350
350
350
degrees
Wind Speed
7
7
7
knots
Visibility
7
10
8.5
nautical miles
Clouds
Clear
Clear
Clear
Temp
75.2
77
76.1
ºF
Dew Point
46.4
46.4
46.4
ºF
Pressure
30.08
30.07
30.075
mmHg
Insolation
648
641.28
644.64
W/m^2
21
Table 4
Photovoltaic Cell Characterization – Voltage and Current
Voltage
[volts]
Current
[milliamps]
Current
[amps]
Power
[watts]
0.06
92.7
0.093
0.006
1.26
91.4
0.091
0.115
2.20
89.8
0.090
0.198
4.00
90.6
0.091
0.362
7.43
77.4
0.077
0.575
8.75
90.1
0.090
0.788
12.42
66.7
0.067
0.828
15.34
47.7
0.048
0.732
16.16
39.1
0.039
0.632
17.02
28.4
0.028
0.483
18.00
6.4
0.006
0.115
18.22
0.6
0.001
0.011
22
Figure 7. Photovoltaic Cell Characterization – I-V Curve
23
Figure 8. Photovoltaic Cell Characterization – P-V Curve
The efficiency of the solar cell was calculated using efficiency equation below,
given the solar insolation and maximum power output of the cell, and knowing that the
MPT15-150 has an area of 0.038 square meters.
ηpv =
Pout
Pin
=
0.828 W
W
(644.64 2 *0.038 m2 )
m
=3.39%
(14)
A 3.39% efficient cell was well below what was expected and, as determined later
in the study, was well below what was needed to meet the design requirements. As a
result, the idea of modeling PowerFilm thin-film photovoltaic cells in the design
spreadsheet was discarded and the efficiency of the photovoltaic array was left as a
variable. The maximum specific power of the PowerFilm cells was determined to be 3.70
24
W/oz (i.e. 130.43 W/kg) and was used in the design spreadsheet because it was thought to
be representative of thin-film photovoltaic cells.
4.2 Solar Insolation
In order to determine the required efficiency, size, and power output, of the
photovoltaic array, the amount of insolation (solar radiation per unit area) on the earth’s
surface had to be determined. Due to the highly variable nature of solar radiation, the
designer is forced to choose an average value. Luckily, the National Renewable Energy
Laboratory of the United States has generated a National Solar Radiation Database that
contains solar radiation and supplementary meteorological data from 1,454 sites in the
United States and its territories for the years 1991 through 2005 (National Solar
Radiation Data Base 1991-2005 Update). Insolation data collected at the Sacramento
Executive Airport site were analyzed and the results are shown in Figure 9. Data shown
are for a plane horizontal to the earth’s surface.
25
Figure 9. Sacramento Executive Airport Hourly Insolation
The original intent of the design study was to design an aircraft capable of flying
24 hours a day for an entire year and so the minimum hourly insolation was first used for
modeling. It was ultimately acknowledged that adverse weather during the colder months
would make it nearly impossible for a small unmanned aerial vehicle to survive at low
altitude for an entire year. As a result, only the summer months of June through
September, when good weather is common, were considered. Solving for the area
underneath the average hourly summer insolation curve yielded an average daily summer
insolation value of 7141 watt-hours per square meter.
26
Chapter 5
PROPULSION
The propulsion system is comprised of the photovoltaic array (discussed in the
preceding section), charge controller, battery pack, motor controller, electric motor, and
propeller.
5.1 Charge Controller
In order to extract the maximum power from a photovoltaic cell, a charge
controller should be used that takes advantage of maximum power point tracking (MPPT)
technology. As defined in Chin:
The MPPT is a high efficiency electronic DC to DC converter that is
capable of varying the electrical operating point of a solar panel so that it
can deliver the maximum available power regardless of the prevailing
battery voltage. (103)
Maximum power point tracking charge controllers can yield efficiency increases
on the order of 10% to 30%; the only downside is that the additional circuitry involved
increases cost. Electrical efficiency of the charge controller was assumed to be 94%.
5.2 Battery Pack
Lithium-ion polymers batteries are a relatively mature technology and have seen
widespread use in the model aircraft industry and so the battery pack was modeled as
such. The characteristics of lithium-ion polymer batteries of 2 cells and over
manufactured by Thunder Power RC were examined as shown in Table 5 below.
27
Table 5
Lithium-Ion Polymer Battery Cell Characteristics
Number of
Battery Cells
Voltage
[volts]
Average Specific
Power [Wh/oz]
Average Power
Density
[Wh/inch3]
Overall
Rank
2
7.4
4.495
5.046
8
3
11.1
4.495
5.046
8
4
14.8
4.589
5.046
7
5
18.5
4.850
5.620
2
6
22.2
4.827
5.665
1
7
25.9
4.462
5.443
6
8
29.6
4.481
5.474
5
9
33.3
4.660
5.686
4
10
37.0
4.675
5.776
3
The average specific power of the Thunder Power battery packs was found to be
4.615 watt-hours/oz. Further analysis revealed that 4.615 watt-hours/oz was too low. As a
result, the battery pack specific power was assumed to be 7 watt-hours/oz, which is at the
limit of current lithium-ion polymer battery technology. The power density of the battery
pack was taken as 5.665 watt-hours/inch3 which was the average power density of battery
packs of two cells or greater. Battery pack voltage was set at 22.20 volts and photovoltaic
array voltage was set at 26.64 volts (which was 20% greater than battery pack voltage to
allow for charging). However, the design spreadsheet was based on overall power and so
voltage and current were not critical. Battery electrical efficiency was assumed to be 95%.
5.3 Electric Motor, Motor Controller, and Propeller
The electrical efficiencies of the electric motor and motor controller, were
assumed to be 84% and 95%, respectively. In addition, the battery elimination circuitry
28
within the motor controller that allowed the battery to power the entire system was
assumed to have an electrical efficiency of 65%. The electrical efficiencies mentioned in
this chapter were later used in calculating the total required power.
29
Chapter 6
STRUCTURE
A structural analysis was performed on the wing in terms of spanwise bending
and torsion about the quarter-chord point and on the fuselage in terms of bending. A “G”
loading of six times the force of gravity and a factor of safety of 1.5 were used in all
calculations.
6.1 Wing Spanwise Bending
The spanwise load distribution is required to find the maximum bending stress in
a wing. In this study, the spanwise load distribution was used to size the wing spar and
was assumed to be equal to the spanwise lift distribution; the weight of the wing itself
was neglected. Schrenk’s approximation, which assumes that the load distribution of an
untwisted wing is equivalent to the average of an planform lift distribution and a elliptical
lift distribution, was used to find the spanwise lift distribution (Peery 224).
One half of the wing was divided into 20 spanwise stations and the wing chord at
each station was determined. A lift coefficient at each station was calculated for a
trapezoidal planform and then for an elliptical planform using the following equations.
𝐶(𝑦)𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑𝑎𝑙 = 𝐶𝑟 [1 −
4𝑆
2𝑦 2
2𝑦
𝑏
(1 − 𝜆)]
𝑏
𝐶(𝑦)𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 = 𝜋𝑏 √1 − ( 𝑏 ) ; 𝑆 = 2 𝐶𝑟 (1 + 𝜆)
(15)
(16)
Where “y” is the spanwise location, “Cr” the root chord, “b” the wingspan, and “λ”
the tip to chord ratio. The coefficients were multiplied first by the dynamic pressure,
which is equal to one-half the atmospheric density times the flight velocity squared, and
30
then by the unit span to obtain the lift at each station. The lifts at each station were added
together to get the total required lift. The maximum shear force was taken to be the total
required lift and to be located at the wing root. The shear force was assumed to decrease
linearly from a maximum at the wing root to a minimum of zero at the wing tip. The
bending moment at each station was taken to be the shear force multiplied by the unit
span added to the moment of the previous station (from wingtip to wing root). Table 6 as
well as Figure 10 and Figure 11 show the results of using Schrenk’s approximation.
Table 6
Wing Bending Analysis Results
Symbol
Value
Unit
n
6
G
Flexural Strength
230,000
psi
Density
0.054
lb/inch3
Factor of Safety
1.50
Design Strength
153,333
psi
Load Factor
Spar Height
h
0.42
inch
Distance from Neutral Axis
h/2
0.21
inch
Moment of Inertia
I
9.68E-04
inch4
Spar Width
w
0.15
inch
Spar Cross-Sectional Area
0.06
inch2
Spar Linear Density
0.0557
oz/inch
31
Figure 10. Wing Half-Span Lift Distribution
32
Figure 11. Wing Bending Moment and Shear Force
Direct stress due to bending was considered to be the most critical stress on the
wing and so the width of the wing spar was sized to withstand the maximum bending
stress using the equation below.
𝑤=
(𝐼)12
ℎ3
ℎ
2
𝑀( )
; 𝐼=𝜎
𝑑𝑒𝑠𝑖𝑔𝑛
𝑎𝑛𝑑 𝜎𝑑𝑒𝑠𝑖𝑔𝑛 =
𝜎𝑓𝑙𝑒𝑥𝑢𝑟𝑎𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝐹.𝑆.
(17)
Where “w” represents the wing spar width, “h” the wing spar height, “I” the
second moment of inertia, “M” the maximum bending moment, “σflexural strength” the
flexural strength of the carbon fiber material, and “F.S.” the factor safety. The spar height
was assumed to be the maximum thickness of the airfoil, the flexural strength was
assumed to be 230,000 psi (graphitestore.com), and the factor of safety to be 1.5.
33
Determination of the spar width, along with the knowledge of the spar height, length, and
density, allowed the spar weight to be calculated and used in the design spreadsheet.
6.2 Wing Torsion
A torsional analysis was performed on the cross-section of the wing at the
quarter-chord point. The quarter-chord point was assumed be coincident with both the
aerodynamic center and with the wing spar location. Torque from the aerodynamic
pitching moment was the only torque considered to be acting about the quarter-chord
point. Shear stress and angular deflection due to torsion were calculated using the two
equations below (Raymer 459).
𝑇
𝜏 = 𝛼𝑤ℎ2
𝑇𝐿
𝜙 = 𝛽𝑤ℎ3 𝐺
(18)
(19)
Where “τ” is the shear stress, “T” the torque, “w” the spar width, “h” the spar
height, “Φ” the angular deflection, “L” the length of the spar, and “G” the shear modulus.
The terms “α” and “β” are torsion constants and were calculated from Figure 12. The
shear modulus was taken to be 650,000 psi (graphitestore.com).
34
Figure 12. Alpha and Beta
The results of the torsion analysis are shown in Table 7.
Table 7
Wing Torsion Analysis Results
Symbol
Shear Strength
Value
Unit
9500
psi
oz-inch
Torque Due to Pitching Moment
T
-2.282
Spar Height/Width
h/w
2.79
alpha
α
0.265
Beta
β
0.260
Shear Stress Due to Torsion
τ
314.57
oz/inch2
Shear Modulus
G
6.50E+05
psi
Angular Deflection
Φ
-0.57
degrees
Calculated Factor of Safety
FS
30.20
35
6.3 Fuselage Bending
An analysis of fuselage bending was performed in which the moment created by
the tail lift about the aerodynamic center of the wing was used to size the wall thickness
of the fuselage. However, the tail lift was so small, and the flexural strength of the carbon
fiber fuselage tube was so great, that the calculated wall thickness was smaller than could
be realistically used (on the order of 0.001 inches). As a result, the wall thickness of the
fuselage tube was assumed to be 0.015 inches. Results of the fuselage bending analysis
are shown in Table 8.
Table 8
Fuselage Bending Analysis Results
Symbol
Value
Unit
n
6
G
Flexural Strength
272,000
psi
Density
0.055
lbf/inch3
Design Stress
181,333
psi
1,472
psi
Load Factor
Actual Stress
Calculated Factor of Safety
FS
185
Fuselage Outer Diameter
D
3.00
inch
Distance from Neutral Axis
c
1.50
inch
Distance from CG to Tail
36.86
inch
Maximum Bending Moment
2460.41
oz-inch
Moment of Inertia
I
0.15667
inch4
Tube Outer Radius
R
1.5000
inch
Fuselage Inner Radius
r
1.4850
inch
Fuselage Wall Thickness
t
0.0150
inch
Fuselage Cross-Sectional Area
0.1407
inch2
Fuselage Linear Density
0.1238
oz/inch
36
Chapter 7
WEIGHT AND STABILITY
7.1 Weight
The payload pod, the pylon connecting the pod to the fuselage, and the foam core
of the wing, were all assumed to have a density of 1.0 lb/ft3 while the fiberglass wing
covering was assumed to have an area density of 5 oz/yard2. The balsa wood tail was
assumed to have a density of 0.03 oz/inch3. The weight of the solar array and of the
battery pack were left as variables in the design spreadsheet. The cross-sectional area and
weight of the carbon fiber spar were also left as variables, but the density of the spar was
assumed to be 0.054 lb/inch3. The carbon fiber fuselage was taken to have a density of
0.055 lb/inch3.
The weight characteristics of motors manufactured by AXI Model Motors Limited were
Limited were examined and a motor weight trendline was developed as shown in
37
Table 9 and Figure 13.
38
Table 9
Motor Weight Manufacturer Recommendations
Aircraft
Weight [oz]
Recommended
Electric Motor
Weight [oz]
20
2.011
40
2.011
60
2.011
80
2.452
100
3.739
120
3.739
140
5.326
160
6.385
180
6.385
200
7.937
220
7.937
240
11.288
260
11.288
280
7.937
300
11.288
320
11.288
39
Figure 13. Motor Weight Trendline
40
Table 10 shows a summary of the weights and the location of the center of gravity “Xcg”
calculated in inches from the nose of the aircraft.
41
Table 10
Table of Weights
Systems
Ardupilot Mega
Autopilot
Quantity
Weight [oz]
X-Location
(from nose)
[inch]
1
1.60
20.52
32.84
Data Transceiver
1
0.10
20.52
2.05
Radio Receiver
1
0.33
20.52
6.77
Servos
4
2.88
59.11
Propulsion
Quantity
Weight [oz]
20.52
X-Location
(from nose)
[inch]
Electric Motor
1
4.62
1.00
4.62
Propeller
1
3.00
0.50
1.50
Speed Controller
1
3.00
20.52
61.57
Charge Controller
1
2.80
20.52
57.46
Solar Array
1
18.09
33.28
602.02
Battery Pack
1
39.64
813.46
Structure
Quantity
Weight [oz]
20.52
X-Location
(from nose)
[inch]
Wing and Spar
1
17.06
30.26
516.16
Fuselage
Fiberglass Cloth and
Hardener/Resin
1
8.47
34.21
289.66
1
7.31
30.26
221.30
Pod
1
0.68
20.52
13.91
Pylon
1
0.06
20.52
1.26
Tail
1
7.34
Total Weight
[oz]
63.44
Xcg [inch]
465.57
Total Moment
[oz-inch]
116.98
26.92
3149.26
X-Moment
[oz-inch]
X-Moment
[oz-inch]
X-Moment
[oz-inch]
Figure 14, Figure 15, Figure 16, and Figure 17, supply a graphical breakdown of
the weights, with the weight in ounces and the weight percentage listed beneath each item.
42
Figure 14. Overall Weight
43
Figure 15. System Weights
44
Figure 16. Propulsion Weights
45
Figure 17. Structure Weights
7.2 Stability
A simple static longitudinal stability analysis was completed using the weight and
balance data discussed in the preceding section and with the assumption that the aircraft
structure is perfectly rigid. The forces involved are shown in Figure 18 (Simons 140).
46
Figure 18. Longitudinal Forces
The x-location of the wing, i.e. the distance from the nose of the aircraft, was
adjusted to shift the center of gravity to achieve the more efficient loading shown in
Figure 19 (Simons 141) where the tail produces zero lift.
Figure 19. Balanced Longitudinal Moment - Zero Tail Lift
The loading shown in Figure 19 means that the moment about the center of
gravity must equal zero without the tail producing any lift. The equation below expresses
the sum of the longitudinal moments about the center of gravity in terms of coefficients;
this equation was modified from one found in Raymer (486).
47
𝑆
𝐶𝑚𝐶𝐺 = 𝐶𝐿 (𝑋𝑏𝑎𝑟𝐶𝐺 − 𝑋𝑏𝑎𝑟𝑎𝑐𝑤 ) + 𝐶𝑚𝑤 − 𝜂ℎ 𝑆 ℎ 𝐶𝐿ℎ (𝑋𝑏𝑎𝑟𝑎𝑐ℎ − 𝑋𝑏𝑎𝑟𝐶𝐺 ) (20)
𝑤
Where “CmCG” is the pitching moment coefficient about the center of gravity, “CL”
the lift coefficient of the wing, “XbarCG” the x-location of the center of gravity divided by
the wing chord, “Xbaracw” the x-location of the wing aerodynamic center divided by the
wing chord, “Cmw” is the aerodynamic pitching moment coefficient of the wing, “ηh” the
ratio of between the dynamic pressures at the tail and in the freestream, “Sh” the planform
area of the tail, “Sw” the planform area of the wing, “CLαh” the lift-curve slope of the tail,
and “Xbarach” is the x-location of the tail aerodynamic center divided by the wing chord.
This nomenclature remains the same for the other equations in this section.
In order for an aircraft to be longitudinally statically stable, any change in angle
of attack must be countered by a moment sufficient to keep the angle of attack from
diverging. Mathematically, this means that the derivative of the pitching moment must be
negative with respect to angle of attack. The equation below shows the method used to
calculate the pitching moment derivative, modified from that described in Raymer (487).
𝑆
𝐶𝑚𝛼 = 𝐶𝐿𝛼 (𝑋𝑏𝑎𝑟𝐶𝐺 − 𝑋𝑏𝑎𝑟𝑎𝑐𝑤 ) + 𝜂ℎ 𝑆 ℎ 𝐶𝐿𝛼ℎ
𝑤
𝜕𝛼ℎ
𝜕𝛼
(𝑋𝑏𝑎𝑟𝑎𝑐ℎ − 𝑋𝑏𝑎𝑟𝐶𝐺 )
(21)
Where “Cmα” is the derivative of the pitching moment, “CLα” the lift-curve slope
of the wing, “CLαh” the lift-curve slope of the tail, and “Xbarach” is the x-location of the
tail aerodynamic center divided by the wing chord. The partial derivative term is the tail
angle of attack derivative, which was estimated using the equation below. The downwash
angle derivative was taken to be 0.4 using methods outlined in Raymer (496).
48
𝜕𝛼ℎ
𝜕𝛼
𝜕𝜖
= 1 − 𝜕𝛼 ;
𝜕𝜖
𝜕𝛼
≡ 𝑑𝑜𝑤𝑛𝑤𝑎𝑠ℎ 𝑎𝑛𝑔𝑙𝑒 𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒
(22)
The aerodynamic center of “neutral point” of an aircraft is the location about
which there is no change in pitching moment as the angle of attack changes. The xlocation of the neutral point can be determined from the following equation, again
modified from that shown in Raymer (487).
𝑋𝑏𝑎𝑟𝑁𝑃 =
𝑆
𝜕𝛼
𝐶𝐿𝛼 𝑋𝑏𝑎𝑟𝑎𝑐𝑤 −𝜂ℎ ℎ 𝐶𝐿𝛼ℎ ℎ 𝑋𝑏𝑎𝑟𝑎𝑐ℎ
𝑆𝑤
𝜕𝛼
𝑆
𝜕𝛼
𝐶𝐿 𝛼 +𝜂ℎ ℎ 𝐶𝐿𝛼ℎ ℎ
𝑆𝑤
𝜕𝛼
(23)
Finally, the distance from the neutral point to the center of gravity divided by the
wing chord is called the static margin. The equation for the static margin is as follows.
𝐶𝑚𝛼 = −𝐶𝐿𝛼 (𝑋𝑏𝑎𝑟𝑁𝑃 − 𝑋𝑏𝑎𝑟𝐶𝐺 )
(24)
Lennon recommends a static margin of -5% to -10% for acceptable flying
qualities (28). The lower the static margin, the more stable the aircraft. The final design
exhibited a static margin of -6.82%.
49
Chapter 8
DESIGN SPREADSHEET
A design spreadsheet was created to model the aircraft at the minimum power
necessary to maintain steady level flight. Three optimization “loops” were at the heart of
the design spreadsheet, one that solved the for the minimum photovoltaic array efficiency,
one that solved for the minimum battery pack capacity, and one that solved for the overall
weight. The equation below was used to determine the power produced by the
photovoltaic array for a given level of solar insolation.
𝑃𝑃𝑉 = (𝜂𝑃𝑉 𝜂𝐶𝐶 𝜂𝐵𝐴𝑇 )(𝐼𝐴𝑃𝑉 )
(25)
Where “PPV” represents the total power of the photovoltaic array, “ηPV” the
photovoltaic array efficiency, “ηCC” the charge controller efficiency, “ηBAT” the
charge/discharge efficiency of the battery, “I” the solar insolation. “APV” is the total area
of the photovoltaic array and was equated to the planform area of the wing. The total
power required during steady level flight was determined using the following equation.
𝑃𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 = (𝜂
𝑃𝑚𝑜𝑡𝑜𝑟
𝑚𝑜𝑡𝑜𝑟 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑒𝑟 𝜂𝑚𝑜𝑡𝑜𝑟 )
+
𝑃𝑠𝑒𝑟𝑣𝑜 +𝑃𝑟𝑎𝑑𝑖𝑜 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 +𝑃𝑎𝑢𝑡𝑜𝑝𝑖𝑙𝑜𝑡 +𝑃𝑡𝑟𝑎𝑛𝑠𝑐𝑒𝑖𝑣𝑒𝑟
𝜂𝐵𝐸𝐶
(26)
Where “Prequired” represents the total power required for steady level flight, “Pmotor”
the electric motor power, “ηmotor controller” the motor controller efficiency, “ηmotor” the
electric motor efficiency, “Pservo” the total servo power, “Pradio receiver” the radio receiver
power, “Pautopilot” the autopilot power, “Ptransceiver” the data transceiver power and “ηBEC”
the efficiency of the battery eliminator circuitry.
50
The cumulative power stored in the battery pack was found for each hour of the
day by first adding the power produced by the photovoltaic array and then subtracting the
total powered required. The flight was assumed to start at sunrise with the battery pack
fully charged. Figure 20 shows the daily power cycle of the aircraft for two 24-hour
periods.
Figure 20. Daily Power Cycle
The photovoltaic efficiency was adjusted so that the battery pack power at the
start of the first day was equal to the battery pack power at the start of the second day.
The total battery pack power capacity was adjusted so that the power in the battery pack
never reached a negative value. Finally, the difference between an estimated weight and
51
the computed weight of each component was minimized to find the actual weight as
shown in the equation below.
𝑊𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑊𝑔𝑢𝑒𝑠𝑠 𝑤ℎ𝑒𝑛 𝑊𝑔𝑢𝑒𝑠𝑠 − ∑ 𝑊𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = 0
(27)
52
Chapter 9
RESULTS
Numerous design points were generated for aspect ratios of 15, 16, 17, and 20, by
varying the wing loading between 15 to 32 oz/ft2. Aspect ratios of less than 15 did not
permit any solutions for aircraft weighing less than 20 pounds. Aspect ratios of greater
than 20 were excluded due to concerns over structural rigidity. Slender wings are prone
to undesirable aerodynamic deflections and failure without a detailed structural analysis
that is beyond the scope of this study. Table 11 illustrates the lowest permitted wing
loading for a given aspect ratio.
Table 11
Lowest Permitted Wing Loading for a Given Aspect Ratio
Aspect Ratio
Lowest Permitted Wing
Loading [oz/ft2]
15.00
20.00
16.00
17.00
17.00
16.00
20.00
15.00
As wing loading was increased, the minimum required photovoltaic array
efficiency also increased. Wing loadings of greater than 32 oz/ft2 required photovoltaic
array efficiencies that were at the limit or beyond what is possible with current
photovoltaic technology. Figure 21 shows the total aircraft weight versus wing loading.
53
Figure 21. Weight Versus Wing Loading
According to the above figure, wing loadings between 20 and 24 oz/ft2 yield the
lowest aircraft weight regardless of the aspect ratio. Figure 22 shows the power-to-weight
ratio for level flight versus the wing loading
54
Figure 22. Power-to-Weight Ratio Versus Wing Loading
From the previous figures, it is immediately apparent that a higher aspect ratio
results in a lower weight design that requires less power. The benefit of increasing the
aspect ratio appears to have a diminishing return in regard to weight and a constant return
in regard to power-to-weight ratio.
Figure 23 depicts the minimum photovoltaic array efficiency required for the
photovoltaic array to fit within the planform area of the wing.
55
Figure 23. Minimum Photovoltaic Efficiency Versus Wing Loading
Current thin-film technology can achieve efficiencies between approximately
12% and 20% and so wing loadings are limited to 20 oz/ft2 or less if thin-film
photovoltaic cells are to be used. It is interesting to note that aspect ratio has a limited
effect on the minimum photovoltaic efficiency as evident from the close proximity of the
four curves.
Based on the above results, an aspect ratio of 20 was selected for the final design.
A “carpet plot” of design variables was generated in order to further investigate and
optimize the design for aspect ratio of 20. Figure 24 is a carpet plot that depicts the
interaction between different design elements. Each dashed black line represents a single
aircraft design.
56
Figure 24. Carpet Plot – Aspect Ratio 20
Based on this carpet plot, a final design point of aspect ratio 20 and wing loading
18 oz/ft2 was selected because it offered the lowest battery pack power and minimized the
required solar cell efficiency and weight. Table 12 presents pertinent characteristics of
the selected design point.
57
Table 12
Design Point Summary
Design Variable
Aspect Ratio
Wing Loading
Weight
Wingspan
Fuselage Length
Photovoltaic Array Specific
Power
Photovoltaic Array Efficiency
(minimum required)
Photovoltaic Array Power
Battery Pack Specific Power
Battery Pack Power Capacity
Total Power Consumption
Motor Power Consumption
Static Margin
Value
20
18.00
117.00
11.40
5.70
Unit
3.70
watt/oz
13.64%
66.93
7.0
277.45
21.88
15.38
-6.82%
%
watt
watt-hours/oz
watt-hour
watt-hour
watt-hour
%
oz/ft2
oz
feet
feet
58
Chapter 10
SUMMARY
In closing, aspect ratio, wing loading, battery pack specific power, photovoltaic
efficiency, and solar insolation, all have a pronounced effect on the final design of a solar
powered unmanned aerial vehicle. Aircraft weight is inversely related to aspect ratio but
care must be taken regarding the structural rigidity of high aspect ratio wings. A wing
loading that minimizes aircraft weight does not always minimize the power required for
level flight. Utilizing a battery with a high specific power is essential because the battery
may account for 30% to 50% of the total aircraft weight. Minimum required photovoltaic
efficiency is directly related to wing loading. Knowledge of the amount of solar
insolation experienced in the area of intended operation is absolutely essential when
designing for flights exceeding 24 hours duration.
This study has shown that is possible for a solar powered unmanned aerial vehicle
to fly autonomously for 24 hours in steady level flight at 300 feet over Sacramento,
California during the summer months of May through September. A design spreadsheet
was used to implement a continuous design approach, in which the battery pack power,
photovoltaic efficiency, and aircraft weight were determined for a given aspect ratio and
wing loading. The optimum aspect ratio and wing loading to minimize both battery pack
power and photovoltaic efficiency were selected using graphical techniques including
carpet plots.
59
Further research is required regarding the effect of increasing aspect ratio on the
overall design and its efficiency; such research should be coupled with detailed structural
analysis to prevent failure of the wing structure.
60
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