-4
Design and Optimization of Micro Aerial Vehicles
by
Sarah N. Saleh
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2003
@ Massachusetts Institute of Technology 2003. All rights re
ifapST
OF TECHNOLOGY
SEP 1 0 2003
.....
Author ...............
LIBRARIES
Department of Aeronautics and Astronautics
May 9, 2003
Certified by............
i
bJohn
J. Deyst
Professor of Aeronautics and Astronautics
Thesis Supervisor
Certified by...
I'
Certified by.......
........
Sean George
Draper Laboratories
Supervisor
LThesis
/
.....
............
Bernard F. Mettler
Laboratory for Information and Decision Systems
Thesis Supervisor
A
..
Edward M. Greitzer
H.N. Slater Professor of Aeronautics and Astronautics
Chairman, Committee on Graduate Students
Accepted by......
AERO
.A
Design and Optimization of Micro Aerial Vehicles
by
Sarah N. Saleh
Submitted to the Department of Aeronautics and Astronautics
on May 9, 2003, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
This thesis details the optimization and development of two Micro Aerial Vehicles
(MAVs), namely a fixed wing vehicle and a quadrotor vehicle, within the Parent
Child Unmanned Air Vehicle (PCUAV) system developed at MIT and the Draper
Laboratory. The PCUAV system allows up close surveillance using a three-tiered
system, of which the MAVs comprise the lowest altitude tier to the ground. MAVs are
defined by the Department of Defense as having a span of 6 inches, and can be used
to increase situational awareness by obtaining damage assessment and surveillance
information. In addition to these military uses the MAVs can be used for applications
such as search and rescue, air sampling and urban surveillance. A Multidisciplinary
System Design Optimization (MSDO) method was used to optimize each of the vehicle
configurations for a particular mission.
Thesis Supervisor: John J. Deyst
Title: Professor of Aeronautics and Astronautics
Thesis Supervisor: Sean George
Title: Draper Laboratories
Thesis Supervisor: Bernard F. Mettler
Title: Laboratory for Information and Decision Systems
3
4
Acknowledgments
In the Name of God the Most Gracious, the Most Merciful
To only thank a limited number of advisors, friends and family in this section is hard,
since there are many people that have affected me in many ways. So to all my friends
that I have not mentioned below, thank you all for helping me grow and develop
academically, spiritually and socially.
I would like to thank Professor Deyst, for giving me the opportunity of a life time to
study the field of my dreams. For being an advisor not just in my area of study but
in life. Thanks for being such a wonderful role model. My thanks also to Mrs. Deyst
who throughout my studies here has encouraged my growth in many aspects.
Sean- thank you for your all your help, and the countless hours that you spent with
me working on "my models" and the many 2 hour meetings that we would have
early on Wednesday mornings. I appreciate your enthusiasm for my work and your
constant good humor and encouragement.
Professor Mettler- Thank you for the many hours that you put into this work, and a
wonderful helicopter course that provided me with the background to complete this
work.
I would like to thank Brent Appleby and Chris Andersen at Draper Labs for their
direction and guidance throughout the project.
To Don, Dick, Carol, Doris and Phyllis, for all your support and in making my time
at MIT easy and stress free.
To my friends in Calgary who encouraged me to pursue my dreams, especially Dr.
Jason Mukherjee and Dr. Kentfield, who without their advice and efforts I would not
5
be here doing what I love.
Thanks also to the team - who treated me like their little sister! Francois and Thomasthank you both for your leadership and dedication to the team, Sanghuk- thanks for
many precious AVL moments, and the help that you have given to me since I joined
the team, Damien- thanks for your sincerity and care, Anand- thanks for teaching me
the joys and effects of coffee at "Starbooks", Jason- thanks for all your aero stories
and Alex- thanks for teaching me about Russia and Hockey!
To my friends in the Muslim Students' Association and at the Islamic Society of
Boston, JazakumAllah Khairan, for making these few years the best in my life, I will
remember each and everyone of you for everything that you have taught me.
And finally to my family who throughout my life, have encouraged me to follow my
dreams and have nurtured me. To my sisters Mona and Susan- who have been with me
since day one...thanks for making me who I am, and for constantly putting me above
yourselves. To Mummy and Daddy, I couldn't wish for greater parents. Thanks for
giving me the opportunities to grow. Thanks for always being there for me, picking
me up when I have been down and sacrificing your needs for mine. I hope that one
day, I will be able to give to you what you have given to me. May Allah (SWT) give
you the best in this life and the next.
6
Contents
1
2
Introduction & Overview
23
1.1
Background & Motivations . . . .
.
23
1.2
Thesis Contributions . . . . . . .
.
24
1.3
Organization of Thesis
. . . . . .
.
24
1.4
Intended Audience
. . . . . . . .
.
25
PCUAV System
27
2.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.2
Concept Elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.2.1
PCUAV Mission Scenario
. . . . . . . . . . . . . . . . . . . .
28
2.2.2
Key Enablers
. . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.3
Reintegration
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.4
PCUAV Vehicles and Components . . . . . . . . . . . . . . . . . . . .
31
2.4.1
Parent Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.4.2
M ini Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.4.3
Micro Aerial Vehicles (MAVs) . . . . . . . . . . . . . . . . . .
34
2.4.4
Clandestine Mid Air Retrieval System (CMARS)
. . . . . . .
35
2.4.5
Communications & Surveillance . . . . . . . . . . . . . . . . .
36
3 MAV Selection
37
3.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . .
37
3.2
Importance of Micro Aerial Vehicles . . . . . . . . . . . .
37
3.3
Requirements & Mission Definition
38
7
. . . . . . . . . . . .
3.4
4
3.3.1
MAV Requirements ........
39
3.3.2
Mission Definition . . . . . . . .
39
3.3.3
Physical MAV Requirements . .
40
3.3.4
MAV Performance Requirements
41
Current MAVs & QFD Analysis . . . .
42
3.4.1
Current MAVs
. . . . . . . . .
42
3.4.2
QFD Analysis . . . . . . . . . .
42
3.4.3
QFD Results
. . . . . . . . . .
46
51
Optimization Model Design
4.1
Chapter Overview . . . . . . . . .
51
4.2
Problem Definition & Objectives
51
4.3
Mission Definitions
4.4
4.5
. . . . . . . .
52
4.3.1
Fixed Wing Mission
. . .
52
4.3.2
Quadrotor Mission . . . .
53
Module Definition . . . . . . . . .
54
4.4.1
Aerodynamics . . . . . . .
55
4.4.2
Weight . . . . . . . . . . .
55
4.4.3
Propulsion . . . . . . . . .
56
4.4.4
M otor . . . . . . . . . . . . . . . . . . . . .
56
4.4.5
Battery
. . . . . . . . . . . . . . . . . . . .
56
4.4.6
System Structure . . . . . . . . . . . . . . .
58
. . . . . . . . . . . . . . . . .
60
Model Commonality
4.5.1
Design Variables
. . . . . . . . . . . . . . .
61
4.5.2
Design Constants . . . . . . . . . . . . . . .
61
4.5.3
Mission Parameters and Nominal Mission.
4.5.4
Model Analysis Approach
. . . . . . . . . . .
61
. . . . . . . . . . . . . . . . . . . .
62
65
5 Fixed Wing
5.1
Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
5.2
Mission Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
8
5.3
5.4
6
. . . . . . . . . . . . . . . . . .
66
5.3.1
Geometry Calculations . . . . . . . . . . . . . . . . . . . . . .
67
5.3.2
Weight Calculations
. . . . . . . . . . . . . . . . . . . . . . .
75
5.3.3
Aerodynamic Calculations . . . . . . . . . . . . . . . . . . . .
76
5.3.4
Force Calculations
. . . . . . . . . . . . . . . . . . . . . . . .
79
5.3.5
Propulsion Calculations
. . . . . . . . . . . . . . . . . . . . .
80
5.3.6
Motor Calculations . . . . . . . . . . . . . . . . . . . . . . . .
81
5.3.7
Energy Calculations
. . . . . . . . . . . . . . . . . . . . . . .
82
5.3.8
Overall Model Summary . . . . . . . . . . . . . . . . . . . . .
83
. . . . . . . . . . . . . . . .
84
5.4.1
Nominal Vehicle Designs . . . . . . . . . . . . . . . . . . . . .
84
5.4.2
Weight Trends for Nominal Missions
. . . . . . . . . . . . . .
85
5.4.3
Secondary Parameters
. . . . . . . . . . . . . . . . . . . . . .
93
Design & Numerical Implementation
Optimization Study-Results & Analysis
Quadrotor
97
6.1
Chapter Overview.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
6.2
Mission Definition.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
6.3
Design & Numerical Implementation
. . . . . . . . . . . . . . . . . .
98
6.4
6.3.1
Quadrotor Theory
. . . . . . . . . . . . . . . . . . . . . . . .
98
6.3.2
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
6.3.3
Weight Calculations
. . . . . . . . . . . . . . . . . . . . . . .
10 0
6.3.4
Aerodynamic Calculations . . . . . . . . . . . . . . . . . . . .
10 3
6.3.5
Force Calculations
. . . . . . . . . . . . . . . . . . . . . . . .
10 8
6.3.6
Propeller Power Calculations . . . . . . . . . . . . . . . . . . .
10 9
6.3.7
Motor Power Calculations
. . . . . . . . . . . . . . . . . . . .
110
6.3.8
Overall Model Summary . . . . . . . . . . . . . . . . . . . . .111
Optimization Study-Results and Analysis
. . . . . . . . . . . . . .111
6.4.1
Nominal Vehicle Designs . . . . . . . . . . . . . . . . . . . . .
112
6.4.2
Weight Trends for Nominal Mission . . . . . . . . . . . . . . .
113
6.4.3
Secondary Parameters
. . . . . . . . . . . . . . . . . . . . . .
119
9
7
123
Conclusion
7.1
Chapter Overview.
. . . . . . . . . . . . . . . . . . . . . . . . .
123
7.2
Comparative Results . . . . . . . . . . . . . . . . . . . . . . . .
123
7.2.1
Loiter Radius/Hover Comparison
123
7.2.2
Loiter Velocity
. . . . . . . . . .
124
7.2.3
Weight Comparison . . . . . . . .
125
7.2.4
Effect of Parameters
. . . . . . .
126
7.2.5
Qualitative Study . . . . . . . . .
127
7.3
Conclusions . . . . . . . . . . . . . . . .
129
7.4
Future Work . . . . . . . . . . . . . . . .
130
A Battery Macros
133
B Fixed Wing Model
135
C Spar Sizing
139
D Quadrotor Model
141
10
List of Figures
2-1
Multi-tiered System Concept . . . . . . . . . . . . . . . . . . . . . . .
28
2-2
Communications Hierarchy for PCUAV [13]
29
2-3
Phase One of Reintegration
. . . . .
30
2-4
Phase 2, Optical System . . . . . . .
31
2-5
Outboard Horizontal Stabilizer Parent Vehicle in Flight and Disassem-
. . . . . . . . . . . . . .
bled for Transportation in a Van . . .
. . . . . . . . . . . . .
33
2-6
New Generation Mini (NGM) II . . .
. . . . . . . . . . . . .
34
2-7
CMARS Directional Finder
. . . . .
. . . . . . . . . . . . .
35
2-8
Rover with Surveillance Equipment .
. . . . . . . . . . . . .
36
3-1
Mission Overview . . . . . . . . . . .
. . . . . . . . . . . . .
40
3-2
QFD Diagram [4] . . . . . . . . . . .
. . . . . . . . . . . . .
43
3-3
Initial QFD Definition
. . . . . . . .
. . . . . . . . . . . . .
46
4-1
Ragone Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4-2
N 2 Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
4-3
System Simulation
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5-1
Mission Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
5-2
Wing Shapes [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
5-3
Lift and Drag Coefficien Lts Vs. Angle of Attack for Low Aspect Ratio
Wings [16]
. . . . . .
68
5-4
Geometry and Area Calculations for the Fixed Wing MAV . . . . . .
69
5-5
Structural Calculations for the Fixed Wing MAV
. . . . . . . . . . .
71
11
5-6
D eflections . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .
73
5-7
Fixed Wing MAV- Wing Structure [2] . . . . . . . . . . . . .
. . .
73
5-8
Reynolds Numbers for a Range of Vehicle Sizes [20] . . . . .
. . .
77
5-9
Free Body Diagram -Loiter Radius
. . . . . . . . . . . . . .
. . .
79
. . . . . . . . . . . . .
. . .
83
5-11 Fixed Wing Model Block Diagram . . . . . . . . . . . . . . .
. . .
84
5-12 Normalized Weight Distribution Comparison for the Nomina lMis sion
86
5-13 Wing Span Vs. Payload Weight, Nominal Mission . . . . . .
. . .
87
5-14 MAV Weight Vs. Payload, Nominal Missions . . . . . . . . .
. . .
88
5-15 Wing Span Vs. Loiter Time, Nominal Mission . . . . . . . .
. . .
89
5-16 MAV Weight Vs. Loiter Time, Nominal Missions
. . . . . .
. . .
89
5-17 Wing Span Vs. Loiter Radius, Nominal Mission . . . . . . .
. . .
90
5-18 MAV Weight Vs. Loiter Radius, Nominal Missions
. . . . .
. . .
91
5-19 Wing Span Vs. Cruise Distance, Nominal Mission . . . . . .
. . .
92
. . . .
. . .
92
5-10 Fixed Wing MAV (Main Worksheet)
5-20 MAV Weight Vs. Cruise Distance, Nominal Missions
5-21 Secondary Effects on AR and Mission Energy whilst varying payl oad
5-22 Loiter Radius Effects on AR and Mission Energy
. . . . . .
. . .
95
96
6-1
Quad-rotor Mission Definition . . . . . . . . . . . . . . . . .
98
6-2
Quadrotor Model (Geometry and Area Calculations)
. . . .
101
6-3
Quadrotor Assembly
. . . . . . . . . . . . . . . . . . . . . .
102
6-4
Simplified Quadrotor (Cross Section) for Drag Calculations .
104
6-5
Quadrotor Model (Figure of Merit Calculations) . . . . . . .
106
6-6
Quadrotor Maneuvering Forces
. . . . . . . . . . . . . . . .
109
6-7
Quadrotor Model (Main Worksheet) . . . . . . . . . . . . . .
112
6-8
Quadrotor Model Block Diagram
. . . . . . . . . . . . . . .
113
6-9
Weight Distribution Comparison for Nominal Missions
. . .
114
6-10 MAV Weight Vs. Cruise Distance, Nominal Mission . . . . .
115
6-11 Rotor Diameter Vs. Cruise Diameter, Nominal Mission . . .
116
6-12 Weight Distribution Comparison- Cruise Distance . . . . . .
117
12
6-13 MAV Weight Vs. Payload Weight, Nominal Mission . .
118
6-14 Rotor Diameter Vs. Payload Weight, Nominal Mission
118
6-15 Weight Distribution Comparison- Payload
119
. . . . . . .
6-16 MAV Weight Vs. Hover time, Nominal Mission
. . . .
120
6-17 Rotor Diameter Vs. Hover time, Nominal Mission . . .
121
6-18 Weight Distribution Comparison- Hover Time . . . . .
121
7-1
Vehicle Separated Weight Comparison
. . . . . . . . .
125
7-2
Vehicle Weight Comparison
. . . . . . . . . . . . . . .
126
A-1
Battery Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
134
B-i
Geometry and Area Calculations for the Fixed Wing MAV
136
B-2 Structural Calculations for the Fixed Wing MAV
. . . . .
137
. . . . . . . . . . . .
138
. . . . . . . . . . . . . . . .
140
B-3 Fixed Wing MAV (Main Worksheet)
C-1
Spar Sizing Text Example [6]
D-1
Quadrotor Model (Main Worksheet) . . . . . . . . . . . . . . . . . . .
D-2
Quadrotor Model (Geometry and Area Calculations)
D-3
Quadrotor Model (Figure of Merit Calculations) . . . . . . . . . . . .
143
D-4
Quadrotor Model (Velocity Macro)
144
13
141
. . . . . . . . . 142
. . . . . . . . . . . . . . . . . . .
14
List of Tables
3.1
Hierarchy of Requirements Affecting MAV Choice . . . . . . . . . . .
47
3.2
Factors Affecting MAVs
. . . . . . . . . . . . . . . . . . . . . . . . .
49
4.1
Battery Energy Densities . . . . . . . . . . . . . . . . . . . . . . . . .
58
4.2
Design Variables Common to both MAV Optimizations . . . . . . . .
61
4.3
Design Constants Common to both MAV Optimizations
. . . . . . .
62
4.4
Parametric Mission Value Samples
. . . . . . . . . . . . . . . . . . .
62
5.1
Fixed Wing Geometry Related Constants . . . . . . . . . . . . . . . .
70
5.2
Fixed Wing Structural Weight Constants . . . . . . . . . . . . . . . .
72
5.3
Nominal Vehicle Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
5.4
Secondary Variable Trends, Objective: Minimizing Wing Span . . . .
93
5.5
Secondary Variable Trends, Objective: Minimizing Weight
94
6.1
Material Properties and Constants for Weight and Geometric Calcula-
. . . . . .
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103
6.2
Constants for Figure of Merit Calculations . . . . . . . . . . . . . . .
106
6.3
Nominal Vehicle Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
6.4
Variable Trends, Objective: Minimizing Rotor Diameter
. . . . . . .
122
6.5
Variable Trends, Objective: Minimizing Weight
. . . . . . . . . . . .
122
7.1
Loiter Radius Comparison . . . . . . . . . . . . . . . . . . . . . . . .
124
7.2
Minimum Loiter Velocities . . . . . . . . . . . . . . . . . . . . . . . .
124
7.3
Parameter Effects on each Vehicle . . . . . . . . . . . . . . . . . . . .
126
15
16
Nomenclature
a
Vehicle Angle
rn
Efficiency/Figure of Merit
rK
Induced Power Factor
Adef
Required Angular Deflection
Q
Rotor Tip Speed
<$
Bank Angle
p
Density
0-
Rotor Solidity
-cap
Tskin
Cap Stress
Required Skin Thickness
Subscripts
a
Material area
bat
Battery
Cp
Cruise Power
cap
Cap
cf
Carbon Fiber Rods
17
c
Cruise
dc
Cruise Drag
dens
Density
d
Diameter
foam
Foam
foil
Airfoil
fuse
Fuselage
f
Flight
ho
Housing
h
Height
h
Hover
if
Flight Induced
ih
Hover Induced
Loiter
mc
Motor Cruise
mh
Motor Hover
misc
Miscellaneous
ml
Motor Loiter
m
Maneuvering
pay
Payload
PC
Propeller Cruise
18
pf
Propeller Flight
ph
Propeller hover
,1
Propeller Loiter
prop
Propeller
r
Root
skin
Skin
struct
Structure
A
Area
ADj
Component Drag Area
BL
Blade Loading
BW
Battery Weight
c
Propeller Chord
c/R
Propeller Chord Ratio
CD
Fixed Wing Fuselage Drag Coefficient
Cd
Drag Coefficient
CT
Coefficient of Thrust
Cd
Profile Drag Coefficient
Cduse
Fuselage Drag Coefficient
C
_LaxMaximum Coefficient of Lift
CL
Coefficient of Lift
D
Drag
19
Di
Component Drag
DL
Disk Loading
E
Energy
e
Oswald Efficiency
H
Fuselage/Housing
Hid
Fixed Wing Fuselage Length:Diameter ratio
k
Induced Drag Factor
M
Motor
m
Mass
Mb
Root bending moment
N
Number
n
Load Factor
P
Power
R
Radius
Re
Reynolds Number
Re,
Rotor Reynolds Number
S
Area
T
Thrust
t
Time
V
Velocity
V
Volume
20
W
Weight
w
Width
AR
Aspect Ratio
ATA
Avionics Testbed Aircraft
BEMT Blade Element Momentum Theory
CCR Cruise Climb Rate
CMARS Clandestine Mid Air Retrieval Systems
GPS
Global Positioning Systems
L
Load
LCR Loiter Climb Rate
LED Light Emitting Diode
MAV Micro Aerial Vehicle
MDPP MIT Draper Partnership Project
MPIM Mini-Parent Integration Mechanism
MSDO Multidisciplinary system design optimization
NGM New Generation Mini
OHS
Outboard Horizontal Stabiliser
PCUAV Parent Child Unmanned Aerial Vehicle
PDV Payload Delivery Vehicle
UAV
Unmanned Aerial Vehicle
WASP Wide Area Surveillance Projectile
21
WLAN Wireless Local Area Network
y
Deflection
22
Chapter 1
Introduction & Overview
1.1
Background & Motivations
In the last seven years, as military needs grow, the requirement to obtain up close/fine
scale reconnaissance information from a distance has become increasingly evident.
The Massachusetts Institute of Technology (MIT) and The Charles Stark Draper
Laboratory (Draper) responded to this need by forming a technology development
partnership in 1996.
The partnership was formed not only to address the need for up-close surveillance
and designing leading edge innovative systems, but also to allow for graduate students
studying at MIT to be exposed to project engineering and a life cycle of a critical
academic and industrial problem.
The partnership began with the Wide Area Surveillance Projectile Project (WASP),
where students designed a canon-launched folding-wing projectile, which was later
marketed by Draper.
After the WASP project came the Parent Child Unmanned Aerial Vehicle Project,
PCUAV, which still focused on the main objective of the WASP project by providing
close-up surveillance from a distance.
The goal of PCUAV was to create a system that provides an environment that allows
23
a hierarchy of unmanned vehicles to work together to obtain information otherwise
not obtainable by just one of the individual vehicles. These vehicles range from a
large parent vehicle, with a tail span of approximately 21ft, to small micro aerial
vehicles, MAVs, whose lengths can be as small as 6 inches.
In 2002 the PCUAV project came to a successful end, and was followed by the MIT
Draper Partnership Project (MDPP). The purpose of this new project is to continue work in the area of up-close surveillance by looking at areas such as unmanned
precision delivery, coordinated operation of sensor networks and probing ground and
aerial vehicles, areas of research that will allow the set-up of an entire communications
network in hostile environments.
1.2
Thesis Contributions
The work completed for this thesis provides:
" An analysis of current MAV designs on the market
" A software environment for use in the initial design of both a fixed wing MAV
and a quadrotor MAV.
" A multidisciplinary system design optimization of two MAVs
1.3
Organization of Thesis
In chapter 1, we discuss the history of the MDPP and the needs for up-close surveillance.
Chapter 2 outlines the PCUAV system and delves into the vehicles of PCUAV, navigation techniques, and communications and surveillance systems. In this chapter we
also introduce one of the key capabilities of PCUAV: reintegration of two UAVs.
24
Chapter 3 on, focuses on MAVs, specifically with the PCUAV project in mind. Currently available off-the-shelf MAVs and potential mission scenarios, that will enhance
the capabilities of the PCUAV system are examined.
Chapter 4 delves into the design challenges and requirements to set up an Excel optimization of both fixed wing and quadrotor MAVs. We study further the parameters
that constrain the multidisciplinary system design, the design variables, and how to
build optimization models for both MAVs.
Chapters 5 and 6 discuss in more detail the design challenges and theory involved in
building a fixed wing and quadrotor optimization model. We analyze the aerodynamic
theory and design of both the fixed wing and quadrotor MAVs, and set up the Excel
Optimization model. Finally we analyze the results of the optimization for both
vehicles.
In chapter 7, we compare the results from chapters 5 and 6 and quantitatively look at
the factors that would determine the number and type of MAVs needed for a specific
surveillance mission. Finally we conclude our work and discuss potential future work
in this area.
1.4
Intended Audience
This thesis is intended to be read by individuals interested in:
" Multidisciplinary system design optimization (MSDO)
" Flight vehicle design of MAVs
" MAV applications
25
26
Chapter 2
PCUAV System
2.1
Chapter Overview
This chapter presents an overview of the PCUAV project and describes the system's
concepts, requirements, and missions.
2.2
Concept Elaboration
The original motivation for the PCUAV project was to allow someone sitting at their
desk in Boston to take a "virtual walk" through Central Park in New York City (over
two hundred miles away); by using information being relayed back through a fleet
of unmanned aerial vehicles (UAVs). Through this basic idea the PCUAV mission
became to:
"Perform real-time and continuous up-close surveillance of a low altitude cluttered
environment using low-cost assets, from a distance."
The overall architecture of the PCUAV project consists of a fleet of UAVs organized
in a three-tiered system (Figure 2-1). The system is designed so that each vehicle
can be used at different desired altitudes, relaying important information from each
tier and providing the necessary energy for the smaller lower-energy vehicles to be
transported to the area of interest.
27
Tier 1: Parent Vehicle
(20 000 ft)
Tier 2: Mni Vehicles
(10 000 ft)
Tier 3: MLAVs
(200ft)
Figure 2-1: Multi-tiered System Concept
This setup is useful for a number of different missions in which it is hazardous to dispatch humans. These missions include, collecting soil or water samples from nuclear
waste sites, obtaining battle-zone damage assessment information, and for search and
rescue scenarios.
The advantages of using such a system over currently available reconnaissance systems
like the Predator, are as follows:
" The flexibility and modularity of each vehicle on its own allows for reconfiguration of the vehicles for a broad range of missions and deployment platforms.
" Smaller vehicles (micros) can operate for hazardous, up-close surveillance and
are low-cost expendable vehicles.
* Obtain the same high value, long range as the Predator, using the Parent.
2.2.1
PCUAV Mission Scenario
In a typical mission, a parent vehicle would be loaded with two mini vehicles, a
number of payload delivery vehicles (PDVs) and micro aerial vehicles (MAVs), and
enough fuel to last for a trip of up to 350km, with a surveillance/loitering time of
approximately 5 hours over the target. The parent would take off from an airport or
28
an unapproved landing strip, and fly to the area of interest autonomously or remotely.
A communications link is established and maintained with a ground operator from
the time of departure until the time of return. At the site of interest the parent
would deploy the mini vehicles that descend to lower altitudes for surveillance, until
running low on fuel, where the minis would then rendezvous with the parent, and
either redock or refuel.
While the minis gather information, the PDVs and MAVs are deployed to collect
finer reconnaissance information (for example, under-the-tree-canopy surveillance or
obtaining soil samples). These samples are then retrieved by a balloon rendezvous
system with the mini vehicles and brought back to the parent (and later the base
station) using clandestine mid air retrieval systems (CMARS). During the entire
mission a communications system maintains real-time communication between all the
vehicles and the ground station, allowing for redefinition of the mission, if necessary
(Figure 2-2).
PAREP47
*iP TO IVU MLLEZ
-
30u FLc~r
INI
-~~~
"'
30
FEET
UPj~ERAT'MR/
Figure 2-2: Communications Hierarchy for PCUAV [13]
2.2.2
Key Enablers
To be able to perform the mission, we need a number of key enablers:
" A parent vehicle that is capable of long distance flight and carrying payloads
that may have an effect on the overall stability of the vehicle.
" A robust system for reintegration between the parent and mini vehicles.
29
9
A robust and dynamic communications network between all vehicles.
We will look at these key enablers in more detail in later sections.
2.3
Reintegration
601
401
4 201
800
600
40(
2(
y axis
-200
0
200
400
xaxis
Figure 2-3: Phase One of Reintegration
Since both vehicles are unmanned and autonomous, the concept of joining two vehicles in the air, although not new, presents many control and design challenges.
Establishing a routine for both the mini and the parent to follow, for rendezvous, is
critical to the success of the mission, so that the chances of a "mission abort" are
minimized. To overcome this, reintegration is comprised of three phases:
1. Phase 1: Brings both aircraft, the parent and the mini, from arbitrary positions
and velocities in the sky to a point where the parent and mini have a relative
position of 10m.
2. Phase 2: Brings the mini into contact with the parent.
3. Phase 3: Locks the parent and the mini in place.
30
Phase 1 has been demonstrated by PCUAV and we are currently awaiting testing
of Phase 2. The details of Phase 1 can be seen in Figure 2-3 and involve the mini
performing a trajectory that intercepts the parent's position.
Phase 1 is performed using GPS and proportional navigation. Phase 2 begins once
the mini is in the proper position behind the parent. In this phase an optically-based
system is used to bring the mini vehicle from 10m behind the parent to physical
contact with the parent. We use a video camera mounted on the mini vehicle to track
signals from infrared LEDs on the parent vehicle (Figure 2-4) to guide the mini to the
parent vehicle. This system is able to compute the relative position of the aircraft to
an accuracy of a few of millimeters.
Mini
OHS
Sm
optical sensor
measures angles to the target
4kHz Pulse
Diode Array
Figure 2-4: Phase 2, Optical System
2.4
PCUAV Vehicles and Components
This section gives a brief description of the vehicles and the components that make
up the three tiers of PCUAV. These include the parent, the mini, the avionics testbed
aircraft (ATA) and the payload delivery vehicles (PDV), along with the mini-parent
integration mechanism (MPIM), communications and surveillance and avionics.
31
2.4.1
Parent Vehicle
In order to demonstrate the system concepts of PCUAV, the parent vehicle needed
to be able to:
* Navigate autonomously.
" Loiter for 30-60 minutes.
" Maintain speeds suitable for reintegration and provide a stable target for the
mini to dock with.
" Continue flying after docking with one mini.
* Operate from unapproved runways and fields
" Be transportable in a convenient package.
After having studied a number of different vehicle designs, we decided to use the
outboard horizontal stabiliser (OHS) design for ease of reintegration [11] [10] [12].
This design (Figure 2-5) has a number of advantages over a conventional design,
since:
1. It has a unobstructed space behind the parent, as the tails are well outboard of
the main wing, reducing interference of the parent and the mini, and allowing
a large area for the docking of the mini with the parent.
2. More lift is possible with the same size wing as a conventional aircraft, since
the tails are positioned in the wing tip vortices, allowing the tail to lift.
3. The aircraft is still controllable if one of the tails is lost.
4. The OHS can be built in a modular fashion, allowing for easy transportation
(Figure 2-5).
32
Parent Specifications
Wingspan
=
174 in
Chord = 21.25 in
Height = 40 in
Length = 90 in
Tail-span
=
Weight
35 lbs
=
240 in
Moki 2.10 cu. in. Engine 5 hp
Figure 2-5: Outboard Horizontal Stabilizer Parent Vehicle in Flight and Disassembled
for Transportation in a Van
2.4.2
Mini Vehicle
The requirements for the mini vehicle were as follows:
" Fly and navigate autonomously.
" Maintain a speed appropriate for reintegration.
" Maneuver to be able to "hit" a target on the parent for reintegration.
" Minimize detrimental effects on the flight of the parent.
In order to satisfy the requirements, the mini vehicle was designed to feature a pusher
propeller, a vertical direct force fin, and flaperons that can produce both rolling
moments and direct lift forces. The pusher configuration decreases the likelihood of
propeller strike when the mini approaches the parent from behind, and also clears
an area for a probe to protrude from the nose of the mini for reintegration.
The
vertical fin with its associated control surface, over the center of gravity of the aircraft,
creates the possibility of moving side to side without yawing or banking, when the fin
surface deflection is combined with both aileron and rudder deflections. Similarly, it
33
is possible to make the plane move up and down with the combination of flaperons,
elevator and throttle; without pitching or changing airspeed.
Mini Specifications
Wingspan
=
100 in
Chord = 11 in
Height
=
25 in
Length = 65 in
Weight
=
15 lbs
0.91 cu. in OS Engine
Figure 2-6: New Generation Mini (NGM) II
2.4.3
Micro Aerial Vehicles (MAVs)
Two types of MAVs were examined to provide even closer surveillance information.
These vehicles could be used to drop off sensors; however, their primary use is surveillance and to act as accurately-placed communications nodes. A fixed wing vehicle
and a rotating hovering vehicle (quadrotor) were designed and optimized, and will be
addressed in following chapters in greater detail.
To carry out their mission it is necessary for both vehicles to meet the following
requirements:
" Be capable of image detection (surveillance).
" Have sufficient obstacle avoidance for operation in cluttered environments.
" Be deployed from the parent or mini vehicles.
" Have minimum impact on the deployment vehicle (small size and weight)
34
2.4.4
Clandestine Mid Air Retrieval System (CMARS)
During the course of a typical mission it is desirable to be able to recover sensors
or soil samples from the ground. A clandestine mid air retrieval system (CMARS)
was developed by PCUAV to provide a cost-effective solution to recovering elements
from the ground.
The system consists of a balloon to carry the desired package,
an RF transmitter attached to the balloon, and a directional receiver onboard the
rendezvousing aircraft.
To collect a soil sample, for example, first a mini or MAV would deliver a collector
from the parent to the site of interest. A sample would be gathered by the collector,
the balloon would inflate bringing the collector to the altitude of the mini, where
an RF transmitter would send an omnidirectional signal. The receiver on the mini
would find the bearing toward the transmitter and steer the mini towards it. Finally
the mini would then fly through a cable that connects the sample to the balloon, and
retrieve the sample at the wing-tip while cutting away the balloon.
We designed, constructed and tested a transmitter and directional receiver. The receiver uses four antennae in a pyramidal orientation as seen in Figure 2-7. Differential
signal strengths among the antennae are used to determine the direction of the receiver with respect to the antenna; i.e., when the strengths are equal, the transmitter
is directly ahead of the mini. This system could also prove useful for reintegration
with the parent as a supplement to both the GPS and optical navigation systems.
Figure 2-7: CMARS Directional Finder
35
2.4.5
Communications & Surveillance
The surveillance system consists of a computer stack separate from the one used for
navigation, a video camera, and a WLAN (Wireless Local Area Network) system.
The system was tested and flown in both the ATA and the NGM (New Generation
Mini). We first demonstrated the capability to take video images from the air and
transmit them via a WLAN to a laptop computer on the ground. The pictures were
recorded, compressed into JPEG form, and transmitted to the laptop at a rate of one
frame every two seconds.
The second feature used a camera placed on the ground, which transmitted images
to a UAV overhead which relayed them to the laptop. At the same time, the laptop
operator could move the ground camera via commands sent back through the aircraft.
The third feature demonstrated was the capability to send and receive images from
both the aircraft and the ground cameras simultaneously.
The last feature demonstrated was placing the ground camera on a ground rover so
that the rover can be operated by the laptop with a signal relayed through the aircraft.
The final surveillance concept to be demonstrated will combine all the concepts with
GPS, so the aircraft can be made to orbit a moving rover based on its GPS position,
allowing the user to view images from the rover and the aircraft simultaneously.
Figure 2-8 shows the rover and the ground camera used for surveillance.
Figure 2-8: Rover with Surveillance Equipment
36
Chapter 3
MAV Selection
3.1
Chapter Overview
In this chapter we study the potential roles of MAVs. We describe MAVs currently
available on the market, and discuss which MAVs would best suit the PCUAV system,
in terms of the mission definition and criteria. We then assess the potential vehicles
using a Quality Function Deployment (QFD) Matrix.
3.2
Importance of Micro Aerial Vehicles
The U.S. government has focused considerable resources on small UAVs, as they
offer a number of advantages over larger UAVs for missions that do not require large
payloads or long endurance. Some of these advantages include:
" Low cost and expendability.
" Low radar signatures that make them hard to detect.
" Low operating costs due to sufficient automation that eliminates the need for
highly trained ground crews;
" deployment from an aerial platform.
37
"
Increased "team work" among a group of UAVs, including MAVs, by facilitating
greater communication and coordination in a mission, by dividing labor among
the vehicles.
" Increased communication capability since the MAVs can be used as mobile
communication relays.
MAVs can be used for a variety of missions either working alone or within a team
framework, like the PCUAV system. Examples of these missions include: reconnaissance surveillance target acquisition (RSTA) activities, search and rescue, and communication relay, in which minimum human intervention is a key element. Within the
PCUAV framework MAVs have become an integral part of the proposed system; providing under-the-tree-canopy surveillance and communication relays, and allowing for
more information from a greater standoff distance, with minimal human intervention
[21].
3.3
Requirements & Mission Definition
The challenge of developing an MAV that meets the requirements both of a military
mission-being hand-launched by a soldier-and could be used within the PCUAV
system, led to a number of criteria that had to be met.
For the purpose of this thesis though, we will concentrate on the MAV in the PCUAV
system, and discuss missions where the MAV is dropped from a carrier vehicle. The
final MAV design however, could also be used by ground forces. Deployment from an
aerial platform offers the following advantages:
" Extended range of smaller lower energy vehicles by providing a platform to
transport the MAVs to the site of interest, "piggybacking".
" Simple launch, no bungee or catapult is needed.
" A faster surveillance chain to provide more timely information.
38
3.3.1
MAV Requirements
The following list outlines the requirements of a successful mission:
" Stealth: the vehicle must be small enough to be hard to detect.
" Durability: the vehicle must withstand being dropped from high altitudes and
must be able to survive falling to the ground.
" Surveillance: the vehicle must be capable of steady and slow flight for image
collection.
" Obstacle Avoidance: the vehicle must be capable of avoiding buildings and trees
and be able to navigate through cluttered environments.
" Deployment: the vehicle must be deployable from a carrier UAV.
" Endurance: the vehicle must have a minimum endurance of 30 minutes (in a
surveillance mode) and a 3km cruise ingress and egress distances.
3.3.2
Mission Definition
The MAV will be deployed from a carrier UAV. It will then fly to an area of interest,
which may be obscured or cluttered, and as such is not visible by high altitude assets.
The MAV will collect information from that area by either loitering or by hovering
over the "hot-spot" and then flying far enough away from the area of interest as to
leave no trace where it will "die" or lay dormant. During each of its phases (Figure 31) the MAV will be able to communicate to the ground station, via the parent and
the mini vehicles, relaying important surveillance information.
Mission Scenarios
Some potential mission scenarios include:
1. Urban Surveillance: Low-range MAVs could be dropped from the carrier UAV
(very close to the area of interest, i.e., less than 5km away). The MAV would be
39
Deployment Phases:
Phase 1: Drop from Parent vehicle (20,000ft), autonomous startup
for transition between fall and horizontal flight at specified altitude
(200ft).
Phase 2: Horizontal flight to area of interest (cruise).
Phase 3: Surveillance of area of interest (loitering/ circular flight),
preferably for a minimum of 10 minutes.
Phase 4: H orizontal flight to area of "death".
LPHASE4
Figure 3-1: Mission Overview
able to fly forward, and navigate around cluttered buildings to allow close-up
(real-time day and night imagery) surveillance and battle damage assessment.
The MAV could land on buildings creating a potential communication relay and
possibly a surveillance capability as well.
2. Cluttered Environments: MAVs could be deployed from the carrier vehicle and
fly to an area that is chemically hazardous, dropping off various chemical sensors
that could potentially be retrieved by CMARS, as described in chapter 2.
In each mission, one of the main requirements for the MAV is to fly close to the
ground (at an altitude of less than 150m), for a short time providing extremely upclose surveillance. This requires vehicles that are small, maneuverable, low cost, and
expendable.
3.3.3
Physical MAV Requirements
Size & Volume, Storage Capability, & Deployment
An MAV is defined by the Department of Defense (DoD) as being a vehicle with a
wingspan of 6 inches or less. The packaging and size of the MAV is important to the
40
mission since the payload capacity of the carrier UAV is limited, and so the size of the
payload on the MAV is key. (For the purpose of this thesis the mission requirements,
in terms of flight time, carry greater weight than the DoD-imposed size constraints on
the MAV). Along the same line, it is important that the design of the MAV results in
a vehicle that is easily packaged for deployment and whose deployment is automated.
Weight
The weight of any aerial vehicle is a major concern in its design. For our mission and
design however, the weight of the MAV carries even greater penalty, for two reasons.
1. The heavier the vehicle structure the shorter its surveillance time will be; because less battery weight can be carried, implying less endurance for the aircraft.
2. The number of vehicles that can be carried by the carrier vehicles depends on
the size and the weight of the MAVs, and will affect the aggregate endurance
time of the carrier and the surveillance information gained from the MAVs.
Payload
The weight and physical size of the payload, affect all aspects of the model. Therefore
the payload weight and size is factored into the optimization, and its effects can be
seen in both the drag and weight calculations.
3.3.4
MAV Performance Requirements
We now discuss a number of requirements conducive to a valuable mission. Although
a design may be found so that the MAV can fly to obtain surveillance information, it
is rendered moot if the MAV is unable to reach the area of interest. Therefore, the
performance requirements listed below are set in tandem with mission requirements:
1. Deployment: the MAV must be able to start autonomously and stabilize itself
after being dropped from a particular height.
41
2. Cruise Distance: the MAV must be able to fly a predetermined distance from
the drop point to the area of interest, and after performing surveillance, fly to
some area of its "death".
3. Loiter or Hover Flight: the MAV must be able to fly at a speed that ensures
quality surveillance information for a specified mission duration.
4. Climb: the MAV must have enough energy to be able to climb a certain distance.
3.4
3.4.1
Current MAVs & QFD Analysis
Current MAVs
There are a number of vehicles potentially suitable for the mission described above.
Each vehicle uses a different propulsion method, having its own advantages and disadvantages.
For the purpose of this study, four different flight vehicles will be analyzed:
e Rotorcraft Vehicles
" Fixed Wing Vehicles
" Ducted-Fan MAVs
" Parafoil Vehicles
In order to determine which of the designs would be best to further research, a Quality
Functional Deployment (QFD) matrix was used.
3.4.2
QFD Analysis
A QFD is a tool that works to translate customer needs into vehicle requirements
and enables the designer to prioritize requirements (especially for conflicting requirements). It also helps eliminate human biases in choosing one method over another.
42
As such, the QFD is an invaluable tool in selecting the MAVs that are worth further
investigation for the PCUAV system.
"A QFD is a graphical technique that translates customer needs into parameters or
attributes of the product and its manufacturing and quality control processes [4]."
In general a QFD matrix is set-up as in Figure 3-2.
Correlation Matrix
Tecnical Requirements
"Hows"
Customer
Needs
Relationship Matrix
o
"Whats"
Determines technical requirements
priorities using need importance
weightings
rjQ
Technical Requirement Priorities
Quantifications of Technical Requirements
"How much?"
Benchmarking: Assesment of engineering
competitive capabilities
Technical or regulated constraints/
considerations
Figure 3-2: QFD Diagram [4]
Not all the functions of the QFD are needed for our research; and so we will use only
the relevant areas of the QFD to determine which vehicles are best studied for our
43
research. The QFD allows a direct comparison of the different elements within the
design, so it is necessary to first determine which components of an MAV are critical
to the success of the mission, and then use this information to evaluate each MAV
design option. The QFD requirements comprising the main technical specifications
and customer needs are listed below.
Technical Requirements
" Engine Autonomous Start: Since the MAV will be dropped from a carrier vehicle, it must be capable of autonomous start-up.
" Auto-control/Onboard Navigation: For the mission defined, the MAV must be
able to self-navigate with an onboard navigation system for autonomous control
and obstacle avoidance.
" Range: Vehicle efficiency is necessary for longer flight times, and ingress/egress
distances.
" Surveillance Flight Speed: The MAV must be able to fly at a speed that facilitates image gathering.
" Carrier UAV Deployment: The MAV must be deployable from carrier vehicles.
" Sensors: Multiple sensors are necessary to fly autonomously and negotiate obstacles.
" Multi-tasking: MAVs should be capable of obtaining surveillance information
and act as communication nodes as well.
" Small-Scale System: All onboard systems must be on the micro scale, so that
they can be packaged within the small MAV.
" Payload (MAV size to Payload weight ratio): The MAV must be capable of
carrying an effective surveillance payload.
" Light- Weight Structure: For maximum efficiency the vehicle structure must be
light weight.
44
"
Number of Vehicles Deployed: The greater the number of deployable vehicles,
the more surveillance information obtainable.
" Instrument Calibration: The MAV must be capable of auto-calibration once
deployed from the carrier vehicle.
Customer Needs
Significant Capability Gain
" Reliability: MAVs must satisfy some required level of probability of mission
success.
" Durability: The mission requires that the MAVs be deployable from a
carrier vehicle and capable of subsequent flight.
" Surveillance (loiter or hover) time: The minimum duration for a surveillance mission is specified as 30 minutes.
" Autonomous Obstacle Avoidance: The MAV must be able to negotiate
obstacles in cluttered environments.
" Low Altitude Flight (under canopy): To obtain close-up information it is
necessary that the MAVs be capable of flying under tree canopies and/or
around buildings.
" Stealth: As the MAV will often be flying in hostile environments, it must
travel undetected.
" Adverse weather and day-night capabilities: The MAV must function in all
weather conditions in both daylight and darkness.
Goals
* Fast Response Time: The mission definition (e.g., obstacle avoidance) dictates that the MAV have a fast maneuver response time.
" Multiple Scenario Capability: The MAV must be deployable from airborne
and ground carrier vehicles, the former being our primary mode of interest.
45
Communication Links: The MAV must serve as a communication node or
9
link to relay information collected during a mission.
The technical requirements and customer needs can be seen in Figure 3-3 with their
corresponding weights.
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a)
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70
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Figure 3-3: Initial QFD Definition
3.4.3
QFD Results
From the QFD matrix, we review the top six factors that affect the choice of MAV.
These factors, previously defined, and their respective scores, can be seen in Table 3.1.
The higher the score for each factor, the more important that requirement becomes for
the vehicle, and as such is given greater weighting when deciding which final vehicle
46
to study.
Factor
Score
Range Distance
270
Surveillance Time
270
Ease of Control
237
Engine Autonomous start
210
Carrier Deployment
180
Payload Weight Fraction
174
Table 3.1: Hierarchy of Requirements Affecting MAV Choice
Each vehicle is then given a score in terms of the ease of achieving each of the above
mentioned factors, with 1 being the easiest and 10 being the most difficult. From the
values obtained, the vehicle design with the fewest points becomes the most desirable.
A summary of these points is shown in Table 3.2.
The following summarizes the rationale behind the empirical scores given to the different vehicles for each factor, with their respective score in brackets after the description.
Engine Autonomous Start
" Rotor-craft: Electric motors can be used, however, there is a greater chance
of failure since there are more motors (3)
" Ducted Fan: One electric motor can be used (2)
" Fixed Wing: One electric motor can be used (2)
" Parafoil: No need for a motor (1)
Flight Range (minimum 3000m)
e Rotor-craft: Small size tough to get a relatively long flight range (3)
47
"
Ducted Fan: Low with current designs available (5)
" Fixed Wing: Easy to get forward flight range (1)
" Parafoil: Dependent on external factors (8)
Surveillance Capability (minimum 30 minutes)
" Rotor-craft: Built to hover (1)
" Ducted Fan: With current designs available (5)
" Fixed Wing: Not able to hover but able to fly slowly (6)
* Parafoil: Not able to actually hover in one place but can deploy many, to
"fake" a sustained presence in one area (8)
Ease of Control
" Rotor-craft: Relatively easy to control, once deployed (3)
" Ducted Fan: Relatively hard to control, once deployed (6)
" Fixed Wing: Easy to control once deployed (1)
" Parafoil: Very dependent on external factors (9)
Carrier Deployment (Storage and Deployment)
" Rotor-craft: If mounted outside affects carrier performance, may not be
practical to mount inside of carrier (storage for 2-4 vehicles) (5)
" Ducted Fan: If mounted outside affects carrier performance, may not be
practical to mount inside of carrier (storage for 2-4 vehicles) (6)
" Fixed Wing: Relatively easy to store (inside) and deploy (3)
" Parafoil: Easy to store and deploy (1)
Payload Weight Fraction
* Rotor-craft: larger vehicle able to carry mid-sized payload (4)
48
"
Ducted Fan: larger vehicle probably able to carry smaller payload (6)
" Fixed Wing: small vehicle, small payload (2)
" Parafoil: small payload (2)
Cost/Complexity
" Rotor-craft: Off-the-shelf model could be used and modified (4)
" Ducted Fan: New design necessary (8)
" Fixed Wing: Off-the-shelf model could be used and modified (2)
* Parafoil: Off-the-shelf model could be used and modified (1)
Factor/Vehicle
Rotorcraft
Ducted Fan
Fixed Wing
Parafoil
Autonomous start
3
2
2
1
Range Distance
3
5
1
8
Surveillance Time
1
5
8
8
Ease of Control
3
6
1
9
Carrier Deployment
5
6
3
3
Payload Weight Fraction
4
6
2
2
Cost
4
8
2
1
SCORE
23
38
19
32
Table 3.2: Factors Affecting MAVs
From the results (Table 3.2) we see that the fixed wing and the rotor-craft MAVs
seem to be the most likely vehicle designs for further investigation.
After further
investigation a quad-rotor design was chosen over a helicopter or other rotor-craft
designs, for it was determined that the quad-rotor was easier to package and control
than other rotor-craft designs.
The fixed wing vehicle and the quadrotor will be
discussed in further detail in later chapters.
49
50
Chapter 4
Optimization Model Design
4.1
Chapter Overview
In this chapter we form the basic framework which will be used for the optimization.
We describe the constraints, variables and parameters that affect both vehicles and
study the commonalities between the two chosen MAV designs.
4.2
Problem Definition & Objectives
As we have seen in previous chapters the main goal of the PCUAV system is to obtain
detailed information from a distance. Using MAVs it is possible to get very close from
a distance, since the MAVs are able to fly at low altitudes, under tree canopies and in
cluttered environments. The mission definition therefore requires that we minimize
the size and/or weight of the MAV.
Objective: Minimize Weight and Size to satisfy mission constraints
In order to achieve this objective, a detailed mission definition, design variables,
constraints and parameters were chosen. These will be described in more detail in
the following sections.
51
Mission Definitions
4.3
Since the two vehicles chosen for the study are fundamentally different (i.e., one is
based on hover flight and the other on forward flight) it is necessary that some sort
of base mission be designed for both vehicles so that they may later be compared.
As mentioned previously, it was decided that the mission should be separated into
four different flight phases:
1. Phase 1: Drop from the carrier vehicle, autonomous start-up for transition
between free-fall and forward flight.
2. Phase 2: Forward flight to the area of interest.
3. Phase 3: Surveillance of the area of interest.
4. Phase 4: Forward flight to area of 'death'.
4.3.1
Fixed Wing Mission
For the purpose of this thesis, Phase 1 will not be looked at in great detail. However,
deployment ideas will be discussed at a general level.
Phase 1
Deployment from a larger carrier UAV necessitates a low weight solution with autonomous start up capabilities.
The carrier volume is a stringent constraint for
packaging of the MAV. The fixed wing will be designed as a flying wing, and so
deployment from the carrier UAV can take advantage of its gliding ability until its
motor is started.
Phase 2
In this phase, the fixed wing must fly horizontally and also be able to climb a minimum set distance. This ingress/egress capability will be parameterized via a distance
52
constraint. A climb margin will be built into the flight performance of the vehicle to
simulate a climb portion of the distance.
Phase 3
This phase is more complicated for the fixed wing MAV than for the quadrotor MAV,
since a flying wing cannot hover. To overcome this, the fixed wing is constrained to
follow a loiter parameter with a specific loitering radius. By doing this we are able to
achieve hover like conditions where the fixed wing can circle over the area of interest,
at a slower velocity. This provides a larger area of surveillance than a hovering vehicle
but still provides detailed information about one particular point. One facet of the
fixed wing study will be to determine the effect on the vehicle design as the loiter
radius is decreased, and therefore increasing the maneuver requirements.
Phase 4
Since the MAV may be working in military situations, where one would not want to
leave trace of the MAVs, it is necessary that the MAV has enough energy to leave the
area before it 'dies'. This distance is included in the same constraint as the phase 2
distance parameter.
4.3.2
Quadrotor Mission
Phase 1
Unlike the fixed wing, the quadrotor does not lend itself readily to being deployed
from a carrier vehicle. Some methods to overcome this are as follows:
" Parachute deployment until the quadrotor lands on the ground in the correct
orientation where it can then take off.
" Adding a lifting body into the design of the quadrotor to enable the vehicle to
be able to glide to the area of interest, similar to how the fixed wing would.
53
"
Have the quadrotor auto-rotate while being dropped until it is able to continue
the other phases of the mission.
" Have a foldable vehicle framework for compactness that allows for easy deployment.
Phases 2 and 4
Compared to the fixed wing MAV these phases of the mission are harder for the
quadrotor as its main design intent is to be able to hover. Typically the quadrotor
will expend more energy in forward flight than a fixed wing vehicle. These phases are
defined using the same mission constraints as for the fixed wing vehicle for ingress
and egress.
Phase 3
Loiter is still defined by the time of flight parameter, however loiter velocity and
maneuvering radius lose their meaning with the quadrotor since the MAV has the
capability to hover.
4.4
Module Definition
Before delving into the design theory and implementation of the model it is necessary
to divide the design into smaller separate modules.
These modules represent the
multi-disciplinary aspects of the optimization, and the links between each discipline
within the design of the MAV.
The following modules were determined necessary to fully define the basic model.
Aerodynamics - Vehicle Weight - Propulsion - Motor - Battery
These modules are further defined below, and more detail about the theory behind
each module, for both the fixed wing and the quadrotor, can be found in the fol54
lowing chapters. The ultimate goal of the optimization is to calculate the two main
performance variables, namely, the system weight and required mission energy. We
do this by varying the geometry of the vehicle, and selecting the required battery
size/capacity while meeting constraints set in areas such as endurance and range.
4.4.1
Aerodynamics
The primary use of this module is to calculate the power required for each segment
of the mission.
This module contains all the main aerodynamic calculations and
calculates the L/D efficiency of the fixed wing, and the figure of merit calculations
for the quadrotor system.
4.4.2
Weight
Weight directly influences the endurance of the MAV, so weight estimates are produced for all major vehicle components.
" Structural Weight: Considers the basic structure and fabrication of the MAV,
and varies during the optimization depending on vehicle geometry.
" Battery Weight: Is directly related to the energy and power requirements for
each mission segment, coupled with the calculated energy density of the battery.
" Propulsion Weight: Accounts for the motor weight and its dependency on the
required mission segment power. Motor weight relations are taken from information describing a substantial group of RC-class electric motors.
" Payload Weight: The payload weight is used as a mission constraint, and is
set by requirements of an anticipated mission. The payload weight consists of
both the avionics/controls weight and the payload weight (i.e. the surveillance
package, a camera). For the nominal mission the payload weight was chosen at
a value of 60g, which is a consistent value based on prior MAV programs [7] [5].
55
4.4.3
Propulsion
This module directly links into the aerodynamic calculations to determine the power
required for each mission segment, and feeds this information into the motor module.
4.4.4
Motor
At this stage the model assumes a constant propulsive efficiency demonstrated by
typical RC motors. The primary output of this module is the power required by the
motor, which links to the battery module. For both the fixed wing and the quadrotor
MAVs we use the following equation, that reasonably describes the weight of small
scale RC motors:
Motor Weight
Where Wt,
=
Wt, + K * Power
=
(4.1)
14 g and K = 0.5 g/W [1].
The motor weight is scaled with the required power. A linear relationship with power
(using a fixed motor weight/power) has been to shown to describe small scale RC
motors. Specific values for the equation were generated from [1].
4.4.5
Battery
Choosing the appropriate battery is key to the endurance of the MAV. In this module
we calculate the energy density of the battery.
The energy density calculation is based on performance charts of specific power versus
energy density for a variety of battery chemistries.
These charts (Figure 4-1) are
called Ragone Plots, and allow a wide variety of energy sources to be compared. The
diagonal lines in a Ragone plot have units of time so that the required weight for a
constant discharge situation can be compared for different energy storage devices [19].
Empirical formulae for 4 types of general batteries; Lithium Oxyhalide, Lithium Ion,
56
Nickel Metal Hydride or Nickel Cadmium; have been extracted from several sources
and are used to model the tradeoff between battery capacity and power requirements.
1000
400
400
A
Ni-Cd
_
Ag-Zr1
200
High tomnerature
systerns
Ni-Zn
100BO
0
60
LeadPci d
-
40-
20
-
Alkaline-
mrnaqanese
-
2n-air
Heavy dDuy
SLeclanche
04
Low-drain
1
-telance
,lithium
\ 2n-MgD
0-4-
10
100
1000
Energy Density, Wh/Kg
Figure 4-1: Ragone Plot
Since battery information is an integral part of the optimization it is separated into a
macro that is used by the optimization. The macro enables a choice of the above mentioned batteries and then solves for the energy densities, and mass densities dependent
on the battery chemistry. See Appendix A for the battery information macro.
Ragone plots show that an exponential relationship exists between the energy density
and the specific power.
General exponential expressions for the battery's energy
57
density as a function of specific power can be modelled by:
Energy Density
ED = Ale A2Specific
(4.2)
Power
Where A1 and A 2 are constants.
Energy Density
Battery Type
Lithium Oxihalide, LiO
561.15e-o.oo
22
*specific
power
Lithium Ion, Li-Ion
100e-0.0017 *specific power
Nickel Metal Hydride, NiMH
6 0 e-0.0017*specific power
Nickel Cadmium, NiCad
4 8 e-0 001
7
*specific power
Table 4.1: Battery Energy Densities
Table 4.1 shows the equations used for each battery. These equations represent average values taken from a variety of commercial sources. The important aspect of the
batteries for the optimization model is the general trade-off between the discharge
rate and the energy density of the battery. Since, as the discharge rate is increased,
the total energy that can be drawn from the battery decreases. The reason for this
is the current increase causes heating losses in the battery because of the battery's
internal resistance. As the current draw (discharge rate) from the battery increases,
more energy goes into heat. Another important aspect is the general performance differences between commercial batteries and exotic type batteries available at a greater
cost. In further studies other power sources could be included in the same module
for comparison.
4.4.6
System Structure
Now that we have a general idea of the modules that will be used we may model the
overall simulation using an N 2 diagrams.
58
N2 Diagrams
An N2 Diagram can be used to develop and organize interface information, and provides a visual representation of the flow of information through the simulation architecture.
Using an N2 matrix (Figure 4-2) we can better see that the module order is designed
so that there are no feedback loops within the module simulation suggesting that the
run-time of the optimization will be short and that the modules are well organized.
Weght
1
Motorn
Baiey
-
ou pu
Figure 4-2: N2 Diagram
System Simulation
Figure 4-3 simplifies the N 2 Diagram and shows the overall system simulation, and
how the modules follow on from one another.
An initial design, with a wing span and mission times for example, is entered into
the model, which then uses this information to calculate the weight of the entire
59
SYSTEM
SIMULATION
DESIGN
WEIGHT
AERO
PROPELLER
MOTOR
BATTERY
OBJECTIVE
TRADE
SPACE
EXPLORATION
TOOL
OPTIMIZER
Figure 4-3: System Simulation
vehicle. The vehicle weight is then used to determine the thrust and lift needed and
other variables in the aerodynamic module. These feed information into the motor
and battery modules that determine energies needed to perform a certain mission.
The entire process is then iterated to find the optimal objective. More details of this
process can be found in the following chapters.
Model Commonality
4.5
The basic structure of the model can be seen in both the the N2 diagram (Figure 4-2)
and system simulation (Figure 4-3). This basic structure is maintained for both the
fixed wing and the quadrotor vehicles. Differences in the models will be discussed
in the following chapters. The following however will be true for both optimization
models:
" Both MAVs will fulfil the same mission, specified by the same constraints and
parameters.
" The base optimization will be performed using similar variables and the objective will be to minimize the total weight and the size (rotor diameter for the
quadrotor and span for the fixed wing) of both vehicles.
" Models will share the same level of fidelity where possible.
" Models will use the same generic battery performance models and battery chemistry types.
60
* The models use identical relations between motor weight and power, as well as
the same constant motor efficiency.
4.5.1
Design Variables
Design variables common to both vehicles include the driving dimensions (i.e. the
span or the rotor diameter), the coefficients of lift, the time in loiter, the motor weight
and the battery weight, as can be seen in Table 4.2. Greater details for each model
will be described in their respective chapters.
4.5.2
Design Constants
Table 4.3 shows the constants that are common to both vehicle optimization studies.
These constants are standard or design chosen, for example, the motor efficiency.
Parameter
Symbol
Wing Span
b
Rotor Diameter
Dr
Coefficient of Lift
CL
Time in loiter
tj
Battery Weight
Wb
Motor Weight
Wm
Table 4.2: Design Variables Common to both MAV Optimizations
4.5.3
Mission Parameters and Nominal Mission
There are three parameters common to both vehicles that will be looked at during
the optimization, and a fourth parameter, the loiter radius, for the fixed wing vehicle
(Table 4.4).
For the nominal mission though, these parameters will be kept constant at:
61
Parameter
Value, SI
Symbol
1.226kg/m
p
Air density
3
rlm
0.75
Battery Types
Battype
Li-Ion, LiO, NiCad, NiMH
Viscosity of Air
p
1.8 x 10- 5m 2 /s
Gravity
g
9.81m/s 2
Motor Efficiency
Table 4.3: Design Constants Common to both MAV Optimizations
Parameter
Value Ranges
Payload Weight
[20 40 60 80 100]g
Loiter Time
[10 20 30 40 50]minutes
Loiter Radius
[5 10 15 50 100]m
Range Distance
[1000 2000 3000 4000 5000]m
Table 4.4: Parametric Mission Value Samples
PW: 60g - Loiter Time: 30 mins - Range D: 3000m - Loiter R: 10m
4.5.4
Model Analysis Approach
The optimization procedure was run a number of times for two design objectives:
1. Minimize Overall Weight: Find the minimum fixed wing MAV weight that
fulfills the mission constraints for cruise distance, loiter time, loiter radius and
payload capacity
2. Minimize Span: Find the minimum size fixed wing MAV that fulfills the mission constraints for cruise distance, loiter time, loiter radius and payload capacity
For the optimization study we chose to vary one mission constraint parameter (Table 4.4) while fixing the others to the nominal mission values, seen above. A second
62
layer of parameters, the battery type, was used to examine how the vehicles optimum design characteristics were altered as the energy density of the battery was
increased. For each run, both objectives were analyzed, minimizing rotor diameter
and minimizing the weight of the quadrotor and the fixed wing vehicles. This approach allows us to understand how each parameter affects the vehicle's overall design
in a comprehensive manner.
The optimizer was run for each objective until a convergence criteria was met, i.e.,
the optimizer reaches the maximum number of iterations or the optimizer finds a
solution that satisfies all the constraints.
63
64
Chapter 5
Fixed Wing
5.1
Chapter Overview
In this chapter we discuss the design challenges and theory involved in developing
a fixed wing model. We focus on the aerodynamic theory sufficient to capture the
dynamics and design of a fixed wing MAV. We later analyze the results of the optimization and observe trends specific to the fixed wing nominal mission.
5.2
Mission Definition
In chapter 4 we defined a general mission scenario, and now we determine the necessary specifics for a fixed wing mission. An important characteristic of our prototype
mission is the ability to hover or gain surveillance information of a specific area.
However, the fixed wing vehicle is not capable of hovering, so to "mimic" hover flight
conditions we defined a loiter velocity and radius.
Figure 5-1 shows in greater detail the defined mission. Where:
" Phase 1: deployment from the carrier vehicle.
" Phase 2: cruise flight to the area of the interest.
" Phase 3: circular flight (fixed loiter radius to mimic hover flight).
65
Deployment Phases:
Phase 1: Drop from Parent vehicle (20,000ft), autonomous startup
for transition between fall and horizontal flight at specified altitude
(200ft).
Phase 2: H orizontal flight to area of interest (cruise).
Phase3: Surveillance of area of interest (loitering/ circular flight),
preferably for a minimum of 10 minutes.
Phase4: Horizontal flight to area of "death".
I
/P
H A SE3
IV1,
PHASE 2PHS1
Figure 5-1: Mission Overview
9 Phase 4: cruise flight to the area of "death".
Design & Numerical Implementation
5.3
In this section we define the equations needed to model the flight aerodynamics and
overall design of the vehicle. We then set up the optimization model by dealing with
each of the separate module sections defined in chapter 4, and their related equations.
We first make the following assumptions to simplify the fixed wing model design and
set-up:
1. The fixed wing was modelled assuming a basic trapezoidal planform.
2. Vehicle drag characteristics were calculated using component buildup coupled
with empirical estimates of wing aerodynamics.
3. Component weight equations were determined using relational attributes that
were functions of power, energy, and geometric characteristics (see Chapter 4).
66
4. Battery performance was determined by characteristic discharge curves defined
for specific battery chemistries.
5. Low Reynolds number flight regimes (Re O(104)) and characteristics are assumed.
Initial designs for the fixed wing vehicle are determined using basic aerodynamic
principals [3]. The following sections delve into the details of the model, at the end
of each module definition the inputs and the outputs are summarized.
5.3.1
Geometry Calculations
Wing Shape Selection
Before building an optimization model it is first necessary to decide on the general
design of the MAV that the optimization will be modelled around. Two of the main
aspects of the general design are the wing and the airfoil shapes.
Torres and Mueller [16] discuss a series of experiments to asses various wing shapes
suitable for micro sized vehicles and low Reynolds number flight. The paper discusses
the merits of 4 different wing shapes at aspect ratios of 1 and 2 (Figure 5-2).
Rectangular
Zimmerman
Inverse Zimmerman
Elliptical
cs8S
ziml
zimlitiv
ell1I
zimn inv
e112
AR 1f-
AR=')
zM2/
c4s8
A112
Figure 5-2: Wing Shapes [16]
Figure 5-3 shows that the rectangular and inverse Zimmerman planforms have modestly better performance than the other AR = 1 wings [16]. Since both wings perform
67
Ia
12S
Im
Ina -
cis
-
olmZ
*
IlmzI
0:5
a o
02S
-
Q-8:50
l0
-025.
-20
a
.10
-
0
0
4p
-
Alpha (degrees)
zm
na
a (
10
Alpha (degrees)
a
ad
a.
I
-3:
Fir
4i 4
a16]
0+
-
0
Alpha (degrees)
-CEO103
0
Az
.
t?
0.0A
~~caw
I-
0
-0
4
Alh
(degees
0
1
2
an
Alpha-(degrees)
Figure 5-3: Lift and Drag Coefficients Vs. Angle of Attack for Low Aspect Ratio
Wings [161
well, we decided to use a rectangular shaped wing even though it has a larger maximum dimension than the Zimmerman type wings, since it offers simplicity in both
setting up the optimization model and building.
Geometry and Area Calculations
Now that we know the wing type we will use, we describe the geometry and area
calculations needed for the model. The Excel model (Figure 5-4) shows the module
used for these calculations.
The model uses the following equations as intermediate steps to solve for the main
objectives of minimizing the weight and span of the MAV. Some designer defined
68
Geometry and Area Calculations
Geometry
Symbol
Est. Rotor Radius
Number of rotors
Number of blades
Rr
Value
Units
b
0.0497 m
.0000
2.0000
Prop Chord Ratio
CMR
0.2000
Prop Chord
C prop
0 0099 m
ai
7.82 in
1.96 in
0 39 in
Fuselage Volume Calculation
1000.0000 kgftm 3
Paylioad mass density
paydens
Battery Volume
Payload Volume
Vbat
Vpay
0.0000 mA3
0.0001
2.71 in'3
3.66 in^3
Motor height
Mh
0.0508 m
2-00 in
Motor diameter
Motor Volume
Total Fuselage Volume
Md
Vm
Vho
0.0254 m
0.00003 m^3
0 0001 m^13
4 0000
IFuselage Lenghl -o-Offmelsr Hid
Fuselage diameter
Fuselage height
Fuselage Frontal Area
Fuselage matenal Area
1 00 in
1
1.57 in' 3
7.94 in^3
Hh
Hd
Sh
Ha
0
0
0
0
0346
1384
0009
0075
m
m
m^2
m^2
1.36
5.45
1.46
11 66
in
in
in2
in2
Weight Information
mfarea
Prop. MOl.
m/Pa
0.7500
Housin mt M/Pa
Weight of fuselage
Weight of prop
mlHe
Wfus
Wprop
2.0000 kgim^%2
0.0150 kg
0.0007 kg
15.04 g
0.74 g
Miscellaneous Weight
Wrrdsc
0.0160 kg
15.78 g
Fuselagedrag coefficert
C..D
OA00
ToW DrMg Are
D
0.0004
lq$n*2
Fuselage Drag
m^2
0.58
in^2
Figure 5-4: Geometry and Area Calculations for the Fixed Wing MAV
constants are used in these calculations and can be seen in Table 5.1.
Estimated Rotor Radius
wing span
4
bb
4
R4
(5.2)
Propeller Chord
c
=
R,.f~
(5.3)
Fuselage and motor volume calculations are determined in this section by using density relations seen below:
69
Symbol
Value
Number of Rotors
N,
1
Number of Blades
Nb
2
Prop. chord Ratio
c/R
0.2
Battery Mass density
Pbat
Battery dependent
Payload Mass Density
Ppay
Motor Height
Mh
5cm
Motor Diameter
Md
2.5cm
Fuselage Length:Diameter Ratio
Hid
4
Constant
1000kg/m
pprop
0.75kg/n
Housing. mtl. Mass/Area
pL
2kg/m
Fuselage Drag Coefficient (frontal area)
CD
Prop. mtl. Mass/Area
3
2
2
0.4
Table 5.1: Fixed Wing Geometry Related Constants
Battery Volume
Vbat
=nbat
Vpay
=
(5.4)
Pbat
Payload Volume
mpay
(5.5)
ppay
Motor Volume
M= )
Vm
M_
(5.6)
The total volume is given by:
Total Fuselage Volume
VhO
=
Vay + Vm+
Vat
(5.7)
From the total fuselage volume, geometries are determined using a cylindrical relationship (assuming a length:diameter ratio,
70
Hid).
StuciuralaiighCiiasiieso
st*Uralw margn=
mincapthiciae
mm sid thickness
DalletionAnge Ragsfre
load
=
aree=
aspectratio
OM%
lbs
7.824
3447
3.447
in
strueelipral
choeaenetsee.1
in
Deflection=
Rtinithickness=
Capstrem =
32 775g"e
I*"ays
[I70
in
benes"Y
0
O d"g
lbs
Roo bandigmomnent=
Capload=
Required
Capaam
RequiredCapnifh =
Capthickness=
ShearloadShear ama=
Reqthckness=
SkmtMckness=
0017in
CW111,115114-
CapM/vTotalm=
SkinWrotalt
12.434in-b
24.0
lb
Nonnawired
43.120
83398
0.(S ir52
0.02410
=
3.179 lbs
in-2
D.0fXB1 in
O.KE2
0O070 in
1.87%
Edmanted
Fuam
Foamvolumne=
.347 in
sn
=
Volume
kgin3
Esmarted Sln Fabric
0 31B7
9083
JOB
5.M.
RE9
109ire3
Cap
i
0.577
W03
001740m^2
2t.9m inW2
2270
0517 in
346034psi
03278 kg/me0 024E kgWO3
24.581W"
DAU
in
6.
6.W
Is Mi
shaotloe$s
019%
Esiti.aled SparCap
Dallectenlamdarsq=
a
medduu
do
cab spar uirsy
esp
in
0(335
SkinWotalW =
1.112%
0.377
Toel Perceraage
-
492%
ill
3
,AN kg
1.24%
Figure 5-5: Structural Calculations for the Fixed Wing MAV
Puselage Diameter
1
4
H
3
i
Cr
(5.8)
Fuselage Length
HI = HdHId
(5.9)
Fuselage FrontalArea
2
Hd
2
(5.10)
Fuselage Material Area
Ha
=
lrHdH
(5.11)
Now that we have the geometries and areas we use this information to model the
weight and structure of the vehicle. We ensure that the weight is properly scaled with
geometry and structural constraints. The next section describes the development of
the structures module (Figure 5-5) also seen in Appendix B.
71
Value
Constant
15%
Thickness: Chord
Minimum Cap Thickness
0.02 in
Minimum Skin Thickness
2 layers (0.0037 in)
9
10
Ievel
Required Deflection Angle
0.1 degrees
15 Msi
Cap Modulus
10000psi
Design Shear Stress
Carbon Spar Density
2000kg/m
3
Skin Density
1500kg/m
3
Foam Density
35.24kg/n
3
Table 5.2: Fixed Wing Structural Weight Constants
Structural Calculations
Based on a spar sizing procedure (Appendix C) developed by Drela
[6] we are able
to reasonably predict the size of the spar needed, the amount of foam and skin fabric
used in the wing. The following section outlines some of the equations and constants
determined by the designer (Table 5.2).
The load on the wing is determined by the weight of the vehicle and a g level margin,
Stevel:
Load
L
= gieve, .W
(5.12)
Figures 5-6 shows the geometry used in the calculation of the deflection angle, <5
on the wing generated by the lift load and determines the maximum allowable wing
deflection for structural reasons [6].
The wing structure design is based on a simple spar cap construction (Figure 5-7)
and the equations required for sizing the spar are as follows:
72
y
b/2
Figure 5-6: Deflections
The maximum deflection,
Adef,
on the wing is constrained by the deflection angle
that the wing sees during loading, and results in a conservative estimate of the wing's
deflection, y.
.4-5* WovEN
(No-r
W41- DIIE tr 0 rA L
eAescN "sMP/~s
4eTuh. AM-OIL)
Figure 5-7: Fixed Wing MAV- Wing Structure [2]
Required Deflection
tan#
Adef.
(5.13)
2
Deflection
b
Y
=
Adef
tr
=
-Croot
(5.14)
Root Thickness
t
(5.15)
Cap Stress
4 - cap modulus -t
ocap
b
73
Adef
(5.16)
Root Bending Moment
Mb =
Lb
4
(5.17)
Cap Load
Mb
Leap
(5.18)
tr
L -b
4tr
(5.19)
Required Cap Area
Lcap
(5.20)
9cap
The necessary required cap width is limited to a maximum of 20% of the root chord
and is used to calculate the cap thickness.
Cap Thickness
A
teap
=
cap
(5.21)
ceap
The cap volume and weight are calculated from the geometry determined in the
structural calculations.
Cap Volume
Vcap
2
- Acap - b
(5.22)
Vcap pcarbon spar
(5.23)
=
Cap Weight
Wcap
=
The skin weight was determined by a minimum gauge limitation of two layers of
fabric. The wetted area of the wing is used to calculate the wing skin weight.
Skin Weight
Wskin
=
2.2 - Warea
74
- rskin - Pskin
(5.24)
The foam weight is estimated from the internal volume of the wing, using the airfoil
cross-sectional area, Afoi:
Foam Volume
(5.25)
-b
Af 0
Vfoam
q-t-c-b
=
t
- - -c
=
2
C
(5.26)
-b
(5.27)
Where q is approximately 0.65 for most airfoils [3].
Foam Weight
Wfoam
5.3.2
Vfoampfoam
=
(5.28)
Weight Calculations
The total weight section is split up into five separate sections:
Payload, Battery and Motor Weight are discussed in chapter 4 as they share the
same characteristics and values for both the fixed wing and the quadrotor vehicles.
Miscellaneous Weight The miscellaneous weight section is calculated in the "Geometry and Area" worksheet (Figure 5-4) and takes into account the estimated weight
of the fuselage and the weight of the propeller. The calculations are based on the
wetted skin area of the fuselage and the propeller.
Fuselage Weight
W5us
Ha Pfuse
2
(5.29)
m2
(5.30)
Propeller Weight
Aprop skin - pprop
Wprop
=
N
A.
Nb- (Rr Cr) - Pprop kg I
-I
75
(5.31)
(5.32)
and therefore the total miscellaneous weight is given by:
Miscellaneous Weight
Wmisc
=
Wprop + Wfus
(5.33)
Structures Weight The structures weight was separated into three main components, spar cap weight, skin fabric weight and the foam weight. Material densities
and load analysis was used to estimate the weights of each component as a function
of vehicle dimensions examples of the equations used are shown in Equations 5.23,
5.28, 5.24.
Summary of Weight Inputs and Outputs
Inputs: b, Pmotor, Pbat, Ppay
Output: Weight
5.3.3
Aerodynamic Calculations
MAVs operate in low Reynolds Number (20,000 to 100,000) over their entire flight
envelope (Figure 5-8). The flow over airfoils in this regime is difficult to model (e.g.
effects such as hysteresis stall due to laminar separation bubbles). In practice it is
possible to conservatively account for the effects of low Reynolds number by assuming
large parasitic drags, modest maximum lift coefficients, and additional terms for
induced and body/fuselage drag [151.
The maximum coefficient of lift was chosen
from an average performing airfoil section at Reynolds Number 80,000 and was set
at 1 [18].
Max. Coefficient of Lift, CLmax = 1
76
Figure 5-8: Reynolds Numbers for a Range of Vehicle Sizes
[201
Since the MAV tends to fly at a near stall velocity due to its high parasitic drag, the
minimum velocity is set using the stall speed multiplied by a safety factor of margin
(typical of takeoff requirements).
Vmin = 1.2 V8Wn
The optimization model makes the assumption that the fixed wing MAV is maneuvering for the entire loiter section of the mission, and so provides us with a conservative
estimate of mission time. Maneuvering is taken into account using a load factor,
which is calculated from the required loiter radius (see Figure 5-9).
Load Factor
n
=
+
--- 2
(gR)
(5.34)
Drag Calculations and Assumptions
Drag relations are calculated from basic empirical relations based on geometry and
Reynolds Numbers [17]. The drag coefficient is composed of profile and induced drag
contributions.
77
Profile Drag Coefficient
Cdo
=
Cdfuse + {Co + Cd(Re)}wing
(5.35)
Cruise Drag Coefficient
= 0Cao
d
+ kCL
C
(5.36)
Oswald Efficiency
e = 0.9{1.78(1 - 0.045ARO-68) - 0.64}
(5.37)
Induced Drag Factor
k = 0.007 +
1
7reAR
(5.38)
Reynolds Number
Re
pCV
p
(5.39)
The total drag area of the fuselage is calculated using the fuselage frontal area and a
constant
CD
as follows:
Fuselage Drag Coefficient
CD -
CD fuse
Sf
(5.40)
wing
Lift Over Drag
L
D
=CL
(5.41)
CD
These equations were used for both loiter and cruise flight conditions.
Velocities
The cruise and loiter velocities are calculated below:
Cruise Velocity
2W
"c VC pC,, A =A(5.42)
Maneuvering Velocity
Vm
2nW
=
CW
pCL,A
78
(5.43)
Summary of Aerodynamic Inputs and Outputs
Inputs: CL, n, k,
Cds
Outputs: CD, L/D, Cruise and Loiter Velocities
5.3.4
Force Calculations
From the free body diagram we can see that the loiter radius can be found in the
following way:
R
Figure 5-9: Free Body Diagram -Loiter Radius
Loiter Radius
V2
g
n2 -1
(5.44)
Bank Angle
= =1 -
Cos<p
n
(5.45)
Cruise Drag
W
_
(5.46)
Loiter Drag
D,
=
79
nW
(5.47)
Summary of Force Inputs and Outputs
Inputs: n, Vc, V 1, 7
Outputs: Cruise and Loiter Drags
5.3.5
Propulsion Calculations
The climb angle was set at, y = 15 degrees. This is used throughout the cruise part
of flight. By assuming that the MAV is constantly climbing, we obtain a conservative
estimate of the energy actually needed for the mission.
Cruise Climb Angle
CCR
=
Vsiny
(5.48)
LCR
=
Visin-y
(5.49)
Loiter Climb Rate
In order to be able to determine the total energy that the battery needs, the amount
of power needed for the propeller in loiter and cruise flight conditions must first be
calculated. The cruise drag component deals with steady cruise flight and the loiter
flight component compensates for a climb margin. We find these two powers in the
following way.
Cruise Propeller Power
=
DcVc + W - Vimb
The propeller power needed for loiter is given by a similar equation.
80
(5.50)
Summary of Propulsion Inputs and Outputs
Inputs: D, Vc, V 1 , 7
Outputs: Cruise and Loiter Propeller Powers
5.3.6
Motor Calculations
We use the propeller power to calculate the power needed by the motor.
This is
determined by assuming an efficiency for the motor of 75%.
Cruise Motor Power
PPC
PMC
77M
(5.51)
From motor power values we can then find the power densities that are then used
to find the final endurance of the fixed wing MAV, for both cruise and loiter flight
segments.
Cruise Power Density
P
Peruisepower
BW
(5.52)
The motor power and motor power density for loiter flight conditions are given by
similar equations to 5.51 and 5.52 respectively.
Summary of Motor Inputs and Outputs
Inputs: Pc, Pz, r/m
Outputs: Cruise and Loiter Motor Powers and Cruise Battery Density
81
5.3.7
Energy Calculations
With all the calculations previously detailed, we can find the total energy necessary
for cruise and loiter flight conditions by using the following equations.
Cruise Energy
Ec = Pc te
(5.53)
Loiter Energy
=
El
P
(5.54)
tj
Which yields the total energy necessary for both flight conditions:
Total Energy
= Ec + El
Etotai
(5.55)
and the average power density given by:
Average Power Density
Etotai 60
Ppower
total
ttotal
-
BW
BW
(5.56)
Which is then used by the battery module to compute the battery energy density and
therefore the battery weight.
Energy Density
Penergy
=
f
Pdens}
(5.57)
Battery Weight
Wbat
penergy -Etotai
Summary of Energy Inputs and Outputs
Inputs: t, Pc, P,
Outputs: Battery Weight
82
(5.58)
Overall Model Summary
5.3.8
Figure 5-10 shows the main Excel optimization sheet that was used. Figures 5-4
and 5-5 show the secondary sheets discussed previously. Details of these sheets can
be seen in Appendix B.
FiinsmfgValhiMSkis
Verlees Costariln
inmihn-asnrs
W5Vit khFUNMem
~~i
CnstraltMS
PW
WeOWh
Payload
controls
PropulsionWeight
Structural Weight
Empty Welght
-111
1yetaIM*Vmini
MotorEflency
Propeereinciency
Net Efficiency
PW
SW
EW
staDit
na
eta
:,undts
k
0.1994
0.0142
0.0300
0.294
........
60.00
inits
17291 9
25.47
15.78
199.38
141 g
29.97
299.2 a
kg
kg
kg
90
g
5.40
5.23
356
c
Wing loading
W_8
1574 kg~n^2
rine
Msawmi tC00esit
C#maQ
Coinclent ofdrag(Cruise) Code
Coefficient of drag (loiter) Cdt
Prolie drag coeflictent
induced dragfactor
su5
4
Cdo
K
as
ro
4.514 MIS
07
1 .22
1.08
64.31
L/D-dopt =
LID_popt=
5379
CL-dopt=
CL popt=
0571
LID crutSa=
LUDLoiter=
Aspect ratio=
oswald=
Reynolds#
0.1452
0.1887
0.0531
01828
-ywitit
Equal
Z.026
4i658
0.909
5.181
4.837
2.270
0.900
104703
min
Ma. 1.00E-01
IO
1.00E5
1.00E.0
9d
17.23 deg
9.99degis
0.5480 N
0.5949 N
Dc
Di
Powers
Propeller power (cruise)
Ppl
17,207 W
17.121 W
Motor power (cruise)
Port
22.B28 W
PowerDensityforcruise
Power Density forloiter
Pml/OW
132.69 WYOM|
132.02 Wilkg
Enor
Energyforcruise
EnergytOr loter
Energytoatal
AweragePower density
Ec
El
Etot
afeiyType Name
Batterymas
energy density
Total batteryenergy
Barrype
mens
Ede ns
Ebet
NIMH
3900.00 kg/m^3
71.00 W/Kg
12.432 Wh
Timein Cruise
te
1597 seet
1800.00 sec
Propeller power(loiter)
MAior
Motor power (loiter)
Battey
adensity
Time In Loiter
Cruise Range
,
o
1.0470
Farces
Cruise Drag
LoerDrag
g
^n2
kNA3
100.00 m
Loiter Radius =
Load factor (n)
Bank Angle
Turn Rate =
0.5625
00-*03.kg
0 088 m
Denity ofair
4
tfter)=
Weighto
nig spar
Wing Chord
Aerentss
19.78 trIS
1744 rn/s
16.29 rn/c
168
am MIs
2.49
0.78
VlC
Vt
Vcstai
Vcloitsr
Climb aor e=
Cmb rate (rtse)
Clmb rate
7.924 In
-
Vutecmia
CriseVloioety
Loiter Velocity
1Sta;Veocitycruise
SUa1Velocity loiter
VCVStall
V-Vitall
V1ba-Vt-tai
Totaikein
te
Ppc
III
ier
1.018W91
11.414 Wh
12.432 Wh
132.076 Wl(g
icIe
Etatdi
2.66 min
30.00 min
3000 m
9.94 bat"s
30
S7d1
Figure 5-10: Fixed Wing MAV (Main Worksheet)
The model may be expressed using a block diagram seen in Figure 5-11.
This block diagram provides details of each of the variables and how they are used
as inputs and outputs of each module.
83
D,
i,V, T
Figure 5-11: Fixed Wing Model Block Diagram
5.4
Optimization Study-Results & Analysis
The reader will recall from Chapter 4 that two objectives were studied. The following
sections outline our results from the optimization runs.
5.4.1
Nominal Vehicle Designs
Table 5.3 shows the weights and spans for nominal vehicles of differing battery type,
that are capable of 30 minutes of loiter flight, a loiter radius of 10m, 3000m of
egress/ingress flight, and able to carry a 60g payload.
As can be seen from Table 5.3 for the nominal mission, the smallest size vehicle, with
a LiO battery, has a wing span of 24cm, and a weight of 230g. We find that as we
decrease the battery performance the vehicle size and weight increases greatly. In fact
we see that the solver is unable to find a solution for the nominal mission with the
NiCad battery. For missions that are close to the nominal mission i.e for a payload of
56g (instead of 60g) or a loiter radius of 11m (instead of 10m), the optimizer is able
to find a solution, however the solutions close to the nominal mission are extremely
84
Objective
Minimum Span
Minimum Weight
Battery Type
Span, m
Weight, kg
Span, m
Weight, kg
LiO
0.24
0.23
0.35
0.15
NiMH
0.46
0.31
0.52
0.26
NiCad
no soln.
no soln.
no soln.
no soln.
Table 5.3: Nominal Vehicle Sizes
sensitive and a large vehicle geometry results. The designer therefore has to make the
necessary tradeoffs between cost (for the batteries) and the size of the vehicle. This
will be discussed further in Chapter 7.
5.4.2
Weight Trends for Nominal Missions
From Figure 5-12 we see that the weight distributions for each of the objectives vary
greatly. In the upcoming sections we will make observations about both objectives
separately. Since a vehicle solution could not be found for the NiCad nominal mission,
the nominal mission is set at a slightly lower loiter time of 29 minutes.
Minimum Weight Objective:
Varying the battery type (i.e. the energy density) reveals some interesting trends in
the weight distribution. We see that with high specific energy batteries the payload
accounts for most of the total weight, followed by the empty weight of the vehicle.
As the specific energy of the battery becomes lower we see that the payload weight
increases to nearly 40% of the total, while the payload weight fraction decreases to
approximately 20%. The rise in battery weight accounts for the decrease in percentage
for the payload weight, while the empty weight remains fixed.
Summary: There is a direct trade-off between battery weight fraction and the payload
capacity.
85
Weight Distributions Comparison
for Objective Scenario and Battery Types
100% 90%
80%
U)
C
0
70%
60%
0 Payload Weight
50%
N Motor Weight
40%
E Battery
3 Empty Weight
.8;
Weight
30%
20%
10%
UO
NiMH
NiCad
LiO
NiMH
NiCad
Min b
Min Wt
Battery Types and Objectives
Figure 5-12: Normalized Weight Distribution Comparison for the Nominal Mission
Minimum Span Objective:
The driving variable in the minimizing weight objective was the battery weight, we
see this trend also in the minimizing span objective but to a lesser extent. Again,
the empty weight percentage remains almost constant and the percentages that are
most affected are the payload weight and the battery weight. Since minimizing the
weight is not the main objective, we see that the battery weight naturally takes up
a greater percentage of the overall weight, but the optimizer reduces the span. We
observe that for both objectives for the NiCad battery that the optimizer solves for
one vehicle geometry as it becomes over constrained by the mission parameters.
Summary: By minimizing the span you pay a penalty in the payload capacity.
86
Payload Weight Study
We can see from Figure 5-13 that as the payload increases the wing span increases
in a quasi-linear fashion. We see the same trend with the MAV weight (Figure 5-14),
however, this trend is less linear and seems more pronounced than for the wing span
objective. The reason for this is the cost penalty associated with adding payload and
how the battery and motor weight determine the weight of the vehicle.
Figure 5-13: Wing Span Vs. Payload Weight, Nominal Mission
Summary: The solution to vehicle geometry and weight increase with requiredpayload.
As the battery performance decreases the sensitivity of the vehicle geometry to payload
weight increases.
87
MAV Weight Vs. Payload Weight
0.7
-
-
-
-
--
-
-____
--
___
-
-
- ___ -
--__
__
0.6
0.5
UO-Min b
-+-
-a--UO-Min Wt
0.4
NiMh- Min b
NIMH-Min Wt
10.3
-
NiCad-Min b
~-~NiCad-Min Wt
0.2
0.1
0
0
20
40
60
Payload (g)
80
100
120
Figure 5-14: MAV Weight Vs. Payload, Nominal Missions
Loiter Time
As the loiter time is increased we see the wing span and MAV weight increase (Figures 5-15 and 5-16). As the battery characteristics become poorer, i.e. the discharge
rate is higher and the specific energy lower, we see a non-linear increase in the weight
and the span. Using NiCad and NiMH batteries the maximum mission loiter time for
the vehicles was 29 minutes and 45 minutes respectively. This further demonstrates
the vehicle design sensitivity to battery performance.
Summary: The non-linearity comes from the battery discharge characteristicsand the
feedback of the energy requirements depending on the weight of the vehicle, and so the
poorer the battery density the greater the non-linearity.
88
Wing Span Vs. Loiter Time
0.9
0.8
0.7
-0~~-~~~~~~-~~~~~
0.6
+- UO-Min Wt
iUO-Min b
0.5
NiMH-Min wt
NiMH- Min b
0.4
*Nia-n
0.2
0.1
0
0
10
20
40
30
50
60
Loiter Time (mins)
Figure 5-15: Wing Span Vs. Loiter Time, Nominal Mission
Figure 5-16: MAV Weight Vs. Loiter Time, Nominal Missions
89
Wt,
Loiter Radius
We see in Figures 5-17 and 5-18 that as the loiter radius becomes tighter, the mission
becomes harder to fulfill. With the NiCad and NiMH the solver can not even find a
solution for a 10m or 5m loiter radius respectively. We know that the wing span has
a large role to play in the maneuvering ability of the fixed wing vehicle, and we see
(Figure 5-17) that there is a large variation in the wing span from a 5m - 20m loiter
radii. As the radius increases from 20m on, we see that the wing span almost remains
constant. The penalty that is paid in size to be able to "mimic" hovering capability
will be discussed further in chapter
7. We also observe, Figure 5-18 that for the
minimizing span objective there is a minimum weight that occurs at a loiter radius
of approximately 15m, after this "dip" the weight increases over the loiter radius
range, this increasing trend, will plateau as the loiter radius becomes less crucial to
the mission. We see the increase in weight since a greater penalty is paid on the size
of the MAV in the minimizing span objective than on the weight of the vehicle.
Wing Span Vs. Loiter Radius
0.8
-
-
____-___________-_____
0.7
0.6
0.5
-+-
UO-Min Wt
-E
UO-Min b
NiMH-Min Wt
NiMH- Min
b
NiCad-Min b
0.3 ---
NiCad-Min Wt
0.20.1
00
20
40
80
60
100
120
Loiter Radius (m)
Figure 5-17: Wing Span Vs. Loiter Radius, Nominal Mission
90
Weight of MAV Vs. Loiter Radius
-
0.6 --
0.5
-+-
--
UO-min diam
UO-min wt
NiMH-min diam
20.3-
M-MH-min wt
.
M-NiCad0.2
---
min diam
NiCad- min wt
0.1
0
0
20
80
60
40
100
120
Loiter Radius (m)
Figure 5-18: MAV Weight Vs. Loiter Radius, Nominal Missions
Summary: The maneuverability constraints have the strongest influence on the size
of the MAV because the small turn radii dictate a large required maneuvering acceleration. This added load increases the required wing area of the fixed wing, resulting
in a larger span and weight.
Cruise Distance
Figures 5-19 and 5-20 show that as the cruise distance increases the wing span and
weight of the MAV increase. Again, the better the battery the less of a change in the
weight and the wing span, in fact for the LiO battery the results remain constant,
implying that the cruise distance has a very small affect on the size of the MAV.
Summary: Cruise distance has minimal affect on the design of the MAV since an
optimal velocity is found for the range of cruise distances tested.
91
Wing Span Vs. Cruise Distance
0.9
0.8
0.7
-+-UO-Min b
+LO-Min Wt
NiMH-Min b
NiHM-Min
d-Mm WtW
0.4 - . --N
w---NiCad-Min b
-+-NiCad- Min Wt0.2
0.1
0
0
1000
4000
3000
2000
Cruise Distance (m)
5000
6000
Figure 5-19: Wing Span Vs. Cruise Distance, Nominal Mission
Figure 5-20: MAV Weight Vs. Cruise Distance, Nominal Missions
92
Minimizing b
Payload
Loiter Time
Loiter Radius
Cruise Distance
Lift Coeff. (Cruise)
const.
Lift Coeff. (loiter)
const.
Time in Cruise
11
const.
const.
const.
4
1
Loiter Velocity
4
ii
Cruise Velocity
4
f
Mission Energy
2f1
4
Table 5.4: Secondary Variable Trends, Objective: Minimizing Wing Span
5.4.3
Secondary Parameters
Table 5.4 and 5.5 show the general trends of some of the secondary variables with
respect to the parameters. From this information we see which variables most affect
the design of the MAV. We see the following observations:
" The coefficient of lift in loiter always reaches its maximum value.
" The coefficient of lift in cruise flight decreases with minimum span objective.
* The coefficient of lift in cruise flight increases as the mission difficulty increases.
" The coefficient of lift is maximized and so the only way to increase the acceleration is to increase the velocity which impacts the loiter radius as a function of
V2 and so we see no solution for small loiter radii.
Aspect Ratio
We also looked at the aspect ratio as part of our secondary study. From the aspect
ratio we can see trends in efficiency (i.e. L/D) and the specific energy of the battery
needed.
We see that for most of the parameters varied, with the exception of the loiter radius,
which will be discussed separately, the aspect ratio and the mission energies follow the
93
Minimizing Wt
Payload
Loiter Time
Loiter Radius
Cruise Distance
Lift Coeff. (cruise)
4
4
4
4
Lift Coeff. (loiter)
const.
const.
const.
const.
Time in Cruise
4
1
4
f
Loiter Velocity
4
I
f
Cruise Velocity
4
f
f
f
4
r
Mission Energy
1
Table 5.5: Secondary Variable Trends, Objective: Minimizing Weight
same trends. Figure 5-21 shows that the harder the mission, the more mission energy
is needed, although this result is expected, what is interesting is that depending on
the objective, the LiO battery may need the least or the most amount of energy.
When minimizing the weight of the MAV we find that the NiCad battery has the
higher values for the mission energy, and the LiO battery needs the least. This trend
is then reversed for the minimizing span objective, now, the LiO battery needs the
most energy. This same trend is seen when we look at the aspect ratios. The reason
for this is that for the LiO battery the cost of providing energy is less, the design
therefore exploits this economic fact and takes advantage of this "cheaper" energy
to use a more "expensive" design. Although the same trends are seen for all battery
types, the NiCad battery exhibits a slightly different trend since vehicle solutions are
not found for the nominal vehicle.
As we study the effects of each of the other parameters, payload weight, loiter time
and cruise distance we see similar trends. The loiter time affects the overall design of
the MAV the most, followed by the payload weight and finally the cruise distance. An
understanding of these results helps the designer in designing an appropriate mission
that balances the payload weight, loiter time, and ingress/egress parameters.
The loiter radius (Figure 5-22) does not follow the same trends mentioned above.
Although we see the same trends in the amount of energy needed for the different
battery types or the aspect ratio growth, the results are not as linear compared to
94
Wight
Aect RedoV. Payload
AMpeclAdo VL Payload
Weight
Objedlve: M*imze Weight
3.5
32
--
a
-
2-5
ba
11:
1 .52
0
2D
40
OD
SO
100
0
120
2-1A1
21)
SO
40
SO
10D
12D
-W viewS (9
Mabskn
Ehrgy V. Payload Weight
Ob5ecv.
Mbp.Wh
sp..
101
0
20
40
00
BID
100
120
-a VtW (
Figure 5-21: Secondary Effects on AR and Mission Energy whilst varying payload
the other parameters. With decreasing loiter radius we see a sharp increase in the
mission energy when minimizing the weight, and the opposite when we minimize the
wing span. The aspect ratio remains fairly constant when minimizing the weight
of the MAV, but when minimizing the span we see that the aspect ratio increases
greatly at a small loiter radius and then decreases to a minimum at approximately
15m, and then gradually increases. This is because the larger the aspect ratio, the
greater the weight penalty seen, and the more mission energy required, and a lower
specific energy is needed by the battery. From basic aerodynamics, we know that the
higher the aspect ratio, the better the lift over drag, and thus the efficiency of the
vehicle, however there is also a weight penalty associated with a higher aspect ratio.
This effect is seen in Figure 5-22.
95
Aspect RaIs Vs.Loller Radius
Obleaive: nniize Weigh
Ampa
adnVvI
Rdspe
42.5
0.54-
0
20
40
el
el
140
120
0
20
e
40
so
to0
120
Loner
fadus(m)
'3
isslon EnergyVs.Loier Radius
MiesionEnergyVs.LatterRadius
Obleclve: irize Weightt
2
ObGlsve:
n
nimize WingSpen
25-
S
I
0
20
40
60
90
100
12D
10
0
Lonernuntnnl
2
O
40
0
1O
M
120
LonernReduson
Figure 5-22: Loiter Radius Effects on AR and Mission Energy
Secondary Variables TRends Summary
1. The mission energy increases as the mission constraints increase.
2. The loiter velocity decreases as the radius decreases, which increases the wing
area and reduces the wing loading.
3. The lift coefficient in loiter reaches a maximum allowable value due to parasitic
drag, power relations and maneuvering requirements.
96
Chapter 6
Quadrotor
6.1
Chapter Overview
In this chapter, as in chapter 5, we discuss the design challenges and theory used to
develop a quadrotor optimization model. We focus on the aerodynamic theory that
captures the vehicles performance and design. We later analyze the results of the
optimization and observe trends specific to the quadrotor nominal mission.
6.2
Mission Definition
Before we delve into the optimization model design of a quadrotor MAV, lets revisit
the mission scenario in more detail.
As we saw in chapter 4, in order to achieve a surveillance mission the MAV must be
able to fly in three different flight regimes:
1. Travel to and from the area of interest: For the nominal mission we will define
this to have a value of 3000m, phases 2 and 4 in Figure 6-1.
2. Hover Flight
(for surveillance of area): For the nominal mission this value will
be set at 30 mins, phase 3 (Figure 6-1).
97
3. Climb: A thrust margin is used to account for the added energy needed for
climb, phase 2 (Figure 6-1).
--..
.
1
2
1 Dropfromparent
vehicle to grond
2, imbphase to
area ofitterest
4
3
3 Hove over
areaofinterest
4. Quise Hightto areaof death
Figure 6-1: Quad-rotor Mission Definition
Design & Numerical Implementation
6.3
6.3.1
Quadrotor Theory
In this section we define the equations used to model the flight performance. In a
similar manner to the fixed wing vehicle we then set-up the optimization model by
dealing with each the modules defined in Chapter 4.
We first make assumptions to simplify the optimization model:
1. The quadrotor was modelled as a multi-rotor system, without interference effects, using basic helicopter theory [141.
2. Rotor performance was determined using momentum theory coupled with a
blade element method (BET) [14].
3. Vehicle drag characteristics were calculated using simplified component build-up
98
4. Component weight equations were determined using relational attributes that
are functions of power, energy, and size characteristics.
5. Battery performance was determined by characteristic discharge curves defined
for specific battery chemistries (Chapter ??.
6.3.2
Definitions
Before delving into the optimization we first introduce fundamental definitions that
are used throughout these sections.
Rotor Thrust Coefficient: The non-dimensional rotor thrust coefficient is defined
as follows:
T
CT =pA(QR) 2
(6.1)
Rotor Solidity: The rotor solidity represents the ratio of the lifting area of the
blades to the area of the rotor, and is used in the figure of merit, and profile drag
calculations.
-
NbcR
(6.2)
Profile Drag: Profile drag is the drag incurred from forces acting on the blade during
flight. It is used in a number of calculations, from the figure of merit calculation to
the drag calculations.
C =
oCdo
d
(6.3)
8
The profile drag is a function of the blade Reynolds number [14].
Profile Drag
f(Re)
Cdo
99
(6.4)
Reynolds Number
Re,
PvtipCrotor
(6.5)
Loadings: The blade and disk loadings were not used directly in the optimization
but were used to verify results.
Blade Loading
BL = p
-b
(6.6)
T
DL = A
(6.7)
pAb(QR)2
Disk Loading
The following sections describe the different models used in the optimization model
as described in chapter 4. Each subsection will end with a summary of the inputs
and outputs to the module.
6.3.3
Weight Calculations
Weight plays a large role in the overall performance of a hovering vehicle, and as
such, needs to be dealt with in a comprehensive manner. Figure 6-2 shows the Excel
spread sheet used to perform the weight calculations. The total weight of the vehicle
is split up into four separate parts:
Payload, Battery and Motor Weight are discussed in chapter 4 as they share the
same characteristics and values for both the fixed wing vehicle and the quadrotor.
Structural Weight: The structural weight is separated into three main components;
the weight of the rods that support the majority of the structure, the central housing,
and the weight of the propellers (Figure 6-3). Material densities are used to estimate
the weights of each component as a function of vehicle dimensions.
The structural weight was calculated in the "Geometry and Area" Calculations Excel
spreadsheet (see Appendix D and Figure 6-2) using the following calculations:
100
--
Geometry and Area Calculations
17.35 in
0.5016 m
Length of Arm
Larm
Rod Length-to-Diameter
riod
Thickness of Arm (OD)
IProp Chord
Tip to Tip lenth
Tarm
Cprop
Ltotal
0.0201 m
0.0882 m
1.0031 m
paydens
0.0000 kg/n
0.0005 mA3
0.0001
Payload mass density
Battery Volume
Payload Volume
Total Housing Volume
}Housing Length-to-Diameter
Housing diameter
Housing height
Housing Area
Housing material Area
Vbat
Vpay
Vtot
0.0006 mA3
Hid
2.0000
0.0708
0.1416
0.0100
0.0394
0.0508
0.0254
0.0013
m
m
mA2
mA2
m
m
mA2
0.0101 mA2
Hh
Hd
Sh
Ha
Motor height
Mh
Motor diameter
Motor Area
Rod Area
Md
Sm
Sr
19.75 in
25.0000
0.790 in
3.47 in
39.49 in
30.39 inA3
3.66 inA3
34.05 inA3
2.79
5.58
15.55
61.06
2.00
1.00
2.00
15.60
in
in
in2
in2
in
in
in2
in2
Weight Information
Prop. mtl. m/area
Housing mtl. M/Pa
Weight of rods
Weight of prop
Weight of housing
lWeight entire structure
0.7500 kg/m^2
m/Pa
m/Ha
200 kg/m^2
0.3479 kg
0.2331 kg
0.0788 kg
0.=$91g-
WCf
Wp
Wh
Wstruct
347.85
233.13
78.79
659.76
g
9
9
9
DRAG
OveraU coleefcient of Drag
1.0000
CD
0.0554 mA2
0.0920 mA2
0.1475 m^2
Dp
Estimated drag (pressure)
,Estimated drag (skin friction) Df
D
Total Drag Area
85.94 inA2
142.66 inA2
228.59 inA2
Figure 6-2: Quadrotor Model (Geometry and Area Calculations)
101
-
---
- -
7
Z.V-
Figure 6-3: Quadrotor Assembly
Structures Weight
Wstruare
=
Wh+W,+Wc5
(6.8)
Where the component weights were calculated using a mass per unit area expression
for the housing and the propeller, and for the carbon fibre rods, a mass per unit
length:
Housing Weight
Wh
(6.9)
Shphusin [kg]
Rod Weight
Wef
NrLProd
[kg]
(6.10)
Propeller Weight
Wprap = NbNrRCproppy
M2
(6.11)
The densities used are from material standards or from practical weights from [5].
They are presented in Table 6.1. Table 6.1 also shows designer set constants that
were used for the geometry calculations given in Figure 6-2.
Summary of Weight Inputs and Outputs
Inputs: R,, N,, Nb, Propeller R:c
102
Material
Symbol
Value
2
Propeller Density
pprop
0.75kg/m
Payload Mass Density
ppay
1000kg/m 3
Housing Skin Density
Ph
2 kg/m
2
Rod Density
Prods
interpolated from std. data
Housing length: Diameter
Hid
2
Rod Length: Diameter
Rid
25
Motor Height
Mh
0.05m
Motor Diameter
MD
0.025m
Table 6.1: Material Properties and Constants for Weight and Geometric Calculations
Output: Weight of MAV Structure
6.3.4
Aerodynamic Calculations
This section presents the aerodynamic characteristics of the model, namely the calculations for drag, flight velocities, and maneuvering considerations.
Drag Calculations and Assumptions
There is little information currently available on the drag characteristics of quadrotors. To estimate the drag acting on the vehicle we used an approximation based on
total drag area.
The quadrotor design was divided into four principal drag areas (Figure 6-4):
1. The main housing (carries avionics, payload and batteries)
2. The motors
3. The connector rods
4. The blades
103
BIde
Motor
head
Qudrotor DagSimplifition
Comector
Rods
ManHousing
TOP VIEW
SIDE VIEW
Figure 6-4: Simplified Quadrotor (Cross Section) for Drag Calculations
The following assumptions were made in order to simplify the drag calculation:
" Low Reynolds Number Flight Regime (Re 0(104), defined at the rotor)
" Motor size remains constant (however, weight can vary as a function of the
vehicle size)
" Rod length is sized based on the housing radius and the propeller size.
It
includes a margin to ensure that there is no interference between the housing
and the propeller.
Skin friction drag (tangential to the body) and pressure drag (perpendicular to the
body) have the most effect on the MAV. In the drag calculation we assume that the
skin friction drag accounts for approximately two thirds of the drag [8].
Drag for each component is calculated using:
Component Drag Area
CDSi
ADj
(6-12)
Component Drag
Di =
[pV2SCDi
2
(6-18)
It is necessary to find an approximation for the drag coefficient values for each section.
Hoerner [8], states that for a cylinder and circular/square plates at low Reynolds
104
numbers (Re 0(104)) CD is approximately equal to 1. The total drag force can then
be calculated using the following equation.
Total Drag
1
Dtotai =PV
2
2
CD{Sh + 4Sm + 4 Sb ±
4Sr}
(6.14)
The motor frontal area remains constant and at a height of 1 x 2 inches (a large value,
resulting in conservative estimates for the drag). The connector rods are scaled with
the size of the vehicle by varying the rod thickness linearly with length, and calculating
the mass per unit length of the rods as a function of thickness. The main housing
is sized by determining the battery and payload volume including the avionics. The
resulting drag estimate is conservative, and provides a means to calculate the required
thrust as a function of flight speed.
Summary of Aerodynamic Inputs and Outputs
Inputs: Rr, Nr, Nb, Propeller Chord Ratio
Output: Total Drag Area
Figure of Merit Calculations
It is more difficult to define an efficiency factor for a rotorcraft, than with the fixed
wing vehicle because many more parameters are involved.
One way of overcoming
this problem is to use a combination of Momentum and Blade Element Momentum
Theory (BEMT) to calculate a Figure of Merit. The figure of merit is equivalent to
a static thrust efficiency, and is defined as the ratio of the ideal power to the actual
power required.
Figure of Merit
Ideal Induced Power
Real Induced Power
105
+ Profile Power
...........
FigureOfMOriCalculdens
65FL91
g
945.96in12
34.71in
640.71g
946.90in2
34.71in
1.2
Bide o lerr alT
Bla eft
02
Owde
of ber- aob
1.2
O66
0.2
c5
cle
ElIada
Blade number =
Nb
2
CT design =
Ct
Bladechord
Solidity(Bc/pil) =
Bladeloading
=
Discloading
c
sigma
BL
DL
0.0127
0.0682
m
0.127
o 100
Rotor speed=
Reynolds#=
omega
Re
Cdblade=
LoDblade
Cd_b
Blade speed=
BS
Elad
3.471in
10.296Nkn*2
58.275rad/s
154978
5%
rpm
0.03211
18.684
25.885
84.27 is
eis
Cpi=
Cpv
=
0.001016
Cp.tot=
0.(01730
0.6
= Nb
numiber
2
CT design=
Ct
Bladechord
=
Solidity
(Bc/pir) =
Bladeloading=
Discloading
c-b
sigma
BIL
DL
Rolorspeed=
Reynolds
#
Cdblade
=
LolDblade=
omega
Re
Blade speed
BS
00127
0M2 m
0.127
1D.100
10.519 N/re2
59 007 rad/s
i
12.391 W
21.938
W
6M36rpm
0-03194
18.788
26.00 mis
E5.33ft/s
0.001016
0.E50B
0001727
FgsiEpm esit=
Power
Ideal
Pind + Pprofile
g
3.471in
15W95
Cd-b
IJD-b
Cpi
CpW
=
Cp~jot
11(iE011
IdealPower
P ind+ Pprolle
e*b
Cb
5A20 W
9.216W
Figure 6-5: Quadrotor Model (Figure of Merit Calculations)
Constant
Value
Blade Efficiency Factor
1.2
Blade c/r
0.2
Blade C
0.6
Number of Blades
2
Table 6.2: Constants for Figure of Merit Calculations
1 5
f
9/l5
1
(6.16)
+G
-*+2Td
8~
where from Blade Element Theory:
Coeficient of Thrust
oCL
CT-
6
(6.17)
Figure 6-5 shows the Excel sheet used to calculate the figure of merit and Table 6.2
shows the designer defined constants that are used for the calculations.
Expressions exist for all the unknown parameters based on blade element methods
106
and an assumed propeller operating state.
Summary of Figure of Merit Inputs and Outputs
Inputs: Blade efficiency factor, g, CL, N,
Output: Figure of Merit
Velocities
There are three types of velocities that we must look at in this model:
" The flight velocity
" The hover induced flight velocity
" The cruise/ascending flight induced flight velocity
The flight velocity is varied during the optimization and is used to obtain optimum
quadrotor designs.
The flight and hover induced velocities are dependent on the flight velocity and are
calculated based on simplified momentum theory
[91:
Flight Induced Velocity
Vif =
V2ih
v(ICc, COS a)
2
+
(6.18)
(V ...
sin a + if)
Hover Induced Velocity
_
Vih
=
107
T
2 p-A
(6.19)
An iterative scheme is used to solve the induced velocity in forward flight, and the
vehicle angle of attack, a, (with respect to the free stream velocity)is calculated from
the forces acting on the vehicle.
tan a
=
D
W
(6.20)
Summary of Velocity Inputs and Outputs
Inputs: T, a, Voc
Outputs: Vif, Vih
6.3.5
Force Calculations
The hover thrust, maneuvering thrust, and flight drag are the main forces the quadrotor experiences in the various mission stages.
Hover Thrust: In hover flight the thrust is simply the weight of the vehicle.
Th =
=
mg
(6.21)
W
(6.22)
Maneuvering Thrust
The maneuvering thrust is the thrust needed to support both the weight of the quadrotor and to overcome drag of the vehicle while flying at an angle (Figure 6-6) for cruise
flight conditions. The flight/maneuvering thrust is calculated in the following manner:
Maneuvering Thrust
T.
1
Thover
Cos a
108
(6.23)
Thrust
a
Drag
Weight
Figure 6-6: Quadrotor Maneuvering Forces
As with the fixed wing vehicle a load factor is used when calculating the maneuvering
thrust and is given by:
Load Factor
n
1
cos a
(6.24)
Summary of Force Inputs and Outputs
Inputs: T, a, D
Outputs: Tm, Th
6.3.6
Propeller Power Calculations
To determine the total energy that the battery needs, the power needed for the
propeller in cruise and hover flight conditions must be calculated. It is given by the
following equations:
Propeller Hover Power
PPh = Nr ThVih
77h
A similar equation is used for cruise flight conditions.
109
(6.25)
Summary of Propeller Power Inputs and Outputs
Inputs: T, a, Vih, 'qh, 77f, Nr
Outputs: Powers: Pph, Ppf
6.3.7
Motor Power Calculations
The propeller and motor powers are needed to calculate the final endurance of the
quadrotor. The motor power is calculated using an estimate for the motor efficiency,
nm, and the required propeller powers.
Motor Hover Power
Pmh
(6.26)
7M
The power density can then be found by dividing the motor powers by the battery
weight as we see below.
Motor Hover Power Density
mh
Pmh
Bpower,
= BW
(6.27)
Similar equations for both the motor cruise flight power and cruise flight power density
are used.
Summary of Motor Power Inputs and Outputs
Inputs: Pph, ' pf
Outputs: Motor Powers and Power densities
110
Energy Calculation
The total energy that is needed for the mission is then calculated using the following
equation:
Total Energy
Ett = Eh +Ef
=
Pmh* th+ Pmf * tf
(6.28)
(6.29)
This value is then used to calculate the total battery size needed, using macros given
in Appendix D. The battery energy density is computed on the basis of the required
power, and is used to compute the battery weight required for a total mission.
Summary of Energy Inputs and Outputs
Inputs: Power and time
Output: Endurance
6.3.8
Overall Model Summary
Figure 6-7 shows the Excel optimization that was used and can be seen in more detail
in Appendix D.
The model may also be expressed using a block diagram (Figure 6-8).
As with the fixed wing vehicle this block diagram provides details of each of the variables and how they are used as inputs and outputs of each module for the quadrotor.
6.4
Optimization Study-Results and Analysis
The reader will recall from Chapter 4 that two objectives were studied. The following
sections outline our results from the optimization runs.
111
Conslants
2 Varilabtles
4 '
5
E
E
0
D
C
BB
A
1 QuadRaterVarilesuand Parmee
Units
0.061rg
6 PeyloadWigt
7 Cor*0lstate
PLW
CW
Weght_
10 Propulsion
PW
1.508rkg
12 TolalM
lota
2
13
14 Ehciencias
15 6 lergel6ncy
160
el
0.760
etah
etaL.c
0440
wacmpos
HoverInduced
Velocity Vifn
Forces
&h rotr)
HoverThrust
Ftightdrag
Th
6.2854N
1.4223N
222857
ManeuveringThrust
Tin
Rtddd3 N
M11 u -INig
Flight angle
Af
9
1.22 lggre3
Cd
1.0253
Power.
0.61032m2
i
12.75 deg
Loadfactor (h)
34.705 In
Ar
2.-J mis
0.84 mWs
Flight induced Velocity
0.00 g
1394.31g
114.50g
108.81 g
650.76a
0.441
28
29 Dragcoefitcient=
30 Tllust Meti
N
N
ve
units
60.000
ftk
1?
Efficiency
18 TotalHover
19 TotalCruiseEfliciency
20
21i
22
23
rotorarea
24 individual
25
26 Aerodynaics
27 De sar=
Ii
II
Constraints
elipiNmini
hVweit
L
L
K
K
J
I
N
H
13
G
F
F
Q
0.642
1.15
946.98irA2
506.99
in*2
Propeller
hoverpower
Propeller
light power
Pph
W
87.753
Ppr
64561 W
Mlotor
Motorhoverpower
Motorflightpower
Pmh
PmBW
117.004 W
96.061W
e3.92Wg
51.74 6Wkg
PowerDensltyfor
hover PnVOVV
PowerDensity
forflight PrnBW
321
j2~Suronavvia"
1.3043
0115
0.0
Equal
0.45
rab"s
Max
.
".D
EeW
Min
I.0E-6
1.00E-0
1.80E-06
Energy
forhover
Energyfbrfilght
Energytotal
Eh
58.502 t
Ef
Etot
14.735Whk
BAeyTwe#
1.
73.237Wit
78.259 WKg
Averagepowerdensty
.OO
.
BatType
aftry Type: Narne
mders
Batterymassdensity
Balleiyenergydensily Edens
Ebat
Totalbattery
energy
NiCad
2600M.00
kgn*3
52.53WhKg
73.237 Wh
EaBUtSic
TimeInHover
Time In Flight
CruiseRange
TOllthusbtheak
ih
if
el"Wr
metl
1800.00sec
616.25se
30.00min
1027 min
3000 m
2411.25&Zecis
0"I hW=
51
sigma=
I 00E-06
Figure 6-7: Quadrotor Model (Main Worksheet)
6.4.1
Nominal Vehicle Designs
Table 6.3 shows the weights and rotor diameter for a nominal quadrotor vehicle, that
is capable of 30 minutes of hover flight, 3000m of egress/ingress flight and carries a
payload of 60g.
As can be seen from Table 6.3, for the nominal mission we can see the smallest size
vehicle, with a LiO battery has a rotor diameter of 10cm (which implies an overall
vehicle size of approximately 24cm) and a weight of 510g. As we decrease the battery
performance though, we find that the vehicle size and weight increases greatly. The
designer therefore has to make the necessary trade-offs between cost (for the batteries)
and the size of the vehicle penalty paid on the carrier vehicle. This will be discussed
further in Chapter 7.
112
D,TI,V, T
Figure 6-8: Quadrotor Model Block Diagram
Objective
Min. Weight
Min. Rotor D
Battery Type
Rotor D, m
Weight, kg
Rotor D, m
Weight, kg
LiO
0.21
0.22
0.10
0.51
NiMH
0.45
0.58
0.37
0.79
NiCad
0.88
2.22
0.84
2.44
Table 6.3: Nominal Vehicle Sizes
6.4.2
Weight Trends for Nominal Mission
Figure 6-9 shows the weight distribution for a nominal mission, i.e. a cruise distance
of 3000m, hover time of 30 minutes and a payload capacity 60g. The trade-off between
the payload weight and battery weight, the two aspects of weight that show the most
change, can be seen from the figure.
Although there is a general increasing trend in the percent of weight used for some
weight aspects; battery weight, motor weight and structures weight, the payload
weight contribution decreases and the structures weight seems to remain fairly constant for the different battery types.
113
Weight Distributions Comparison
for Objective Scenario and Battery Types
100%
-
90/
800%
0
70%
OPayload
3
Weight
600
5
50%-N
*
D3Structures Weight
Motor Weight
40/6 -
Battery Weight
30%
20%
10%
0%
LiO
NiMH
Ni~a
LiO
NiMH
Ni~ad
Min Diameter
Min Weight
Battery Types and Objectives
Figure 6-9: Weight Distribution Comparison for Nominal Missions
The weight break down shows us clearly how the vehicle tradeoffs the energy (battery
weight) and the size of the vehicle (payload weight/structures weight).
It is interesting to note that the variations depending on the objective are not as
pronounced. When minimizing the rotor diameter as the main objective, we see that
in comparison to the minimize weight objective the battery weights stay within a 10
percent value of each other for the different battery chemistries. This emphasizes the
penalty that is associated with increasing the battery weights when minimizing the
rotor diameter for certain missions.
Summary: We see that the higher the energy density the higher the payload weight
fraction, and that when minimizing the diameter of the quadrotorthat the optimizer
substitutes payload weight fraction for a smaller dimension.
114
Figure 6-10: MAV Weight Vs. Cruise Distance, Nominal Mission
Cruise Distance
Figures 6-10 and 6-11 show the weight and the rotor diameter of the quadrotor versus
the cruise distance.
It can be seen from the graphs (Figures 6-10 and 6-11) that there is a higher penalty
to go to a larger size or faster speed than to increase the cruise distance, this is seen
since the rotor diameter grows in a constant fashion for both the LiO and NiMH
batteries and to a certain extent for the NiCad battery. The figure exemplifies that
the battery chemistry is important and affects the size of the vehicle a great deal. The
cruise velocity remains constant for each of the battery types which is an interesting
finding since it reveals that there is an optimum cruise velocity regardless of distance.
From Figure 6-12 we see that for the LiO battery the weight distribution is not
affected by varying the cruise distance. As we decrease the energy density of the
battery however, and look at the NiCad battery we see that the battery weight takes
a greater portion of the weight distribution at a decrease in the motor weight and
115
Rotor Diameter Vs. Cruise Distance
1.6
---
1.4
1.2
--
-
1
1
E
a 0.8 -
NiHM-min wt
-*-
0.6
--
~0.4
UO-min diam
UO-min Wt
NiMH-min diam
NiCad-min diam
NiCad
-
0.2
0-
0
1000
4000
3000
2000
Cruise Distance (m)
5000
6000
Figure 6-11: Rotor Diameter Vs. Cruise Diameter, Nominal Mission
the payload weight distribution, since the NiCad battery seems to be insensitive
to the cruise distance, because there is not enough energy compared to the loiter
requirement.
Summary: The cruise distance has minimal affect on the design of the MA V and does
not affect the weight distribution, as an optimal cruise velocity is found, since energy
requirements are not very high. There is also a near direct substitution of the battery
weight fraction to the payload. The poorer the battery energies the more non-linear
the results become.
Varying Payload Weight
Figures 6-13 and 6-14 show the affect of increasing the payload weight for the two
objectives, of minimizing weight and rotor diameter respectively. As the payload
weight is increased the rotor diameter and weight increase in a linear fashion for
all battery types. Again depending on the battery chemistry the effects are more
pronounced, and can be seen in Figures 6-13 and 6-14.
116
Weight Distributions Comparison for Cruise Distance and Battery Type
100%
90%
80%0 Payload Weight
A
0
3 Structures Weight
0.
500/0-
0
40N
71n
N btor Weight
Battery Weight
20%
10%
0%
L
iO %
1000m
NiCad
L
N
NCad
LiO
3000m
N@&I Mad
5000m
Battery Types and Cruise Distances
Figure 6-12: Weight Distribution Comparison- Cruise Distance
From Figure 6-15 we see the same trend as for the cruise distance, where the battery
weight increases drastically in order to respond to the tougher mission.
Summary: There is a tradeoff between the payload weight and the rotor diameter, and
that is seen heavily in the minimizing rotor diameter objective. The results found were
nearly linearsuggesting that a constant payload fraction is found.
Varying Hover Time
Figures 6-16 and 6-17 show the Weights and Rotor Diameters Versus increasing the
hover time respectively.
By varying the hover time, we see non-linear results, that increase in their nonlinearity as the battery energy density decreases. It is interesting to note that the
solver could not find a solution for a 50 minute hover time when minimizing the weight
for the NiCad battery. This is because energy required is a function of weight and
117
Figure 6-13: MAV Weight Vs. Payload Weight, Nominal Mission
Rotor Diameter Vs. Payload Weight
1.2 - - -
-
-
-
- -
~ - ~ ~ ~ ~ ~ ^-
- - - - - - - -
1
E
0.8
,
0.6
S--UO- Min diarn
UO-min Wt
NiMH-min diam
NiMH-min Wt
-----
'
0.2
NiCad-min diarn
NiCad- min wt
-
00
20
40
60
80
100
120
Payload Weight (g)
Figure 6-14: Rotor Diameter Vs. Payload Weight, Nominal Mission
118
Weight Distributions Comparison for Payload Weights and Battery Types
100%
90%
S-700% C
o
P
ayload Weight
13 Structures Weight
E Motor Weight
Battery Weight
61
40%/6 -
10% LiO
NiMH
NiCad
LO
NiMH
NiCad
LO
60g
20g
NiMH
NiCad
1O0g
BatteryTypes and Payload Weights
Figure 6-15: Weight Distribution Comparison- Payload
flight times, and so eventually the battery is unable to support its own weight, since
its weight increases at a greater rate than the energy supplied. Again, this proves to
us that the battery chemistry plays a large role in the optimization process.
Figure 6-18 shows that the hover time largely affects the weight distributions, since
even the highly exotic batteries show an increase in weight for an increase in hover
time, unlike when the cruise distance was varied.
Summary: There is a greaterpenalty to supply energy to the to the battery than to
increase the size of the quadrotor
6.4.3
Secondary Parameters
Tables 6.4 and 6.5 show the general trends of some of the secondary variables with
respect to the parameters.
From this information we can see which of the variables most affect the size of the
119
Weight of MAV Vs. Hover Time
5
4.5
4
3.53E 2NiMH-min
2.5
2-*-DNiCad-
-+-UO-min diam
LiO-min wt
diam
- NiMH-min wt
min diam
X
--
1.5-
0.5
NiCad- min wt
-
0
0
10
20
30
40
50
60
Hover Time (mins)
Figure 6-16: MAV Weight Vs. Hover time, Nominal Mission
MAV. We make the following observations for the diameter minimization design:
" Cruise velocity remains constant for the cruise distance optimizations and so
suggests that there exists an optimum velocity for all distances.
" The energy required for cruise (ingress and egress) flight is always minimized,
as it seems to have large penalty on the cruise distance.
" The flight speed is not sensitive to the payload weight, there seems to exist a
higher penalty to going to a higher speed then to going to a larger payload.
" For all battery types when running the optimizer for the minimizing weight
objective, a constant cruise velocity is found,since a penalty in weight is higher
than the penalty for increasing the power.
" The hover time and payload weight seem to have a greater effect on the results
than does the cruise distance.
120
Figure 6-17: Rotor Diameter Vs. Hover time, Nominal Mission
Weight Distributions Comparison for Hover Time and Battery Types
100%
80%
C
.2
60%
1 Payload Weight
40%
*Battery
O Structures Weight
.0
U
'5
PU
0 Motor Weight
20%
0%
LiO
INiMH
10 min
INiCad
LiO
i NiMH
INiCad
30 mins
Battery Types and Hover Time
LiO
NiMH
NiCad
50 mins
Figure 6-18: Weight Distribution Comparison- Hover Time
121
Weight
Minimizing D
Cruise D
Payload
Hover Time
Time in Cruise
f
4
ii
4
Cruise Velocity
const.
Hover Induced Velocity
4
f
4
Flight Induced Velocity
4
f
4
Flight Angle
4
4
4
Table 6.4: Variable Trends, Objective: Minimizing Rotor Diameter
Minimizing Wt.
Cruise D
Payload
Time in Cruise
#
~ const.
Hover Time
const.
Hover Induced Velocity
const.
const.
4
Flight Induced Velocity
const.
const.
4
Flight Angle
const.
4
4
Table 6.5: Variable Trends, Objective: Minimizing Weight
* The hover time parameter shows that the vehicle grows exponentially
,
since
there is an increase in required battery energy discharge and there is also an
increase in energy needed and so to provide for these two growths, the vehicle
becomes very large (no longer in the micro, as defined by the DoD, scale).
122
Chapter 7
Conclusion
7.1
Chapter Overview
This chapter compares both vehicles and discusses the effects that each vehicle would
have on the air deployment mission. We determine when it is necessary to send in a
quadrotor, because of its hovering capabilities, as opposed to a fixed wing vehicle and
then discuss and compare which vehicles are most effected by the parameters tested.
We also qualitatively look at how each vehicle affects the carrier vehicle. Finally we
conclude our work and look at future work in this area.
7.2
7.2.1
Comparative Results
Loiter Radius/Hover Comparison
In the simulations the algorithm could not find a solution for small loiter radii of 5m
and 10m for the fixed wing vehicle and the poorer battery chemistries, NiMH and
NiCad. In these cases there is, therefore, a minimum loiter radius that the fixed wing
can operate. These results can be seen in Table 7.1. We look at the overall weight
of the MAV since it is a better indication of the penalty that it will have on the
carrier than the size of the vehicle, as innovative techniques can be used to design
folding/smaller vehicles etc.
123
Objective
Minimize Span
Minimize Weight
Battery Type
Weight (kg)
Loiter R (m)
Weight (kg)
Loiter R (m)
LiO
0.2245
6
0.51
4
NiMH
0.59
9
0.8
8
NiCad
2.25
11
2.4
11
Table 7.1: Loiter Radius Comparison
Battery
Velocity (21)
Weight (g)
LiO
6.3
300
NiMH
7.1
399
NiCad
8.7
570
Table 7.2: Minimum Loiter Velocities
From these results we see that the poorer the battery characteristics the larger the
minimum loiter radius. If the mission dictates that the MAV must be able to loiter
under a certain radius/ must hover, then we can conclude from these results which
vehicle should be used. Characteristics that dictate which vehicle should be sent are
discussed in Qualitative Section.
7.2.2
Loiter Velocity
Similar to the loiter radius/ hover comparison analysis we studied the minimum loiter
velocity values for a nominal fixed wing mission and the minimize weight objective.
The results of this study can be seen in Table 7.2.
Although the results are relatively similar for each of the batteries we observe that the
loiter velocities are very sensitive to the maximum angle of attack and lift coefficient.
This result is also observed with the loiter radius.
124
7.2.3
Weight Comparison
It is interesting to compare the proportion of weights of each of the vehicles to the
two MAVs. From Figures 7-1 and 7-2 we can see the following:
" The fixed wing weight remains fairly constant when decreasing the quality of
the battery unlike the quadrotor which seems to exponentially increase
" The fixed wing MAV has a larger percentage of payload weight than for the
quadrotor. For the quadrotor the battery weight carries the largest percentage,
since a rotor is less efficient than a wing in producing lift, and so compensates
for this deficiency by increasing the battery weight available to the MAV.
" With poorer battery chemistries one is unable to satisfy the mission under
reasonable MAV weight constraints for the quadrotor MAV, however, with the
fixed wing, although the MAV grows its weight still remains reasonable.
Weight Comparison
--
2.5
-
-
--
-_
_
-_
-
-
2-
-+-Battery Weight
--- Motor Weight
Structures Weight
payload weight
-total weight
1.5
0.5
0 Fixed wing
Quadrotor
LiO
Quadrotor
Fixed wing
Quadrotor
Fixed wing
NiCad
NiMH
Vehicle and Batlery Type
Figure 7-1: Vehicle Separated Weight Comparison
125
Weight Distribution Comparison
10%
80%
70%
60%
0 payload weight
o Structures Weight
50%-
0 Motor Weight
E Battery Weight
40% .5
30%20%
10%
Quadrotor
Fixed wing
Quadrotor
Fixed wing
Quadrotor
NiMH
UO
Fixed wing
ACad
Battery and Vehicle Type
Figure 7-2: Vehicle Weight Comparison
7.2.4
Effect of Parameters
For each of the vehicles the parameters had a different effect on the final design of
the vehicle. Table 7.3 shows which vehicle was most affected by the various mission
parameters tested. The results were computed by perturbing the mission parameters
around the nominal mission parameters and recording the effect to the weight of the
vehicles.
It is interesting to note that for both the fixed wing MAV and the quadrotor, the
Parameter
Fixed Wing MAV
Quadrotor
Loiter Radius
1
N/A
Loiter/Hover Time
2
1
Payload Weight
3
2
Cruise Distance
4
3
Table 7.3: Parameter Effects on each Vehicle
126
order in which each of the parameters affects the vehicle design is the same, with
of course the exception of the loiter radius for the fixed wing vehicle. In the three
parameters that are common to both vehicles we see that the loiter time has the
greatest affect on the overall size of the vehicle, followed by the payload weight and
the cruise distance.
The overall design/size of the MAV is a result of the energy incurred during the
mission. The battery chemistry chosen has a large effect on the energy and hence the
overall design of the vehicle since, energy is a function of the battery weight, which
in turn is a function of both the required energy and also the rate of discharge of the
energy (power). We also reveal that NiCad batteries are not suitable for a nominal
mission for the fixed wing vehicle.
With the hover time, we see a large energy penalty and so, when varying the hover
time, it has a greater effect on the design. The payload weight has the next greater
effect on the MAV design and has less penalty on the energy needed and thus the
overall MAV design. The cruise distance doesn't change the overall size of the vehicle
since the expenditure of energy for cruise is small in comparison to the other variables.
7.2.5
Qualitative Study
In this section we look at a top level comparison of both the fixed wing vehicle and the
quadrotor and see the tradeoffs between the two vehicles. We separate characteristics
that are important to any defined mission especially if the vehicles are being used
within a fleet of vehicles.
Ability to Land and Take off The ability of a vehicle to take off and land is
invaluable, since the MAV may potentially be able to land in an area, lay dormant
for a while, and potentially work as a communications node. In doing so one is able
to gain more information about a hot-spot. A fixed wing MAV does not have this
capability and so if this was necessary for the mission, then, a quadrotor would have
to be sent in. Even though there is a greater penalty paid on the carrier vehicle by the
127
quadrotor, the designer needs to assess the benefits gained for a particular mission
based on the information that would be gained and the weight penalty on the carrier
vehicle.
Minimum Loiter Velocity The quadrotor vehicle is able to maneuver at a much
slower velocity than the fixed wing vehicle and as such is not only able to gain more
information, but is a more suitable platform to mount the camera; allowing for better
quality surveillance information to be obtained.
Maneuverability and Control The maneuverability and control of the vehicle is
an important facet for under tree canopy surveillance and other confined environments
since the vehicle must be able to avoid obstacles. Since the quadrotor is a hovering
vehicle and capable of loitering with small radii it is a better for maneuvering in
challenging environments than the fixed wing .
Deployment Since the fixed wing vehicle is able to "naturally" glide, the vehicle
would be easier to deploy than the quadrotor and would not need stabilization. On
the other hand, the quadrotor would need some form of stabilization. This could be
in the form of an added lifting body to the design of the quadrotor or a parachute
deployed to stabilize the vehicle until the quadrotor can fly on its own, which of course
would add complexity and weight to the vehicle.
Penalty on Carrier Vehicle Penalty on the carrier vehicle is better defined in
terms of weight, since as mentioned previously it is possible to "shrink" the overall
size of a design by using innovative techniques such as folding wings. Bearing this in
mind, we still find that the quadrotor has a greater penalty on the carrier vehicle as
it has to carry more batteries and motors for the same mission as the fixed wing, so
unless the mission requires that the vehicle needs to hover and land it is better to
send in a fixed wing MAV.
128
7.3
Conclusions
In this thesis we have described the design and implementation of a multi-disciplinary
system design optimization for a fixed wing and quadrotor MAV. We have discussed
the benefits of a fixed wing MAV over a quadrotor MAV and have determined when
it is best to deploy a fixed wing vehicle as opposed to a quadrotor MAV.
From our results we made the following key observations:
" There is a large trade off between the payload weight and the size of the vehicle
and the mission endurance.
" The order in which the parameters studied affect the vehicle design is:
1. Loiter radius
2. Hover time
3. Payload weight
4. Cruise distance
The loiter radius parameter plays the primary role in the design of the fixed
wing vehicle, and therefore provides the differentiating factor between sending
in a quadrotor or a fixed wing vehicle.
" The battery selection is also crucial to the design of the MAV. The more exotic
the battery (i.e. the higher the energy density), the smaller and lighter the
vehicle to fulfill a given mission, and the better endurance. NiCad batteries will
not fulfill the nominal mission and so are not a good choice for this particular
fixed wing scenario. The designer must therefore make the tradeoff between the
cost of the battery and the performance for a particular mission.
" For a mission where greater emphasis is placed on being able to maneuver
through a cluttered area then a hovering vehicle (quadrotor) is better deployed
to achieve the goals of the mission.
129
7.4
Future Work
This thesis allowed. us to layout the basic framework to design MAVs for particular
missions.
In the future implementation of such a framework will require a more
detailed analysis. We will separate this section into 3 areas; model enhancements, a
top level analysis, and fabrication and test.
Model Enhancements
There are features that could be added to the model to increase the functionality and
fidelity of the model. These include:
" Inter-software link: Link the optimization model using a software package like
Oculus with a CAD package like Pro/Engineer.
" MSDO: Couple higher fidelity aerodynamics and structural models with the
current performance estimates/design algorithms, for example including the
rotor speed for the quadrotor as a design variable.
Top Level Analysis
In order to gain a more quantitative feel for how each vehicle would affect the air
deployment mission, the following areas should be considered:
" Packaging Model: Couple vehicle packaging within the carrier vehicle to the
overall optimization process.
" Sensitivity Analysis: Perform a more elaborate sensitivity analysis of the design
variables and vehicle parameters.
" Cost Analysis: Couple the vehicle costs with the optimization.
130
Fabrication and Test
As with any hypothetical design it is good to be able to physically test the theory
and assumptions used in the analysis. There are several design issues that require
prototype testing for validation and analysis.
" Fabricationof theoretical vehicle models: collect data to enhance performance
and weight models.
" Deployment Analysis: Detailed design and test of deployment options
" Camera Platform:Detaileddesign and test of image quality for two vehicles to
create metrics for use in the optimization.
131
132
Appendix A
Battery Macros
The following diagram shows the battery macros used in both the fixed wing and
quadrotor optimizations.
133
04
Elk & 5-I
1 rAt FawL*~ fDshlU Hli EM; &*1-Trr 1Crn±-w H-ah
------_,
-------
Tunttion flatT7]De(btwpe3
-
taomf~ Excel
Cbects
qj
*1et
Case btvp
-io
flmtryp
2
Batryp
Case 3
Case
s~w9wok
"Li-Tom"
Case 4
'g-Lftse
Btrvp
"
Constant'
13denl
Fiunctton edens(btV~e,
vil)On
j3S~llib ModIt
2J
A0-*1CftJ"
3elecr~ Case btype
case 1
edens - 561.15
7
mde"WO
I
Case
.00 17
*ExpC-O.i
017
pdtes
3
edens
Cnz= 4
90
e
Cse
Chefi73_i7
Err(-C.OOZZ I pdltma
Em(-
edens = 120
tver7,
21(
*e GD
Kp(-O I0017
*pdezo)
*pdean)
Else
Ead Seinct
F-ti-n =dorm (bnvpe:
L'.,
2COC k4/n 3
Select Cse btype
Case 1
wens
2000
C. e 2
Cse
3
=dn
3900
Case 4
adn
3000
&d Slet
End Pinction
Figure A-i: Battery Mac~ro
134
:C-ad c
Ul
"K
Appendix B
Fixed Wing Model
135
Geometry and Area Calculations
Geometry
Symbol
Est. Rotor Radius
Number of rotors
Number of blades
Prop Chord Ratio
Prop Chord
Rr
Geometrv
Value
Units
7.82 in
1.96 in
Nr
Nb
c/R
0.0497 m
1.0000
2.0000
0.2000
C_prop
0.0099 m
0.39 in
Payload mass density
paydens
1000.0000 kg/m"3
Battery Volume
Payload Volume
Vbat
Vpay
Motor height
Motor diameter
Mh
Md
Motor Volume
Total Fuselage Volume
Vm
Vho
:ilais
0.0000 m^3
0.0001
0.0508
0.0254
0.00003
0.0001
4.0000
Fuselage Length-to-Diameter Hid
Fuselage
Fuselage
Fuselage
Fuselage
diameter
height
Frontal Area
material Area
Weight Information
Prop. mt. m/area
Housing mtl. M/Pa
Weight of fuselage
Weight of prop
Miscellaneous Weight
m
m
m^3
m^3
Hh
Hd
Sh
Ha
0.0346 m
0.1384 m
m/Pa
r/Ha
Wfus
Wprop
Wmisc
0.7500
2.0000
0.0150
0.0007
0.0168
CD
D
0.4000
0.04 mA2
0.0009 mA2
0.0075 m^2
2.71 inA3
3.66 ir^3
2.00 in
1.00 in
1.57 in^3
7.94 in^3
1.36
5.45
1.46
11.66
in
in
in2
in2
kg/m^2
kg/mA2
kg
15.04 g
kg
kg
15.78 g
0.74 g
Fuselage Drag
Fuselage drag coefficient
Total Drag Area
0.58 in^'2
Figure B-1: Geometry and Area Calculations for the Fixed Wing MAV
136
Structural Weight Calculations
lbs
in
in
in
0.636
7.824
3.447
3.447
structural margn =
I layers
10.000
0.1 deg
6.357 lbs
26.967 in^2
2.270
0.00370 in
Root thickness =
Cap stress =
Required Cap area
Required Cap width =
Cap thickness =
Cap volume =
Cap weight CapW/TotaWl =
r
0.00695 in^2
0.347 in
0.020 in
0.109 inA3
3.564 g
8.A04 kg
1.24%
16| kgrn*3
2.2rb8*3
35.20 kg/mA3
0.0005 kg/in^3
faam density =
Estimated Skin Fabric
Shear load =
Shear area =
Req thickness =
Skin thickness =
Skin weight -
in
12.434 in-lb
24.48 lb
kg/in^3
32.775 g/in^3
0.577 g/in3
3.179
in*2
0.00031
in
000370
in
5.396
g
SkinWt/TotalWt =
Normalized
43.120
83.398
0.02410
0.619
0.035
0.377
1.24%
kg
1.87%
Estimated Foam
Foam volume =
Foam weight -
9.063
5.234
0.5152
SkinWt/TotalWt =
1.82%
Total Percentage =
4.92%
Figure B-2: Structural Calculations for the Fixed Wing MAV
137
lbs
0.00032
B.5154
0.517 in
3460.34 psi
Root bending moment =
Cap load =
0.03278
0.01740 m^2
0.00087
0007
carbon spar density =
0.02458 kg/in^3
24.581 g/in*3
Estimated Spar Cap
Deflection lamda.req =
Deflection =
15 Msi
10000 psi
2W kgmrn*3
design shear stress
skin density =
0:0%
15.0%
0.02 in
thickness/chord =
min cap thickness
min skin thickness
g-leve =
Deflection Angle Required =
load =
area =
aspect ratio =
Structural Characteristics
cap modulus =
inA3
g
kg
Structural Weight Calculations
lbs
in
in
in
0.636
7.824
3.447
3.447
U.U-I.ft
KgilrrJ
32.775 g/in^3
skin desity =
0.0246B kg/in*3
24.680 grW3
0.0037
in
2.Xffkit'9
foam density =
35.2gkg/m^3
luau
area =
aspect ratio =
OGM;Rkgfin^3
0.577 glir-3
0.orf lub
26.967 inA2
2.270.
0.01740 m^2
Estimated Sin Fabric
Shear load =
Shear area =
Req thickness
Skin thickness =
Sidaweigh-
Estimated Spar Cap
Deflection lamda req=
Deflection =
0.007
0.07 in
Root thickness
Cap stress =
0.517 in
3460.34 psi
3.179
lbs
0.009
in*2
(100031
0 00370
in
in
8
kg
SkinWtfTotaPMt =
1.87%
Normalized
Root bending moment =
Cap load =
12.434 in-lb
24:048 lb
43120
83.398
0.00695 inA2
0.347 in
S 000in
0.02410
0.689
0.035
O109 inA3
0-377
Esimated Foam
Foam volume =
Required Cap area =
Required Cap width
Cap thickness =
Cap volume =
Cap weigt CapVA/TotalW=
9.063
5,234
8.1A5
SkinWtfTotalW=
1.82%
Total Percentage =
492%
124%
CM* kg
1.24%
Figure B-2: Structural Calculations for the Fixed Wing MAV
137
irA3
g
kg
Appendix C
Spar Sizing
139
pcaling
test results to winchproof RC giler spar
Mark Drela
Feb 15 00
This spar sizing procedure is based on the test data
obtained by loading spar samples to destruction.
Typical two-meter glider example...
Tc =
:
sparcap thickness
0.028 in
(4 plies,
commonly sold as 0.030 in)
conservative I think)
Design cap stress : sigma = 140000 psi (still may bemargin
Included)
tau = 12000 psi 50% safety
Design shear stress:
500 psi 50% safety margin for 4 lb balsa)
Allowed core stress: sigc =
Heavier balsa can withstand proportionately larger si
in tension,
Note: The bottom spar cap is
c.
and can surely tolerate
The bottom cap
at least 200000 psi or even 300000 psi stress.
thickness can therefore be 0.021 In (3 plies) or even 0.014 in
conditions at wing root:
=
=
=
wing span
wing load
spar height
cap modulus
:
:
:
:
bending mom.:
M = b F/B = 1560 lb-in
cap load
:
:
P = M/h
b
F
h
E
78 in
160 lb
0.9 in
2.OxlOA7 psi
(2 plies).
(winch line force)
(9% airfoil with 10 In chord)
(for common T-300 carbon fiber)
= 1733 lb
= 80 lb
s = F/2
shear load
: Ac = P / sigma - 0.0124 inA2
required cap area
:
required cap width
required shear area :
required skin thick.:
w
=
Ac / Tc
As - s / tau
Ts - As / 2h
- 0.44 in
- 0.0067 inA2
(2 layers of 1.5 oz glass)
= 0.0037 in
estimated core compressive strength: sigc estimated tip deflection: d = bA2 sigma / (4
This particular case may call for a reduction
stress sigma to get proportionately lower tip
tau As / h w = 200 psi
E h) = 12 in (yikes!)
in the allowable
deflection.
(no problemo!)
The spar will then be stronger than necessary but that
has to be accepted.
Ideally one wants to taper the spar dimensions so as to maintain constant
This will give minimum weight for a given strength.
sigma and tau.
Assuming the cap thickness Tc and spar height h are roughly constant,
the relative spar width and shear skin thickness should taper as follows:
center
..
midspan
..
tip
w
~ 1.0
0.56
0.25
0.06
0.0
0.0
0.25
0.50
0.75
1.0
TS simple linear taper of w is OK, but gives unnecessary strength
Ts will obviously need to be stepped --(and weight) outboard.
from 2 layers in the middle dropping to 1 layer at midspan.
If w is constant, then the sparcap thickness Tc should taper the same
way as w above.
sizing wood spars
The sizing example above can also be followed for sizing
spar caps and shear webs in traditional I-beam wood wings.
The fol lowing minor definition changes must be made.
I got the wood properies out of an old book on wood
aircraft structures.
h = spar height measured between cap section midpoints
=
total height
-
single cap thickness
wood shear web area
Ts = As/h wood shear web thickness
As =
E = 1.3x10A6 psi
= 200 psi
tau
sigma = 5000 psi
(spruce)
(for 4 lb balsa.
(spruce)
scale up for larger densities.)
Notes:
* tau and sigma are values at failure. Reduce these to get some safety margin.
* The same ideal spanwise taper rates apply. Typical existing wood spars are grossly
oversized outboard relative to the center.
* Much more modest winch loads will need to be chosen with wood, else the spar will end
up wider than the airfoil chord!
Figure C-1: Spar Sizing Text Example [61
140
Appendix D
Quadrotor Model
C
B
A
VWr sanipaiirmtS
I QuadNWter
2 VanablesOnestans
4
alithiemIn
6
Payftrad
Weight
10
Pro isin We1
Gm
F
Consranim
Unfst
0.0ekag
PiW
units
60.00g
1394.31 g
114.50 g
1508.81 6
11
12 TotalMAVweight
lolm
666.76g
2226.57g6
2.2286kg
111111
--Vi
Hoverinducedavelocae
Flight induced Velocily,
VW
Fercs (mr reur)
HoverThrust
Flightdrag
Maneuvering
Thrust
Th
Di
TM
FlIght angle
M
2.05
rnis
0.84mWS
6,2854N
1.4223 N
N
6.4443
13
14 Emcmncles
15 Meler
16
17
16 TotalHover ciency
18 TotalCruisEniciency
m0
12.75 deg
1.0253
Loadfactor(n)
etaji0h4
elafc
0.441
20
21 EltiWueeO
ulY
A
24 ndlvidualroraa
26
34.705in
ernanics
o
in1
1226 JW3j
27 Deedew arle
28
29 Dragcoetlsciente
30 fust Marg
Cd
1.15
32 tmenmyVarieas
~3j"
1. 39 g10.
0.,1145kg
MinEWeiht
36 Rolordiameler
otolors
37 Nlumber
36 Tirme
InHawr
35
30.0minul10.3 mule
4.882 rnis
39 Time inFligh&
606.99n*2
U 42
31
hower
power
Propeller
PropellerlIght power
Pph
Ppf
87.753 W
MAior
Motorhover
power
Motorlight power
Prnh
Pmf
W
117.004
84.561W
94598 lnr2
Cansralis
Max
Equal
-- .1145
30
Min
.00-06
.6&6
1306
1.00 00
96081 W
PowerDensoilrhoer PromlW
PowerDensily
forRight PmoEW
Eh
Ef
Energy
forIlight
ECot
Energy
total
powerdensity
Awerage
Energyforhover
Balry Type:Name
Ballerymass density
sallery energydensly
Totaltaery energy
BatType
mdens
Timein Hover
TImein Flight
CruiseRange
In
It
Teualeintha,
B3.92WUg
Wkg
61.74
58.502 WI
14.735Wh
73.237Wh
76.259W4g
ICad
2800.00 kghn3
52.53WhNKg
Edens
Ebat
73.237 Wh
1800.00
sec
616.25sec
3000 m
241,25 SSml
11167 ma
51 sigma=
52
1.00&-06
Figure D-1: Quadrotor Model (Main Worksheet)
141
30.00rnin
10.27rMin
Geometry and Area Calculations
17.35 in
Length of Arm
Larm
Rod Length-to-Diameter
Thickness of Arm (OD)
Prop Chord
Tip to Tip lenth
rod
Tarm
Cprop
Ltotal
Battery Volume
Payload Volume
Total Housing Volume
lHousing Length-to-Diameter
Housing diameter
Housing height
Housing Area
Housing material Area
Motor height
Motor diameter
Motor Area
Rod Area
Vbat
0.5016 m
19.75 in
25.0000
0.0201 m
0.0882 m
1.0031 m
0.790 in
3.47 in
39.49 in
0.0005 m^3
0.0001
0.0006 mA3
Vpay
Vtot
Hid
30.39 inA3
3.66 in*3
34.05 inA3
20000
Hh
Hd
Sh
Ha
0.0708 m
0.1416 m
0.0100 mA2
0.0394 m^2
Mh
Md
0.050B m
Sm
Sr
0.0254 m
0.0013 mA2
0.0101 m^2
rndPa
0.7500 kg/m-2
m/Ha
2.0000
0.3479
0.2331
0.0788
2.79
5.58
15.55
61.06
2.00
1.00
2.00
15.60
in
in
in2
in2
in
in
in2
in2
lWeiaht Information
Prop. mitl. marea
Housing ml. M/Pa
Weight of rods
]Weight of prop
IWeight of housing
WeIght entire structure
DRAG
Overall coeeflicient of Drag
Estimated drag (pressure)
Estimated drag (skin friction)
Tetal Drag Area
Wcf
Wp
Wh
Wstruct [
kg/mA2
kg
kg
kg
.69kg
1.0000
CD
0.0554 mA2
0.0920 mA2
D_p
D-f
0
0.1475
IA2
347.85
233.13
78.79
659.76
g
g
g
g
85.94 in*2
142.66 in^2
228.59 in^2
Figure D-2: Quadrotor Model (Geometry and Area Calculations)
142
- -
MEN
-
7-
W
Figure of Medt Calculadein
656.91 g
945.98 in^2
34.71 in
640.71 g
945.98 inA2
34.71 in
Bsde off face=
Blade ec=
Blade cl=
Blade numnber =
ta
clr-b
Cl b
l
CTdesign =
Ct
c-b
Blade chord =
Solidity (8c/pi*r) = sigma
EL
Blade loading
DL
Disc loading
Rotor speed =
Reynolds #=
Cd blade =
LoDblade =
Blade speed =
Cpi
CpV
Cptot
omega
Re
Cd b
L/Db
BS
2
0.0127
0.0882 m
0.127
3.471 in
0.100
10.298 N/mA2
58.275 rad/s
154978
0.03211
18.684
25.685 m/s
0.001016
0.000511
0.001730
556.5 rpm
84.27 it/s
00b
ch~b
Ci-b
Nb
1.2
0.2
0.6
2
Ct
CT design =
cb
Blade chord
Solidity (Bc/pi*) = sigma
Blade loading = BL
DL
Disc loading
0.0127
Rotor speed =
Reynolds #=
Cd blade =
LoD blade
Blade speed =
Cpi =
Cpv=
Cptot
F4g"r of Merit -
Figue of MeritIdeal Power =
jPjnd + P_profile
8ade ll'factor m
Blade eOr
Bladec0 =
Blade number =
1.2
0.2
12.881 W
21.938 W
Ideal Power =
P-ind + P_profle
omega
Re
Cd b
L/D..b
BS
0.082 m
0.100
10.569 N/m2
59.007 rad/s
156925
563.5 rpm
0.03194
18.78
26.8 m/s
0.001016
0.000508
0.01727
1Mu
5.420 W
9.216 W
Figure D-3: Quadrotor Model (Figure of Merit Calculations)
143
3.471 in
0.127
85.33 ft/s
4 Ele Edit Yiew Insert Fgrmat Debug Run ools 6dc-ns Window telp
INi-.al X na.
.ais
IV
W9
eLni,coln
F"
F(Genwo
J unction
VRAProject (MDRW7 0
El
B
JFcrosaftExcelObjec ts
IMSheeti (DeigCAalc
I5het2d(aterWtrc
Sheet3W(Firt Ca
L- tj
aw
heet4 (GeomAn
ThsWorkbook
Modules
vi(thrust, rotorarea, vel,
Rem
Rem
-alculates
Inducedgel
4e4Rs
of rotor
induced velocity
from
4
parameters
Rel
rho - 1.226
Pi = 3.1415
eps = 0.001
vihover -
-.4
angle)
(thrust
/
(2
*
rho *
rotorarea)) ^
0.5
old = vihover
counter = 0
vi
resid
=
1#
Rem calculate parallel and perpendicular vehicle speed
* Cos(angle * Pi / 180)
* Sin(angle * Pi / 180)
vpara - vel
vperp = vel
Rem Do loop to iterate on induced velocity until residual
Do
vTOT =
Pp-
(vpara ^ 2
vi = vihover ^ 2
resid
- Abs((vi -
InCadued
vi
old
If
-
counter +
counter > 10000
vi
(vperp + vi
viold)
/
old)
^
2)
^
0.5
vi)
vi
-
counter
+
/ vTOT
1
Then
= counter
Exit Do
End If
Loop Until resid < 0.001
End Function
Function vih(thrust,
Rem
rotorarea,
vel,
angle)
Rem Calculates induced velocity of rotor in hover
Rem
rho vih
=
1.226
(thrust
/
(2
*
rho * rotorarea))
0.5
End Function
Figure D-4: Quadrotor Model (Velocity Macro)
144
is
small
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