Coaxial Rotary-Wing Mini Aerial Vehicle Aeromechanics Alexander P. K. Hall
A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy
UAV Group School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney March 2009
Declaration I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material previously published or written by another person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of the University or other institute of higher learning, except where due acknowledgement has been made in the text.
Alexander Hall
30 March 2009
i
ii
Abstract Alexander Hall The University of Sydney
Doctor of Philosophy March 2009
Coaxial Rotary-Wing Mini Aerial Vehicle Aeromechanics This thesis presents novel methodology for analysing the aeromechanical performance of small coaxial helicopters for use as Unmanned Aerial Vehicles. Fundamentally, the focus of this work is on developing a simple yet robust analysis methodology for investigating the aeromechanical behaviour of highly dynamic coaxial rotors. In particular, focus is placed on creating a method which is computationally inexpensive yet retains accuracy. By retaining these objectives throughout the development process, a design tool with characteristics which are beneficial to platform design optimisation has been created. Specifically, a Proxflyer type rotorcraft was chosen as the desired target of investigation. This platform places particularly challenging requirements on any analysis methodology used. The combination of highly dynamic flapping coaxial rotors, which are positioned in close proximity, places high demands on aerodynamic modelling. This is made more challenging by low Reynolds number at which the rotors are operating. In this region, there is little known about the flow characteristics which drive rotor performance. Original analysis methodology has been developed to encapsulate these effects. New analysis methods for modelling coaxial rotor interaction as well as highly dynamic rotor flapping has also been developed. A method which accounts for the interaction between coaxial rotors has been developed for use within Blade Element Momentum Theory. This method is characterised as Velocity Augmentation, which operates by mapping rotor effects between the coaxial rotors. Verification of this theory was conducted and shows that the computational model agrees well with experimental tests. To account for complex rotor dynamics, a model which represents the flapping of the rotor blades was developed. This model allows the rotor characteristics which effect flapping performance to be investigated. The developed analysis methodology has been applied to the study of the stability, controllability and efficiency of Proxflyer type rotorcraft. Two studies centred on this rotorcraft type show that the developed analysis can be used for configuration design and optimisation. Firstly, an existing rotorcraft configuration has been studied with improvements seen in both stability and efficiency. Secondly, a new rotorcraft configuration has been analysed with results leading to good performance in stability, controllability and efficiency. Through these studies, the new analysis methodology is shown to give rise to many new avenues of research, and also provides important new techniques for the analysis and design of Coaxial Rotary-Wing Mini Aerial Vehicles.
Project Publications Full Paper Reviewed Hall, A., Wong, K.C. and Auld, D., “Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory”, Proceedings of the 7th Australian Pacific Vertiflite Conference on Helicopter Technology, Melbourne, Australia, 9 - 12 March, 2009 *Received best paper award.
Hall, A. and Wong K.C., “Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors”, Proceedings of the 3rd Australasian Unmanned Air Vehicles Conference, Melbourne, Australia, 9 - 12 March, 2009 Hall, A. and Wong, K.C., “Development of an Analysis Package for Increased Stability Rotary-Wing Micro Air Vehicles”, Proceedings of the 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, Victoria, March 19-22, 2007
Extended Abstract Reviewed Hall, A., Wong, K.C. and Auld, D., “Analysis and Conceptual Design of a Novel MAV Rotorcraft”, Proceedings of the 34th European Rotorcraft Forum, Liverpool, England, 2008 Hall, A., Wong, K.C. and Auld, D., “Coaxial Aero-Mechanical Analysis of MAV Rotorcraft with Rotor Interaction for Optimisation”, Proceedings of the 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, Canada, 2008 Hall, A., Wong, K.C. and Auld, D., “Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation”, Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA-2006-7076
iii
Acknowledgements Over the past four years I have both enjoyed and hated the process of completing my PhD. Although I have always thoroughly enjoyed working on coaxial helicopters, I almost always took the road less travelled. And with the support and guidance of my supervisors, KC and Doug, have turned my ideas into something useable. For this I thank them. I appreciate the encouragement and support that my family has shown over the neverending last four years. Mum, for always listening to me (for better or worse) when I needed it, as well as for being put through the painful task of reading all my draft chapters. James, for annoying me as an older brother should. Liz and Pat, for coming to Sydney to distract me from my project, always when I needed it. And, Dette and Sarah for giving me the drive to get a real job. Alana has my deepest thanks and appreciation for her support through the crunch time of this project. She has given me someone to laugh, smile and joke with, as well listening to my occasional rants, and telling me that I am just being silly. It certainly has been a much easier and more enjoyable ride with her. To all my friends who have supported me over the never ending four years, I thank you. In particular, Brett for being my coffee dealer; and Kane and Stu (Alexander) for tempting me to distraction, oh so many times. My office-mates (Peter, Josh, Angus, Juan and James) over the years have provided me with not only good company, but a wall to bounce ideas off. This is especially useful when you have created one too many problems for yourself. And lastly, but not least, Stuart and Duncan for distracting me so much, that I needed the full four years!
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The helicopter approaches closer than any other vehicle to fulfillment of mankind’s ancient dreams of the flying horse and the magic carpet. Igor Sikorsky
Engineers like to solve problems. If there are no problems handily available, they will create their own problems. Scott Adams
Contents Declaration
i
Abstract
ii
Project Publications
iii
Acknowledgements
iv
Contents
vi
List of Figures
xiv
List of Tables
xxiii
List of Symbols
xxv
List of Abbreviations
xxviii
1 Introduction 1.1
1.2
1
Thesis Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.3
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Rotary-Wing Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1
Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1.1
Conventional . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.2.1.2
Coaxial . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
vi
CONTENTS
vii 1.2.1.3
Tandem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.2.1.4
Multi-Rotor . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Rotary-Wing UAVs . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.3
Proxflyer Rotorcraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.4
Rotary-Wing Conventions and Definitions . . . . . . . . . . . . . . . . . . .
9
1.5
Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
1.5.1
Summary of Completed Work . . . . . . . . . . . . . . . . . . . . . .
10
1.5.2
Chapter Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.5.2.1
Chapter 2 - Background and Motivation . . . . . . . . . . .
11
1.5.2.2
Chapter 3 - Blade Element Momentum Theory . . . . . . .
12
1.5.2.3
Chapter 4 - Coaxial Rotor Interaction Modelling . . . . . .
12
1.5.2.4
Chapter 5 - Interaction Model Verification . . . . . . . . .
12
1.5.2.5
Chapter 6 - Blade Flap Modelling . . . . . . . . . . . . . .
12
1.5.2.6
Chapter 7 - Coaxial Rotorcraft Analysis . . . . . . . . . . .
13
1.5.2.7
Chapter 8 - Design Studies . . . . . . . . . . . . . . . . . .
13
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
1.2.2
1.6
2 Background and Motivation
14
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.2
Problem to Solve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.3
Configuration Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2.4
Coaxial Helicopter Configuration . . . . . . . . . . . . . . . . . . . . . . . .
18
2.4.1
Existing Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.4.2
Benefits and Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.4.3
Configuration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
23
Helicopter Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.5.1
Rotor Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.5.2
Rotor Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.5.3
Rotorcraft Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.5.4
Analysis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.6
Design Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.5
CONTENTS
viii
3 Blade Element Momentum Theory
36
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.2
Basic Blade Element Momentum Theory . . . . . . . . . . . . . . . . . . . .
37
3.2.1
Hover and Vertical Flight . . . . . . . . . . . . . . . . . . . . . . . .
40
3.2.2
Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.2.3
Aerodynamic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.2.4
Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
3.2.5
Example Implementation of Basic Theory . . . . . . . . . . . . . . .
45
3.3
Tip Loss Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
3.4
Multiple Blade Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.5
Translational Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.6
Aerodynamic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.7
Problem Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.8
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
4 Coaxial Rotor Interaction 4.1
63
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.1.2
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
Background and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.2.1
Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
4.2.2
Available Options . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
4.2.2.1
Empirical Relations . . . . . . . . . . . . . . . . . . . . . .
65
4.2.2.2
Vortex Methods . . . . . . . . . . . . . . . . . . . . . . . .
67
4.2.2.3
Additional Methods . . . . . . . . . . . . . . . . . . . . . .
68
4.2.2.4
BEMT Methods . . . . . . . . . . . . . . . . . . . . . . . .
68
Summary and Method Choice . . . . . . . . . . . . . . . . . . . . . .
70
4.3
Overview of Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
4.4
Rotor Interaction Method within BEMT . . . . . . . . . . . . . . . . . . . .
73
4.5
Simple Test Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4.6
Method Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.2
4.2.3
CONTENTS
4.7
4.6.1
Centred Around Hover . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.6.2
Static Streamtube . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.6.3
Steady State Flow Between Rotors . . . . . . . . . . . . . . . . . . .
82
4.6.4
Incompressible Inviscid Flow . . . . . . . . . . . . . . . . . . . . . .
83
Full Method Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4.7.1
Convergence Procedure Outline . . . . . . . . . . . . . . . . . . . . .
83
4.7.2
Geometric Calculation Outline . . . . . . . . . . . . . . . . . . . . .
84
4.7.3
Geometric Calculation Explanation . . . . . . . . . . . . . . . . . . .
87
4.7.3.1
Azimuth Location . . . . . . . . . . . . . . . . . . . . . . .
87
4.7.3.2
Flap Angles
. . . . . . . . . . . . . . . . . . . . . . . . . .
88
4.7.3.3
Radial Location . . . . . . . . . . . . . . . . . . . . . . . .
89
4.7.3.4
Stream Contraction Angle . . . . . . . . . . . . . . . . . .
94
4.7.3.5
Vertical Separation . . . . . . . . . . . . . . . . . . . . . .
96
4.7.3.6
Radial Interpolation . . . . . . . . . . . . . . . . . . . . . .
98
Implementation Method . . . . . . . . . . . . . . . . . . . . . . . . .
99
4.7.4
4.8
ix
4.7.4.1
Pre-Loop Calculations . . . . . . . . . . . . . . . . . . . . .
100
4.7.4.2
Loop Calculations . . . . . . . . . . . . . . . . . . . . . . .
100
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
5 Interaction Model Verification
105
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
105
5.2
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
5.2.1
Rotor Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
5.2.2
Rotor Drive Mechanism . . . . . . . . . . . . . . . . . . . . . . . . .
109
5.2.3
Load Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
5.2.4
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
112
5.2.5
Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
5.3
Coded Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
5.4
Test Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
5.5
Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
5.6
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
123
CONTENTS 5.6.1
Constant Upper Rotor Speed . . . . . . . . . . . . . . . . . . . . . .
125
5.6.1.1
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
5.6.1.2
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
Constant Lower Rotor Speed . . . . . . . . . . . . . . . . . . . . . .
129
5.6.2.1
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
5.6.2.2
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
131
Separation Comparison . . . . . . . . . . . . . . . . . . . . . . . . .
133
5.6.3.1
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
5.6.3.2
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
Problems with Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
142
5.7.1
Rotor Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
142
5.7.2
Blade Twist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
143
5.7.3
Section Aerodynamic Data . . . . . . . . . . . . . . . . . . . . . . .
145
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
146
5.6.2
5.6.3
5.7
5.8
x
6 Modelling of Blade Flapping
147
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
147
6.2
Modelling Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
147
6.3
Rotational Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . .
148
6.3.1
Axis Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
149
6.3.2
Blade Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
150
6.3.3
Gravity Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
151
6.3.4
Inertial Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
152
6.3.5
Blade Rotational Moment of Inertia . . . . . . . . . . . . . . . . . .
152
Blade Pair Flapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
153
6.4.1
Blade Pair - Blade Load . . . . . . . . . . . . . . . . . . . . . . . . .
156
6.4.2
Blade Pair - Gravity Load . . . . . . . . . . . . . . . . . . . . . . . .
156
6.4.3
Blade Pair - Inertial Load . . . . . . . . . . . . . . . . . . . . . . . .
157
6.4.4
Blade Pair - Rotational Inertia . . . . . . . . . . . . . . . . . . . . .
158
6.5
Method Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
158
6.6
Rotor to Aircraft Axis Transformation . . . . . . . . . . . . . . . . . . . . .
161
6.7
Example Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
162
6.8
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
165
6.4
CONTENTS
xi
7 Rotorcraft Analysis
168
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
7.2
Entire Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
169
7.2.1
Analysis Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . .
169
7.2.2
BEMT Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
172
7.2.3
Interaction Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
174
7.2.4
Blade Dynamics Analysis . . . . . . . . . . . . . . . . . . . . . . . .
176
7.2.5
Analysis Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . .
177
7.3
Analysis Package Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
178
7.4
Methods of Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
182
7.4.1
Analysis Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
182
7.4.1.1
Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
7.4.1.2
Control Authority . . . . . . . . . . . . . . . . . . . . . . .
183
7.4.1.3
Gust Response . . . . . . . . . . . . . . . . . . . . . . . . .
184
Input Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
186
7.4.2.1
Blade Configuration . . . . . . . . . . . . . . . . . . . . . .
186
7.4.2.2
Rotor Configuration . . . . . . . . . . . . . . . . . . . . . .
187
Aircraft Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
187
7.5.1
Rotor Cyclic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188
7.5.2
Fully Controlled Rotor . . . . . . . . . . . . . . . . . . . . . . . . . .
188
7.5.3
Flapping Feedback Rotor . . . . . . . . . . . . . . . . . . . . . . . .
188
7.5.4
Flapping Feedback and Partial Control
. . . . . . . . . . . . . . . .
188
7.5.5
Flapping Feedback and Full Control . . . . . . . . . . . . . . . . . .
189
7.6
Control Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
189
7.7
Flapping Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
191
7.8
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
191
7.4.2
7.5
8 Design Studies
193
8.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
193
8.2
Design Study Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
194
8.3
Analysis Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
CONTENTS
8.4
8.5
8.6
8.7
xii
8.3.1
Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
196
8.3.2
Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
196
8.3.3
Controllability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
199
Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
200
8.4.1
Blade Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
200
8.4.2
Rotor Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
201
8.4.3
Rotorcraft Configuration . . . . . . . . . . . . . . . . . . . . . . . . .
202
8.4.4
Control Configuration . . . . . . . . . . . . . . . . . . . . . . . . . .
202
8.4.5
Design Variable Summary . . . . . . . . . . . . . . . . . . . . . . . .
204
Design Study 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
204
8.5.1
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
205
8.5.2
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
206
8.5.3
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
208
Design Study 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
210
8.6.1
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
211
8.6.2
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
215
8.6.3
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
218
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Conclusion
219 223
9.1
Project Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
223
9.2
Major Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
224
9.2.1
Rotor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
225
9.2.2
Individual Blade Analysis . . . . . . . . . . . . . . . . . . . . . . . .
225
9.2.3
Blade Flapping Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
225
9.2.4
Rotor Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
226
9.2.5
Control Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
226
9.2.6
Flapping Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . .
227
9.3
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
227
9.4
Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
228
A Rotary Wing Definitions
230
CONTENTS
xiii
B Interaction Model Verification Appendix
239
C Blade Flapping Appendix
254
D Design Study Appendix
266
E Author’s Publications
282
References
344
List of Figures 1.1
Yamaha R-Max Unmanned Helicopter. . . . . . . . . . . . . . . . . . . . . .
7
1.2
Proxflyer - Rotorcraft range. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3
Proxflyer - Mosquito Twin-tail. . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.1
Gyrodyne QH-50 DASH Aircraft. . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2
Kamov Ka-27SP - Anti-Submarine Aircraft. . . . . . . . . . . . . . . . . . .
19
2.3
AirScooter G70 UAV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.4
E-flite - Blade CX2 Radio Controlled Aircraft. . . . . . . . . . . . . . . . .
21
2.5
Proxflyer - Mosquito Aircraft. . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.6
Comparison of Single and Coaxial Rotor Performance. . . . . . . . . . . . .
23
2.7
Comparison of Conventional and Coaxial Rotor Heads. . . . . . . . . . . . .
24
3.1
Grouping Rotor Blades Together. . . . . . . . . . . . . . . . . . . . . . . . .
37
3.2
Individual Induced Velocities for each Blade Element. . . . . . . . . . . . .
38
3.3
Element Geometric Definition. . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.4
Momentum Theory Flow Development.
. . . . . . . . . . . . . . . . . . . .
41
3.5
Blade Element Aerodynamic Diagram - Hover. . . . . . . . . . . . . . . . .
43
3.6
Blade Element Aerodynamic Diagram - Climb. . . . . . . . . . . . . . . . .
44
3.7
Element Thrust Force Diagram. . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.8
Element convergence procedure. . . . . . . . . . . . . . . . . . . . . . . . . .
46
3.9
Example BEMT procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
3.10 Basic BEMT Induced Velocity Distribution. . . . . . . . . . . . . . . . . . .
48
3.11 Basic BEMT Normal Force Distribution. . . . . . . . . . . . . . . . . . . . .
48
3.12 Basic BEMT Tangential Force Distribution. . . . . . . . . . . . . . . . . . .
49
xiv
LIST OF FIGURES
xv
3.13 Basic BEMT Angle of Attack Distribution. . . . . . . . . . . . . . . . . . .
49
3.14 Prandtl Tip Loss Correction Factor Distribution. . . . . . . . . . . . . . . .
51
3.15 Prandtl Tip Loss Factor Distribution. . . . . . . . . . . . . . . . . . . . . .
51
3.16 Normal Force Distribution with Prandtl Tip Loss Factor. . . . . . . . . . .
52
3.17 Tangential Force Distribution with Prandtl Tip Loss Factor. . . . . . . . . .
52
3.18 Multiple Blade Breakup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.19 Multiple Blade Induced Velocity Distribution. . . . . . . . . . . . . . . . . .
54
3.20 Multiple Blade Thrust Distribution. . . . . . . . . . . . . . . . . . . . . . .
55
3.21 Translational Flight Velocity Diagram. . . . . . . . . . . . . . . . . . . . . .
56
3.22 Helicopter Axis System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.23 Effect of Translation on Blade. . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.24 Translation Velocity Blade Components. . . . . . . . . . . . . . . . . . . . .
59
3.25 Blade Angle of Attack Quadrants. . . . . . . . . . . . . . . . . . . . . . . .
60
4.1
Induced velocity influencing effect on coaxial rotors. . . . . . . . . . . . . .
72
4.2
Steady-state coaxial streamtubes. . . . . . . . . . . . . . . . . . . . . . . . .
73
4.3
Coaxial streamtubes with blade flapping.
. . . . . . . . . . . . . . . . . . .
74
4.4
Iteration upon coaxial influence. . . . . . . . . . . . . . . . . . . . . . . . .
75
4.5
Element convergence error. . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4.6
Influence BEMT flow analysis. . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.7
Simple BEMT algorithm procedure. . . . . . . . . . . . . . . . . . . . . . .
77
4.8
Basic rotor interaction procedure. . . . . . . . . . . . . . . . . . . . . . . . .
78
4.9
Simple implementation, influence between blades. . . . . . . . . . . . . . . .
79
4.10 Thrust Distribution with Influence. . . . . . . . . . . . . . . . . . . . . . . .
81
4.11 Thrust Distribution without Influence. . . . . . . . . . . . . . . . . . . . . .
81
4.12 Extended Implementation Diagram. . . . . . . . . . . . . . . . . . . . . . .
84
4.13 Rotor interaction procedure with geometric calculations. . . . . . . . . . . .
85
4.14 Rotor Location Differences. . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4.15 Azimuth Influence Location. . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
4.16 Flap Location Calculation Diagram. . . . . . . . . . . . . . . . . . . . . . .
89
4.17 Coaxial Streamtubes with Straight Assumption. . . . . . . . . . . . . . . . .
90
LIST OF FIGURES
xvi
4.18 Upper Radial Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.19 Lower Radial Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
4.20 Slipstream development across rotor. . . . . . . . . . . . . . . . . . . . . . .
95
4.21 Streamtube contraction across rotor. . . . . . . . . . . . . . . . . . . . . . .
96
4.22 Vertical separation between rotor elements. . . . . . . . . . . . . . . . . . .
97
4.23 Radial Interpolation Regions. . . . . . . . . . . . . . . . . . . . . . . . . . .
98
4.24 Pre convergence loop procedure. . . . . . . . . . . . . . . . . . . . . . . . .
100
4.25 Influence Velocity Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . .
101
5.1
Experimental Test Rig - Assembled for Use. . . . . . . . . . . . . . . . . . .
107
5.2
Experimental Test Rig - Drawing.
. . . . . . . . . . . . . . . . . . . . . . .
108
5.3
Experimental Test Rig - Rotor Blades. . . . . . . . . . . . . . . . . . . . . .
109
5.4
Experimental Test Rig - Assembled Rotor. . . . . . . . . . . . . . . . . . . .
110
5.5
Experimental Test Rig - Motor and Gearbox. . . . . . . . . . . . . . . . . .
111
5.6
Experimental Test Rig - Mini 45 Load Cell. . . . . . . . . . . . . . . . . . .
112
5.7
Experimental Test Rig - National Instruments DAQ. . . . . . . . . . . . . .
114
5.8
Experimental Test Rig - Motor Speed Pickup. . . . . . . . . . . . . . . . . .
115
5.9
Experimental Test Rig - Motor Speed Filter. . . . . . . . . . . . . . . . . .
116
5.10 Experimental Test Rig - Brushless Speed Controller. . . . . . . . . . . . . .
116
5.11 Experimental Test Rig - Servo Controller. . . . . . . . . . . . . . . . . . . .
117
5.12 Experimental Test Rig - Test Interface.
. . . . . . . . . . . . . . . . . . . .
117
5.13 Cambered Flat Plate Aerofoil Diagram. . . . . . . . . . . . . . . . . . . . .
118
5.14 Cambered Flat Plate Aerofoil Aerodynamic Data. . . . . . . . . . . . . . .
120
5.15 Test Schedule Sample - Commanded Rotor Speed. . . . . . . . . . . . . . .
121
5.16 Test Schedule Sample - Resulting Load Cell Thrust. . . . . . . . . . . . . .
121
5.17 Full Range Sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
122
5.18 Full Range Sample with Region Averages. . . . . . . . . . . . . . . . . . . .
124
5.19 Thrust Readings - Upper Rotor Speed 2000RPM - 50mm Separation. . . . .
125
5.20 Thrust Readings - Upper Rotor Speed 2000RPM - 10mm Separation. . . . .
126
5.21 Thrust Readings - Upper Rotor Speed 2000RPM - 150mm Separation. . . .
126
5.22 Variation from Experiment - Constant Upper Rotor - 50mm Separation. . .
127
LIST OF FIGURES
xvii
5.23 Variation from Experiment - Constant Upper Rotor - 100mm Separation. .
128
5.24 Variation from Experiment - Constant Upper Rotor - 150mm Separation. .
128
5.25 Experiment and Code Trend Fits - 50mm Separation, Constant Upper Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
5.26 Experiment and Code Trend Fits - 100mm Separation, Constant Upper Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
5.27 Experiment and Code Trend Fits - 150mm Separation, Constant Upper Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
5.28 Thrust Readings - Lower Rotor Speed 2000RPM - 50mm Separation. . . . .
131
5.29 Thrust Readings - Lower Rotor Speed 2000RPM - 10mm Separation. . . . .
132
5.30 Thrust Readings - Lower Rotor Speed 2000RPM - 150mm Separation. . . .
132
5.31 Variation from Experiment - Constant Lower Rotor - 50mm Separation. . .
133
5.32 Variation from Experiment - Constant Lower Rotor - 100mm Separation. .
134
5.33 Variation from Experiment - Constant Lower Rotor - 150mm Separation. .
134
5.34 Experiment and Code Trend Fits - 50mm Separation, Constant Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
5.35 Experiment and Code Trend Fits - 100mm Separation, Constant Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
136
5.36 Experiment and Code Trend Fits - 150mm Separation, Constant Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
136
5.37 Separation Variation - Upper Rotor 0RPM, Lower Rotor 1500RPM. . . . .
137
5.38 Separation Variation - Upper Rotor 500RPM, Lower Rotor 1500RPM. . . .
137
5.39 Separation Variation - Upper Rotor 1000RPM, Lower Rotor 1500RPM. . .
138
5.40 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 1500RPM. . .
138
5.41 Separation Variation - Upper Rotor 2000RPM, Lower Rotor 1500RPM. . .
139
5.42 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 0RPM. . . . .
140
5.43 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 500RPM. . . .
140
5.44 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 1000RPM. . .
141
5.45 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 1500RPM. . .
141
5.46 Separation Variation - Upper Rotor 1500RPM, Lower Rotor 2000RPM. . .
142
5.47 Variation of Rotor Speed - Slower Speed.
. . . . . . . . . . . . . . . . . . .
143
5.48 Variation of Rotor Speed - Higher Speed. . . . . . . . . . . . . . . . . . . .
144
5.49 Variation of Blade Twist Distribution. . . . . . . . . . . . . . . . . . . . . .
145
LIST OF FIGURES
xviii
6.1
Simplified Flapping Axis System - Centre Flapping. . . . . . . . . . . . . .
150
6.2
Simplified Flapping Axis System - Offset Flapping. . . . . . . . . . . . . . .
151
6.3
Moment Derived from Blade Lift. . . . . . . . . . . . . . . . . . . . . . . . .
151
6.4
Moment Derived from Element Gravity Load. . . . . . . . . . . . . . . . . .
152
6.5
Moment Derived from Element Inertial Load. . . . . . . . . . . . . . . . . .
153
6.6
Calculation of Blade Rotational Inertia. . . . . . . . . . . . . . . . . . . . .
153
6.7
Closeup of Proxflyer Aircraft Types Rotor Hub. . . . . . . . . . . . . . . . .
154
6.8
Breakup of Blade Pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
155
6.9
Blade Pair Axis Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . .
155
6.10 Blade Pair - Blade Load Calculation. . . . . . . . . . . . . . . . . . . . . . .
156
6.11 Blade Pair - Gravity Load Calculation. . . . . . . . . . . . . . . . . . . . . .
157
6.12 Blade Pair - Blade Load Calculation. . . . . . . . . . . . . . . . . . . . . . .
157
6.13 Blade Pair - Inertia Calculation. . . . . . . . . . . . . . . . . . . . . . . . .
158
6.14 Time simulation procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
6.15 Rotor to Aircraft Axis Flap Angle Transformation. . . . . . . . . . . . . . .
162
6.16 Pitch Flapping Superposition. . . . . . . . . . . . . . . . . . . . . . . . . . .
163
6.17 Roll Flapping Superposition. . . . . . . . . . . . . . . . . . . . . . . . . . .
163
6.18 Example Gust Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
164
6.19 Blade Flapping Response - 5ms−1 . . . . . . . . . . . . . . . . . . . . . . . .
165
6.20 Rotor Flapping Response - 5ms−1 . . . . . . . . . . . . . . . . . . . . . . . .
166
6.21 Rotor Flapping Response - Steady State Angles. . . . . . . . . . . . . . . .
166
7.1
Aircraft and Rotor Axis Overlaid on Proxflyer. . . . . . . . . . . . . . . . .
170
7.2
Aircraft and Rotor Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171
7.3
Rotor Axis - Top. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
172
7.4
Rotor Axis - Bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
173
7.5
Blade Element Aerodynamic Diagram with Additional Components. . . . .
174
7.6
Disc Thrust Contour - Translational Wind. . . . . . . . . . . . . . . . . . .
175
7.7
Disc Thrust Contour - Cyclic Application. . . . . . . . . . . . . . . . . . . .
176
7.8
Blade Element Aerodynamic Diagram with Augmenting Velocity. . . . . . .
177
7.9
Flapping Velocity Assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . .
177
LIST OF FIGURES
xix
7.10 Diagram to Analyse Aircraft Configuration. . . . . . . . . . . . . . . . . . .
179
7.11 Diagram to Simulate Aircraft Motion. . . . . . . . . . . . . . . . . . . . . .
180
7.12 Diagram to Get State-Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . .
181
7.13 Rotor Performance for Varying Rotor Speeds. . . . . . . . . . . . . . . . . .
183
7.14 Rotor Performance for Varying Collective Control. . . . . . . . . . . . . . .
184
7.15 Rotor Performance for Step Cyclic Input. . . . . . . . . . . . . . . . . . . .
185
7.16 Rotor Performance for Pulse Gust Input. . . . . . . . . . . . . . . . . . . .
185
7.17 Blade Radial Chord and Twist Distribution. . . . . . . . . . . . . . . . . . .
187
7.18 Blade Control Connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
189
7.19 Aileron Blade Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
190
7.20 Elevator Blade Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
190
7.21 Flapping Feedback Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . .
192
8.1
Destabilising Moments Caused by Gust. . . . . . . . . . . . . . . . . . . . .
194
8.2
Control Force Availability. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
8.3
Example Rotor Speed Sweep. . . . . . . . . . . . . . . . . . . . . . . . . . .
197
8.4
Example Rotor Collective Sweep. . . . . . . . . . . . . . . . . . . . . . . . .
197
8.5
Stability Test Gust Input. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
198
8.6
Stability Test CG Moments. . . . . . . . . . . . . . . . . . . . . . . . . . . .
198
8.7
Controllability Test Cyclic Input. . . . . . . . . . . . . . . . . . . . . . . . .
199
8.8
Controllability Test CG Forces. . . . . . . . . . . . . . . . . . . . . . . . . .
200
8.9
Blade Design Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
201
8.10 Rotor Position Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
203
8.11 Proxflyer Mosquito Rotorcraft. . . . . . . . . . . . . . . . . . . . . . . . . .
205
8.12 Design Study 1 - Baseline Gust Response. . . . . . . . . . . . . . . . . . . .
207
8.13 Design Study 1 - Design Variant Performance Plot. . . . . . . . . . . . . . .
209
8.14 New Rotorcraft Configuration - Translation. . . . . . . . . . . . . . . . . . .
212
8.15 New Rotorcraft Configuration - Rotation. . . . . . . . . . . . . . . . . . . .
212
8.16 New Rotorcraft Configuration - Fast Translation. . . . . . . . . . . . . . . .
213
8.17 Design Study 2 - Rotor Blade. . . . . . . . . . . . . . . . . . . . . . . . . . .
214
8.18 Design Study 2 - Example Power Plot. . . . . . . . . . . . . . . . . . . . . .
216
LIST OF FIGURES
xx
8.19 Design Study 2 - Example Power Plot. . . . . . . . . . . . . . . . . . . . . .
216
8.20 Design Study 2 - Example Power Plot. . . . . . . . . . . . . . . . . . . . . .
217
8.21 Design Study 2 - Power vs Stability Comparison. . . . . . . . . . . . . . . .
219
8.22 Design Study 2 - Power vs Controllability Comparison. . . . . . . . . . . . .
220
8.23 Design Study 2 - Proposed General Configuration. . . . . . . . . . . . . . .
221
A.1 Convention Helicopter with Axis System. . . . . . . . . . . . . . . . . . . .
231
A.2 Convention Helicopter Axis System Wire-frame. . . . . . . . . . . . . . . . .
232
A.3 Coaxial Helicopter with Axis System.
. . . . . . . . . . . . . . . . . . . . .
233
A.4 Coaxial Helicopter Axis System Wire-frame. . . . . . . . . . . . . . . . . . .
234
A.5 Four Bladed Rotor with Axis System. . . . . . . . . . . . . . . . . . . . . .
235
A.6 Four Bladed Rotor Axis System Wire-frame. . . . . . . . . . . . . . . . . .
236
A.7 Rotor Blade with Axis System. . . . . . . . . . . . . . . . . . . . . . . . . .
237
A.8 Rotor Blade Axis System Wire-frame. . . . . . . . . . . . . . . . . . . . . .
238
B.1 Verification Plots - 50mm Separation, Constant Upper Rotor Speed. . . . .
243
B.2 Verification Plots - 100mm Separation, Constant Upper Rotor Speed.
. . .
244
B.3 Verification Plots - 150mm Separation, Constant Upper Rotor Speed.
. . .
245
B.4 Verification Plots - 50mm Separation, Constant Lower Rotor Speed. . . . .
246
B.5 Verification Plots - 100mm Separation, Constant Lower Rotor Speed. . . . .
247
B.6 Verification Plots - 150mm Separation, Constant Lower Rotor Speed. . . . .
248
B.7 Verification Plots - Separation Variation, Constant 0 RPM Lower Rotor Speed.249 B.8 Verification Plots - Separation Variation, Constant 500 RPM Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
250
B.9 Verification Plots - Separation Variation, Constant 1000 RPM Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
251
B.10 Verification Plots - Separation Variation, Constant 1500 RPM Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
252
B.11 Verification Plots - Separation Variation, Constant 2000 RPM Lower Rotor Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
253
C.1 Test Implementation Flapping Response - 0ms−1 . . . . . . . . . . . . . . . .
255
C.2 Test Implementation Flapping Response - 1ms−1 . . . . . . . . . . . . . . . .
256
C.3 Test Implementation Flapping Response - 2ms−1 . . . . . . . . . . . . . . . .
257
LIST OF FIGURES
xxi
C.4 Test Implementation Flapping Response - 3ms−1 . . . . . . . . . . . . . . . .
258
C.5 Test Implementation Flapping Response - 4ms−1 . . . . . . . . . . . . . . . .
259
C.6 Test Implementation Flapping Response - 5ms−1 . . . . . . . . . . . . . . . .
260
C.7 Test Implementation Flapping Response - 6ms−1 . . . . . . . . . . . . . . . .
261
C.8 Test Implementation Flapping Response - 7ms−1 . . . . . . . . . . . . . . . .
262
C.9 Test Implementation Flapping Response - 8ms−1 . . . . . . . . . . . . . . . .
263
C.10 Test Implementation Flapping Response - 9ms−1 . . . . . . . . . . . . . . . .
264
C.11 Test Implementation Flapping Response - 10ms−1 . . . . . . . . . . . . . . .
265
D.1 Design Study 1 - Design 1 Gust Response. . . . . . . . . . . . . . . . . . . .
266
D.2 Design Study 1 - Design 2 Gust Response. . . . . . . . . . . . . . . . . . . .
267
D.3 Design Study 1 - Design 3 Gust Response. . . . . . . . . . . . . . . . . . . .
267
D.4 Design Study 1 - Design 4 Gust Response. . . . . . . . . . . . . . . . . . . .
268
D.5 Design Study 1 - Design 5 Gust Response. . . . . . . . . . . . . . . . . . . .
268
D.6 Design Study 1 - Design 6 Gust Response. . . . . . . . . . . . . . . . . . . .
269
D.7 Design Study 1 - Design 7 Gust Response. . . . . . . . . . . . . . . . . . . .
269
D.8 Design Study 1 - Design 8 Gust Response. . . . . . . . . . . . . . . . . . . .
270
D.9 Design Study 1 - Design 9 Gust Response. . . . . . . . . . . . . . . . . . . .
270
D.10 Design Study 1 - Design 10 Gust Response. . . . . . . . . . . . . . . . . . .
271
D.11 Design Study 1 - Design 11 Gust Response. . . . . . . . . . . . . . . . . . .
271
D.12 Design Study 2 - Design 1 Performance Plots. . . . . . . . . . . . . . . . . .
272
D.13 Design Study 2 - Design 2 Performance Plots. . . . . . . . . . . . . . . . . .
272
D.14 Design Study 2 - Design 3 Performance Plots. . . . . . . . . . . . . . . . . .
273
D.15 Design Study 2 - Design 4 Performance Plots. . . . . . . . . . . . . . . . . .
273
D.16 Design Study 2 - Design 5 Performance Plots. . . . . . . . . . . . . . . . . .
274
D.17 Design Study 2 - Design 6 Performance Plots. . . . . . . . . . . . . . . . . .
274
D.18 Design Study 2 - Design 7 Performance Plots. . . . . . . . . . . . . . . . . .
275
D.19 Design Study 2 - Design 8 Performance Plots. . . . . . . . . . . . . . . . . .
275
D.20 Design Study 2 - Design 9 Performance Plots. . . . . . . . . . . . . . . . . .
276
D.21 Design Study 2 - Design 10 Performance Plots. . . . . . . . . . . . . . . . .
276
D.22 Design Study 2 - Design 11 Performance Plots. . . . . . . . . . . . . . . . .
277
LIST OF FIGURES
xxii
D.23 Design Study 2 - Design 12 Performance Plots. . . . . . . . . . . . . . . . .
277
D.24 Design Study 2 - Design 13 Performance Plots. . . . . . . . . . . . . . . . .
278
D.25 Design Study 2 - Design 14 Performance Plots. . . . . . . . . . . . . . . . .
278
D.26 Design Study 2 - Design 15 Performance Plots. . . . . . . . . . . . . . . . .
279
D.27 Design Study 2 - Design 16 Performance Plots. . . . . . . . . . . . . . . . .
279
D.28 Design Study 2 - Design 17 Performance Plots. . . . . . . . . . . . . . . . .
280
D.29 Design Study 2 - Design 18 Performance Plots. . . . . . . . . . . . . . . . .
280
D.30 Design Study 2 - Design 19 Performance Plots. . . . . . . . . . . . . . . . .
281
D.31 Design Study 2 - Design 20 Performance Plots. . . . . . . . . . . . . . . . .
281
List of Tables 3.1
Basic BEMT Implementation Aircraft Geometry . . . . . . . . . . . . . . .
47
3.2
Basic BEMT Implementation Rotor Performance . . . . . . . . . . . . . . .
48
3.3
Rotor Performance with Prandtl Tip Loss Modelling . . . . . . . . . . . . .
50
3.4
Example Aerodynamic Data for NACA0012 . . . . . . . . . . . . . . . . . .
61
4.1
Simple Implementation Data . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.2
Simple Implementation Results . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.1
Test Rig Rotor and Blade Dimensions . . . . . . . . . . . . . . . . . . . . .
109
5.2
Test Rig Motor Specifications . . . . . . . . . . . . . . . . . . . . . . . . . .
110
5.3
Test Rig Motor Load Cell Specifications . . . . . . . . . . . . . . . . . . . .
113
5.4
Load Cell Calibration Error . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
5.5
Tested variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
6.1
Blade Flapping Implementation Aircraft Geometry . . . . . . . . . . . . . .
164
8.1
Design Variable Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
204
8.2
Design Study 1 - Base Rotorcraft Geometry . . . . . . . . . . . . . . . . . .
206
8.3
Design Study 1 - Baseline Rotorcraft Performance . . . . . . . . . . . . . .
206
8.4
Design Study 1 - Design Variations Analysed . . . . . . . . . . . . . . . . .
207
8.5
Design Study 1 - Performance Results . . . . . . . . . . . . . . . . . . . . .
208
8.6
Design Study 2 - Fixed Rotorcraft Geometry . . . . . . . . . . . . . . . . .
214
8.7
Design Study 1 - Design Variations Analysed . . . . . . . . . . . . . . . . .
215
8.8
Design Study 1 - Analysis Results
. . . . . . . . . . . . . . . . . . . . . . .
218
B.1 Verification Results - Separation 50mm . . . . . . . . . . . . . . . . . . . . .
240
xxiii
LIST OF TABLES
xxiv
B.2 Verification Results - Separation 100mm . . . . . . . . . . . . . . . . . . . .
241
B.3 Verification Results - Separation 150mm . . . . . . . . . . . . . . . . . . . .
242
List of Symbols Letter Symbols: Rotor area A AzInf Influencing blade offset position Influence rotor blade position Azrtr Number of blades B c Blade element chord Rotational damping constant C Blade element sectional drag coefficient Cd Blade element sectional lift coefficient Cl Blade element sectional pitching moment coefficient Cm Influence offset in slipstream direction d Influence perpendicular offset in slipstream direction dP Blade element drag dD Blade element lift dL Blade element mass dm Blade element pitching moment dM Blade element width dr Blade element thrust dT Blade element rotor plane normal force dTN Blade element rotor plane tangential force dTT Prandtl tip loss factor F f Prandtl tip loss intermediate factor Fx , Fy , Fz Force in the X, Y and Z directions g Acceleration due to gravity Distance from CG to rotor hub h Influencing horizontal direction H Moment of inertia I Rotational moment of inertia J Rotational spring constant K Streamtube development factor kd l1 , l2 Control linkage lengths m Aircraft mass mB Mass of rotor blade Mx , My , Mz Moment in the X, Y and Z directions Blade radius R xxv
LIST OF SYMBOLS r s S T V Vh VM VT Vv VX VY VZ w W Y X, Y, Z
Blade element radial location Distance from rotor plane in streamtube direction Streamtube cross-sectional area Thrust Influencing vertical direction Blade element total horizontal velocity Blade element flapping motion velocity component Blade element translation speed Blade element total vertical velocity Translational X velocity Translational Y velocity Blade element vertical climb speed Average downstream streamtube velocity increment Blade element resultant velocity Rotor hub vertical offset from CG X, Y and Z directions
Greek Symbols: α Blade element angle of attack β Blade flap angle dβ Flapping increment γ Rotor streamtube contraction angle ∆p Average disc pressure change ηef f ect Influence effectiveness Blade element incidence angle θ Blade element geometric control increment dθ ν Blade element induced velocity νinf Blade element influencing velocity Average rotor induced velocity ν¯ ρ Air density φ Blade element inflow angle ψ Blade position Rotor rotational speed Ω ω Rotor rotational speed Subscripts: bld C dif f F lap G Gravity Inertial Load l, Lower opposing
Blade Control Difference Flapping Geometric Gravity Load Inertial Load Blade Load Lower Rotor Opposing rotor
xxvi
LIST OF SYMBOLS P air Root rtr T ip u, U pper
Blade flapping pair Blade Root Rotor Blade Tip Upper Rotor
xxvii
List of Abbreviations BEMT CBRNE CFD CG Code DASH Ex MAV RC RPM RDTE RWUAV UAV VTOL
Blade Element Momentum Theory Chemical, Biological, Radiological, Nuclear, Explosive Computational Fluid Dynamics Centre of Gravity Coded Implementation Drone Anti-Submarine Helicopter Experimental Mini Air Vehicle Radio Controlled Revolutions per Minute Research, Design, Test and Evaluation Rotary-wing Unmanned Aerial Vehicle Unmanned Aerial Vehicle Vertical Takeoff and Landing
xxviii
Chapter 1
Introduction 1.1
Thesis Introduction
Unmanned Aerial Vehicles (UAVs) are a widely recognised modern aircraft type. They have become regarded by engineers, operators and the public as a necessity within the modern aerospace environment. This thesis focuses on the analysis and design of the Proxflyer type rotorcraft for use as an UAV. The Proxflyer is an inherently stable rotorcraft with much potential for use as a UAV.
1.1.1
Overview
Unmanned Aerial Vehicles provide an excellent base for many aerospace applications. However, for UAVs, often less resources are devoted to development of the airframe with a greater portion assigned to systems development and operation. This is especially the case for smaller UAV design and operation. In general, aerospace platforms require that significant resources are assigned to their design and development. Due to legislative requirements of manned aircraft more a larger financial commitment is assigned to this process. Restrictions placed on the design and operation of UAVs are often less stringent than those placed on a manned aircraft. At present there are few separate guidelines for the design and operations of UAVs. They are often either placed into a category with manned aircraft, for larger UAVs, or they are classed as a smaller aircraft where restrictions placed on operations
1.1 Thesis Introduction
2
only. As a result of this the development of systems and aircraft operation often has higher priority. More often than not this results in airframe design becoming a second thought. The background of the UAV designer influences the approach heavily. Should the primary focus of the designer be systems and control the structured development of the airframe is often overlooked. an example of this is Bermes et. al. [1]. By focusing on CG shifting as a source of control, they have overlooked the majority of platform design in favour of testing a new control mechanism. In contrast however, Bouabdallah et. al. [2] present an aircraft with similar design characteristics and used a more structured approach to the UAV design process. This aircraft was designed from the outset with the focus placed on the platform as a whole. Whereas the UAV presented by Bermes et. al. concentrates on their field of expertise rather than a global approach to the design. These examples show the two ends of the spectrum which can result when designing similar aircraft. Due to the emphasis placed on the operation of UAVs good design methodology is often neglected. With a result being sub-optimal flight performance or stability. A “control system fixes all” attitude frequently pervades the design and manufacture of smaller UAV platforms. This attitude disregards magnification of stability and performance issues which is seen when reducing the scale of a flight platform. However use of a sound set of regulations and a structured design process, including an appropriate level of analysis, can minimise this type of effect. This approach is similar to the adage “Measure twice, cut once!”, which more often than not eliminates future unseen problems.
1.1.2
Goals
The primary goal of this thesis is to use structured design methodology to investigate, analyse and design the new Proxflyer rotorcraft configuration. This is in contrast to developing a new methodology for designing UAVs. This is achieved through the development of a design and analysis tool for the specific Proxflyer configuration. An additional goal of this project is to use the analysis tool for a variety of applications. These applications include being able to explore improvements to the existing configuration, and to propose new design configurations based on the Proxflyer. Although these two goals may seem somewhat similar, in fact they are not. Generally analysis of a single configuration with the goal of improving the design requires a more detailed analysis tool. While the
1.1 Thesis Introduction
3
development of a new configuration requires a tool which can be used to rapidly analyse many design iterations. Ultimately the goal of this project is a combination of the these two goals. Insomuch as to develop an analysis tool which can be used both within a structured design process, and for specific configuration analysis. Focus is placed on using a structured design methodology to complete this goal. As only a single rotorcraft configuration is considered the tool developed is simplified. The resulting design and analysis tool will not be a comprehensive tool encapsulating all facets of rotary-wing design. But rather will focus on analysing the Proxflyer rotorcraft with the aim of appropriate fidelity and low computational expense.
1.1.3
Objectives
Developing an effective analysis and design tool dictates that specific objectives be used. This set of objectives is used throughout the entire thesis project and summarises the thesis as a whole. A majority of the objectives detail the specific rotorcraft (Proxflyer) configuration and flight conditions which are examined. Additional objectives and/or restrictions may be used as the thesis continues, and will be defined when used. The objectives of this project include, but are not limited to, the following list:
• Coaxial Rotary-Wing Vehicle; • Mini Air Vehicle (MAV) Category; • Performance Analysis; and • Stability and Controllability Analysis.
Although these objectives set the overall scope of the project, they do not outline enough detail to begin analysis tool development. To begin this formulation the design features of the aircraft, to be analysed, need to be discussed. These features detail the aircraft design features which effect overall performance and thus need to be examined with accuracy; and are outlined in the following list:
• Rotor Aerodynamics;
1.2 Rotary-Wing Aircraft
4
• Rotor Aerodynamic Interaction; • Analysis of Blade Flapping; • Aircraft Flight Performance; and • Control Modelling. Construction of an analysis tool which is flexible requires that a number of different objectives be met. These objectives allow the analysis tool to be formulated in a way which makes it useful for the two applications, specific analysis and general design, discussed previously. The objectives which need to be met within the development of the analysis tool are listed below: • Analysis Accuracy; • Ease of Use; and • Computational Efficiency. A flexible, useful and efficient analysis and design tool was constructed to ensure that the analysis tool and the entire project meets these objectives. This also ensures that a good methodology is maintained when the design tool is used for configuration development.
1.2
Rotary-Wing Aircraft
A brief outline of the design and construction of rotary-wing aircraft is made before proceeding with the development of the analysis and design tool. While not an exhaustive survey of rotorcraft types, it is general enough to provide grounding for further development within the thesis. This section outlines the various forms of which a rotary-wing aircraft can take, including both manned and unmanned aircraft variants.
1.2.1
Configurations
The following are the four general rotorcraft configurations available to a designer, each of these are summarised in the following sections.
1.2 Rotary-Wing Aircraft
5
• Conventional; • Coaxial; • Tandem; and • Multi-Rotor. In addition to a general description of these configurations a subsequent discussion on the use of rotary-wing aircraft as UAVs is made.
1.2.1.1
Conventional
A conventional rotary-wing aircraft is the configuration which most people would identify as a helicopter. This configuration has a main rotor used for producing lift to support the vehicle, and a tail rotor to balance the main rotor torque. These rotorcraft range in size from large heavy lift aircraft, such as the Sikorsky S-64 Skycrane [3]. To medium sized transport aircraft, such as a Bell 47 [4]. And finally down to smaller autonomous UAVs, such as the Scheible Camcopter [5].
1.2.1.2
Coaxial
A coaxial helicopter has two main rotors positioned about the same axis and no tail rotor. The two main rotors also provide torque balance and yaw control. For a given lifting capacity this rotorcraft is smaller than a conventional helicopter due to the extra lift provided by the second rotor. Examples of this aircraft include the manned Kamov Ka-32 [6] and the small radio controlled Proxflyer [7].
1.2.1.3
Tandem
Tandem rotor helicopters are similar to a coaxial helicopter as they have two main rotors and no tail rotor. However the main rotors about two separate axes. Whether the rotors overlap or not depends on the design. The rotors can either be positioned on the front and back of the aircraft, like the Chinook [8]. Or can alternatively be positioned on either side of the aircraft, such as the Osprey V-22 [9], when configured in vertical flight mode, or the Kaman K-Max helicopter [10].
1.2 Rotary-Wing Aircraft 1.2.1.4
6
Multi-Rotor
Multi-rotor rotorcraft have three or more rotors. Which differentiates them from either coaxial or tandem designs. Once again the balance of power produced by the rotors is used to provide torque balance and yaw control. This aircraft is not as common as other rotary-wing designs. Although early attempts to construct a viable helicopter used this configuration. The most common form which this configuration takes is a quad-rotor platform, with an excellent example shown by Hoffman et. al. [11].
1.2.2
Rotary-Wing UAVs
Rotary-wing aircraft can prove to be extremely useful when used as UAVs. The range of configurations used for rotary-wing UAVs is similar to that of manned rotorcraft. Flexibility of operation, which is seen in larger manned aircraft is likewise seen in similar unmanned variants. A rotary-wing UAV gives operational characteristics which can benefit a large variety of mission types. As such this aircraft type has been used in several different unmanned applications such as surveillance, exploration and communications. One of the most widely utilised rotary-wing UAV platforms is the Yamaha RMax, shown in Figure 1.1. This aircraft was originally developed for use as an agricultural crop spraying aircraft in the early 1980’s. Following its initial operation this platform has been developed into several different variants. including surveillance and research. The size, cost and infrastructure required to operated this aircraft is large. Therefore, it is not always suited for use within some missions especially where total project cost is a factor. As a results other rotary-wing UAVs have been developed to fill the void. Many rotary-wing UAVs were first developed to be used for missions where a larger aircraft would also be useful. This is no longer the case. Recently there has been an increasing trend to produce smaller rotary-wing UAVs. This is in part due to the cost of development, purchase and operation. However, this is also due to a larger rotorcraft’ inability to operate within tighter mission environments now being explored. Missions which have these requirements often lend themselves to operate a smaller UAV. However, smaller rotary-wing UAVs have significant stability problems which need to be solved. Therefore analysis of stability, controllability and efficiency of this aircraft type is of increasing importance.
1.3 Proxflyer Rotorcraft
7
Figure 1.1 – Yamaha R-Max unmanned helicopter. Photo courtesy Yamaha [12].
Figure 1.2 – Range of three different sized Proxflyer type rotorcraft. Photo courtesy of Proxflyer [7].
1.3
Proxflyer Rotorcraft
Within this thesis the Proxflyer type rotorcraft [7] is the primary platform which is examined. Figure 1.2 shows three different sized Proxflyer rotorcraft, while figure 1.3 shows a closer view of the larger Mosquito twin-tail Proxflyer. Due to its’ unique design features, such as its’ inherent stability, this rotorcraft does not fit entirely within a single category outline in the previous section. The features which contribute to the unique design are discussed below. Inherent Rotorcraft Stability The Proxflyer rotorcraft concept was the first inherently stable rotorcraft [13]. The combination of the coaxial rotor design and the passive
1.3 Proxflyer Rotorcraft
8
Figure 1.3 – Proxflyer Mosquito Twin-tail rotorcraft. Note the unique rotor hub design and the twin upwards facing tail rotors. Photo courtesy of Proxflyer [7]. flapping blades allows the rotorcraft to maintain stability without active control. Paired Flapping Rotor Blades Both of the four bladed rotors are broken up into two blade pairs. Each blade within each pair flaps in unison, they experience the same flapping deflection, rate and acceleration. The free-flapping nature of these pairs contributes to the inherent stability. Uncontrolled Rotors Both of the two rotors’ on the Proxflyer have no control, either collective or cyclic. Therefore they only respond passively to external disturbances. Upwards Facing Tail Rotor The primary control which the Proxflyer has available is from either one or two upwards facing tail rotors. These rotors provide control by applying a pitching moment to the rotorcraft, thus allowing the aircraft to be pitched.
Any of the single features listed above are not exclusive to the Proxflyer type rotorcraft. However the combination of them allows this rotorcraft to operate with inherent stability. Thus this makes the Proxflyer rotorcraft an interesting subject for further study. This is
1.4 Rotary-Wing Conventions and Definitions
9
especially true when considering possible applications as a UAV operating within urban environments.
1.4
Rotary-Wing Conventions and Definitions
There are many conventions which are used across the entire range of rotary-wing aircraft. First is the definition of the controls used by these aircraft within both operation and analysis. Although these terms are usually defined for a conventional configuration, they are also applicable to any of the other configurations. Each of the controls listed and then briefly summarised below. • Rotor Speed Control; • Rotor Collective; • Rotor Cyclic; and • Yaw Control. To control the vertical position of the aircraft, both speed control and collective can be used. Speed control of the main rotor/s is governed by the throttle setting, which provides power to the meet the rotors’ requirement. This control is generally only used to control the rotor lift when collective control is not used. Collective control changes the pitch setting of all rotor blades simultaneously. This can then be used to control the total lift which is produced by the rotor, and in controls the vertical position of the aircraft. Directional control of a rotorcraft is through use of both cyclic and yaw control. Cyclic control allows the lift on the main rotor to be directed by changing the blade pitch setting cyclically around the rotor. This control allows the aircraft to either pitch or roll, and subsequently allows the aircraft to be translated. Secondary directional control is provided by Yaw control about the vertical axis. Yaw control allows the direction of the nose of the aircraft to be controlled directly, which is achieved by varying the torque balance from the main rotor. Torque balance is typically controlled by placing a smaller second rotor on the aircrafts’ tail boom. This rotor produces a force in the opposite direction to that of the main rotor
1.5 Thesis Layout
10
torque. Listed below are the most common methods for balancing a main rotors resultant torque. However, there are other methods which can be used to balance the torque from the main rotor which are not listed here. • Directing Engine Exhaust; • Using a Coanda Effect Over the Tail Boom; or • Coaxial or Multiple Rotors.
Apart from the conventions used within rotary-wing aircraft operations, various parameters need to be defined for analysis and design. There are too many definitions for a detailed listing to appear here. However, the major areas which need to be defined to carry out rotorcraft analysis are listed below. And a more detailed description is provided in Appendix A. • Rotor Definitions; • Blade Definitions; and • Airframe Definitions.
1.5
Thesis Layout
The primary focus of this thesis is the analysis and development of small rotary-wing UAVs. A special focus is centred on the analysis of the Proxflyer rotorcraft for operation within urban environments. Focus is also placed on completing the analysis with simplicity and efficiency kept in mind. To do this a framework as discussed previously has been used. To facilitate the flow and understanding of this thesis an initial summary of the work completed and the thesis’ overall layout is made.
1.5.1
Summary of Completed Work
As the amalgamation of the various analysis techniques used in this thesis has not been commonly used, a summary of the work completed initially sets the scene.
1.5 Thesis Layout
11
The analysis techniques which have been used are designed for implementation with little computational overhead. Each of the major areas of interest listed below are further expanded within the chapter summary section 1.5.2. The full impact of each area is outlined in full within the remainder of the thesis. The analysis areas which have been focused on are summarised in the following list:
• Extended Blade Element Momentum Theory (BEMT); • Coaxial Rotor Interaction; • Blade Dynamics; • Combined Rotor Aeromechanics; and • Rotor Performance.
Each analysis areas makes up a small part of the overall development in this thesis. In isolation each technique plays only a single part of the overall analysis. However when combined the full impact of each technique is seen, and allows a structured analysis and design package to be formed. A summary of the structure of the thesis, including a brief description of each of these analysis areas is made in the following section.
1.5.2 1.5.2.1
Chapter Layouts Chapter 2 - Background and Motivation
This chapter presents a summary which includes developing the need for, and use of, a small coaxial Rotary-Wing UAV. A summary of the various aspects of helicopter analysis in terms of both aerodynamics and dynamics is completed. This summary is then related to the analysis of UAV helicopters and the applicability to smaller rotary-wing UAVs. Finally, the need to conduct either specific configuration or general design optimisation is also presented. This chapter sets the scene and direction for the entire project, and further defines many of the desired outcomes of the project.
1.5 Thesis Layout 1.5.2.2
12
Chapter 3 - Blade Element Momentum Theory
Analysis of helicopters is dominated by the complex aerodynamics surrounding the rotors. Many rotor aerodynamic analysis methods require significant computational overhead and development. This type of analysis is often counter-intuitive, especially in relation to configuration selection and design. To alleviate this problem, a step back from complex analysis has been taken. As a result an analysis method which requires less overhead, but can still replicate a wide range of flight conditions, has been chosen. The flexibility, usability and accuracy of Blade Element Momentum Theory (BEMT) lends itself to this task, and is shown within this chapter. Methods for adopting non-standard analysis configurations, many of which are used throughout this thesis, are also discussed.
1.5.2.3
Chapter 4 - Coaxial Rotor Interaction Modelling
One of the significant problems associated with analysis of coaxial helicopter is the analysis of rotor interaction. This is especially so when a simplified analysis model such as BEMT is chosen. A new method for analysis of coaxial rotor interaction has thus been developed. This chapter explains the theory and working behind this method for analysing coaxial rotor interaction with BEMT. A great deal of care is taken to show the simplicity, usability and accuracy of this method.
1.5.2.4
Chapter 5 - Interaction Model Verification
This chapter presents the verification of the rotor interaction method. The test apparatus built to perform these tests is shown, as well as the process used to test within the limitations of the analysis method. The drawbacks of the method are highlighted to show areas in which improvement can be made. However, the overall benefit of this method is shown, especially with the overall project goals kept in mind.
1.5.2.5
Chapter 6 - Blade Flap Modelling
Proxflyer type aircraft have rotors which flap to a higher degree than many conventional helicopter rotors. This aircraft uses this high range of flapping motion to provide a stabilising
1.6 Summary
13
mechanism for the aircraft. To model the flapping of these blades simple rotational equations of motion, which can include many external effects, are used. This chapter summarises the development of this theory to analyse all required effects and the implementation of this method into the analysis tool.
1.5.2.6
Chapter 7 - Coaxial Rotorcraft Analysis
This chapter explains the assembly of these methods and the workings of the analysis tool as a whole, as well as its overall structure. The assembly of the separate analysis methods was completed in a structured manner to keep complexity to a minimum. This chapter also discusses the various implementations which the analysis tool can be used to investigate.
1.5.2.7
Chapter 8 - Design Studies
Two design studies are presented in this chapter to illustrate the developed tool as both an analysis and a design tool. These design studies show how the tool can be used to either design or improve a rotorcraft configuration. Firstly, an existing configuration is examined with the goal of improving its efficiency and stability. The second design study examines developing a working design from a new configuration concept.
1.6
Summary
This chapter has provided a summary of the overall theme of this thesis. An basic introduction into the use of rotorcraft platofrms as UAVs has been made. Special focus has been made on for small coaxial rotorcraft and how they can be used as an UAV. The general features of the Proxflyer rotorcraft has been made, and the motivation as to why it provides an interesting subject to study has been listed. This has then been linked to the development of an analysis and design tool. Only a small amount of detail pertaining to each of the areas of interest has been outlined. Each section within this thesis focuses primarily on a single facet of MAV rotorcraft analysis. As such, a significantly more interesting level of detail is included within each chapter. In turn each chapter outlines a progressively developing description of the overall MAV rotorcraft analysis tool. This is then combined together and two design studies are summarised.
Chapter 2
Background and Motivation 2.1
Introduction
Development of new aircraft configurations generally requires that a large amount of data be analysed. To implement this analyses in an appropriate manner, and especially for configuration optimisation 1 , the operational region of the aircraft must be defined. Requirements that configuration optimisation place on an analysis tool differ, sometimes significantly, to those for optimisation of an existing design. This chapter discusses the motivation to develop a new rotary-wing UAV platform for operation within urban environments. Special emphasis is placed on how this motivation effects the development of an analysis and design tool for this category of aircraft. By relating the operational goal of the aircraft to its performance, any unique requirements, performance or operation, of the aircraft are established before the analysis tool is constructed. Thus can be included within the analysis tool’s structure.
2.2
Problem to Solve
Over recent years, Unmanned Aerial Vehicles (UAVs) have become increasingly utilised in a multitude of application. The variety of missions in which UAVs can be used is as 1
For this thesis configuration design or optimisation are used interchangeably. They both refer to the process of determining the overall design, not details.
2.2 Problem to Solve
15
varied as the number of configurations available. For civilian UAV operations, Okrent [14] suggests that there are four main mission areas: Scientific; Emergency; Surveillance; and Communications. While the US Department of Defence [15] has likewise suggested that military operations for unmanned systems could include: Reconnaissance and Surveillance; Target Identification and Designation; Counter-Mine Warfare; and Chemical, Biological, Radiological, Nuclear, Explosive (CBRNE) Reconnaissance. As would be expected, there is a large overlap between civilian and military UAV uses. Each of the mission types listed above outlines only the general characteristics of each mission. However, the operational environment also needs to be defined. A large portion broad mission types are applicable to operations within urban environments. Vick et al. [16] explores flight operations within urban environments and concludes that over the coming years, this type of operation will only increase in frequency. By examining the conclusions proposed by Wright [17] and Vallance [18], it can be seen that any operation within an urban environment is either unsuitable or difficult for existing aircraft. Urban environments place tough operational and, more importantly, flight requirements on any vehicle of any scale. Perhaps the biggest problem for an aircraft operating within this environment is the turbulent unsteady atmosphere. The characteristics of the atmosphere within an this environment is often unknown and unpredictable. Rotach [19] states that during daylight hours, the atmosphere surrounding urban buildings is typically unstable. And likewise, Nakamura and Oke [20] determined this environment to be dominated by micro-scale effects. They go on to state that problems within this atmosphere include: Wind Buffeting; Wind Chill; Heat Stress; Driving Rain; Blowing Snow and Sand; and Pollutants. All these factors greatly effect operation of vehicles, especially small, within this environment. Difficulties which UAVs face within urban environments extend beyond operational and atmospheric. The effects of turbulence and gusts become far more problematic when reducing scale from larger manned aircraft to smaller unmanned platforms. Watkins and Vino [21] state that UAVs and smaller Micro Air Vehicles (MAVs) are immersed within the microscale atmospheric effects as discussed above. Thus, smaller aircraft operating within this region will be more heavily influenced by these atmospheric characteristic. Atmospheric influences such as these need to be considered when defining the operation which an aircraft is to undertake.
2.3 Configuration Options
16
A majority of UAVs used within an urban environment will, at some stage during the mission, be required to perform steady positioning for surveillance, monitoring or relay. Holding a steady position within an unstable atmosphere is extremely difficult. In addition to maintaining steady position effective operation in an urban environment requires that aircraft be capable of flying around buildings, trees and other dynamic obstacles. Due to these factors Bohorques et al. [22] suggest that many missions in this environment also require good maneuverability. Thus, a cluttered flight space; turbulent unstable air; and highly dynamic obstacles are the main problems associated with operating within this environment. Designing a smaller UAV which can operate effectively in this demanding environment becomes difficult. There are many factors which need to be kept in mind from the start of the design process. This process is made more difficult when the range of aircraft configurations is also taken into account. To find a configuration which best meets these needs a variety of different configurations need to be investigated. A summary of existing UAVs which can be used for applications within urban environments is discussed in the following section (2.3).
2.3
Configuration Options
There are a range of UAV configurations which can be used for the mission discussed previously. Howard and Kaminer [23] state that there are three main areas into which a military UAV can be classified: Tactical UAVs; Vertical Takeoff and Landing (VTOL) UAVs; and Endurance UAVs. Tactical UAVs can be used for large scale battlefield surveillance operations over a wide flight region. VTOL UAVs are most suited to missions where either hover or slow translational flight is required. And finally, Endurance UAVs are used when long flight times are required for reconnaissance type missions. For missions based within an urban environment, and often independent of the mission specifics, VTOL UAVs are most suitable. VTOL UAVs can often be used for urban operations independent of mission type, with the most familiar configuration being the helicopter. A study by Shim et al. [24] presented a conventional helicopter, the “Berkley UAV”, to test possible uses within this environment. Likewise, Nordberg et al. [25] presented the development of a vision system for a Yamaha RMax helicopter within cluttered (urban) environments. Additionally, Whalley et al. [26]
2.3 Configuration Options
17
used a pair of RMax Helicopters to show the development of this platform type within a military framework. A common thread throughout these applications is the use of commercial off-the-shelf airframes. Conventional helicopter platforms are often used when focus is placed control system development, rather than the aircraft itself. Thus, the control system is used to compensate for atmospheric and platform instabilities rather than only the aircraft itself. Although conventional helicopters are often the first choice for VTOL UAVs, they are not always the best choice. For missions which require both hover, speed, range and endurance; a tail sitter aircraft can perform extremely well. The T-Wing aircraft presented by Stone and Clarke [27] is a configuration which could potentially perform well an urban environment. Likewise Wong et al. [28] discuss the stabilisation of a Mini Tail-Sitter UAV which could find use within confined urban environments. Both of these platforms have the benefit of use in multiple roles, however still has the drawback of requiring higher complexity control systems to maintain stability. Apart from helicopter and aeroplane type platforms, there are a wide range of VTOL aircraft which use novel concepts. The Cypher UAV, presented by Murphy and Cycon[29], uses a ducted fan arrangement to give a highly maneuverable platform. This UAV is suggested to be used for law enforcement, operating primarily within urban environments. Many of the platforms already discussed are large. However if a smaller platform is required, there is also a range which have been developed. Young et al. [30] discuss a wide range of smaller UAV configurations whose main mission applications surround the urban environment. Some of the platform types reviewed are: Quad-Rotor Configurations; Morphing Configurations; Tilt-rotors; and Coaxial Configurations. Each of these configurations is generally based on a rotorcraft. Out of all the configurations available for urban missions, perhaps the most appealing option is the coaxial rotorcraft. Recently this configuration has attracted a large amount of interest. This includes manned aircraft such as the Sikorsky X2 [31]; and smaller UAVs such as the AirScooter UAV [32]. As an UAV this configuration has all the benefits of a conventional helicopter, and the additional benefit of a smaller footprint due to the elimination of a tail-rotor. In addition to these general features, there are many aspects of this platform configuration which make it an excellent choice as an urban UAV.
2.4 Coaxial Helicopter Configuration
2.4
18
Coaxial Helicopter Configuration
Coaxial helicopters have two rotors centred about the same axis, rotating in opposite directions. The range of uses for this type of platform is vast. And the number of platforms which have been previously developed is likewise large. However, there is much which is still unknown about this configuration.
2.4.1
Existing Aircraft
Coaxial helicopters have been used since the original effort to construct a viable rotarywing aircraft. Gessow and Myers [33] (pp. 5-8) show that designers such as Berliner, Pescara and Breguet all initially used this designs to attempt VTOL flight. Once successful “conventional” (main and tail rotor) helicopters were developed, the coaxial design became a less favoured configuration. Despite this, from 1946 until 1969 the Gyrodyne company produced a range of coaxial helicopters. These aircraft were used as drones in anti-submarine ship board operations [34]. An example is shown in Figure 2.1. Perhaps one of the most notable producers of manned coaxial helicopters is the Russian company Kamov [6]. Kamov have produced a range of coaxial helicopters which recently include the: Ka-25, Ka-27, Ka-32 and Ka-52 aircraft. Figure 2.2 shows the Ka-27 operating as a ship-based anti-submarine aircraft. Besides the large coaxial helicopters, there has also been much development of smaller coaxial rotorcraft platforms. The aforementioned AirScooter UAV [32] is a good example of a moderate sized platform, shown in Figure 2.3. When the scale of the aircraft is reduced further, the number of available platforms increases. The E-Flite [36] Blade CX2, shown in Figure 2.4, is an example of a radio controlled (RC) coaxial helicopter designed for the indoor hobby market. As discussed in section 1.3, a coaxial aircraft of particular note is the Proxflyer UAV aircraft developed by Petter Muren [37] (shown in Figure 2.5). This aircraft uses articulated flapping rotor pairs to increase its inherent stability. And has been observed to perform well in a moderately turbulent atmosphere. The platforms listed within this section are only a small number of the known coaxial helicopters. Coaxial helicopters range from large manned aircraft, to small Mini Aerial Vehicles (MAVs). Properties of each in terms of flight characteristics, performance and
2.4 Coaxial Helicopter Configuration
Figure 2.1 – Gyrodyne QH-50 Model. Used as a Drone AntiSubmarine Helicopter (DASH). Photo courtesy of Gyrodyne Helicopter Historical Foundation [34].
Figure 2.2 – Kamov Ka-27SP Aircraft used as a ship-based antisubmarine aircraft. Photo courtesy of Wikipedia [35].
19
2.4 Coaxial Helicopter Configuration
Figure 2.3 – AirScooter Corporation G70 Gas UAV. Photo courtesy AirScooter Corporation [32].
20
2.4 Coaxial Helicopter Configuration
Figure 2.4 – E-flite Blade CX2 radio controlled aircraft. Photo courtesy E-flite [36].
Figure 2.5 – Proxflyer Mosquito aircraft. Photo courtesy Proxflyer [7].
21
2.4 Coaxial Helicopter Configuration
22
design vary widely. Thus, an examination of general benefits and drawbacks is completed in the next section.
2.4.2
Benefits and Drawbacks
One of the major benefits of a coaxial rotorcraft is the reduction in aircraft size as well as the footprint. This is achieved through the elimination of the tail and tail-rotor structure. Previous designs with not tail rotors include the NOTAR and fenestron concepts. These methods increase the weight or complexity of the tail design, and this sometimes outweighs the benefit. By positioning the two rotors about the same axis there is a major reduction in size over other multi-rotor platforms, such as a quad-rotor. However, the benefits of this platform type extend far beyond size. An increase in lifting capacity for a given rotor diameter is a major performance benefit of the coaxial configuration, as shown in Figure 2.6. This figure shows theoretical lifting capacity for single and coaxial configuration 2 . By compacting the size of the coaxial rotors, more lifting capacity can fit within a given size (rotor diameter). This is beneficial if a compact payload needs to be transported within the aircraft fuselage. By eliminating the tail rotor, the rotorcraft now becomes symmetric about the pitch and roll axes. This eliminates many of the adverse cross coupling effects which are experienced by other rotorcraft designs. A significant increase in control power can also be achieved, and is shown when only one rotor is used to provide control. If both rotors are controlled, this further increases the control power. Again this allows the size of the aircraft to be further reduced. All of these factors allow the design to perform in a superior manner to that of a conventional helicopter configuration of a similar size. There are, however, a number of drawbacks with the coaxial configuration. For instance stability issues, which conventional helicopter experience, are carried over to coaxial configurations. These issues are difficult to eliminate without major rotor or configuration changes. Mechanical complexities, which can be introduced into the design, is another major difficulty which is introduced to the coaxial rotorcraft. Running concentric rotating shafts can be difficult if the rotor speed is high, as problems with friction and serviceability can occur. Designing and building control linkages for two rotors instead of one can also 2
These results were generated with the analysis tool developed within this thesis
2.4 Coaxial Helicopter Configuration
23
Figure 2.6 – Performance comparison of Single and Coaxial rotors with the same diameter, chord and rotor speed. Values generated with the analysis tool developed in this thesis. be extremely complicated. This increase in complexity can be seen through the comparison of the Kamov Ka-26 and Sikorsky S-92 rotor heads, as shown in Figure 2.7. In addition to mechanical complexities, analysis of aerodynamic interaction between coaxial rotors in close proximity can be difficult during design. A method has been developed to characterise this effect for small coaxial rotorcraft, and is presented in chapter 4. Drawbacks of the coaxial configuration are not insurmountable. The advantages of the configuration outweigh the difficulties. However, to overcome the design difficulties detailed analysis of the configuration must be performed to ensure that these benefits are achieved.
2.4.3
Configuration Analysis
Analysis of coaxial rotorcraft configurations is difficult, while similar to conventional helicopters does differ in certain key areas. There are three major areas which affect the performance of coxal rotorcraft analysis: rotor aerodynamics, rotor dynamics and rotorcraft dynamics. Analysis of coaxial helicopter rotor dynamics and rotorcraft dynamics does not differ greatly from conventional helicopters. However, aerodynamic analysis of coaxial
2.4 Coaxial Helicopter Configuration
(a) Kamov Ka-26 rotor head. Courtesy Jean-Patrick Donzey [38].
(b) Sikorsky S-92 rotor head. Courtesy David Monniaux [39].
Figure 2.7 – Comparison of rotor heads of a conventional and coaxial rotor system. Increased complexity is seen within the coaxial rotor head.
24
2.4 Coaxial Helicopter Configuration
25
rotors has additional complexities which are not experienced with single rotor configurations. Therefore, a summary of coaxial aerodynamic analysis is made within this section. An excellent summary of various aspects of research pertaining to coaxial rotor aerodynamics has been collated by Coleman [40]. This document summarises both theoretical and experimental research activities. The most significant problem for aerodynamic analysis of coaxial rotorcraft is how to analyse the interaction between the rotors. Thus, the majority of both experimental and theoretical research has focused on this area. Analysis of coaxial rotors is very similar to analysis of coaxial propellers, and is used to expand the range of usable data and research. The study performed by Harrington [41] is a commonly used source of coaxial rotor experimental data. This study examines the static thrust and torque performance of a large coaxial rotor. When compared to coaxial rotors, coaxial propeller analysis and experiments is a larger source of test data. Both Chung et al. [42] and Wainauski and Vaczy [43] examine the performance of counter rotating coaxial propellers. By combining these three sources, and other sources, a range of experimental data which can be used for comparison is compiled. Theoretical and computational analysis of coaxial rotor interaction can likewise also draw on both rotors and propellers. Anikin [44] presents the aerodynamic performance surrounding a coaxial helicopter configuration. Colehour et. al. [45] present a strip theory method for analysing the performance of coaxial propeller. While Allen and Korkan [46] present a method for predicting both the performance and acoustics of a coaxial propeller configurations with non-uniform flow. And finally, Cho and Williams [47] present a panel method based analysis of coaxial propellers. Each of these studies, both theoretical and experimental, give good insight into the analysis of coaxial rotors. However, this also highlights the complexity of aerodynamic analysis of coaxial rotors. Thus, to analyse a UAV coaxial helicopter configuration, an appropriate aerodynamic analysis tool needs to be chosen.
2.5 Helicopter Analysis
2.5
26
Helicopter Analysis
The range of helicopter analysis begins with simple first order analysis such as actuator disc theory. And ends with multifaceted comprehensive analysis with a tool such as CAMRAD. Likewise, the range of analysis applications also varies from simple load predictions to complex full aircraft analyses. A simple analysis which may look at only one of these aspects in isolation, while a comprehensive tool will more than likely use two or three concurrently. A brief summary of each of these areas is given in the following sections 2.5.1 to 2.5.3.
2.5.1
Rotor Aerodynamics
All analysis of rotorcraft configurations is dominated by the aerodynamics surrounding the rotor/s. Accordingly there is a large volume of research and development which concentrates on this area. There are many texts which cover a great deal of the theory surrounding rotor aerodynamics. Most notable of there are texts by Gessow and Myers [33]; Johnson [48]; Leishman [49]; and Stepniewski and Keys [50]. Each of these texts provides a good background to simple theories such as Blade Element Momentum Theory; Vortex Theory; and Potential Theory. They often extend this explanation to the other areas of interest (Rotor and Rotorcraft Dynamics). However, they do not cover more complex theories or comprehensive analyses. Perhaps the simplest rotor analysis tool is developed from Blade Element Momentum Theory. This method uses both aerodynamic and momentum theory to analyse loading on either rotors or propellers. While the method is often thought of as a rough sizing tool, with minor changes it can be developed into an excellent analysis method. Azuma and Kawachi [51] use momentum theory which shows excellent functionality and has lower computational expense than other analysis such as vortex methods. The thesis author has previously shown how BEMT can be extended to include external effects including rotor interaction and motion [52, 53, 54, 55, 56, 57]. Implementations of this basic theory show how a simple, computationally inexpensive, analysis tool can be used to tackle complex analyses. A more detailed rotor aerodynamic analysis method is vortex methods applied to the rotors and blades. Vortex wake models examine analysis and dynamic mapping of the rotor
2.5 Helicopter Analysis
27
wake to determine a rotor’s performance. This analysis has been used by Gaonkar and Peters [58] to analyse blade stability during flight. While Kunz and Hodges [59] use a similar methodology implemented within a comprehensive analysis package ‘GRASP’. In comparison, for practical applications, Peters and HaQuang [60] present a methodology for analysis of sidewards flight. A more recent study which focuses on analysis of vortex ring state has been presented by Chen and Prasad [61]. Vortex ring state has extremely complicated flow characteristics, and is often difficult to model. These examples show that vortex methods are not the most complicated or computationally expensive analysis method. However, for more general configuration design and development the complexity may be too great. Previously, the computational cost of implementing a highly refined CFD model has been too great. Therefore, other methods which prescribe more of the flow properties were used. In recent years, developments in both computer power and CFD codes have allowed their use within rotor aerodynamic analysis. Common uses of CFD for rotorcraft is performing either performance, vibration or aeroacoustic analysis. All of which give performance benefits to an existing rotorcraft. Lee et al. [62] examine a high fidelity rotor model during hover for structural analysis and improvement. While Datta et al. [63] focus on analysis of vibration loads using CFD. Both of these investigations look at the aerodynamic and structural interactions within the rotor. In contrast to this, Renaud et al. [64] conduct an acoustic analysis of blade vortex interaction using CFD as the primary tool. A common thread between these studies is although they produce excellent fidelity the computation expense required is high. As many helicopter analyses are examining unsteady flows, CFD simulations require a number of rotor revolutions to properly develop the flow model. For optimisation and design many configuration variations need to be examined. The extra computation required with CFD is then further extended for this operation type. Again, CFD has been shown to be an effective analysis tool, however it comes with a high computational price. There are many different rotor aerodynamic analysis methods, each of which has their own benefits and drawbacks. However, the main differentiating factor is “accuracy vs cost”. For an analysis with an aim to improve performance of an existing design CFD would be the obvious choice. However, for the design of a new configuration a less computationally expensive method such as BEMT may be a better choice. The choice of analysis needs to
2.5 Helicopter Analysis
28
be made depending entirely on the type of project and resources available.
2.5.2
Rotor Dynamics
Compared to aerodynamic analysis, the range of different methods available for the investigation of rotor dynamics is much more limited. Treating blade motion with classical mechanics is probably the most simple analysis method. This is shown in the papers by the thesis author, which analyse the flapping motion of a Proxflyer type aircraft [54]. Extension of the analysis to include both flapping and lagging of the blades increases the complexity significantly. To model rotor dynamics during helicopter pitch and roll motions, Rosen and Isser [65] use a more thorough implementation of these simple equations of motion. Finally, Turnour and Celi [66] use a flexible rotor blade model to analyse blade dynamics within a full aircraft simulation. Once again, the choice between accuracy and cost needs to be made with respect to the specific analysis being undertaken.
2.5.3
Rotorcraft Dynamics
Analysing the dynamics of helicopter configurations is similar to analysing fixed-wing aircraft, however is often more complicated. Complexities are often introduced when analysis of accurate rotor aerodynamics and dynamics are desired within the same model. Thus, complexity is once again tied to the accuracy of the rotor model. The complexity of a flight dynamics simulation with refined aerodynamics is highlighted in Theodore and Celi [67]. Here, a free wake model is applied to a hingeless rotor to refine predictions of flight dynamics. Further complexity is also introduced if dynamic analysis of blade dynamics is included. Once again, Theodore and Celi [68] show a study which includes refined aerodynamics and flexible blade dynamics within the analysis. This study begins to show the complexities which an rotorcraft dynamic analysis can reach. This level of complexity is often required when examining the flight characteristics or handling qualities. Guglieri and Celi [69] discuss a theoretical study to examine the handling qualities of hingeless rotors in steady turns. Studies such as these help to examine the flight characteristics within a computer simulation. Therefore help to predict future rotorcraft refinements before flight testing is conducted.
2.5 Helicopter Analysis
29
Often analyse of real-world situations requires a higher level of fidelity of analysis. A common problem for helicopter operations is the difficulty of transporting slung loads. Reddy et al. [70] have examined the simulation of slung loads below a Chinook. Analyses such as this can be used to help operational personnel to determine safe working criteria. In a study such as this, increased complexity is required for accurate investigation of all possible flight performance issues. A less complex dynamic simulation can be used to design flight controllers. While a less complex simulation may be used within the process of the flight controller design, the simulation used is often a subset of a complex full simulation. This type of analysis is especially important when designing new UAV configurations. By already having obtained a less complex dynamic model, Zanetti et al. [71] use this model to design and test a new feed-forward controller design for a rotary-wing UAV. Many studies within this area focus on analysis of a specific rotorcraft and flight configuration. For more general configuration design, a full simulation may not be required. This is especially true if the key response characteristics can be identified before analysis is conducted, e.g. when examining rotor loading responses which dominate rotorcraft motion, such as around hover. Although hover is an extremely complicated flight condition rotor loading will initially control aircraft performance. This is a type of analysis where it may not be necessary to expend the computational resources for a full simulation. This is especially the case if only general trends of performance are being examined.
2.5.4
Analysis Summary
Analysis of helicopters and rotary-wing vehicles cover a wide variety of techniques and complexities. For any analysis of these configurations it is especially important to identify the required complexity. For example, an analysis which has a goal of improving performance of an existing design, such as Robinson and Brocklehurst [72], higher complexity and fidelity analysis may be preferred. However, if a more general configuration design is undertaken, such as Datta et. al. [73], a less complex analysis approach may be used. A trade-off must be made between complexity of the analysis being performed; the required fidelity of the results; and the time available for the analyses. Once this trade-off has been made, the choice of the specific analysis methods to be used can be made.
2.6 Design Optimisation
2.6
30
Design Optimisation
Effective design of an aircraft requires that a balance between many competing factors be reached. The previous section (2.5) shows only rotor aeromechanics and rotorcraft dynamics. Although this is only a subset of the full analysis, it provides a large range of both design variables and performance measures. Providing a balance between aerodynamic performance; aircraft stability; and control authority for a rotorcraft can be difficult. For a configuration design process, Design Optimisation provides a convenient methodology for reaching this balance. An excellent summary of design optimisation of rotorcraft is shown within a survey by Celi [74]. Within this comprehensive survey Celi outlines many of the goals of helicopter optimisation. He also discusses that although some design problems may appear to be a single discipline, in reality most are almost always multi-disciplinary. One of the most salient points that Celi makes is that many practical problems still cannot be modeled with enough accuracy due to computational restraints. This then has an adverse effect on the performance of the optimisation process. An important first step to introduce optimisation within the rotorcraft design process is to ensure that the analysis matches reality. By examining the structural design of rotor blades, Davis and Weller [75] investigated improving a blade’s dynamic response. Most importantly they have set up tests to verify the performance of the analysis model. This helps to ensure that the optimisation criteria which were chosen accurately reflect the physical model, thus giving confidence in both the analysis tool and the optimisation procedure. Full design of a helicopter requires that a wide variety of different characteristics from different disciplines be taken into account. This can be completed within an optimisation procedure by using a multidisciplinary design optimisation process. Adelman and Mantay [76] present one of the first integrated design optimisation procedures focused on helicopter design. This paper outlines the goals and procedures for optimising with respect to performance, vibration and weight. As a parallel to this paper, Chattopadhyay et al. [77] show a more focused application. They display the procedure and results of an optimisation process to minimise blade weight and hub shear force. This study combines an existing analysis package, CAMRAD, with and existing optimiser, CONMIN. The procedure used shows how existing analysis packages can be used to perform design optimisation with promising
2.6 Design Optimisation
31
results. In addition to more general configuration design; optimisation can be used to improve a specific performance issue. Structural loads can be improved through use of optimisation. For a hingeless rotor the loads seen at the hub can be particularly problematic. Lim and Chopra [78] use an aeroelastic analysis and an optimiser to improve loads seen at the hub of this rotor type. In particular this study shows an increase in optimisation algorithm performance by using a sensitivity analysis. An 80% reduction in computation time is seen by using this method. This shows that not only is the choice of analysis important, but also the formulation of the optimisation procedure. In addition to general flight performance or airframe design, optimisation can be used to improve more detailed problems. For this type of process, the logical implementation of an analysis method by an optimiser can be extremely useful. Aeromechanical instability of rotor blades can cause server flight handling problems. Hathaway and Gandhi [79] examine this situation, and the application of optimisation algorithms to help reduce these adverse effects. They use various structural and aerodynamic analyses tools to develop a model which includes all necessary effects. They then applied an optimisation procedure to minimise aeromechanical instability. Finally, the performance of an entire UAV configuration can be improved by using optimisation. Jun et al. [80] attempted to improve performance of a coaxial UAV by using a robust design procedure. This is especially relevant as it introduces the additional factor of Operational Uncertainty within the analysis. By including operational uncertainty within the design process, an attempt to characterise potential future difficulties is included within the analysis. This is a good example of how optimisation can be used to analyse and improve every facet of a configuration. The above examples have shown the utility, flexibility and benefit of using optimisation within the helicopter design process. Design optimisation can be applied to improve almost any feature of a rotorcraft. From improving specific flight performance or stability issues, to helping find an optimum configuration for a new rotorcraft concept. Ensuring that the optimisation functions as desired is an integral part of the design process. Each of the papers discussed above use benchmarks to ensure that the analysis and optimisation tool performs in this manner. Thus for any new analysis implementation this type of procedure must also be conducted.
2.7 Summary
32
Not every analysis tool is suited for use with optimisation. An analysis tool may be computationally too expensive for use with an optimiser. Or may only reflect a small subset of the entire range of analysis, whereas an optimiser may need to include a much wider range to find an optimal result. To be suited for use with an optimiser, an analysis tool should be developed around a framework which is similar to the typical optimiser. Salas and Townsend [81] propose a framework can be adopted when developing an analysis tool for use with an optimiser. This framework suggests that the areas of interest during development should include: Architectural Design; Problem Formulation Construction; Problem Execution; and Information Access. Isaacs et al. [82] also suggest that increased computational efficiency can be achieved with this formulation and optimum communication between analysis tool and optimiser. Optimisation is an extremely useful process which can be used with many aspects of design. It is especially useful for improving existing designs; reduce problematic flight characteristics; or developing new design configurations. Careful attention must be paid to reducing the computational expense of the process. Total computation time can often be reduced by minimising the number of function evaluations needed, or more importantly, by reducing the cost of each analysis evaluation.
2.7
Summary
Clearly there is a present and future need for small rotorcraft UAVs which can operate within urban environments. Both military and civilian organisations require UAVs for urban operations of surveillance and monitoring. However, the current range of aircraft available for such missions do not always perform optimally. Difficulties which these aircraft face vary, but any aircraft flying within this region will experience environmental factors which include: • Wind Buffeting and Turbulence; • Wind Chill and Heat Stress; • Driving Rain, Blowing Snow and Sand; • Pollutants; and
2.7 Summary
33
• Moving Obstacles. To develop an aircraft which can perform well within this domain, a new design process needs to be explored. Factors which need to be considered are not always immediately apparent, therefor a systematic procedure needs to be followed to ensure all design goals are taken into account. Surveillance and monitoring operations require that line-of-sight communications be maintained. Within urban environments buildings, trees, bridges and other aircraft can either block or interfere with line-of-sight communication and surveillance. Therefore, an aircraft which circles above these obstacles may intermittently loose contact with a target. As a result, a platform which can hover in one position, move to another and continue surveillance without loosing target acquisition is preferred. This typically results in use of a rotary-wing platform. Rotary-wing aircraft can take many different forms. Broadly, there are four types of configurations which can be used: Single Rotor Configurations; Coaxial Rotor Configurations; Tandem Rotor Configurations; and Multi-Rotor Configurations. Each of these types has benefits and drawbacks, and is used for a preferred operational scenario. However, to make a choice between these configurations further definition of mission specification and requirements is needed. Ideally, a helicopter configuration used within an urban environment should be capable of multiple missions. Such a rotorcraft could be used for stationary observation as one mission, or target tracking and pursuit in another. These two missions require a rotorcraft to not only stably, but also be able to maneuver. This requires a configuration which has a good balance between stability and controllability. Additionally a rotorcraft operating within these bounds must be able to fly in as much of the airspace as possible. This is to ensure that the rotorcraft be able to fit between buildings; under trees and bridges; and most importantly have the possibility of entering confined spaces. Both conventional helicopters and quad-rotor aircraft perform well in terms of their flight performance. However, both configurations suffer from poor stability and require significant stability augmentation for hover. Thus requiring complex control system. A promising alternative is that of coaxial rotorcraft, and provide a very promising base configuration for operations within urban environments.
2.7 Summary
34
A base coaxial configuration generally has two standard helicopter rotors placed one on top of the other. However, other coaxial rotorcraft configurations provide better performance. Most promising of these is the Proxflyer [7] type configuration. This aircraft is small, efficient and stable; and may be used for autonomous urban operations. To design a rotorcraft of this type, an analysis tool which represents the unique rotor dynamics needs to be developed. To adequately analyse this rotorcraft type the following features will need to be modeled: • Flapping Rotor Pairs; • Coaxial Rotor Interaction; • Possibility of Independent Cyclic/Collective Pitch Control; and • Low Reynolds Number Aerodynamics. Once these features are represented accurately the analysis tool can be used to examine any given aircraft configuration of this type. And then new coaxial rotorcraft configurations and designs can be developed. An optimisation process can help to reduce the time spent manually analysing various configurations to find an optimum. However to use optimisation with a specifically developed analysis tool, the following features should be included: • Ease of Use; • Flexibility of Analysis; • Accuracy of Analysis; and • Low Computational Overhead. To streamline any design optimisation process the above factors should be used. These goals will help to drive the analyses development, and ensure that the desired outcomes are achieved. The goal of this thesis is to investigate rotorcraft which can operate within an urban environment effectively. To do this, a new configuration, the Proxflyer type rotorcraft is used as a base. However, the development of such rotorcraft requires a custom developed analysis
2.7 Summary
35
tool. This analysis tool may be used within design optimisation. Therefore, characteristics of the tool include: simplicity; ease of use; accuracy; and computational expensive proportional to the accuracy required.
Chapter 3
Blade Element Momentum Theory 3.1
Introduction
Blade Element Momentum Theory (BEMT) was origninally developed as a method to analyse the loading distributions of various actuation discs. Johnson [48] presents and excellent summary of the development and workings of BEMT. BEMT has been used for the analysis of both helicopter rotors and propellers. Archer [83] suggested that the Wright brothers may have used some form of the analysis method during their aircraft development. Blade Element Momentum Theory analyses rotors or propellers by breaking each of the blades into distinct sections. As both aerodynamic and momentum solutions are developed for each elemental section, the method is can be expanded to include many effecrts. In addition to the simple rotor analysis, the method lends itself to include external effects such as Blade Flapping (Chapter 6) and Rotor Interaction (Chapter 4). This chapter presents a basic summary of the Blade Element Method as a whole. Following a summary of the basic rotor analysis with BEMT; additions to the basic theory are outlined, which include:
• Tip Loss Modeling; • Multiple Blades; • Translational Flight; and • Extendability.
3.2 Basic Blade Element Momentum Theory
37
Figure 3.1 – Basic theory treats all blades in a single rotor as a single unit. All seeing the same flow conditions. Each of these sections plays a key part in developing an analysis which can analyse wider range of flight conditions. In addition to outlining the analysis method, the limitations associated with BEMT are also discussed.
3.2
Basic Blade Element Momentum Theory
Blade Element Momentum Theory is used as a basis for all analysis performed throughout this thesis. To begin this process the basis on which this method is derived must be outlined. Basic BEMT commonly groups all blades together for a single analysis. This makes the assumption that all blade experience the same flow (shown in Figure 3.1), and makes no room for dynamic analysis. Although this is not ideal for complete aircraft analysis, the base of this theory must be explained. Each of the blades within a rotor is broken up into a number of elements for individual analysis. Each element is analysed in turn, and then collectively summed to determine the total rotor performance. As indicated previously, the analysis of a rotor with Blade Element Theory differs to the analysis of a propeller. BEMT can be used for both rotor and propeller analysis. A propeller has a high rotational component associated with its flow, which is not as pronounced in many rotor flows. To take
3.2 Basic Blade Element Momentum Theory
38
Figure 3.2 – Individual Blade Elements with discrete induced velocity components for each element. this into account, the analysis of a rotor with Blade Element Momentum Theory commonly neglects an induced rotational component which is present in propeller analysis. BEMT assumes that a rotor performs like an actuator disc, which has a discrete energy increase as the flow passes across the disc plane. To model this increase in energy across the plane an induced velocity ,ν, is used (as described in chapter 1 of [84]). Each of the blade elements has its own induced velocity component, as shown in Figure 3.2. By assigning each element its own induced velocity, and thus discrete loading, a better representation of the rotor’s loading can be made. Once each blade has been broken into elements, the geometry for each element must be found. Figure 3.3(a) shows the location of an element with respect to the rotor mast. Both the radial location and the angular speed of the element must be known to determine a its velocity diagram. Momentum Theory (Section 3.2.2) and Aerodynamic Theory (Section 3.2.3) require that the geometric dimensions of the element are known. An elements chord (c), width (dr) and geometric incidence angle (θ) are defined in Figure 3.3(b). The following sections (3.2.1 to 3.2.4) discuss the derivation of the finer points of the method. This includes the limitations of the methods and the derivation of the actual algorithm. This includes the following points: • Flight Region; • Momentum Theory; • Aerodynamic Theory; and • Implementation.
3.2 Basic Blade Element Momentum Theory
(a) Element Position
(b) Element Geometry
Figure 3.3 – Complete element geometric definition.
39
3.2 Basic Blade Element Momentum Theory
3.2.1
40
Hover and Vertical Flight
The basic implementation of blade element momentum theory is restricted to modeling either hover or vertical flight. This restriction does not allow any rotorcraft dynamics, other than a steady climb or descent, to be modeled. Although the base method is restricted to vertical flight, it will be shown in later sections that the Blade Element Method can be expanded to include Translational Flight (Section 3.5) and Multiple Blades (Section 3.4). This allows a wider range of flight conditions to be considered, and thus gives greater room for expansion.
3.2.2
Momentum Theory
By applying conservation of momentum, Momentum Theory allows the prediction of the thrust produced by an actuation disc. As a flow travels towards and away from a rotor (the streamtube), the area which is effected by the rotor contracts. Contraction of this flow is caused by the increase in energy across the rotor disc plane. Figure 3.4 shows the flow development from far upstream, to far downstream of the rotor. At the disc plane the effect of the rotor is seen as a discrete increase in velocity by the mean induced velocity component, ν¯. Full development of the flow is then seen far downstream with an effect of twice the mean induced velocity, represented by w. Momentum theory contributes to BEMT by modeling the increase in energy over the rotor. By analysing the conservation of momentum theory on both sides of the disc, an estimate for the thrust produced by the rotor can be determined. The following is adapted from Johnson [48] with respect to Figure 3.4, and shows the derivation to find a blade elements’ induced velocity using momentum theory. The following equation (3.1) is found by applying conservation of momentum between the disc plane and downstream. Here A represents rotor area; VZ , climb velocity; ν¯, average induced velocity; and S1 , downstream area.
(VZ + ν¯)A = (VZ + w)S1
(3.1)
With the previous equation a representation for the thrust produced by the entire rotor
3.2 Basic Blade Element Momentum Theory
41
Figure 3.4 – Development of flow across rotor plane with momentum theory. can be found. This is shown below (equation 3.2), where T represents thrust; ∆p, pressure change; ρ, air density; and dA, dT and dr represent element area, thrust and width.
T = ∆pA = ρ(VZ + w)wS1
(3.2)
It is assumed that the velocity increment far downstream from the rotor (w) is twice that of at the rotor ([48] page 39), thus w = 2¯ ν . This is not the case for all situations, but is true for a rotor with uniform inflow. Analysing an actuator disc with momentum theory produces this situation. Applying this relation to the above Equations 3.1 and 3.2, Equation 3.3 is now found.
T = 2ρA(VZ + ν¯)¯ ν
(3.3)
Considering that ν¯ represents the mean induced velocity with respect to the disc area, Equation 3.3 can be further reduced. The analysis of the entire rotor is then broken down into elemental rings. By applying the
3.2 Basic Blade Element Momentum Theory area integral, ν¯ =
R
42
νdA/A, the thrust produced by an elemental flow ring (shown in Figure
3.1) with constant induced velocity, ν can be found (Equation 3.4).
dT = 2ρdA(VZ + ν)ν
(3.4)
This is then further expanded with dA = 2πrdr, giving the following equation 3.5.
dT = 4πρrdr(VZ + ν)ν
(3.5)
This procedure has been summarised from Johnson [48]. For a more detailed explanation of the momentum theory analysis of an actuation disc, a more detailed text should be examined. Although this procedure allows the calculation of elements’ (flow annulus’) thrust, the increase in energy (ν) is unknown. To determine this increase in energy, aerodynamic theory is used.
3.2.3
Aerodynamic Theory
The momentum theory described in the previous section can predict an element’s thrust, but requires an estimate for the induced velocity. To determine the induced velocity aerodynamic analysis of the blade element is used. By using both of these theories an element’s induced velocity can then be converged upon. To visualise the aerodynamic analysis of an element an aerodynamic vector diagram is used. Within this thesis all velocity diagrams of this type are drawn with velocities meeting at the trailing edge, not the aerodynamic centre. Hover analysis is the most simple flight region in which to analyse the aerodynamics of an element, and is visualised in Figure 3.5. Within this analysis, there are only two velocity components which play a role: the Rotational Velocity Ωr and the Induced Velocity ν. To determine an estimate for the thrust produced by the element, the lift and drag of the section firstly need to be found (equations 3.6 and 3.7).
1 dL = Cl ρW 2 cdrB 2
(3.6)
3.2 Basic Blade Element Momentum Theory
43
Figure 3.5 – Aerodynamic diagram for Blade Element analysis during hover.
1 dD = Cd ρW 2 cdrB 2
(3.7)
Each of the above two equations use the resultant velocity component, W ; element chord, c; element width, dr; and number of blades, B. The resultant velocity is found by taking the resultant of the velocity diagram, as shown in equation 3.8. The sectional lift and drag coefficients (Cl and Cd ) are found in independently of BEMT (discussed in section 3.6).
W =
p ν 2 + (Ωr)2
(3.8)
To adjust for vertical flight, the aerodynamic diagram is redrawn to include the vertical velocity component, and is shown in Figure 3.6. This is accounted for by adding the extra vertical velocity component, VZ , into the derivation of the resultant velocity, shown in equation 3.9.
W =
p
(VZ + ν)2 + (Ωr)2
(3.9)
Once the lift and drag components have been found for either hover or vertical flight, the thrust can be found. Figure 3.7 shows the resolution of the forces from lift and drag, to normal and tangential thrust components. Lift and drag forces are resolved into the Thrust Normal (dTN ) and Thrust Tangential (dTT ) forces using Equations 3.10 and 3.11 respectively.
3.2 Basic Blade Element Momentum Theory
44
Figure 3.6 – Aerodynamic diagram for Blade Element analysis during vertical climb.
dTN = dL cos φ − dD sin φ
(3.10)
dTT = dL sin φ + dD cos φ
(3.11)
The equations listed above allow an aerodynamic estimate for the thrust of a blade section to be made. This is then combined with the momentum theory to converge upon the sections induced velocity. Implementation of this technique is discussed in the following section 3.2.4.
3.2.4
Implementation
Momentum and aerodynamic theories do not complete the implementation of BEMT. By assuming an induced velocity, each of these independent theories can produce an estimate for the element’s thrust component. To find an element’s loading, the correct induced velocity must be known. An iterative method using both theories is used to find a stable induced velocity solution for the blade section. An iterative method allows a simple yet robust algorithm to be produced to converge upon a section’s induced velocity. To facilitate this, the equations derived in the previous sections must be rearranged and an implementation needs to be outlined. To begin an initial estimate of the sections induced velocity is made. This can either be
3.2 Basic Blade Element Momentum Theory
45
Figure 3.7 – Diagram used to illustrate resolution forces on element. a prior value or a nominal value, such as 1ms−1 . By starting with this estimate an initial estimate for the elemental thrust can be found. From this, a better estimate for the induced velocity can then be found. This is continued until the new estimate for ν is within error (for example 1e−10 ) of the current value. This procedure is shown in figure 3.8, and outlines the procedure used to find a stable estimate. The procedure listed above allows the induced velocity across any given section to be found. Using this induced velocity the elements lift (dTN ); drag (dTT ); and pitching moment (dM ) can be found using equations (3.6-3.11). Defining the loading for the entire disc only requires that this procedure be applied to each blade element.
3.2.5
Example Implementation of Basic Theory
The previous sections outline the theory, equations, and implementation of BEMT. This section shows an example implementation of BEMT. Although a procedure for finding an element’s induced velocity has been given, a procedure for analysing an entire rotor has not. The procedure shown in figure 3.9 outlines that used for this example, or any BEMT, implementation. The geometry used for this example BEMT implementation is shown in Table 3.1. This example rotor has been analysed by using the procedure shown previously. The performance
3.3 Tip Loss Modelling
46
1. Define initial estimate for the induced velocity, ν. Either through an initial guess or calculation. 2. Enter convergence loop to find the induced velocity of the blade section: (a) Using current induced velocity (νn ), calculate thrust from aerodynamic aerofoil theory (equation 3.10). (b) Calculate new estimate for induced velocity (ν( n + 1)) using momentum theory (equation 3.5). Re-arranged and shown below as equation 3.12. 0 = (4πρrdr)ν 2 + (4πρrdrVZ )ν − dT
(3.12)
(c) Compare current (νn ) and new (ν( n+1)) estimates for convergence. Convergence occurs once difference between estimates is below predefined limit ( 10( − 10)). Exit loop once converged. 3. Once converged value of induced velocity is found, continue with calculating element forces.
Figure 3.8 – Procedure to converge on an elements induced velocity. of this rotor is shown in Table 3.2. Figures 3.10, 3.11 and 3.12 show the: induced velocity; blade lift; and blade drag distributions. Although the blade pitch is high (30◦ ), this does not likewise result in a high angle of attack. Figure3.13 shows that the angle of attack (α) varies between 4 and 6 degrees.
3.3
Tip Loss Modelling
Basic blade element momentum theory models blade lift proportional to the radial location. However, lift along rotor blades should drop to zero at the tip, which BEMT does not model. To correct for the losses which should be present a method for modeling the tip losses needs to be used. A commonly used method for modeling tip losses within BEMT is the Prandtl Tip Loss Model (PTLM). This method determines an induced velocity correction factor, F , which corrects the analysis to include tip loss. Equations 3.13 and 3.14 are used to determine this correction factor, where R is the rotor radius; r the element radius; and φ the inflow angle. This factor augments the aerodynamic calculations, as shown in equation 3.15). These
3.3 Tip Loss Modelling
47
1. Define all rotor characteristics, as listed below: • Root and Tip Radii: RRoot , RT ip • Root and Tip Chord: cRoot , cT ip • Root and Tip Geometric Pitch: θRoot , θT ip • Rotor Speed: Ω • Climb Speed: VZ • Number of Blades: B • Number of Sections: n 2. Define geometry of each individual blade element: • Radius (r), Chord (c) and Twist (θ); linear interpolation between root and tip. • Horizontal element velocity (Vh = Ωr). 3. Loop through blade elements, 0 → n (a) Converge on induced velocity for section. (b) Define element loading, dT n, dT t, dM . 4. Combine individual element forces and moments to find performance (L, Q and P ) for entire rotor.
Figure 3.9 – Procedure used for the example BEMT calculation.
Table 3.1 – Geometry of Aircraft used for basic BEMT implementation. Parameter Tip Radius Root Radius Tip Chord Root Chord Tip Pitch Angle Root Pitch Angle Climb Speed Number of Blades Number of Elements Rotor Speed
Value 300 mm 100 mm 30 mm 30 mm 30◦ 30◦ 0ms−1 4 100 1500 RPM
3.3 Tip Loss Modelling
48
Table 3.2 – Rotor performance for basic BEMT implementation. Parameter Thrust Torque Power
Value 2.3114 N 0.1002 Nm 15.7462 W
Figure 3.10 – Distribution of Induced Velocity across rotor blade for Basic BEMT implementation.
Figure 3.11 – Distribution of Normal Force across rotor blade for Basic BEMT implementation.
3.3 Tip Loss Modelling
Figure 3.12 – Distribution of Tangential Force across rotor blade for Basic BEMT implementation.
Figure 3.13 – Distribution of Angle of Attack across rotor blade for Basic BEMT implementation.
49
3.3 Tip Loss Modelling
50
Table 3.3 – Rotor performance for basic BEMT implementation with Prandtl Tip Loss Modelling. Parameter Thrust Torque Power
Tip Loss 2.1404 N 0.0913 Nm 14.3392 W
No Tip Loss 2.3114 N 0.1002 Nm 15.7462 W
% Difference -7.4 % -8.9 % -8.9 %
equations have been suggested in Leishman [49], but implemented in the form derived by from Moriarty & Hansen [85].
F =
2 cos−1 (e−f ) π
(3.13)
B R−r 2 r sin(φ)
(3.14)
f=
1 dL = Cl ρW 2 cdrBF 2
(3.15)
These equations model the correction factor as an elliptical distribution from root to tip. This elliptic model leaves the majority of the blade unmodified, but reduces the effectiveness of the blade towards the tip. A normalised distribution of the correction factor is shown in Figure 3.14. The same example implementation as section 3.2.5 has been used to illustrate the effect of PTLM on simple BEMT analysis. Figure 3.15 shows the Tip Loss Factor distribution across the radius of the rotor blade. It can be noted that the shape of this distribution is similar to that of the previous figure (3.14). Although, as the last element is not centred at the blade tip the correction factor does not reach zero. Likewise, as root-cutout has not been modelled there is no change at the root. While Figures 3.16 and 3.17 show the normal and tangential force distributions across the rotor blade. Finally, Table 3.3 shows the performance of the rotor with and without tip loss modelling. This comparison is not designed to show a comparison with experimental data. Rather, it is to show the inaccuracy in performance predictions if no tip loss model is used. Whilst not a comparison with experiment, this example shows the change in performance by introducing tip loss modeling. The computational cost which tip loss model imposes is
3.3 Tip Loss Modelling
Figure 3.14 – Prandtl Tip Loss Factor, F , plotted against normalised radius. Taken from Moriaty & Hansen [85].
Figure 3.15 – Distribution of Prandtl Tip Loss Factor across rotor blade for Basic BEMT implementation.
51
3.3 Tip Loss Modelling
Figure 3.16 – Distribution of Normal Force across rotor blade for Basic BEMT implementation with Prandtl Tip Loss Factor.
Figure 3.17 – Distribution of Tangential Force across rotor blade for Basic BEMT implementation with Prandtl Tip Loss Factor.
52
3.4 Multiple Blade Analysis
53
Figure 3.18 – Breakup of the rotor into separate blades for analysis. insignificant compared to the benefit it provides. From here onwards all implementations using blade element momentum theory include tip loss modeling.
3.4
Multiple Blade Analysis
Often BEMT is only used for performance analysis of rotor configurations in hover or vertical flight. Extending the method to include an ability to analyse each blade in isolation is the first step to allow dynamic rotor analysis. This is extremely important when blade flapping (chapter 6) and coaxial rotor interaction (chapter 4) are introduced. Simple BEMT assumes that all blades experience the same flow, and thus act together. When dynamic conditions, such as translational motion, are considered all blades do not experience the same flow. Thus they must be analysed individually. Analyse the rotor as separate blades requires that the streamtube also be separated. It is assumed that each blade will cover an equal part of the streamtube. Likewise, for momentum analysis each elemental annulus will be broken up equally. The breakup of the annulus into individual blades is shown in Figure 3.18. To implement the change from the previously presented basic theory (3.2) to multi-blade theory only a small change is made. Each blade now represents an equal part of the streamtube individually. Thus the analysis is altered to represent this change. Both the momentum (equation 3.5) and aerodynamic analysis (equations 3.17 and 3.18) are divided by the number of blades, B, to represent this change. The resulting equations are shown below (equations 3.16 to 3.18).
3.4 Multiple Blade Analysis
54
Figure 3.19 – Distribution of Induced Velocity for Simple and MultiBlade Theory for the same rotor.
dT =
4πρrdr(VZ + ν)ν B
(3.16)
1 dL = Cl ρW 2 cdr 2
(3.17)
1 dD = Cd ρW 2 cdr 2
(3.18)
To demonstrate that these equations are applicable for analysis surrounding hover, sample calculations have been made. Hover calculations have been made for the same four bladed rotor using multiple blade and basic analysis. Figures 3.19 and 3.20 show the Induced Velocity and Thrust distributions respectively for both basic and multiple blade analysis. Figure 3.19 shows that the induced velocity for both analyses are identical. In addition figure 3.20 shows that the total thrust distributions are identical, with each individual blade distribution making up one quarter (as there are 4 blades) of this total. These results are as expected.
3.5 Translational Flight
55
Figure 3.20 – Distribution of blade thrust for Simple and MultiBlade Theory for the same rotor.
3.5
Translational Flight
Basic BEMT allows for vertical flight, but makes no allowances for translational flight. Blades in different locations around the rotor will experience different velocity components. To include translational flight multiple blade analysis must be already in use. As translational flight may involve aircraft tilt, vertical velocity components are also included. Translational flight affects the analysis of the rotor by changing both the horizontal and vertical velocity components at each element. This is implemented by adding an extra translational velocity component, VT , to the velocity diagram, as shown in Figure 3.21. The magnitude of VT will change sinusoidally as the blades travel around the rotor disc. Figure 3.23 shows the variation of VT around the rotor from positive to negative effect. And also shows zero effect for blades oriented parallel to the translational velocity. Total relative aircraft motion is found by combining the translation and wind at the aircraft CG in the body fixed axis system. A body fixed axis system is centred at the aircraft CG with X, Y and Z axes located in the nose, starboard and downward directions respectively. This is shown in figure 3.22. And is then mapped to each blade. Figure 3.24(a) shows the
3.6 Aerodynamic Data
56
mapping of the horizontal translation components to the horizontal component applied to the blade, and is found with equation 3.19.
VT = VX sin ψbld + VY cos ψbld
(3.19)
In comparison to the horizontal component, the vertical component, VZB EM T , is mapped directly from the aircraft climb speed, VZ . Figure 3.24(b) shows the vertical motion of the helicopter, and the corresponding BEMT vertical velocity. By defining each of these components, the motion of the aircraft can be included within the analysis of each of the blades individually.
3.6
Aerodynamic Data
Blade element momentum theory does not include a method to determine aerofoil properties. Therefore it is heavily reliant on accurate aerodynamic data. As the method treats each element in isolation, only 2D sectional aerodynamic data is needed. Within the basic implementation, only the lift and drag coefficients (Cl and Cd ) are called for. However, to find blade pitching moment the pitching moment coefficient (Cm ) is also needed. Fidelity of BEMT is dependant on the fidelity of the aerodynamic data used. On the lower end of the spectrum, Cl can be found as a direct function of angle of attach (α) and Cd as
Figure 3.21 – Diagram showing all velocity components within translational flight.
3.6 Aerodynamic Data
57
Figure 3.22 – Helicopter axis system, including body and earth axis systems. Original image from Wikimedia [86]. a function of Cl . Such a simple function is unlikely to include stall effects which should be included. An example this is shown in equations 3.20 and 3.21 (coefficients are examples only). Representation of this type is unlikely to be accurate enough for more than rough analysis.
Cl = 2πα
(3.20)
Cd = 0.008 − 0.003Cl + 0.01Cl 2
(3.21)
To improve the quality of the aerodynamic model, data from either experimental tests or Computational Fluid Dynamics (CFD) can be used. This data is used as a simple lookup table, and a example of this is shown in table 3.4. Fidelity of this method is derived by ensuring the accuracy of the source data. Only a small range of aerodynamic data is required for a simple hover analysis. However once the analysis range is extended to either translational motion or other effects, the range must be further extended. Should conditions such as reverse flow or fast climb and/or descent be encountered, the range of aerodynamic data must be extended. In these situations, the required aerodynamic data may be required from all four quadrants of angle of attack. Figure 3.25 shows the four quadrants derived from differing components of VZ and VT , which result in each α region. Thus a full range of aerodynamic data over the range
3.7 Problem Areas
58
Figure 3.23 – Changing effect of the translation of the craft on individual blades around the rotor. −180◦ ≥ α ≤ 180◦ is required.
3.7
Problem Areas
Although BEMT performs well for hover analysis, there can be significant problems for regions outside of hover. Because the method relies on an iterative solution of induced velocity for each section, numerical singularities can arise under certain flow conditions. For example, should the element pitch angle (θ) be less than the inflow angle (φ), the section will produce thrust downwards. When momentum theory in standard form is solved for this situation the solution produces imaginary numbers, and the method fails. To allow for these flow regions to be analysed, a different numerical approach should be used. A solution to this problem is to break up the analysis into four separate regions. Each
3.7 Problem Areas
59
(a) Horizontal Component
(b) Vertical Component
Figure 3.24 – Velocity breakup as seen at blade for translational motion.
(d) 4th Quadrant
(c) 3rd Quadrant
(b) 2nd Quadrant
Figure 3.25 – Diagram showing four angle of attack regions for a blade section, produced by different velocity components.
(a) 1st Quadrant
3.7 Problem Areas 60
3.7 Problem Areas
61
Table 3.4 – Example aerodynamic data for a NACA0012 section. Taken from Abbott & von Doenhoff [87]. α −18◦ −16◦ −8◦ 0◦ 8◦ 16◦ 18◦
Cl -1.75 -1.6 -0.8 0.0 0.8 1.6 1.75
Cd 0.045 0.035 0.018 0.01 0.018 0.035 0.045
Cm -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1
of these regions has been derived from equation 3.12 and are listed in equations 3.22-3.25. No Vertical Motion, Positive Thrust. VZ = 0, dT ≥ 0, r > 0, dr > 0 s ν=
dT πρrdr
(3.22)
No Vertical Motion, Negative Thrust. VZ = 0, dT < 0, r > 0, dr > 0 s ν=−
−dT πρrdr
(3.23)
Vertical Motion, Negative Thrust. VZ 6= 0, dT > 0, r > 0, dr > 0 ν=
−πρrdrVZ −
p (πρrdrVZ )2 + 4dT πρrdr 2πρrdr
(3.24)
p (πρrdrVZ )2 + 4dT πρrdr 2πρrdr
(3.25)
Vertical Motion, Positive Thrust. VZ 6= 0, dT ≥ 0, r > 0, dr > 0 ν=
−πρrdrVZ +
By examining the vertical speed (VZ ) and the section thrust (dT ) potential problems can be caught before they occur. Each of the flow regions has a unique configuration which is listed above, with its appropriate solution. Once the flow region has been found, the appropriate solution for momentum analysis component can be implemented.
3.8 Summary
3.8
62
Summary
This section has discussed using Blade Element Momentum Theory for analysing loading of helicopter rotors. It has been shown that although BEMT has its origins within simple analysis of rotors, it can be extended to include a larger range of conditions; from multiple blade analysis to aircraft translation and other external effects. In later chapters extension to include Coaxial Rotor Interaction (Chapter 4) and Dynamic Blade Flapping (Chapter 6) is shown. By combining these effects, a single analysis package for Coaxial Rotorcraft has been constructed (Chapter 7). The simplicity of the method presented here may seem too basic for detailed performance analysis. However, Blade Element Momentum Theory is based on solid physical principles and thus gives a rotor analysis method with excellent characteristics.
Chapter 4
Coaxial Rotor Interaction 4.1
Introduction
Accurate prediction of the performance of coaxial rotors requires that the interaction between the rotor pair be taken into account. This chapter describes the new analysis method that has been developed to accomplish this task. The description begins with a description as to how the method fits with BEMT (section 4.4). It then outlines of the initial basic analysis concept (section 4.5) and assumptions (section 4.6). And finally concludes with a full description of the formulation and implementation of the full analysis technique (section 4.7).
4.1.1
Overview
Similarly to conventional helicopters, coaxial helicopters are difficult to analyse both in terms of their dynamics and complex aerodynamics. However, the complex flow patterns surrounding coaxial rotors makes analysis of this configurations loading characteristics, and thus performance, difficult. With most rotor analysis tools, there is no direct method for modeling the interaction between coaxial rotors. Including a rotor interaction model will improve aerodynamic analysis of coaxial rotors and rotorcraft. By having a better understanding of the performance of coaxial rotors, a better judgement of the initial design and sizing of these aircraft can be made. Furthermore, improvements in the prediction of rotor loads will likewise improve
4.2 Background and Methods
64
other areas of analysis, including flight dynamics. As coaxial rotorcraft have now become an increasingly favoured platform configuration for VTOL UAVs, any improvement in the prediction of rotor loads of these aircraft will improve the process of their design.
4.1.2
Goals
A number of goals were keep in mind during the development of rotor interaction method presented within this chapter (and thesis). These goals ensured that the analysis tool meets the requirements for use within configuration design and platform optimisation. Each of these goals are briefly outlined below.
Blade Element Momentum Theory: This theory is a commonly used method for determining the performance of propellers and rotors. This analysis theory is used as the base framework for all analysis within this thesis. Accordingly, it must also be used as the analysis framework for modeling the interaction between the coaxial rotors. Computational Efficiency: Efficiency of the interaction model and its computational algorithm is of high priority. Generally rotorcraft dynamic simulations require a large number of time-steps, and likewise loading evaluations. Thus the any enhanced efficiency within any part of the computational implementation will reduce computation time. Accuracy: The accuracy of the analysis method must be maintained so as to ensure it can be used as a tool to perform platform analysis and design. As a practical engineering tool for configuration design the accuracy should be within approximately 90%. Proxflyer Analysis: As the focus of this thesis surrounds the Proxflyer type aircraft, the analysis method used must be able to analyse this aircraft type. Including the highly dynamic rotor blade motion and high flapping angles.
4.2
Background and Methods
As suggested by Coleman [40] research into the design and analysis of coaxial rotorcraft is not new. The first formally recognised coaxial rotorcraft design was produced by Henry
4.2 Background and Methods
65
Bright [88] in 1861. Development of these platforms, along with associated design and analysis techniques, continued throughout the 20th century. To begin the development of a new analysis technique an understanding of existing methods must be know. A selection of these techniques are discussed in the following sections.
4.2.1
Previous Work
There are two branches of research surrounding the analysis of coaxial rotorcraft performance; theoretical and experimental. Larger manned helicopters have been the focus of much of the previous theoretical and experimental research, and despite the scale difference were found to be useful during the development of the analysis method presented in this chapter. There has only been a limited number of investigations which have directly focused on coaxial rotor interaction. More often than not both propellers and rotors can be examined using similar (or the same) analysis methods. An excellent example of this is Blade Element Momentum Theory (which was outline in the previous chapter 3). Thus research which focuses on coaxial propellers was also considered in addition to that of coaxial helicopters (discussed in section 4.2.2). Three research areas (listed below) have been chosen to be expanded upon, and is completed in the next section. • Empirical Relations; • Vortex Methods; • Additional Methods; and • BEMT Methods.
4.2.2 4.2.2.1
Available Options Empirical Relations
The most simple option to account for the interaction between coaxial rotors is to apply an empirical correction to isolated rotor analysis. This could be affected by calculating
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the performance of the two rotors in isolation, then applying a known correction factor to augment the thrust and torque coefficients (or values directly).
CTcoaxial = CTisolation × Kthrust
(4.1)
CQcoaxial = CQisolation × Ktorque
(4.2)
Equations 4.1 and 4.2 show thrust and torque coefficients in isolation being augmented to produce an estimate for coaxial rotor performance. However, the correction factors used (KT hrust and KT orque ) need to be determined separately for each aircraft configuration analysed. Thus, this method is not readily feasible for analysis of many different configuration. Both Wainauski and Vaczy [43]; and Harrington [41] provide a range of experimental data produced from tests of coaxial rotor performance. This and other experimental data may be used to produce a relationship which represents the correction factor for a specific rotor. Below is a list of some of the important characteristics which influence coaxial rotor interaction. These factors are considered as a key part of the interaction method presented in section 4.7. • Rotor speed; • Number of blades; • Climb speed; • Blade flapping (if any); • Rotor separation; and • Blade geometry. Applying correction factors to augment rotor performance is an extremely simple approach for this analysis. However, it is not feasible for use within this thesis for two reasons. Firstly, the augmenting factor will be dependant on aircraft configuration and will be difficult to calculate or predict for changing configurations. Secondly, to analyse the dynamic flapping motion of the Proxflyer’s rotor blades, the moment produced by the rotor blade itself is required. A correction factor, applied to the global coefficients, does not facilitate this level
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of detail. Therefore correction factors are not suitable for analysing the blade motion of a Proxflyer type aircraft.
4.2.2.2
Vortex Methods
Vortex methods are commonly used for the analysis of rotor aerodynamics. Krothapalli et. al. [89] used vortex tube theory to analyse dynamic inflow within manoeuvring flight. Streamtube flow characteristics within this region of flight are extremely complicated and an analysis method which can handle these complications is needed. Theodore and Celi [67, 68] have also used vortex methods as the basis of their analysis of equally complex flow regions. Their use of vortex methods provides increased accuracy in aerodynamic modeling, thus ensuring the accuracy of their subsequent analysis. From these implementations of vortex methods on conventional helicopters, it can be seen that they are only used when a higher degree of accuracy is required. The transition from a single rotor to a coaxial pair of rotors increases the complexity of analysis regardless of the method chosen. It can be seen from the study by Anikin [44] that the complexity of both the mathematics and flow patterns is high when vortex analysis is used for coaxial platforms. Accuracy of the analysis is maintained through the use of vortex methods. However, the increased complexity of the analysis method can offen outweigh the increased accuracy. Likewise, Griffiths and Leishman [90] also use a vortex based method for analysing dual rotor interference and ground effect. This study also shows that while accuracy is maintained with vortex methods, complexity of the algorithm and implementation is high. Vortex methods show promise for accurate analysis of coaxial rotors. However the complexity of the method, in terms of algorithm implementation, is too high for this thesis. This is due to there being no convenient method for combining vortex methods into BEMT, as required by this thesis. Additionally, the computational expense required by vortex methods is higher than that of BEMT. Thus making many aerodynamic evaluations, as required by configuration design, is not feasible.
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Additional Methods
The method presented by Colehour et. al. [45] shows promise as a starting point for the development of a rotor interaction model. They present a method which uses strip theory and Euler-equation methods to model the interaction between high speed counter-rotating propellers. By calculating and applying influence coefficient matrices, the influence of one rotor on the other can be found. Their results show that the method (when used accurately) predicts an increase in performance of counter-rotating propellers (CRP). Compared with other analysis methods, such as vortex methods, the simplicity and accuracy of this method provides a good basis as a starting point for coaxial rotor interaction modelling. Cho and Williams [47] used a frequency domain panel method to analyse the interaction between counter-rotating propellers. They represent the interaction between the propellers by applying a calculated augmenting velocity component. This augmenting component is found by using influencing coefficients and pressure differentials. The equations used by Cho and Williams are reproduced in Equations 4.3 and 4.4.
VF = AF F · ∆pF + AF R · ∆pR
(4.3)
VR = ARF · ∆pF + ARR · ∆pR
(4.4)
By basing their method on the differential pressure over each propeller, Cho and Williams use a direct relation between the influence and the performance of each propeller. Furthermore, it also provides a direct feedback between the rotors by using influence coefficients to create the augmenting velocities. This feedback provides an excellent method for representing coaxial rotor interaction.
4.2.2.4
BEMT Methods
There are few theoretical studies which have focused on using BEMT to analyse coaxial rotors. However, there are two notable examples. The first being a study by Valkov [91], and focuses on the analysis of hingeless rotors. Valkov presents models for analysis of both axial and forward flight. To apply an influence between the rotors, Volkov uses a direct mapping of velocity from one rotor to the other. This takes the form of adding an extra
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component of velocity to the vertical component within the analysis, as shown in Equation 4.5.
VN = VZ + ν(r) + νinf (r)
(4.5)
However,a function to find the influencing velocity also needs to be found. Valkov approaches this by using an augmented mass balance over the rotor with an empirical fit to an interaction coefficient, ε. The influence velocity component (νinf ) is found by multiplying the induced velocity (ν), from the opposing rotor, by the empirical interaction coefficient (ε) as shown in Equation 4.6.
νinf = ν(r)ε(d)
(4.6)
A rotor’s effect on the freestream is dependent on the distance from the rotor. Likewise the influence from one rotor on another will also depend on the inter-rotor spacing (d). Thus, interaction coefficients are dependent on the spacing between the rotors. The total normal velocity is then applied to a non-iterative BEMT method, which uses a prescribed solution to the force balance over both rotors. The interaction method used within this thesis (outline in section 4.3) is similar to the method presented by Volkov. However, there are a number of notable differences. First and foremost, Volkov only applies the method to non-flapping rotors. As analysis of Proxflyer rotors requires that high flap angles be taken into account, this exact form cannot be used. Secondly, to reduce numerical computation Volkov uses a BEMT method which requires no iteration to solve. Although iteration is used to determine a stable solution for the influence, a prescribed solution is used to find the actual BEMT solution. Whereas the interaction method presented within this thesis uses iteration for finding both the interaction and BEMT solutions. Despite these differences, Valkov’s method is most similar to the method used within this thesis. A more recent study using BEMT analysis of coaxial rotors was presented by Leishman and Ananthan [92]. Leishman and Ananthan presents analysis of coaxial rotors for finding an optimum planform configuration for axial flight. As with the study by Volkov, Leishman and Ananthan apply an influence from one rotor to the other as a function of induced
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velocity. However, they only apply influence from the upper rotor to the lower and not lower to upper. This has been chosen because the effect of the lower rotor on the upper would be minimal. By using this model there is no mutual influence between the rotors. This eliminates a component of influence, which although minimal is necessary. They also present a benchmark of this method against experimental and CFD results. This benchmark process shows that the total rotor performance agrees well. The distribution of loads over the rotor blades is also shown to agree well with the benchmarks. The two methods discussed above use BEMT to model influence between the rotors in much the same manner. However both studies have no method for accounting for tilted rotors which are seen on the Proxflyer rotors. This is the most crucial element needed for analysis of this aircraft. To fit with the BEMT method presented within Chapter 3 an interaction method needs to work with a non-prescribed solution. Both of the methods presented above use a prescribed non-iterative solution for the BEMT analysis. As a starting point for the development of a specific interaction model both of the previous studies serve as a good starting point.
4.2.3
Summary and Method Choice
Each of the methods discussed in the previous section (4.2.2) show good performance when modeling coaxial rotor interaction. Except for the two methods directly based on BEMT they do not necessarily lend themselves for use with BEMT. To fully define which aspects of these methods will be used, comparison with the base analysis method (BEMT) must be made. Blade element momentum theory uses an iterative process to converge on a rotor’s effect on the freestream. By using an induced velocity component (ν), BEMT directly models the change in the freestream due to the rotor. To continue to be consistent with BEMT as the base analysis method, use of both an iterative process and manipulation of the freestream velocity parameters have been used. By generating an effect from one rotor to the other, the methods used by Colehour et. al. and Cho and Williams provide convenient methods for modelling rotor or propeller interaction. These methods, however, do not provide an obvious method for inclusion within BEMT. Neither of the methods provides a means for calculating the driving parameter behind the influence. The methods used by Valkov and Leishman and Ananthan suggest
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that a mapping of the induced velocity from one rotor to the other can be used. These methods use geometric mapping of the streamtube to find influencing parameters. Likewise the method presented within this thesis also uses geometric mapping to locate and calculate influencing between Proxflyer type rotors. For BEMT to include coaxial rotor interaction, effects between the rotors need to be included within the analysis. To model this effect an augmenting parameter will be used. An augmenting parameter, νinf , will represent the influence of the induced velocity of one rotor on the other. A steady state flow representation is found by converging on a stable induced velocity distribution across both rotors including influence. The method in its entirety is described in the following sections.
4.3
Overview of Method
The method developed to model the interaction between coaxial rotors can be described as Velocity Augmentation, where each rotor influences the other (shown in Figure 4.1). Specifically, the model uses scaled induced velocities to apply influence between the rotors, as shown in equations 4.7 and 4.8. The theory behind and algorithm of these equations is shown in section 4.7. A rotor influences the flow both upstream and downstream of the rotor. Therefore in a coaxial rotor pair, each rotor must have some degree of influence upon the other. Thus many properties of a rotors flow must be considered when calculating this influence. However, contraction of the streamtube is considered to be an independent, as shown in Figure 4.2.
νinf,upper = f n(νlower )
(4.7)
νinf,lower = f n(νupper )
(4.8)
As mentioned above, the influence between rotors is evaluated as a function of the induced velocity on the influencing rotor. The influence depends on a number of factors, related primarily geometry and flow, and include: blade flap angle; rotor separation; radial location; rotor alignment; and stream contraction angle. These factors contribute to the magnitude of the influence, as well its location. Figure 4.2 shows that there is a distinct boundary to the influence region. This is caused by rotor flapping and streamtube contraction. For
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72
Figure 4.1 – Induced velocity influencing effect of coaxial rotors. either of these cases, the location of the streamtube may be offset from the rotor mast. Figure 4.3 illustrates the streamtube offset caused by rotor flapping. Thus a primary factor in determining the influence is to find the influence’s location, which is discussed within section 4.7.3. Once the influencing location has been found the magnitude of the influence is still undefined. The magnitude of the influence is scaled from an induced velocity. Any change in this value, which will change due to influence, will likewise cause a change in influence magnitude. Therefore an iterative procedure must be used to find a global stable solution. Any number of iterations could be used. However, if the distribution of induced velocities over both rotors is converged then the influence will likewise be converged. This is shown in Figure 4.4, where iteration is continued until a global stable solution is found. An example analysis is shown in section 4.5, and is used to give an example of the convergence procedure. From this implementation, figure 4.5 shows the percentage error over the iteration process for a single element. The number of iterations required depends primarily on the level of convergence accuracy required. However, other factors such as flow conditions and blade flap angles also affect the number of iterations. Generally, a single evaluation of the influence parameter is not suitable, and convergence to a define accuracy
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73
Figure 4.2 – Coaxial streamtubes in a steady-state flow pattern. level is required.
4.4
Rotor Interaction Method within BEMT
Velocity augmentation is easily incorporated within Blade Element Momentum Theory. This is because BEMT uses an induced velocity to represent a rotors effect on the freestream. Chapter 3 shows that BEMT has the capability to account for other external effects with minimal modification. Velocity augmentation uses this characteristic to fit within BEMT. Both the theory and framework of its inclusion within BEMT is defined in this section. Inclusion of a parameter to represent the rotor influence is similar to modeling aircraft motion or blade flapping. The influence component (νinf )is included in the vertical component of the flow diagram. The implementation of this within the flow diagram is shown in Figure 4.6. Components which appear as a vertical velocity component are included in
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74
Figure 4.3 – Coaxial streamtubes with an offset, caused by a disturbance from blade flapping. both aerodynamic and momentum analyses. The influence component is included within the aerodynamic (4.9) and momentum (4.10)equations below.
1 dT = CL ρW 2 cdr 2
dT =
4πρrdr(Vv + ν)ν B
(4.9)
(4.10)
It can be seen from the equations above (4.9, 4.10) and the flow diagram (figure 4.6) that νinf is included within the Vv and W components. These components are expanded below in equations 4.11, 4.13 and 4.13.
W =
q Vv2 + Vh2
(4.11)
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75
Figure 4.4 – Example block diagram which shows an overview of the analysis algorithm used, and how the iterative process continues until a stable solution is found.
Vv = VM + VZ + ν + νinf
(4.12)
Vh = Ωr + VT
(4.13)
As stated in Section 4.3, to develop a stable solution for the influence between the two rotors an iterative process must be used. The use of iteration to determine the influence between the rotors fits nicely within the BEMT method. An additional outer iterative loop is used to change from a simple BEMT implementation to an implementation with interaction. An implementation of a simple BEMT method is shown in figure 4.7. To change this into a method designed to model the interaction between coaxial rotors, only two extra steps need to be included. These are:
• Add Outer Influence Convergence Loop; and • Add Calculation for Influence Value, νinf (procedure outlined in section 4.7).
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76
Once these steps have been introduced into the BEMT method, the process used to find a stable distribution is shown in figure 4.8 (with the new steps in bold). This procedure illustrates how the basic BEMT procedure is encapsulated within the complete convergence procedure. In this case as step 2.(a). In either case of Basic BEMT or Influenced BEMT, once a stable distribution has been reached; Lift, Drag and Pitching Moment can be calculated for each element. These values are then used to calculate the performance of either a single rotor or a coaxial rotor pair.
4.5
Simple Test Implementation
This section presents a simple implementation of the velocity augmentation method described in the previous section. The goal of this implementation is to display that the base concept is feasible, and produces reasonable performance predictions. Two factors which must be addressed from the first implementation are: • Are the performance predictions realistic?; and
Figure 4.5 – Convergence error as a percentage of a single element for coaxial rotors in steady hover.
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77
Figure 4.6 – BEMT freestream flow analysis with influence from an opposing rotor included. 1. Define initial guess for Induced Velocities, ν 2. Loop through Rotors, Blades and Sections (a) Converge on Induced Velocity for element i. Aerodynamic Calculation ii. Momentum Calculation iii. Exit if converged 3. Stable Induced Velocity distribution reached
Figure 4.7 – Procedure used for simple implementation of BEMT algorithm. • Does the method allow stable convergence?.
For this example only a single blade on each rotor is considered, much like the simple blade element example. Further simplification is made by only mapping influence between corresponding blade elements. In essence, this simplification applies influence between the nth elements on each blade only (pictured in Figure 4.9). This constraint eliminates any fluctuation within each rotor’s streamtube, and streamtube contraction is also not considered. Each of these simplifications, however, are used within the complete analysis described in later chapters. These simplifications allow the first run test to be coded quickly and will give a good indication as to the potential of the method. For this example interaction analysis the global scheme described in section 4.4 is used. A general overview of these steps is shown in the following procedure.
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78
1. Define initial guess for Induced Velocities, ν 2. Loop to converge on Induced Velocity distribution (a) Loop through Rotors, Blades and Sections i. Calculate influence component, νinf (outlined in section 4.7) ii. Converge on Induced Velocity for element A. Aerodynamic Calculation B. Momentum Calculation C. Exit if converged (b) Check for stable distributions 3. Stable Induced Velocity distribution reached
Figure 4.8 – Example procedure used to combine rotor interaction into the BEMT algortihm. 1. Initialise Data 2. Loop to Converge Induced Velocities with Influence Included 3. Calculate Loading Distribution
Steps one and three are self explanatory. Step two, however, is where the actual implementation is located. This includes determining and applying the influence between rotors. For this example, the influence parameter (νinf ) is calculated as the corresponding induced velocity scaled by an effectiveness parameter (ηef f ect ) which is assumed to be constant (equation 4.14). The effectiveness differs depending which rotor is being influenced. Less than 1 for the lower influencing the upper, and greater than 1 for the upper influencing the lower. The outer convergence process is continued until the entire induced velocity distribution is within tolerance of the previous values.
νinf = νopposing × ηef f ect
(4.14)
To test the initial implementation of the model, a test geometry representing an aircraft needs to be used.
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79
Figure 4.9 – Influence between blades for the simple implementation, shows how corresponding elements influence each other directly. For this implementation, the analysis is assumed to be in steady hover with no external effects. In addition no account for tip loss is made. The data for the first test is shown in table 4.1, and is similar to that used within chapter 3. The only unknown parameter within the data used for the sample analysis is the effect between rotors. Determining this parameter is outside of the scope of this test. Thus an estimate of a 15% change has been assumed. To display the effect that the influence method, analysis with and without influence is made. Table 4.2 displays results for both Table 4.1 – Simple Implementation Data Parameter Tip Radius Root Radius Blade Chord Number of Blades Number of Elements Rotor Speed Effect of Lower on Upper Effect of Upper on Lower
Value 300 mm 100 mm 30 mm 4 100 1500 RPM 0.85 1.15
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80
Table 4.2 – Results of the Simple Implementation. With and Without Interaction Parameter Total Thrust (N) Upper Thrust (N) Lower Thrust (N) Thrust Difference (%) Total Torque (Nm) Upper Torque (Nm) Lower Torque (Nm) Torque Difference (%)
Interaction 14.46 7.61 6.85 11.17 1.19 0.598 0.593 0.775
No Interaction 17.83 8.91 8.91 0.0 1.16 0.58 0.58 0.0
Percentage Difference -18.87 -14.59 -23.12 — 2.5 3.1 2.24 —
sets of analyses. It can be seen that there is a drop in total thrust and an increase total torque. Both of these changes are as expected for two rotors operating in close proximity. The drop in total thrust caused by using this method is approximately 18%. In comparison, Harrington presents data which shows an approximate drop of 15%. This close match shows that the interaction model performs well, even though this is only a rough analysis to test the method. Figure 4.10 shows the differing radial thrust distribution over the upper and lower rotor blades with interaction modeling. In comparison, Figure 4.11 shows the same setup without interaction modeling. The change displayed is also as expected. This example implementation shows that velocity augmentation meets the two criteria previously set out. Firstly, the results agree well with previous experimental results. And secondly, the method converges in a timely manner and is stable. However, the following parameters are included in the full analysis method which will improve its performance.
• Blade flapping; • Multiple blades (including misalignment); • Realistic magnitude model; and • Varying flow characteristics.
4.5 Simple Test Implementation
Figure 4.10 – Thrust distribution over blade with rotor interaction modelling.
Figure 4.11 – Thrust distribution over blade without rotor interaction modelling.
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4.6 Method Assumptions
4.6
82
Method Assumptions
A number of assumptions have been made to simplify the implementation of the full analysis method. Each of these assumptions are discussed in the following sections (4.6.1 to 4.6.4).
4.6.1
Centred Around Hover
The analysis method is primarily designed for use with small unmanned rotorcraft. In particular it applies to the analysis of rotors and aircraft which mainly operate around hover. As the goal of the design process is to improve the stability and controllability of this platform type, there is little call for analysis of the aircraft outside of the hover region. By making this assumption, it allows a number of other assumptions to be made, in particular the static streamtube.
4.6.2
Static Streamtube
The most difficult part of analysing the interaction between coaxial rotors is determining how the streamtubes interact with each other. The velocity augmentation method requires a knowledge of the flow’s location. Thus, being able to map where the streamtube is located important. By mapping the influence location through the use of streamtube geometry, calculation of the influencing parameter is much simplified. Rotor streamtubes change with differing flow conditions. If this were included, the complexity of the analysis would be increased dramatically. To account for this, it is assumed that the axis of the streamtube will always remain perpendicular to the rotor plane, this includes flapping rotors (pictured in figure 4.3). This is valid as the strength of the flow through the rotor will ordinarily be much stronger than external effects. By applying this restriction, direct mapping from one rotor to the other using streamtube geometry is made.
4.6.3
Steady State Flow Between Rotors
Steady state flow between the rotors is assumed to simplify the mapping of induced velocity when blades do not align. When blades do not align a prediction of the induced velocity between the blades needs to be made. This is completed by interpolating the induced
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velocity between the blades. Steady state flow between the rotors assumes that the flow changes little as it travels between the rotors. By assuming this, interpolation of the between the blades can be made.
4.6.4
Incompressible Inviscid Flow
An assumption of Incompressible Inviscid Flow validates the previous assumption. To have static flow between the rotors, there must be negligible compressibility effects. For incompressible flow to be valid, the tip speed should not exceed 0.3 Mach. Therefore, the tip speeds should not exceed approximately 100ms−1 . Small unmanned rotorcraft operate well below this tip speed. Thus, the assumption of Incompressible Inviscid Flow is valid.
4.7
Full Method Explanation
The previous sections illustrate that the velocity augmentation is suited for modeling coaxial rotor interaction. The following sections (4.3 and 4.4) describe a the architecture used within the method. This section describes in detail each of the components required to produce a full Interaction Modelling algorithm within an aero-mechanical rotor analysis. Firstly, an outline of how the final method fits within the blade element method is described. Following this, the calculations required to implement the full method are described in full detail. Finally, this is combined into a complete method which defines the calculations required to find the influencing velocity for each section.
4.7.1
Convergence Procedure Outline
Section 4.4 shows how the interaction modelling method fits within Blade Element Momentum Theory. This section outlines how the required calculations fit within the full method and the BEMT. The simple implementation example did not include any function for adapting to blade misalignment or flapping. To account for this, a set of calculations which account for this geometry is used before the convergence procedure. These calculations are completed before the iterative loops are started. Figure 4.12 shows the location of the geometric calculations
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within the analysis block diagram. This is also shown in the procedure outlined in figure 4.13. Based on previously defined procedures (Section 4.4), this procedure has been altered to include the geometric calculation section. The calculations which are used to define all necessary geometric parameters are discussed in the following two sections (4.7.2 and 4.7.3). The first of these sections defines the general geometric setup and the calculations required to define them. The second section defines the actual calculations that are required, and how they are implemented.
4.7.2
Geometric Calculation Outline
As the rotors rotate the rotors will be out of alignment for the majority of evaluations. Figure 4.14 shows the coaxial rotor pair out of alignment. Furthermore, the rotors flap at once per revolution which also complicates the analysis. Accounting for these misalignments in the rotors and streamtubes can be achieved by developing a simple geometric model. Section (4.6) states the flow between the rotors is assumed to be steady state. Additionally, the flow is assumed to travel perpendicular to the rotor plane itself. This allows the geomet-
Figure 4.12 – Diagram of how required calculations fit within the convergence procedure.
4.7 Full Method Explanation
1. Load in Aircraft States, Rates and Controls 2. Calculate geometric parameters required for Influence Calculation. Use equations 4.15, 4.16, 4.17, 4.22, 4.26, 4.31 and 4.34. 3. Define initial estimate for Induced Velocities, ν 4. Loop to converge on Induced Velocity distribution (a) Loop through Rotors, Blades and Sections i. Calculate influence component, νinf . Use equations 4.37, 4.38 and 4.39. ii. Converge on Induced Velocity for element A. Aerodynamic Calculation B. Momentum Calculation C. Exit if converged (b) Check for stable distributions 5. Stable Induced Velocity distribution reached 6. Calculate Rotor Loading Distributions 7. Calculate Aircraft Forcing
Figure 4.13 – Procedure used for the rotor interaction process with geometric calculations included.
85
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86
ric mapping to be simplified. Thus determining the influencing location for a given blade element is also simplified. The various calculations which are required to determine the geometric mapping are shown in the list below, and are explained in detail in the following section (4.7.3)
• Azimuth Location; • Flap Angles; • Radial Location; • Stream Contraction Angle; • Vertical Separation; and • Radial Interpolation.
Figure 4.14 – Rotors being mapped onto each other, with differences in Azimuth location causing problems with direct mapping.
4.7 Full Method Explanation
4.7.3
87
Geometric Calculation Explanation
Each of the following sections outlines the calculations required to implement the influence method. The purpose, implementation and actual calculations for each set of calculations are discussed.
4.7.3.1
Azimuth Location
One of the initial parameters that needs to be calculated for full implementation is the Azimuth Location. Each of the two rotors have a known Azimuth location with respect to the azimuth origin. However, as the method operates on the assumption that the influence is made through a 2D flow segment, the location of each segment must be known. The ‘zeroth’ blade on each rotor is used to measure the azimuth angle with respect to the aircraft axis system. The relative location of the influenced blade compared to the zeroth blade, in the influencing rotors’ axis system, is required for further calculations. The geometric definition of this is shown in Figure 4.15. In this figure the angles Azbld is the influenced blade’s location with respect to its zero blade; Azrtr is the angle between the zeroth blade on each rotor; AzInf is the angle to the influencing location from the zeroth blade on the influencing rotor; and n defines the blade numbers on the influencing rotor. The relation between these locations is found with equation 4.15.
AzInf = 2π − Azbld − Azrtr
(4.15)
The influencing induced velocity is interpolated between two bounding blades. These bounding rotor blades which contribute to the influence must be found. Figure 4.15 shows an influencing location with its two bounding blades. These bounding blades can be found with equation 4.16. The bounding blade numbers defined with this equation will be used in section 4.7.4.2 to further define the interpolation parameters.
n
π π ≤ Azinf < (n + 1) 2 2
n = 0, 1, 2, 3
(4.16)
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88
Flap Angles
Once the location of the two dimensional influence section is found the flapping angles of both rotors in this plane can be found. This analysis is once again taken in the 2D flow section aligned with the influenced blade. For the influenced rotor the flapping angle is already known. However, the influencing location will more than likely occur between two blades, and thus the influencing flapping angle (βInf ) which must be calculated. Figure 4.16 shows the influencing rotor with an influencing azimuth location marked. Sinusoidal interpolation is used to find the flapping angle this location. The reference point is taken from the ‘zeroth’ blade (shown in figure 4.16). Equation 4.17 is used to calculate the flapping angle with this interpolation, where β1 and β2 are the flapping angles of the two blade pairs.
βInf = β1 cos AzInf + β2 sin AzInf
Figure 4.15 – Diagram of the method for relating the location of an influenced blade with respect to an influencing location.
(4.17)
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Figure 4.16 – Diagram which defines the location of the influencing location between two blades for flap angle calculation. 4.7.3.3
Radial Location
To determine the magnitude of the influence effect the influencing radial location must be known. A two dimensional segment of the streamtube intersecting with the influenced location is used once again. As stated previously, to simplify the streamtube segment two assumptions are made. Firstly, contraction near to the rotor plane it is assumed to be linear. And secondly, in hover the streamtube remains parallel to the rotor, thus at the core there must be no change in direction. Thus the local contraction angle γr ) must vary linearly from the angle at the tip (γ) to zero at the blade root (equation 4.18). Figure 4.17 shows the resulting streamtubes.
γr = γ
r ) R
(4.18)
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Figure 4.17 – Coaxial streamtubes where the assumptions of linear contraction about the rotors has been applied. To find the influencing radii there are two distinct regions. The upper rotor’s streamtube influencing the lower rotor; and the lower rotor’s streamtube influencing the upper rotor. Figures 4.18 and 4.19 show the geometry for determining the radial influence locations on either rotor. As well as the influencing radii (rU or rL ) the distance between radial location along the stream tube (d) must also be found. Analysis of this geometry is broken up into distinct vertical (V ) and horizontal (H) components. To avoid solving simultaneous equations with trigonometric functions, an iterative process to find the radial location and separation is used. The following two sections provide the methods for defining both the radial influence location and the separation between the locations for each rotor. For these sections the following symbols are used, and are defined as follows.
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rU , rL Upper and lower radial location. βU , βL Upper and lower blade flap angles. YU , YL Upper and lower rotor hub length from reference point. d Distance between element and influence location. R Rotor radius. γ Stream contraction angle at tip.
Influence of Upper Rotor For the influence of the upper rotor, the geometry from figure 4.18 is used. Firstly, the relations in the horizontal (H) direction are equated with respect to the origin. This arrives at the relation described in equation 4.19.
rU cos(βU ) = rL cos(βL ) + d cos(βL +
rL π −γ ) 2 R
Figure 4.18 – Geometry describing the influence upon the Upper rotor, required for determining the influencing radial location.
(4.19)
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This is then re-arranged to isolate the straight line distance between the two radial locations (d), resulting in equation 4.20.
d=
rU cos(βU ) − rL cos(βL ) cos(βL + π2 − γ rRL )
(4.20)
Secondly, relations in the vertical direction are then considered. The result of this is shown in equation 4.21.
YU + rU sin(βU ) = YL + rL sin(βL ) + d sin sin(βL +
rL π −γ ) 2 R
(4.21)
Equation 4.20 is then substituted into equation 4.21, and rearranged to form equation 4.22. As the only unknown in this equation is rL , it can be used iteratively to solve for this radius.
0 = YL − YU − rU sin(βU ) + rL sin(βL ) + (rU cos(βU ) − rL cos(βL )) tan(βL +
rL π − γ ) (4.22) 2 R
Influence of Lower Rotor The same procedure as for the upper rotor is used for the the influence of the lower rotor. With the geometry shown in figure 4.19. Equations 4.23 to 4.26 are used with the resulting equation used for iteration being equation 4.26. H Direction
rL cos(βL ) = rU cos(βU ) − d cos(βU +
d=
rU cos(βU ) − rL cos(βL ) cos(βU + π2 − γ rRU )
π rU −γ ) 2 R
(4.23)
(4.24)
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Figure 4.19 – Geometry describing the influence upon the Lower rotor, required for determining the influencing radial location. V Direction
π rU −γ ) 2 R
(4.25)
0 = YU − YL + rU sin(βU ) + rL sin(βL ) − (rU cos(βU ) − rL cos(βL )) tan(βU +
π rU − γ ) (4.26) 2 R
YL + rL sin(βL ) = YU + rU sin(βU ) − d sin(βU +
A simple root finding method is used with equations 4.22 and 4.26 to find the both the upper and lower influencing radii (for each region). However there is a singularity if the influencing location is perpendicular to the influenced blade. This occurs when the influencing flap angle (βInf ) is equal to the stream contraction angle at the influencing location (γP ), and is tested with equation refeqn:RotorInt:VertAlign1. When this situation occurs equating the horizontal components simplifies to equation 4.28. Thus, for this case the root finding method is not needed, and this equation is valid for both the upper and lower rotors.
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94
|βInf − γ
rInf | ≤ 10−2 R
0 = rU cos(βU ) − rL cos(βL )
4.7.3.4
(4.27)
(4.28)
Stream Contraction Angle
When calculating the radial influence location, the stream contraction angle about the influencing rotor is required. The equations derived within the previous section assume that the contraction angle is a constant. However, the actual angle of the streamtube will vary according to changes in geometry and flow parameters. Furthermore, the previous section assumes that the stream contraction around the rotor is linear. This may not be a completely accurate assumption. However as separation distance between the rotors is small, any curvature in the slipstream will be seen as negligible. Defining the contraction angle about the rotor requires a model for the actual streamtube geometry. McCormick [93] suggests a simple model of the slipstream as it moves through the rotor plane. The equation which models the slipstream development factor, kd , is shown in Equation 4.29. Distance from the rotor plane is described by s, and R represents the radius of the rotor.
kd = 1 + √
s2
s + R2
(4.29)
It can be seen from the above equation that the slipstream development factor varies from 0 → 2 as the distance from the rotor varies from −∞ → ∞. This is corollary to the derivation of momentum theory shown by Johnson [48], which describes the increase in velocity through the rotor as 0 → 2ν. Aligning with momentum theory, kd can describe the variation of the velocity of the flow along the stream distance. As the volume flow rate must remain constant along the flow direction (ignoring compressibility), the radius can be found from kd . This is shown in figure 4.20 and in the derivation below, resulting in equation 4.30.
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95
Figure 4.20 – Development of the rotor slipstream as it passes across the rotor plane.
A1 V 1 = A2 V 2 πr1 2 V1 = πr2 2 V2 πR2 ν = πr2 2 kd ν s R2 r2 = kd
(4.30)
Figure 4.21 shows the development of the slipstream and how it can be linearised about the rotor plane. The radial locations above and below the rotor (ru and rd ) shows the radius of the streamtube at points equidistant from the rotor plane (d). From these a linearised contraction angle can be found. The radii of the streamtube are calculated using equation 4.30 twice. Using these values the stream contraction angle can be found using equation 4.31.
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Figure 4.21 – Contraction of the rotor slipstream as it passes across the rotor plane.
γ = tan−1 (
4.7.3.5
ru − rd ) 2d
(4.31)
Vertical Separation
Directly mapping the induced velocity to the influenced blade element does not accurately reflect the stream flow. The separation between the two rotors changes the flow velocity between the rotors. To ensure that the streamtube is accurately modeled, a scaling factor is included. The previous Section 4.7.3.4 gives a factor which reflects this change; the streamtube development factor kd . However, the separation between rotors is needed. The lower rotor influencing the upper rotor is taken to illustrate the separation between the rotors. Figure 4.22 shows an element on the upper rotor being influenced by a location on the lower rotor. The separation between the rotors along the streamtube axis, dP can
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97
Figure 4.22 – Vertical separation between the influenced element on the upper rotor, and the influencing element on the lower rotor. be seen. To find dP the formulae for the direct line separation, d (from equations 4.20 and 4.24), modified by the effective streamtube angle can be used. For the lower influencing the upper rotor Equation 4.32 is used; and upper influencing the lower rotor uses Equation 4.33.
dP =
rL rU cos(βU ) − rL cos(βL ) cos (γ ) cos(βL + π2 − γ rRL ) R
(4.32)
dP =
rU cos(βU ) − rL cos(βL ) rU cos (γ ) rU π cos(βU + 2 − γ R ) R
(4.33)
Once the actual vertical separation distance has been calculated, the strength of the influence can be found. This is found by calculating the streamtube development factor using the separation, dP , as the axial distance; shown in Equation 4.34. This gives a factor which accurately reflects the strength of the influence, kaug . dP kaug = 1 + p dP 2 + R2
(4.34)
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Figure 4.23 – Regions in which the radial interpolation can be location 4.7.3.6
Radial Interpolation
From the Section 4.7.3.3 the actual radial location from which the influence originates has been found. However, this is only one part of the radial location definition. Although Blade Element Momentum Theory represents the distribution over the blade as a number of independent elements, the distribution in reality is a continuous one from blade root to tip. Furthermore, the influencing location will rarely be located on the centre of a blade element. It may in fact be located off the blade. To be able to determine the correct influencing value, the influencing velocity will be interpolated between two bounding radial elements. There are five distinct regions in which the influence can be located. Figure 4.23 shows each of these regions pictured on a six element rotor. Each of these regions has a differing method for defining the influencing velocity. To allow for easy calculation, the actual influencing velocity is interpolated from the element induced velocities. Therefore for each influence velocity there is a differing set of bounds. These bounds are discussed below. Region A: This location is off the rotor at the blade root. There is assumed to be no flow in this region. Therefore it will have no effect on the influence and is set to zero. Region B: This region is located between the root of the rotor and the centre of the first element. As there is no flow at the tip, the influence will be interpolated between 0 and the value of the first element, ν0 . Region C: This region is located in between any two centres of the blade elements. Therefore the influence will be interpolated between the two bounding induced velocities,
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99
νi and νi+1 . Region D: This region is similar to region B, in that it is located between the last element and the tip. Therefore, will be interpolated between the last element, νn , and 0. Region E: Similar to region A, this location is off the tip of the rotor. It has no effect on the influenced rotor, and therefore is set to 0 as well.
If the rotors are flapping in such a way that the influence radial location is found to be negative (on the opposite side of the rotor) the interpolation scheme will not work. To solve this problem the influencing location for this element is set to the opposite side of the rotor. This is implemented by altering the azimuth value by 180◦ and the absolute value of the radial influence location is used. This is shown in equations 4.35 and 4.36. Then normal operation on these values is applied.
4.7.4
AzInf = AzInf + π
(4.35)
rinf = |rinf |
(4.36)
Implementation Method
In the previous sections (4.7.3.1 to 4.7.3.6) the geometric calculations required to determine the influencing velocity have been described. Although these have been described, there is still no single method for determining the augmenting velocity. As the process for finding a stable velocity distribution across the rotors is an iterative process, the augmenting velocity will have to be found many times per loading evaluation. To ensure that the influencing velocity can be found efficiently, interpolation and lookup tables will be used. There are two distinct sets of calculations which are implemented for each loading distribution to be found. As there is a large number of iterative loops to be carried out during the loading calculation, all the complicated calculationsare completed before the looping section. As stated previously, this will then allow the calculation within the iterative process to be minimised. Both the pre-loop and loop calculations are summarised below.
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100
1. Calculated the Slipstream Contraction Angle for each rotor. Use Equation 4.31. 2. Calculate the Azimuth Location Data • For each blade determine the azimuth influence location with respect to the zeroth blade. Use Equation 4.15. • Using the Azimuth Influence Location, define the bounding blades for influence for each element. Use Equation 4.16 3. Define the Influencing Blade locations effective Flap Angle. Use Equation 4.17. 4. Determine the radial location at which the influence is being derived from. This requires iteration to find the location. Use either Equation 4.22 or Equation 4.26. 5. Determine the radial elements from which the influencing velocity will be interpolated. Described in Section 4.7.3.6. 6. Determine the Influencing Velocity augmentation factor from the vertical separation. Use Equation 4.34.
Figure 4.24 – Procedure used for pre convergence loop calculations 4.7.4.1
Pre-Loop Calculations
Calculations which do not depend on the induced velocity distribution are removed from the iterative process. Pre-loop calculations are of geometry parameters which do not change within a single evaluation. These calculations are used to define a set of lookup tables which are then used within the loop calculations. For ease of access lookup tables will contain the required data for each blade element. To find the required parameters to facilitate the loop calculations, the process shown in figure 4.24 is used. This procedure is to be conducted for each blade and element as required.
4.7.4.2
Loop Calculations
Section 4.7.4.1 describes the calculations which are to be conducted before the iterative loop. The iterative loop calculations to find the induced velocity distribution are performed. These calculations are defined in this section.
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Figure 4.25 – Final interpolation diagram for the influencing velocity, between two blades and elements. Each blade element receives an influence from the opposing rotor. This influence is interpolated from the geometry described in the previous sections. Interpolation of the influence is conducted both between two bounding blades and between two bounding radial locations on these blades. Figure 4.25 shows a diagram of the interpolation. This figure shows that three separate interpolations need to be conducted to determine the influence velocity. The final influencing induced velocity is interpolated radially. Equation 4.37 shows the linear interpolation between the two radial induced velocities.
νInf = ν1 + (
ν2 − ν1 )(rInf − r1 ) r2 − r1
(4.37)
Equation 4.37 uses two bounding induced velocities at the influencing azimuth location (ν1 and ν2 ). The two bounding radial induced velocities ν1 and ν2 are interpolated separately between the two bounding blades, locations ψ1 and ψ2 , to the azimuth influencing location
4.8 Summary
102
ψInf . And are interpolated between two induced velocities at each radial location on each blade, ν1,2I,O . This is shown in figure 4.25. Equations, 4.38 and 4.39 are used for this interpolation.
4.8
ν1 = ν1I + (
ν2I − ν1I )(ψInf − ψ1 ) ψ2 − ψ1
(4.38)
ν2 = ν1O + (
ν2O − ν1O )(ψInf − ψ1 ) ψ2 − ψ1
(4.39)
Summary
This chapter has shown the development of a method for modeling the interaction between coaxial rotors. This method has been designed for use with Blade Element Momentum Theory as a analysis technique. Although BEMT may seem a crude analysis technique, the tradeoff between simplicity and accuracy is worthwhile. Furthermore, BEMT has allows for direct inclusion of the interaction modeling using velocity augmentation. Velocity augmentation maps the induced velocity distribution from one rotor to the other. Thus providing a convenient model for rotor interaction, while maintaining the functionality of the Blade Element Momentum Theory. Although the complexity of the velocity augmentation method is minimal, the usability of the method has been maximised. The current implementation of the interaction model has been coded for use with a four-bladed Proxflyer type MAV. However, the method itself is not limited to analysis of this specific platform type. Velocity mapping through geometric relations allows the method to be used for any aircraft configuration. The only requirement for expansion for use with other configurations is that they still meet the base set of assumptions. As the method was designed primarily for use with small rotorcraft, meeting the base assumptions should not be difficult. To make both the development and implementation of this interaction modeling simple a number of factors are not considered within the model. This leaves a number of other areas which could be included in a further expansion of the model, which are discussed below. Swirl Modelling: Currently the interaction model as well as the Blade Element Momen-
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tum Theory used does not include any streamtube swirl effects. Within BEMT swirl is more commonly used for analysis of propellers. Whereas, rotors are usually considered to have flow which has minimal rotation. By neglecting the inclusion of swirl within the model, the addition of a second outer iterative loop has been avoided. Including this second iterative loop would increase complexity of the interaction model. Thus, convergence on a stable induced velocity distribution is not guaranteed. Expanding to include swirl effects would however give a more refined representation of the effects caused by the rotor interaction. Streamtube Model: Improving the methods used to model the streamtube will improve the accuracy of the method. A linear model was chosen to model the contraction of the streamtube. Essentially this was chosen to simplify the calculation of the radial influence location. This assumption is valid if the separation of the rotors is minimal when compared to the rotor diameter. However, if the rotors are not in close proximity, the linearisation of the streamtube is no longer valid. Despite this, when in close proximity the model will be improved if a more refined model of the streamtube is used. Offset Rotors: Although not entirely related to analysis of coaxial rotorcraft, extending the analysis to account for offset rotors is another area of possible expansion. This will allow for analysis of aircraft with overlapping rotors rather than only coaxial aircraft. Platforms with overlapping rotors may possess characteristics which are favorable to differing mission profiles. To account for offset rotors, the geometric mapping of the influencing velocity needs to be extended. These suggestions are outside of the investigation presented here. They are made to highlight areas which could be focused on for further development. Ensuring that the interaction model performs correctly is extremely important. Chapter 5 shows the verification of the interaction model against experiment. This tests the performance of the model in accordance with the restrictions that have been placed on it. Most significant of these restrictions is that all tests are performed around a hover. For these tests a custom test apparatus has been built and used. Now that the development of the interaction model has been completed, it can be introduced into other analysis areas. Chapter 3 previously outlines an in depth discussion of the theory
4.8 Summary
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and implementation of Blade Element Momentum Theory. This chapter briefly touches on the method for including other factors, such as the influence discussed within the current chapter. As a extension to this discussion chapter 6 outlines how the highly dynamic flap motion of the Proxflyer type rotors can be modeled. This is an extremely important factor when considering the performance analysis of this type of aircraft. Finally, chapter 7 discusses the amalgamation of all these factors into a complete analysis tool for Coaxial Contra Rotating Miniature Rotorcraft.
Chapter 5
Interaction Model Verification 5.1
Introduction
Blade Element Momentum Theory was used to formulate the Rotor Interaction Model described in the previous chapter (4). To justify this theory the method itself was benchmarked against physical tests. The goal of the benchmarking process is to ensure that the Rotor Interaction Model is correctly represents the aerodynamic interaction of coaxial rotorcraft. The interaction model is formulated to analyse Proxflyer type rotors operating around hover. It is difficult to verify the performance of the model whilst the characteristic Proxflyer rotors are flapping. To simplify the testing procedure and to ensure that the testing represents a characteristic flight region, the testing has been limited to hover with non-flapping rotors. A coaxial rotor test rig was constructed to benchmark the interaction theory. This experimental apparatus was designed and built with the restrictions on the dynamic motion discussed above kept in mind. Tests have been run over a wide range of rotor speeds and a number of rotor separations. Both of these parameters are restricted by the physical constraints of the test rig itself. Data obtained from these experiments is then compared with data from numerical analysis. From the two sets of data, comparison of the performance of the Rotor Interaction Model is made.
5.2 Experimental Setup
5.2
106
Experimental Setup
This section describes the design and operation of the experimental test rig. Figure 5.1 shows the test apparatus ready for testing. A dimensioned drawing of the test rig without rotors is shown in figure 5.1. To reduce interference from the mounts to the ground the test rig is oriented upside down. This allows the slower moving air to be drawn from below the rotors, where there will be less impact from the mounting structure. There are five major components which combine to makeup the design of the test rig and its operation. These components are as follows. A more detailed explanation and specification of each of these components is discussed in the following sections (5.2.1 to 5.2.5). • Rotor Configuration; • Rotor Drive Mechanism; • Load Sensing; • Data Acquisition; and • Procedural Control.
5.2.1
Rotor Configuration
Significant emphasis has been placed to ensure that the test apparatus reflects a Proxflyer type aircraft. This includes using a four bladed rotor, with highly cambered and twisted blades. The blades used for the rotors are taken from a radio controlled (RC) helicopter; the ‘Outback Rescue’ radio controlled helicopter. This model helicopter was produced by Venom Group International [94], but now is out of production. Figure 5.3 shows a blade from the upper and lower rotors. The Proxflyer type aircraft uses cambered flat plate aerofoils which vary in twist and chord from root to tip. The blades used in the test rig are similar to this in specification, however they have a larger diameter. Dimensions of these rotor blades are shown in table 5.1, the dimensions are for blades mounted in the rotor hubs. Each rotor has four blades mounted to a non-flapping hub. To ensure that minimal blade flapping occurs the blades have been molded to fit within the rotor hub using an epoxy and
5.2 Experimental Setup
Figure 5.1 – Experimental Test Rig - Assembled and ready for use with rotor separation of 50mm.
107
5.2 Experimental Setup
Figure 5.2 – Experimental Test Rig - Dimensioned drawing of the experimental test rig with rotors removed.
108
5.2 Experimental Setup
109
Figure 5.3 – Rotor blades used for verification of the rotor interaction model. flock mix. The molding serves not only to reduce flapping, but also ensures that each of the blades cannot change pitch angle. A fully assembled rotor is shown in Figure 5.4.
5.2.2
Rotor Drive Mechanism
The rotors are mounted on the same side above the gearbox with flow directed upwards, and are driven througha custom built gearbox. Figure 5.5 shows the gearbox housing with motor and rotor shafts. To reduce the rotation speed of the motor to the desired speed, a 4:1 reduction is used. Two AXI-2208-34 brushless motor are used to power each of the rotors. This motor’s specification is shown in table 5.2. It can be seen that at full speed this motor can achieve approximately 12000 RPM. Therefore, with reduction, the rotor will see a maximum speed Table 5.1 – Rotor and blade dimensions used for the test rig. Parameter Number of Blades Rotor Diameter Tip Radius Root Radius Tip Chord Root Chord Tip Twist Root Twist
Value 4 450 mm 225 mm 50 mm 18 mm 32 mm 6◦ 15◦
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110
Figure 5.4 – Fully assembled rotor used for testing the rotor interaction model. Table 5.2 – Specifications for the AXI-2208-24 brushless motor (Model Motors webpage [95]). Parameter Nominal Voltage Maximum Current Speed Configuration Maximum Speed
Value 11.1 V 8A 1100 RPM/V 12210 RPM
for 3000 RPM. Once load is applied to the motor the maximum speed is reduced. For this setup the maximum measured speed is approximately 2250 RPM. To give a margin of safety for the motor, it will be only tested up to a maximum of 2000 RPM.
5.2.3
Load Sensing
A load cell is used to measure the produced forces, which are then recorded by a computer using a data acquisition system. Although only the thrust produced by the rotors is examined, for convenience a six component load cell1 has been chosen. The load cell used is the 1
This load cell was chosen as it has the required accuracy, and was already in use at the university.
5.2 Experimental Setup
Figure 5.5 – Motor and gearbox used to drive rotors through a 4:1 reduction from the brushless motor.
111
5.2 Experimental Setup
112
Mini 45 load cell made by ATI Industrial Automation, and is shown in figure 5.6. Loads produced by the test rig will only be small in comparison to other load sensing applications. For the rotors used produces thrusts of approximately 20N2 . The Mini-45 has the force and moment ranges and resolutions as shown in tables 5.3 and 5.4. Although the maximum force sensing in the thrust direction, FZ , is far in excess of the likely seen thrust; the resolution in that direction is more than adequate. Likewise, the measurement uncertainty (shown in Table 5.4) of the load cell calibration is well within expectations for this measurement.
5.2.4
Data Acquisition
The National Instruments - USB-6251 is used to acquire the load cell voltages, and is shown in figure 5.7. The load cell is connected to the DAQ through a conditioning box, which amplifies and conditions the raw voltages from the load cell. Once the DAQ has acquired 2
This prediction was made using the analysis method developed within this thesis.
Figure 5.6 – ATI-IA Mini 45 6 component load cell used for measuring test rig forces (courtesy ATI - Industrial Automation [96]).
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113
Table 5.3 – Specifications for the Mini-45 6 Component Load Cell (ATI-IA Webpage [96]). Parameter Maximum
Component FX , FY FZ MX , MY MZ
Maximum Value ±290 N ±580 N ±10 Nm ±10 Nm
Resolution 1 32 N 1 32 N 1 1504 Nm 1 3008 Nm
the voltages from the load cell, they are processed by the computer and resolved into forces and moments. In addition to the rotor thrust the rotor speeds are also recorded. For a brushless motor the voltage pulses supplied to the motor itself are read and processed. A schematic of this is shown in figure 5.8. The signal which is produced from this pickup is extremely noisy and therefore must is filtered. As the voltage level of the motor is approximately 11V , the signal voltage is reduced while being filtered. A voltage divider and filter are combined for this process. The resulting circuit is shown in Figure 5.9. Both the load signal and filtered motor speed signal are then processed in LabView to provide useable data. The load cell voltages are processed to produce a set of loads. And the two motor speed signals are processed to determine the frequency of the signal. This allows the motor speed to be determined. Each of these signals is then recorded to file for external post-processing.
5.2.5
Control
During testing it is important to keep the rotors at a constant speed. It is also important to be able to have the rotors reach their test speed as quickly as possible. To control the Table 5.4 – Measurement uncertainty for the Mini-45 6 Component Load Cell (Mini-45 Calibration Certificate [97]). Component FX FY FZ MX MY MZ
Measurement Uncertainty 1.00% 0.75% 0.75% 1.25% 1.50% 1.25%
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114
Figure 5.7 – National Instruments DAQ used to acquire Loads and Motor Speeds. speed of the motors themselves, a brushless motor speed controller with governor mode is used. The Hyperion 20A speed controller has been chosen, and is shown in figure 5.10. To control the setting of the brushless speed controller, a servo controller computer interface was used. The Jimonics SCM18 servo controller, shown in figure 5.11, allows a computer to control servo or motor positions via a serial port interface. The benefit of this device is that it allows the motor speed to be commanded in a single step, rather than the gradual increase produced by a RC transmitter. This allows the setting to be achieved quickly with little transient response. The entire test rig is controlled through a single computer interface created in LabView. For ease of testing a single interface combines: a plot of the load cell wave-form; sensed motor speed; motor control; and data recording. Figure 5.12 shows a the testing interface during operation. All operations required to configure, control, test and record the experimental apparatus are available on this test interface.
5.2 Experimental Setup
Figure 5.8 – Diagram of pickup from brushless motor to sense motor speed.
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5.2 Experimental Setup
Figure 5.9 – Diagram of electronic filter used to sense motor speed. Voltage divider and analogue filter combined to produce a filtered and reduced analogue signal. Both circuits sourced from Wikipedia ([98] and [99]) with tuned component values.
Figure 5.10 – Hacker brushless speed controller with governor mode used to control motor speed.
116
5.2 Experimental Setup
Figure 5.11 – Jimonics SCM18 servo controller interface used to control motor speed controller setting.
Figure 5.12 – LabView interface for controlling operation of the test rig.
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5.3 Coded Test Setup
5.3
118
Coded Test Setup
To compare the analysis method presented in this thesis, numerical results are compared with experimental. However, as the test rig used in unable to test flapping rotors, this was not examined. Other than this all other parameters are similar between experimental and numerical tests. A numerical test without rotor interaction was also conducted to allow relative analysis improvement to be shown. One of the more critical components in the numerical test is the representation of the blade aerodynamics by 2D aerofoil aerodynamic data. The blades used on the test rig are essentially cambered flat plate aerofoils, as shown in figure 5.13. Aerodynamic data for this type of aerofoil at low Reynolds numbers (approximately 40000) is a less researched area. Pelletier and Mueller [100] have published data for flat plate cambered aerofoils down to Reynolds numbers of 60000. The camber of the blades used within Pelletier and Mueller’s study is 4%. This is similar to that of the blades used in the test rig, at approximately 5%. This experimental data has been used to formulate a full set of aerodynamic data for the aerofoils being used. Data provided by Pelletier and Mueller does not cover the required range of ±180◦ . Therefore an extension of Pelletier and Mueller’s data was made. A cambered flat plate is symmetrical about half chord, therefore regions centred on 0◦ and 180◦ are similar but opposite in sign, which is used. Further to this, general potential flow theory has been applied outside these two regions to make a complete data map. Plots of the aerodynamic data are shown in figures 5.14(a) and 5.14(b). This data is not only used for verification of the rotor interaction method, but also is used for the design studies in chapter 8. Tests to determine this
Figure 5.13 – Diagram of the cambered flat plate aerofoils used for physical and coded testing.
5.4 Test Schedule
119
data, either experimental or computational, were deemed outside the scope of this research project.
5.4
Test Schedule
It is essential to ensure that there is a wide variety of data to verify the rotor interaction method. The test rig used for this investigation allows three variables to be varied: upper rotor speed; lower rotor speed; and rotor separation. Table 5.5 summarises the range and interval at which these variables have been tested. All combinations of these variables were tested, resulting in a total of 75 combinations. For each of the test configurations, acquisition of enough samples is essential. To do this a profile of the test speed needs to be defined. In this case the test profile for any configuration is taken as: 0RP M → T estRP M → 0RP M . A sample of this is shown in figures 5.15 (for rotor speed) and 5.16 (for recorded load cell thrust). For each sample of this type two thrust readings are taken; one on the rising edge and the other on the falling edge. This essentially doubles the number of total readings taken for any of the test configurations used. To ensure an accurate array of data was generated for a test configuration, the profile described above was repeated 30 times.
5.5
Post Processing
A sample of the recorded thrust data shown from a single test is shown in Figure 5.16. Electronic noise produced by the load cell itself has been eliminated through a filter within the conditioning box and LabView. However, vibrations caused by the rotors has been transferred to the data file as noise in the thrust measurement. Signal reading with zero rotor speed are relatively noise free, while readings with the rotor/s spinning has a larger Table 5.5 – Variables and the range and interval at which they were tested. Parameter Upper Rotor Speed Lower Rotor Speed Rotor Separation
Upper Value 0 RPM 0 RPM 50 mm
Lower Value 2000 RPM 2000 RPM 150 mm
Interval 500 RPM 500 RPM 50 mm
5.5 Post Processing
120
(a) Cl, Cd
(b) Cm
Figure 5.14 – Lift, Drag and Pitching Moment coefficients for a flat plate cambered aerofoil. Modifications have been made to allow for full domain data.
5.5 Post Processing
Figure 5.15 – Commanded rotor speed profile for sample test schedule.
Figure 5.16 – Resulting load cell thrust profile for sample test schedule.
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5.5 Post Processing
122
noise level. To determine the thrust reading during the test, the data over this region is averaged.
Figure 5.17 – Load cell thrust profile for full range data file.
5.6 Results and Discussion
123
To isolate the test region from the non-test region, the location where the rotor speed changes (turning point) is used. The turning points can be found by examining the rotor speed signal. Equation 5.1 shows that the increasing turning point is found between two threshold values. In this equation, dRP M is the change in rotor speed between samples. Likewise Equation 5.2 shows the threshold values for a decreasing turning point as the negative of the increasing point.
350 ≤ dRP M ≤ 2200
(5.1)
−350 ≥ dRP M ≥ −2200
(5.2)
Figure 5.18 shows the same full range data as figure 5.17 with the test region averages overplotted. It can be seen that there is little variation of thrust measurements over the entire test range. A thrust reading, dTi , canis then be found by taking the difference between each subsequent change in rotor speed. The average thrust for the test configuration is found by taking the average of these readings. Equation 5.3 shows these two process combine. Standard deviation of the experimental readings can also be found from the individual thrust readings. n X
T =
5.6
dTi − dTi−1
i=2
n−1
(5.3)
Results and Discussion
Following physical tests of all desired configurations, numerical analysis both with and without rotor interaction were made. For the interaction method to be valid it must match the experimental results as best as possible. To make comparison between the numerical implementation and experimental results different data combinations are examined. As there are three major variables which are varied through the verification process, there are accordingly three result types which need to be examined. These result types are listed below.
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124
Figure 5.18 – Load cell thrust profile for full range data file with test region averages over-plotted. • Constant Upper Rotor Speed; • Constant Lower Rotor Speed; and • Separation Comparison.
Each of these sections allows the performance of the rotor interaction model to be examined. As the function of the interaction method differs for each of these parameters, they are each examined separately in the following sections (5.6.1-5.6.3). However, before comparison is made a table of the values needs to be examined. Results gathered for each of the combinations of Rotor Separation, Upper and Lower speeds are shown in the following Tables B.1, B.2 and B.3.
5.6 Results and Discussion
5.6.1 5.6.1.1
125
Constant Upper Rotor Speed Results
Figures 5.19 to 5.21 show the variation of experimental results; and numerical results with and without interaction for an upper rotor speed of 2000RPM with rotor separations of 50, 100 and 150mm. Plots of this type for the full range of data are shown in Appendix B. Discussion of these results is conducted in the following section 5.6.1.2. A second order polynomial has been fit to this data, and is used as thrust varies with the square of rotor speed. This fit is used for trend comparison between experimental and numerical results.
5.6.1.2
Discussion
Generally the rotor interaction method agrees well with experimental results for experiments with constant upper rotor speed. Figures 5.19, 5.20 and 5.21 shows the results of the analysis with a constant upper rotor speed of 2000RPM. These plots show that the thrust magnitude prediction agree extremely well with experiment. Further to this, the improvement over
Figure 5.19 – Thrust readings for experiment and code for 50mm separation with an upper rotor speed of 2000RPM.
5.6 Results and Discussion
Figure 5.20 – Thrust readings for experiment and code for 100mm separation with an upper rotor speed of 2000RPM.
Figure 5.21 – Thrust readings for experiment and code for 150mm separation with an upper rotor speed of 2000RPM.
126
5.6 Results and Discussion
127
analysis without interaction is excellent. However, there is still a level of variation when compared to the experimental results. This may be due to several factors such as inaccurate sectional aerodynamic data, geometry, or rotor speed. Problems with the verification are discussed further in section 5.6.3.2. By further processing this data the variation between numerical and experiment results is found. Figures 5.22, 5.23 and 5.24 show this variation for the three rotor separations tested. These plots show a maximum variation of 20%. Reasons for variations of this level are discussed in Section 5.7. Direct comparison of thrust magnitudes is not the only important verification. Of more importance is that the general trend of results matches between analysis and experiment. This is important because it shows that the analysis method includes appropriate physics within the method. By using a second order polynomial fit to both the experimental and code with interaction data, the trend of results can be examined. Figures 5.25 to 5.27 show the trend fits for the three rotor separations with upper rotor speeds kept constant over its rotor speed range.
Figure 5.22 – Code variation from experiment with constant upper rotor speed and 50mm rotor separation.
5.6 Results and Discussion
Figure 5.23 – Code variation from experiment with constant upper rotor speed and 100mm rotor separation.
Figure 5.24 – Code variation from experiment with constant upper rotor speed and 150mm rotor separation.
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129
Examination of the polynomial fit plots it can be observed that the trend of the interaction method matches well with experiment. Over the three separations tested there is no major discrepancy between the experimental and numerical trends. While the fit between the interaction method and experiment is good, agreement is not as good at slower rotor speeds. When the upper rotor is operating at slower speeds the fit is poorer than at higher speeds. This is mostly due to the lower disc loading that is seen at these rotor speeds. This variation is made worse when the lower rotor is also operating at higher speeds.
5.6.2 5.6.2.1
Constant Lower Rotor Speed Results
Figures 5.28 to 5.30 show the three tested rotor separations with a constant lower rotor speed of 2000RPM and varying upper rotor speed. As with the upper rotor, these plots are only a sample and the full range is shown in Appendix B. Examination of this data allows us to investigate the effect that the lower rotor has on the interaction method.
Figure 5.25 – Polynomial trend fit of experimental and code results for 50mm rotor separation with constant upper rotor speed.
5.6 Results and Discussion
Figure 5.26 – Polynomial trend fit of experimental and code results for 100mm rotor separation with constant upper rotor speed.
Figure 5.27 – Polynomial trend fit of experimental and code results for 150mm rotor separation with constant upper rotor speed.
130
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131
Discussion
By examining data for constant lower rotor speed, it can observed again that the interaction analysis method performs well. Figures 5.28, 5.29 and 5.30 show the variation of performance with the lower rotor restricted to 2000RPM. From these plots it can be seen that although agreement between datasets is good, it is not as good as for constant upper rotor. For the 2000RPM case there is a larger degree of variation over the entire upper rotor speed range. This is especially prevalent at slower upper rotor speeds. However, comparing experimental results against numerical analysis with interaction versus without interaction it is seen that numerical analysis with interaction performs much better than without. To examine the performance further variation between experimental and numerical results is plotted. This is shown in figures 5.31 to 5.33. These plots again show that generally the variation away from experiment is less that 20%, and is similar to tests with constant upper rotor speed. However, the location of the maximum variation is seen at a different rotor speed. More variation can be observed at slower upper rotor speeds. Thus, the effect of the constant lower rotor speed is more dominant at lighter disc loadings experienced at slower
Figure 5.28 – Thrust readings for experiment and code for 50mm separation with a lower rotor speed of 2000RPM.
5.6 Results and Discussion
Figure 5.29 – Thrust readings for experiment and code for 100mm separation with a lower rotor speed of 2000RPM.
Figure 5.30 – Thrust readings for experiment and code for 150mm separation with a lower rotor speed of 2000RPM.
132
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133
rotor speeds. Again the trend of the results is examined. Figures 5.34 to 5.36 show second order polynomial fits for constant lower rotor speed. By looking at these plots it can be observed that there is a better trend match with slower lower rotor speeds. The trend agreement decreases as the lower rotor speed increases. However, numerical method agrees well when both upper and lower rotors are at higher speeds. Which is also seen when keeping the upper rotor at a constant rotor speed. As for when keeping the upper rotor at a constant speed, the general trends over the speed range performs consistently at each of the rotor separations. Examination of the trends produced by altering the rotor separations is explored in more detail in the next section.
5.6.3
Separation Comparison
The previous two sections examine the rotor interaction models performance when keeping either of the two rotors at a constant speed and varying the other. It is also important to examine the effect of changing the separation between the rotors.
Figure 5.31 – Code variation from experiment with constant lower rotor speed and 50mm rotor separation.
5.6 Results and Discussion
Figure 5.32 – Code variation from experiment with constant lower rotor speed and 100mm rotor separation.
Figure 5.33 – Code variation from experiment with constant lower rotor speed and 150mm rotor separation.
134
5.6 Results and Discussion 5.6.3.1
135
Results
There are 25 combinations of rotor speeds for comparison of separation. The majority of these plots are displayed in Appendix B. To exhibit changes as the rotor speeds change, plots for varying separation with a lower rotor speed of 1500RPM are used. The plots displayed here are for upper speeds varying from 0RPM to 2000RPM. These plots are shown in figures 5.37 to 5.41 and show the progression from 0RPM to 2000RPM.
5.6.3.2
Discussion
When examining comparison of thrust with either of the two rotors at a fixed speed, it can be seen that agreement is worse for lower rotor speeds. This is also seen when examining the variation due to rotor separation. Figures 5.37 to 5.41 show that for slower upper rotor speeds agreement between experimental and numerical results is poor. However, once the upper rotor speed is increased agreement is improved. At slower upper rotor speeds, there is little difference between numerical results with and
Figure 5.34 – Polynomial trend fit of experimental and code results for 50mm rotor separation with constant lower rotor speed.
5.6 Results and Discussion
Figure 5.35 – Polynomial trend fit of experimental and code results for 100mm rotor separation with constant lower rotor speed.
Figure 5.36 – Polynomial trend fit of experimental and code results for 150mm rotor separation with constant lower rotor speed.
136
5.6 Results and Discussion
Figure 5.37 – Variation of thrust produced with change in rotor separation with lower rotor speed 1500RPM and an upper speed of 0RPM.
Figure 5.38 – Variation of thrust produced with change in rotor separation with lower rotor speed 1500RPM and an upper speed of 500RPM.
137
5.6 Results and Discussion
Figure 5.39 – Variation of thrust produced with change in rotor separation with lower rotor speed 1500RPM and an upper speed of 1000RPM.
Figure 5.40 – Variation of thrust produced with change in rotor separation with lower rotor speed 1500RPM and an upper speed of 1500RPM.
138
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139
Figure 5.41 – Variation of thrust produced with change in rotor separation with lower rotor speed 1500RPM and an upper speed of 2000RPM. without interaction (figures 5.37 and 5.38). While in the mid-range rotor speeds, figure 5.39, the experimental results become closer to that of numerical results with interaction. Furthermore, numerical results without interaction begin to over-predict the thrust prediction. Finally, at higher rotor speeds, 1500RPM and 2000RPM shown in figures 5.40 and 5.41, the agreement in thrust prediction between experiment and analysis with interaction is a very good. More importantly, analysis without interaction are over-predict the thrust produced to a large degree. If the results for upper rotor held constant and changing lower rotor speed are now examined, a similar trend is seen. As the lower rotor speed varies from 0RPM to 2000RPM (figures 5.42 to 5.46) the same change can be seen, but to a lesser degree. The variation between experimental results and numerical results with interaction is much less. For this combination the difference between the analysis without interaction is reduced as the rotor speed increases. This is similarly to the previous discussion as the lower rotor becomes more dominant. Once again this confirms that the rotor interaction method is more accurate at higher rotor speeds.
5.6 Results and Discussion
Figure 5.42 – Variation of thrust produced with change in rotor separation with upper rotor speed 1500RPM and an lower speed of 0RPM.
Figure 5.43 – Variation of thrust produced with change in rotor separation with upper rotor speed 1500RPM and an lower speed of 500RPM.
140
5.6 Results and Discussion
Figure 5.44 – Variation of thrust produced with change in rotor separation with upper rotor speed 1500RPM and an lower speed of 1000RPM.
Figure 5.45 – Variation of thrust produced with change in rotor separation with upper rotor speed 1500RPM and an lower speed of 1500RPM.
141
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142
Figure 5.46 – Variation of thrust produced with change in rotor separation with upper rotor speed 1500RPM and an lower speed of 2000RPM.
5.7
Problems with Verification
At first glance the match between experimental results and numerical results with rotor interaction seems good. However, there is a certain degree of uncertainty with both the experimental and numerical results. To establish the reliability of the verification the major sources of uncertainty must be addressed.
5.7.1
Rotor Speed
The first area of uncertainty is rotor speed. It is difficult to exactly measure the rotor speeds during all samples of a given configuration. To determine how much effect variations on rotor speed have on the solution, characterisation with the numerical analysis tool will be completed. Results are examined for both a slow and fast rotor speed configuration. As the experimental verification has been presented in dimensional values, characterisation is completed likewise. Figure 5.47 shows the thrust profiles for a range of upper rotor speeds with a constant lower
5.7 Problems with Verification
143
rotor speed of 500RPM. The three plots in this figure represent the thrust produced with exact rotor speeds and with an error of ±2.5%. Likewise, Figure 5.48 shows a similar setup with the lower rotor speed of 1500RPM. These plots show that the error is consistent across the entire speed range. For both configurations the maximum error is approximately ±5%. The error seen in the rotor speeds during the test was kept to less than 5%. Thus the maximum possible error seen due to rotor speed would be 10%. Therefore, rotor speed is a factor which does not need to be considered too highly when looking for uncertainty within the verification.
5.7.2
Blade Twist
Blade twist is a factor which could affect the rotor performance to a significant degree. The twist of the blades was measured with the rotors not moving. As the blades are slender, they have minimal structure to withstand twist deformation. Therefore the measured twist will not be correct will change under load. While Finite Element Analysis could be used to
Figure 5.47 – Variation of thrust produced with change in rotor speed due to error in rotor speed measurement. Slow lower rotor speed of 500RPM.
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144
Figure 5.48 – Variation of thrust produced with change in rotor speed due to error in rotor speed measurement. Faster lower rotor speed of 1500RPM. predict this, the complexity and added overhead of completing this makes it unfeasible for this study. Any load applied to these blades will cause the twist on the blade to change. To gain an understanding of the extent to which the thrust will change due to blade deformation, a numerical test is made. It is assumed that there will not be a large change in the twist seen due to loading. Therefore, only a 1◦ change will be applied to the blade. A single lower rotor speed of 1500RPM with a range of upper rotor speeds is tested. Figure 5.49 shows the results from this series of tests. As expected, an increase in blade twist causes an increase in thrust. Likewise decrease in twist causes a decrease in thrust. The thrust change produced by making a 1◦ twist change ranges in a thrust change of between 6% → 13% for increasing angle and 10% → 13% for decreasing angle. The 1◦ causes a twist change of 20% at the tip and 6% at the root. Therefore a thrust change of between 6% and 13% is not too great. However, there is more likelihood of a 1◦ twist change than a rotor speed change. Therefore this does in fact need to be considered.
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145
Figure 5.49 – Variation of thrust produced with change in blade twist due to dynamic load placed on rotor blades.
5.7.3
Section Aerodynamic Data
Aerodynamic data is the most difficult to area of uncertainty to quantify. The sectional aerodynamic data used for verification is based on experimental data. However, this experimental data only covers a small range of Reynolds numbers. This causes a problem as the lowest Reynolds number of the data is well above that of the highest of the experiment. The Reynolds number range that needs to be used for verification is typically very difficult to find data for. The highest Reynolds number is seen at the rotor tip at the maximum rotor speed of 2000RPM, giving a result of 60,000. The lowest is seen at the root at the slowest speed of 500RPM (neglecting no speed) and gives a result of 6,000. This range is extremely large and causes a great deal of trouble at such low Reynolds numbers. Flow at these Reynolds numbers is particularly difficult to characterise. There has been few experimental studies conducted within this region. Therefore, using the data provided by Pelletier and Mueller [100] at a Reynolds number of 80,000 is the best for this configuration. Although there are quantifiable errors in rotor speed and blade twist, the aerodynamic data poses the biggest problem. It is not surprising that the interaction method agrees better at
5.8 Conclusions
146
higher rotor speeds. The uncertainty of the aerodynamic data used makes the agreement shown in the previous sections look even better.
5.8
Conclusions
This chapter has shown an investigation of the verification of the interaction model from chapter 4. Although only a single experimental verification has been conducted, this is more than enough to show the accuracy of the method. Agreement has been shown to be within approximately 20%. This is excellent considering the difficulties and uncertainties encountered within the verification process. Especially when the limitations imposed by the available aerodynamic data is taken into account. Three differing assessments of the experimental data have been made to investigate the method accuracy. These assessments include focusing on constant upper rotor speed, constant lower rotor speed and varying rotor separation. Each of these areas display a different facet of the methods operation. And subsequently show that the accuracy of the method both in raw numbers and trends is excellent for each of these areas. Although the error across each of these areas is not constant, this can easily be accounted for within the uncertainties associated with the testing. The developed coaxial rotor interaction model performs extremely well. Both in terms of its direct accuracy and trends associated with the data. By developing and then verifying this method a greater level of confidence with any future analysis can be held. Although the verification does not extend to examination of flapping rotors, the basis of the method has been tested. This allows the further investigations within this thesis to be continued. Especially being able to analyse a coaxial rotorcraft with flapping rotors with the intention of configuration improvement and design.
Chapter 6
Modelling of Blade Flapping 6.1
Introduction
Rotor aerodynamics are influenced heavily by aircraft motion and blade motion. The dynamic motion changes the local flow conditions at different locations on the rotor. This is especially true for blade flapping, which changes the local vertical velocity of a blade once per revolution. For small unmanned rotorcraft with high flapping ranges this affect will be large in comparison to other flow conditions experienced. To analyse the Proxflyer aircraft (Muren [37]) properly, account must be made for their highly flapping rotors. This chapter shows the model used to account for the Proxflyer’s flapping rotors. This model analyses the flapping dynamics of the rotor blades, and provides input into the aerodynamic analysis. Chapters 3 and 4 show that Blade Element Momentum Theory can include external effects within the analysis; in this case flapping velocity. The flapping model makes use of this characteristic to account for flapping within BEMT.
6.2
Modelling Options
As discussed in previous chapters the goal of this thesis is a simple approach to analysing small unmanned rotorcraft, specifically the Proxflyer rotorcraft. At the heart of this approach is aerodynamic analysis using the computationally simple Blade Element Momentum Theory (chapter 3). As the analysis method for modelling rotor loading is simple,
6.3 Rotational Equations of Motion
148
the method for modelling blade flapping also follows this path. The options considered for modelling the blade flapping are discussed in the following paragraphs. The first and most simple of the two methods is to implement an analysis based on rotational equations of motion. This model may seem too simple to use for analysis of highly dynamic rotors. However, if all forcing and moments are defined correctly this method will perform well. In addition, as there is only one degree of freedom (blade flapping) no crosscoupling terms need to be accounted for. The flexibility allows simplicity to be maintained throughout the analysis. If cross-coupling and higher second order effects are considered a different method needs to be considered. Johnson [48] suggests that Sturm-Liouville theory as a method for solving the differential equations of motion for blade motion. These equations allow a large range of dynamic motion, including in-plane and out-of-plane bending and flapping to be analysed. Although such a model may solve the problems discussed in section 5.7.2, this complexity is exceeds that of this thesis. For a simple analysis of rigid blade flapping deriving these extra modes of motion is unnecessary. Rotational equations of motion complement Blade Element Momentum Theory. The benefits of simplicity and robustness far outweigh the drawback of being limited to rigid blade flapping analysis. Thus, rotational equations of motion are used for modelling the blade flapping of the Proxflyer rotorcraft.
6.3
Rotational Equations of Motion
Modelling the flapping of the blade as rotation about a fixed point allows rotational equations of motion to be used. As a direct extension of Newton’s second law, the rotational acceleration of body is influenced by the rotational force (moment) applied to it. This relation is shown in Equation 6.1.
M = I θ¨
(6.1)
Extending the above relation to include other external effects can be achieved very easily. Rotational spring and damping (K and C) effects contribute to the forcing components
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149
˙ In addition all forcing components are through the rotational position (θ) and rate (θ). included by expanding the applied moment (M ). When expanded, the applied moment includes components for blade lift; gravitational force; and inertial force. These components are caused by differing factors but are equated about the same point. The complete rotational equation of motion to model the blade flapping is shown in Equation 6.2.
IF lap θ¨ + C θ˙ + Kθ = MLoad + MGravity + MInertial
(6.2)
Each of the forcing components as well as the rotational inertia (I) in the above equation need to be defined. To define these components an axis definition for the flapping system also needs to be defined. These components are listed below and are discussed in the following sections:
• Axis Definition; • Blade Load; • Gravity Load; • Inertial Load; and • Blade Rotational Moment of Inertia.
6.3.1
Axis Definition
Although the flapping occurs from the rotor disc plane, the flapping itself uses a substantially different axis system. A general set of axis system have been presented within Appendix A. This does include an axis system for blade flapping and lagging, however for clarity it will be reiterated here. Blade flap angle is always referenced from the neutral blade angle. In most cases (apart from where fixed conning is present) this aligns with the disc plane. A positive deflection is taken in the direction of the normal to the disc plane in the direction of positive thrust. Therefore, the positive flapping is in an upwards direction for all rotor blades (or positions on the rotor).
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150
Generally there are two locations about which a blade can flap. The first configuration is similar to a teetering rotor or a Proxflyer type aircraft. For these aircraft the blades flap about the centre of the rotor disc in line with the rotor shaft. A basic representation of this type of axis system is shown in figure 6.2. The second configuration is where the rotation point is offset from the centre of the rotor plane. This is similar to a conventionally designed helicopter with flapping hinges. This axis system is shown in Figure 6.1. The location of the pivot point with respect to the rotor shaft affects the physical design parameters only. Implementation of the flapping analysis still requires the same procedure, which is independent of the rotation point. Following from the axis definition, Sections 6.3.2 to 6.4.4 define the calculations required to implement the entire analysis for the flapping equation.
6.3.2
Blade Load
The thrust produced by each blade element is used to define the component of forcing moment derived from blade loading (MLoad ). The contribution of a single element on the blade is shown in Figure 6.3. Each blade element has its normal force (Tn ) component multiplied by its radial distance from the rotation point (r). This is then summed to give the total forcing moment contribution from the blade loading, as shown in Equation 6.3.
MLoad =
n X
Tni ri
i=1
Figure 6.1 – Simplified axis system used to model the flapping motion of a single blade about a centre rotation point.
(6.3)
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151
Figure 6.2 – Simplified axis system used to model the flapping motion of a single blade about an offset rotation point.
Figure 6.3 – Rotational forcing produced from elemental blade lift.
6.3.3
Gravity Load
Similar to the blade load, the contribution to the forcing moment due to gravity load is assembled as a sum of its elements. Within the feasible flapping range ( ± 60◦ ) the gravity load will always produce a negative flapping moment. Figure 6.4 shows the gravity load component of an element applied to a flapping blade. To find the total gravitational moment contribution, the gravity force for each element is taken as a moment about the rotation point. This is then summed along the blade to produce a total load, as shown in Equation 6.4. In this equation dm represents elemental mass; g gravity; and r element moment arm. Of course should the aircraft or rotor plane be tilted with respect to the horizontal, this needs to be included within this equation.
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152
n X
MGravity =
−gdmi ri cos (β)
(6.4)
i=1
6.3.4
Inertial Load
To examine the flapping for blades correctly the inertial forces placed upon the blades must be modelled. Inertial load contributes a moment when the blade moves away from its neutral point. This load will always try to move the blade towards the neutral point. Figure 6.5 shows a flapping blade receiving a correcting force from inertial load. As with the Blade Loading and Gravity Loads, the inertial load can be found by summing the components along the blade as shown in equation 6.5.
MInertial =
n X
−ω 2 ri2 dmi cos (β) sin (β)
(6.5)
i=1
6.3.5
Blade Rotational Moment of Inertia
To model a blade’s flapping characteristics, its rotational inertia must be known. Although the rotational inertia of the blade may easily be found from a solid model of the blade, a simpler model is used. Any point mass can have its rotational inertial about any axis found easily by multiplying its mass by rotational distance squared. This technique can also be extended to a distributed
Figure 6.4 – Rotational forcing produced from elemental blade gravity force.
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153
Figure 6.5 – Applied moment on flapping blade produced from inertial component of a single element.
Figure 6.6 – Rotational inertia of a single element contributing to the rotational inertia of the complete blade. mass. An estimate of the blade’s rotational inertia can be found by breaking a structure into a number of elements and summing each elements contribution. For convenience the same distribution as Blade Element Momentum Theory is used. For simplicity the mass distribution (dM ) is assumed to be constant along the length of the blade. Figure 6.6 shows the breaking up the blade into its blade elements. Equation 6.6 is used to calculate the blades inertia.
IF lap =
n X
ri2 dmi
(6.6)
i=1
6.4
Blade Pair Flapping
Section 6.3 shows how rotational equations of motion can be applied to model the flapping motion of a single blade. However, the Proxflyer rotorcraft has blades which flap as pairs
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154
Figure 6.7 – Rotor Hub from the Proxflyer type aircraft showing the joining of opposite blades. not as single blades, as shown in Figure 6.7. The flapping motion of these blades occurs as two ridgidly joined blades, which experience the same flapping motion. Figure 6.8 shows how a the four-bladed Proxflyer type rotor is broken up into two distinct flapping pairs. The blade pairs which are grouped together experience the same flapping deflection, rate and acceleration. As two blades have now been joined to form a single rotational system, the basis of the analysis changes slightly. Although two blades are analysed together BEMT requires that the individual characteristics, as for a single blade, are known. Figure 6.9 shows the definition of the blade pairs axis system. The axis system for a blade pair is defined by the axis system of the first blade. Taken in isolation, a positive deflection of the blade pair will be seen as a positive deflection for first blade and a negative deflection for the second blade. This is shown in equations 6.7 and 6.8.
β1st = βP air
(6.7)
β2nd = −βP air
(6.8)
To be used for a blade pair, the theory shown in the previous section (6.3) requires that each of components be changed slightly. As the blades flap together, it requires that the forcing terms and the flapping inertia be re-evaluated to take this into account. Sections 6.4.1 to 6.4.4 discuss the changes needed to be applied to the previous theory to make the
6.4 Blade Pair Flapping
Figure 6.8 – Proxflyer type aircraft rotor, with blades grouped into flapping pairs.
Figure 6.9 – Definition of the rotational axis for a joined blade pair experiencing the same flapping motion.
155
6.4 Blade Pair Flapping
156
Figure 6.10 – Calculation of the Blade Pair flapping moment contribution due to Blade Loading. extension to blade pair flapping.
6.4.1
Blade Pair - Blade Load
As with the single blade, the contribution to flapping moment is generated from the loading on each element derived from Blade Element Momentum Theory. As each blade is analysed separately within BEMT the loads on opposite blades will differ during flapping and other conditions. The load on each element is transformed into a moment about the rotation point, and summed as show in Figure 6.10. As would be expected this equation shows that if there is no differential loading about the disc there is no mechanism to start blade flapping.
MLoad =
n X i=1 1st
6.4.2
T ni ri −
n X
T ni ri
(6.9)
i=1 2nd
Blade Pair - Gravity Load
Although gravity will have an effect on the flapping of a single blade there will be no or little effect on a pair. Figure 6.11 shows the gravity components being applied to two corresponding elements on a blade pair. As the blades are assumed to be symmetrical about the flapping point, the gravity component of the moment from the each blade will be the same. Thus, the total moment applied to the flapping pair will always be zero.
6.4 Blade Pair Flapping
157
Figure 6.11 – Calculation of the Blade Pair flapping moment contribution due to Gravitational Loading.
6.4.3
Blade Pair - Inertial Load
Calculation of the inertial load for the blade pair is the same as for a single blade. Figure 6.12 shows inertial loads generated from two corresponding element across the blade pair. As these elements have the same mass and radial location, their contribution will be the same. Similarly to the blade load contribution, the inertial load moment is generated by summing the contribution of ll elements on both blades. Equation 6.10 shows the formulae for finding the inertial loading component of the blade pair. This equation uses a negative flap angle for the second blade as would be expected due to the change in axis systems.
MInertial =
n X i=1 1sd
− ω 2 ri2 dmi cos (β) sin (β) +
n X
− ω 2 ri2 dmi cos (−β) sin (−β) (6.10)
i=1 2nd
Figure 6.12 – Calculation of the Blade Pair flapping moment contribution due to Inertial Loading.
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158
Figure 6.13 – Calculation of the Blade Pair rotational inertia.
6.4.4
Blade Pair - Rotational Inertia
As the two blades on each side of the rotation point are similar, individually they will have the same rotational inertia. This is pictured in figure 6.13. Therefore, to find the total inertia for the flapping pair, the inertia for a single blade is double, as shown in Equation 6.11.
IF lap = 2
n X
ri2 dmi
(6.11)
i=1
6.5
Method Implementation
Whether the flapping motion of the blades are being modelled individually or as blade pairs, the implementation is the same. Sections 6.3 and 6.4 show the method for finding the rotational acceleration for the either a single blade or a blade pair. However, this does not allow a continuous tracking of their motion to be found. To allow a continuous record of the blade flapping motion to be found, the equations of motion need to be integrated with respect to time. Once again there are a number of different methods for completing the time integration of these equations of motion. The three most common methods are the Midpoint, Euler or Runge-Kutta integration methods. Press et. al. [101] presents each of these methods as common solutions for computational integration. The Runge-Kutta method is used to numerically integrate the blade flapping motion. Implementation of the Runge-Kutta method is used to predict the next position of a function at a given time step. This requires that the derivative of the equation be found for a given position, as in equation 6.12.
6.5 Method Implementation
159
dy = f (x, y) dx
(6.12)
The derivative of the equation needs to be found to allow the function to be advanced by the time step, h. Runge-Kutta uses four derivatives at different points to estimate the overall derivative. The derivative estimates are shown in the following Equations 6.13 to 6.16.
y˙ 1 = f (xn , yn )
(6.13)
y˙ 2 = f (xn +
h h , yn + y˙ 1 ) 2 2
(6.14)
y˙ 3 = f (xn +
h h , yn + y˙ 2 ) 2 2
(6.15)
y˙ 4 = f (xn + h, yn + h y˙ 3 )
(6.16)
The total derivative for advancing the function is found using equation 6.17. This is then used to advance the function in the same way as any integration scheme, with equation 6.18.
y˙ n =
y˙ 1 y˙ 2 y˙ 3 y˙ 4 + + + 6 3 3 6
yn+1 = yn + y˙ n h
(6.17)
(6.18)
By using the Runge-Kutta scheme to simulate over time the motion of each blade or blade pair, an accurate representation of a blades’ motion can be found. However, to find the motion of the blade, an analysis procedure which includes aerodynamic analysis must be followed. The procedure used for analysing the Proxflyer rotorcraft is shown in figure 6.14.
6.5 Method Implementation
1. Define starting conditions 2. Define simulation time range, tm ax 3. Loop for each time step, while t < tm ax (a) Define current position and rotor states (b) For each derivative estimate: i. Define corrected rotor states ii. Calculate blade loading with blade element theory iii. For each blade pair: A. Define blade load forcing moment B. Define blade inertial forcing moment C. Assembly complete forcing moment iv. Find derivative estimate (c) Average estimate to find total derivative (d) Advance to next time stepm ti+1 = ti + dt 4. Finish simulation
Figure 6.14 – Procedure used to implement time simulation procedure, including Runge-Kutta integrations.
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6.6 Rotor to Aircraft Axis Transformation
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Rotor to Aircraft Axis Transformation
Rotor analysis requires that the flapping angle of the rotor be known with respect to the aircraft axis system. However, the method presented in the previous section calculates the flapping angles with respect to the rotor (or blade pair) fixed axis. To resolve the flap angle with respect to the aircraft axis it is assumed that each of the two pairs will follow the same flapping path around the rotor. And, due to the rotational motion, the flapping will vary in a sinusoidal pattern around the rotor path. These assumptions are valid because the rotation speed is fast enough that any perturbation within the disc will effect both blade pairs almost simultaneously. The flapping angles in the aircraft axis are the same as the blade pairs when the rotor is at zero azimuth angle. This maps directly to blade pair 1 contributing to roll, and pair 2 contributing to pitch. When offset from zero azimuth, both blade pairs combine to form the aircraft axis flapping angles. A sinusoidal function is used to resolve the blade flapping into aircraft axis. The contribution to the roll and pitch flapping angles can then be found by using equations 6.19 and 6.20, shown below.
βP itch = βF lap cos(−ψ)
(6.19)
βRoll = βF lap sin(ψ)
(6.20)
Figure 6.15 shows an example of blade flapping angles for two blade pairs offset from the aircraft axis. The flapping in the aircraft axis system is found by using superposition of the two pairs’ flapping angles. These equations, resulting from this superposition, are shown in equations 6.21 and 6.22, below.
βP itch = β1 cos(−ψ) + β2 sin(−ψ)
(6.21)
βRoll = β1 sin(ψ) + β2 cos(−ψ)
(6.22)
An example of this transformation is plotted in figures 6.17 and 6.16. For this example,
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Figure 6.15 – Transformation of blade pair flap angle from a rotor or blade pair fixed angle to aircraft fixed angle. blade pair 1 has a flap angle of 10◦ , and pair 2 with 2◦ . These figures show the two blade pairs being transformed back to aircraft pitch and roll axis as the azimuth angle is varied. The red line shows Pair 1, the blue Pair 2 and the black line the superposition of the two.
6.7
Example Implementation
A sample implementation has been completed to illustrate the method’s effectiveness. This implementation shows a single Proxflyer type rotor with two blade pairs encountering a sharp edged gust. The general profile of the gust striking the aircraft is shown in Figure 6.18. A hover condition is imposed upon the aircraft before the gust, and the aircraft is restrained to isolate the blade flapping motion. The geometry of the aircraft is the same as in previous chapters, and is shown again in table 6.1. By running the simulation with gust magnitudes varying from 0ms−1 to 10ms−1 , a baseline and range of responses is generated. Figure 6.19 shows the response of the two blade pairs’ flapping motion. This shows that as the blades rotate they experience a varying gust magnitude and thus adopt a sinusoidal flapping motion. As the blades start to flap they are
6.7 Example Implementation
Figure 6.16 – Superposition of two blade pairs to create rotor pitch flapping angle.
Figure 6.17 – Superposition of two blade pairs to create rotor roll flapping angle.
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Figure 6.18 – Profile of the gust used to illustrate the flapping of a Proxflyer type rotor. excited further by the actual dynamic motion of the blade. Once they reach a larger flap angle, the correcting inertial load overcomes the increase in aerodynamic load. As would be expected these two forces come to a balance and there is no further change in the flapping magnitude. Table 6.1 – Geometry of Aircraft used for flapping response test implementation. Parameter Tip Radius Root Radius Tip Chord Root Chord Tip Pitch Angle Root Pitch Angle Climb Speed Number of Blades Number of Elements Rotor Speed Blade Mass
Value 300 mm 100 mm 30 mm 30 mm 11.5◦ 11.5◦ 0ms−1 4 100 1500 RPM 10 g
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Figure 6.19 – Plot of blade flapping response for a 5ms−1 horizontal gust. Figure 6.20 shows the flapping response of the rotor. This plot is generated from the blade pair flapping in Figure 6.19 with the axis transformation in section 6.6 applied. The balance between the inertial and aerodynamic forces becomes even more apparent in this figure through the clear depiction of the steady-state flapping region. Plots of the blade and rotor flapping for the full gust spectrum are shown within appendix C. Figures C.1(a) to C.11(b) show each of the responses to the varying gust magnitudes. Generated from these plots, figure 6.21 shows the relation between gust magnitude and steady-state Pitch and Roll rotor flap deflection. Pitch and Roll flap angles increase with gust magnitude as would be expected.
6.8
Summary
Highly dynamic flapping rotors, such as those seen on the Proxflyer aircraft, experience rotor deflections which normal rotors do not. In contrast to using a complex analysis model which provides a vast range of detail a simpler method, Rotational Equations of Motion,
6.8 Summary
Figure 6.20 – Plot of rotor flapping response for a 5ms−1 horizontal gust.
Figure 6.21 – Steady-state rotor flapping angles for differing gust values.
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has been chosen. This decision has been made to align with the goal to keep the numerical complexity to a minimum. Within the development of this analysis method, inclusions for all major forcing sources has been included. Most importantly blade loading and inertial loads due to the blade rotation have been included. Relating the motion of the blades to the aircraft axis system is important when examining a rotors effect on a platform. A method for relating the dynamic response of the local rotor blade pairs to the aircraft has been developed. This allows the pitch and roll of the rotor disc to be examined. To illustrate the complete workings of this analysis method, a sample set of data has been produced. This data examines the flapping response, both at the local blade and the pitch and roll, for a single configuration over a range of disturbances. This data shows that the flapping analysis model performs as desired.
Chapter 7
Rotorcraft Analysis 7.1
Introduction
As discussed previously, the goal of this thesis is to analyse the rotor dynamics and loading of a Proxflyer type rotorcraft. These aircraft have highly dynamic rotors which allows it to exhibit excellent stability characteristics. The dynamic nature of the rotor flapping also implies equally dynamic rotor loading. Therefore, to be able to investigate aircraft characteristics which contribute to the inherent stability, an accurate representation of both the rotor loading and motion must be available. The previous chapters 3, 4 and 6 outline three aspects of rotor analysis in isolation. This chapter combines these method to allow analysis the Proxflyer as an entire rotorcraft. Further to the investigation of configurations based on the standard Proxflyer configuration are made. Changes to the base configuration may allow aircraft which exhibit more favourable characteristics to be found. Specifically, investigation of similar aircraft with rotor control is desired. By being able to control the rotors directly better control over the aircraft as a whole can be made. This is more preferable than using an upwards facing tail rotor to control the aircraft. In this way new designs can be compared to the original aircraft, to determine if more favourable performance characteristics have been found.
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Entire Package
The next five sections (section 7.2.1 to 7.2.5) describe how the three base analysis techniques play a part in the entire analysis.
7.2.1
Analysis Geometry
The platform geometry that is required for the overall analysis is the rotors position in relation to the aircraft CG, and the geometry of the rotors themselves. As well as actually defining the aircraft axis system and geometry, the restrictions placed upon this geometry must also be defined. Below is a list of the geometry features which must be defined for full analysis. • Upper rotor position; • Lower rotor position; • Blade geometry; and • Blade aerodynamic sectional performance. By examining the physical Proxflyer type aircraft it is seen that the rotor mast always passes through the centre of gravity. It is also be noted that the rotor mast also always remains perpendicular to the aircraft X-Y plane. Both of these points ensure that whilst in steady hover the aircraft remains parallel to the ground. Figure 7.1 shows a picture of a Proxflyer with the rotor mast and axis system highlighted. This layout of the the axis system and rotors has been transferred to a simple line drawing showing the key features in figure 7.2. One of the most important features to highlight within the Proxflyer’s design is the layout of the rotors. The rotors rotate in opposite directions to provide torque balance and yaw control. To standardise the analysis it is assumed that the top rotor will rotate in an anticlockwise direction, as shown in figure 7.3. The bottom rotor must therefore rotate in a clockwise direction as shown in figure 7.4. A further point to note from figures 7.3 and 7.4 is that the pitch and roll flapping directions for both rotors are the same. This is because the axes are derived from the aircraft axis
7.2 Entire Package
Figure 7.1 – Aircraft Axis and Rotor Axis with top and bottom rotors rotating in opposite directions shown overlaid on a Proxflyer type aircraft.
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Figure 7.2 – Aircraft Axis and Rotor Axis with top and bottom rotors rotating in opposite directions.
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Figure 7.3 – Top Rotor Axis with Flapping Pitch and Roll Axis. system. Pitch of the rotor disc being taken about the aircraft Y axis, and roll being taken about the negative X axis. This is similar to standard helicopter analysis. These axis and geometric definitions are carried through the rest of the analysis. The global analysis and results will be related back to these axis definitions.
7.2.2
BEMT Analysis
As discussed in Chapter 3, Blade Element Momentum Theory provides a convenient method for analysing a wide variety of rotor loading configurations. The performance of an entire rotor is analysed with small radial elements on each blade. This allows a distributed flow profile, and therefore a distributed loading profile to be found across the entire rotor. To allow coaxial rotorcraft to be analyed as a whole two additional features must be introduced: wind or translation; and rotor control.
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Figure 7.4 – Bottom Rotor Axis with Flapping Pitch and Roll Axis. By breaking the analysis up into separate blades the rotor can be analysed for asymmetrical flow, control, motion and loading. Wind or aircraft translation can be modeled by adding an additional velocity (VT ) term into the BEMT analysis, shown in figure 7.5. This term only covers flow parallel to the rotor plane, perpendicular flow is already taken into account with the basic analysis. The translation velocity, VT , is found by taking a sinusoidal relation around the rotor ([84] page 141). When this is expanded to consider velocity from both the X and Y directions equation 7.11 is used.
VT = VX cos(ψ) + VY sin(ψ)
(7.1)
Modeling control requires changes to the geometric pitch angle, θ, rather than flow velocities. 1 This relation is for an anti-clockwise rotating rotor. For a clockwise rotor the sign of the VY term is changed to a negative.
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Figure 7.5 – Additional Blade Element components on aerodynamic diagram to model translational flow and control. Additional components are highlighted by boxes. Figure 7.5 shows the additional control pitch angle as dθ. The control pitch angle (dθ) is assembled as in equation 7.2 by using: aircraft collective (θC ); aircraft pitch cyclic (θP ); and aircraft roll cyclic (θR ).
dθ = θC + θP cos(ψ) + θR sin(ψ)
(7.2)
Figure 7.6 shows the thrust contour of a rotor with a translation wind applied. In this figure the rotor is rotating in an anti-clockwise direction and the wind is being applied from left to right. As expected, an increase in thrust on the advancing side and a decrease on the retreating side can be seen. Similar to the wind applied rotor, figure 7.7 shows an application of cyclic input. This rotor is under the same rotational conditions as the previous rotor (excluding wind). Once again, the results are as expected with an increase and decrease in thrust aligned to that of blade pitch.
7.2.3
Interaction Analysis
Blade Element Momentum Theory in its base form does not take interaction between any coaxial rotors into account. An analysis tool used for modelling the Proxflyer’s performance must include rotor interaction. This thesis has presented a method which has been developed
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Figure 7.6 – Thrust contour of rotor disc with a translation wind applied at 3ms−1 . for this purpose. A full explanation for the Rotor Interaction Modelling technique is detailed in Chapter 4. In general terms the rotor interaction modelling technique uses an augmenting velocity, νAug , to account for rotor interaction. This augmenting factor represents the influence between coaxial rotors. As the two rotors are situated within the same stream, they see the same overall flow. However, each rotor imparts energy to the flow, which is modelled as an induced velocity (ν) within BEMT. Each rotor’s induced velocity varies according to the axial distance from the rotor. Therefore, the effect of this induced velocity of one rotor will be seen at the opposing rotor as an influence (νAug ). This is found by using the process outlined in chapter 4. Once the augmenting velocity has been found it is included within the aerodynamic diagram, as shown in Figure 7.8. To implement this system of interaction modelling, a second outer convergence loop is placed outside the original blade element conversion loop. This is due to the augmenting velocity being calculated from the current estimate of the opposing rotor’s
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Figure 7.7 – Thrust contour of rotor disc with a roll cyclic application of 5◦ . induced velocity. The induced velocity from the opposing rotor will continue to change as the interaction is applied. Convergence is performed until the complete induced velocity distribution has stabilised within a preset limit.
7.2.4
Blade Dynamics Analysis
As with the rotor interaction model, analysis of rotor blade dynamics relies upon expansion of simple BEMT. Modelling blade dynamics uses an additional velocity parameter, VM , which represents an elements velocity due to flapping motion. This is shown in figure 7.9, and the corresponding relation is shown in equation 7.3. The inclusion of this component within the analysis is already shown in Figure 7.8.
˙ VM = βr
(7.3)
As discussed in chapter 6, rotational equations of motion are used to model blade flapping.
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Figure 7.8 – Blade Element Theory aerodynamic diagram shown the inclusion of the rotor interaction augmenting velocity.
Figure 7.9 – Element flapping velocity being assembled from the rotational velocity. If all forces are modeled the response of the blade will accurately represents its real motion. The form of this theory that is used is shown in equation 7.4. This equation represents how ¨ is influenced by the applied moments (Mrot ) the rotational acceleration of the blade (β) and inertia (J). It is integrated twice to find the flapping angle response of the blade with respect to time.
J β¨ =
7.2.5
X
Mrot
(7.4)
Analysis Limitations
Rotorcraft motion is difficult to simulate without knowing the intricate higher order effects. Therefore, rather than simulating an entire aircraft’ motion, only rotor motion is considered. By examining the rotor dynamics in sufficient detail a generalised representation of the
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rotorcraft performance can be found. The validity of this reasoning must be shown for this method to be used. The motion of this small UAV rotorcraft is generally centred on hover or slow translation. Therefore, this implies that there will be little change in the rotor wake due to the translation motion. If this is assumed to be true, it is also true that the performance of the rotorcraft will be dominated by the rotors themselves. Hence, a significant portion of the rotorcraft performance can be modelled without the need for large aircraft translation or rotation. This leads to the restraint of the rotorcraft about the CG, thus fixing it to a hover configuration. Not modelling the full aircraft dynamics is not necessarily a problem when examining a rotorcraft’s performance to various inputs. A steady wind or gust input can still be simulated from any direction. These inputs are modelled by resolving the wind/gust into components and applying them to the model as described in the previous section (7.2.2). A similar method is used to apply control to the rotor to test the rotorcraft’s control authority. Although the full rotorcraft motion cannot be examined, a wide range of other affects can be analysed.
7.3
Analysis Package Usage
The complete analysis package requires that a implementation strategy be used. To do this all the major components of the analysis package are amalgamated into a single procedure. Figure 7.10 shows how all the components combine together to form a single analysis tool. The key parts to the the analysis method are contained within the ‘Simulation’ block of the procedure. The simulation procedure contains the method used to analyse the dynamics of the rotorcraft rotors. Mapping these dynamics involves the integration from one state to the next over a given time-step. This can be seen within figure 7.11, which shows the generation of the aircraft state-rates and then using this data to integrate to the next state. As discussed in section 6.5, the Runge-Kutta method is used to perform the time integration. This involves taking four estimates of rotorcraft rates and then averaging them to produce the final rate vector. The remainder of the analysis method is contained within the ‘Get Integration State-Rate’ block.
7.3 Analysis Package Usage
Figure 7.10 – Block diagram to illustrate the procedure for analysing a given aircraft configuration.
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Figure 7.11 – Block diagram to illustrate the procedure for simulating the crafts motion over a given time period.
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Figure 7.12 – Block diagram to illustrate the procedure to assemble a state-rate for any given aircraft state and rate.
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The remainder of the analysis method is contained within the assembly of the state-rates. This includes each of the analysis techniques previously discussed. Figure 7.12 shows the method used to assemble the total rate vector at a given time. BEMT is used to model both the rotor loading and interaction. Rotor loading is then used to assemble the global forcing applied to rotor and platform. And finally, the state-rates can be assembled from the global forcing, as per the equations of motion. This procedure describes the method for implementing the analysis techniques which are used. However, there are other areas in which an explanation is required for full implementation. Each of these areas is covered in the following sections.
7.4
Methods of Use
As the analysis tool allows simulation of a wide variety of configurations the bounds in which the tool can be used need to be defined. Ultimately this tool allows a globally or locally optimal aircraft configuration to be found. Therefore a range of aircraft configurations and setups are able to be tested. To test the configurations the response to external inputs are modeled. Corollary, the rotors’ dynamic response to these inputs must be found. The following two sub-sections describe the criteria to which candidate aircraft designs are compared.
7.4.1
Analysis Criteria
As has been discussed in previous sections, the performance of new aircraft designs with respect to existing aircraft is of interest. Although there are a large number of criteria which can be examined, only the major criteria are detailed here. Each of the items listed below are discussed in the following three sections. • Efficiency; • Control Authority; and • Gust Response.
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Figure 7.13 – Plot of the rotor performance over a range of rotor speeds centred about the hover speed. 7.4.1.1
Efficiency
To ensure that the rotorcraft being analysed has a high efficiency, the power consumed during hover can be examined. Once the aircraft in question has been trimmed for hover, the performance about hover can be examined. This includes examining the thrust produced and power required. By sweeping both collective and rotor speed, the performance of the platform can easily be gauged. Figure 7.13 shows the performance of a sample rotor with respect to rotor speed. As would be expected the thrust and power vary with the change in speed. Similarly, figure 7.14 shows the rotor performance with respect to varying collective control. This plot shows that the rotor blades are operating near stall. As a small increase in collective reduces the thrust produced. These two parameters allows a quick comparison of any efficiency differences between rotors.
7.4.1.2
Control Authority
Similar to efficiency, control authority examines rotor performance by using control. This is tested using rotor controls to simulate a response to control input. This allows the level
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Figure 7.14 – Plot of the rotor performance over a range of collective control angles centred about the hover speed. of control authority to be examined from the rotors response and overall performance. By applying a step cyclic input the transient and steady-state rotor response can be found. A sample response of this type is shown in figure 7.15. By examining the steady state rotor deflections the control authority can be easily examined. The transient response can be checked to determine if any intermediate adverse effects are experienced.
7.4.1.3
Gust Response
The base Proxflyer platform is noted for its stability and gust rejection. Therefore, analysis of response to gust inputs is also made. By applying a pulse wind input to the aircraft, the response of its rotors to a gust can be examined. This gust response can be gauged by the maximum magnitude of rotor deflection. Figure 7.16 shows a rotor’s response to a pulsed gust input. This shows that the rotor returns to the original position after some transient response. This can be further examined to ensure that the damping of the rotor motion is adequate as not to transmit any adverse effects to the platform.
7.4 Methods of Use
Figure 7.15 – Plot of the rotor response to a 5◦ cyclic step input.
Figure 7.16 – Plot of the rotor response to a 3ms−1 pulse gust input.
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Input Criteria
For the rotorcraft type under examination there are only a limited number of design parameters which can be changed. As the bulk of the analysis is dominated by rotor performance, the design parameters are mainly associated with the rotors themselves. For analysis of similar rotorcraft at hover, aircraft mass and rotor speed will likewise be similar. Therefore, for comparative analysis these parameters are eliminated. The remaining parameters are broken into two subsets; blade configuration and rotor configuration. Each of these subsets of parameters of are detailed below, and discussed in the following two sections.
• Blade Configuration: – Root and Tip Radius; – Chord Distribution; – Twist Distribution; and – Mass Distribution. • Rotor Configuration: – Flap Damping; and – Flapping Feedback Parameters.
7.4.2.1
Blade Configuration
Varying the blade configuration of any design will significantly alter its performance. Therefore this can be used to either create a completely new design, or find a optimum version of an existing aircraft. For the analysis tool created, the blade configurations are assumed to be linear from root to tip. Thus, once the root and tip radii are set, parameters at any radial location are known. Figure 7.17 shows the linear distribution of a sample blade from root to tip. In addition, the mass distribution of the blades is assumed to be constant, which has been discussed in section 6.3.5. This is assumption has been made to simplify the range of input geometry for the rotor blades.
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Figure 7.17 – Distribution of the blades’ Chord and Twist with respect to radial location. 7.4.2.2
Rotor Configuration
As discussed previously, rotor configuration is more restricted than the blade configuration. First and foremost, changes to the rotational spring or damping of the rotor blade can be made. By altering the spring or damping of the blade flapping, the blade response will obviously be affected. In addition to these parameters, the geometry of any the control linkages used can also be changed. This is discussed in the following sections, 7.5, 7.6 and 7.7.
7.5
Aircraft Configurations
One of the goals of this thesis is to improve upon the design of the base Proxflyer configuration. Therefore, changing design parameters on the original rotorcraft is not the only method for improving the design. Changing the base rotorcraft design may be advantageous. Therefore, changes to configuration are also considered as an option for improving performance.
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By allowing changes to various rotorcraft configuration parameters more options for improvement are introduced. There are many different options available for analysis of new rotorcraft configurations. The options that are considered for inclusion on new designs are listed and outlined below.
7.5.1
Rotor Cyclic
Many simple radio controlled rotorcraft only include cyclic control. Including cyclic control on this rotorcraft design allows for a better control of directional performance. This allows the pitch of the blades to be controlled to direct the thrust vector, and allows the rotorcraft to be translated through direct use of the rotor.
7.5.2
Fully Controlled Rotor
As with a conventional helicopter, introducing full control to both rotors is considered. This includes both collective and cyclic control. Controlling both rotors gives a higher degree of control to the rotors and to the rotorcraft itself. By introducing this control the overall authority of the rotorcraft should be increased.
7.5.3
Flapping Feedback Rotor
If flapping rotor blades are restrained from a pitch control lever, the blade pitch will vary with changing flap angle. This type of rotor is referred to within this thesis as a Flapping Feedback Rotor. The response of the Flapping Feedback Rotor will vary with different geometric configurations. Thus, changing this geometry will likewise change the performance of the base Proxflyer rotorcraft.
7.5.4
Flapping Feedback and Partial Control
Introducing controlled rotors to a Proxflyer type rotorcraft will be difficult as the pitch levers must be connected to a control mechanism. Thus, introducing either collective or cyclic control will almost always introduce flapping feedback. Once again depending on the geometry chosen, different rotor responses and rotorcraft performance will be experienced.
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Figure 7.18 – Control linkage connection from rotorcraft controls to rotor blade.
7.5.5
Flapping Feedback and Full Control
If control is introduced to Proxflyer type rotors it is sensible to include both collective and cyclic control. This is because there is little extra complexity required to introduce collective as well as cyclic. If this full control, and thus flapping feedback (as discussed in the previous section), are used on both rotors the new rotorcraft configuration will have many options for control. This design option is used in the next chapter (8) within the second design study.
7.6
Control Modelling
The Proxflyer uses an external, upwards pointing, small propeller to apply a pitching moment to the platform. This pitching moment is small compared to the rotor inertia, and has been observed to not be very effective. To increase control authority, additional control methods are needed. The most promising option for increasing control authority is to directly control to the rotors themselves. Although introducing this control is complex, this is outweighed by its benefit. In the previous section it has been stated that the rotors can either be partially or fully controlled. Partially controlled rotors use collective control to change in pitch of the rotor blades. While fully controlled rotors use a combination of collective and cyclic control. Full control allows the rotor to be pitched and rolled in addition to controlling thrust with collective. Figure 7.18 shows how the control linkage is connected to the blade. Figures 7.19 and 7.20 show the change around the rotor of blade pitch for cyclic roll and pitch respectively. This control method is the same as for conventional helicopters.
7.6 Control Modelling
Figure 7.19 – Blade pitch angle with geometric, collective and aileron controls implemented.
Figure 7.20 – Blade pitch angle with geometric, collective and elevator controls implemented.
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7.7 Flapping Feedback
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Flapping Feedback
Generally, implementing control on the Proxflyer type rotor will be difficult without flapping feedback. Aside from allowing the application of external control, flapping feedback passively augments the flapping of the rotor. Flapping feedback occurs as a change to the blade pitch angle that is proportional to the flapping angle. This extra component of blade pitch changes the lift produced by the blade. As two blades are coupled together on opposite sides of the rotor, they experience equal but opposite angle changes. Thus giving an increase to one side and a decrease in lift to the other. Likewise causing a change to the flapping moment that the blade experiences. By augmenting the blade flapping, rotor flapping is able to be sustained for longer. This allows more gust energy to be absorbed, or allows the rotors to adopt a sustained flapping angle during control application. Flapping feedback is introduced to the rotor in much the same way as control itself. Figure 7.21 shows a similar diagram to the control linkages with flapping feedback parameters marked. The length from rotor hub to pitch link is represented by l1 , and the length of the pitch link length by l2 . This diagram shows that with changing flapping angle, the blade pitch will also change. The change in pitch angle with respect to flapping angle is represented by equation 7.5 below.
dθ = sin−1 (
l1 sin(β) ) l2
(7.5)
It can be seen from the diagram and equation that the authority provided by the flapping feedback will varies with the control linkage lengths. These control linkage lengths, l1 and l2 , also change the gain for the control input. Therefore, to implement this system a balance between the two criteria need to also be met.
7.8
Summary
By combining each of the analysis techniques, outlined in the previous chapter, into a single analysis tool many different rotorcraft configurations can be investigated. This combination of the three main analysis techniques has been shown within this chapter. Correct order
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Figure 7.21 – Diagram of Flapping Feedback implementation and parameters which effect its’ gain. of implementation and use is extremely important when combining each part into a larger tool. By showing this order and usage, a better understanding of the techniques used and the application to a specific rotorcraft design has been gained. Although this tool may be applied to any coaxial rotorcraft, with small changes, it has been specifically formulated for the Proxflyer rotorcraft. Direct application to the base rotorcraft has been shown, as well as methods for how the analysis is able to be expanded to include additional design features. Areas such as the application of full rotor control and flapping feedback have been shown. These design features may allow the base rotorcraft design to perform much better. However, further analysis of these designs and the effect on the base rotorcraft need to be studied. The design variables available for manipulation as well as performance measures have been discussed. This includes design parameters which are available for change on both the rotors and the complete rotorcraft. To examine the effect which these parameters allow, characteristic measures of the rotorcraft performance have also been shown. Once all of these factors have been brought together a wide variety of rotorcraft can be analysed and improved.
Chapter 8
Design Studies 8.1
Introduction
Previous chapters outlined the development of a comprehensive yet computationally inexpensive coaxial rotorcraft analysis tool. However, only simple analysis examples have been shown within the development chapters. To fully display the functionality of the analysis tool it is used within a full design study. This chapter uses two design studies to demonstrate the flexibility and usability of the developed analysis as a design tool. The first design study illustrates the analysis tool by optimising the design of an existing rotorcraft similar to the Proxflyer platform. The second study demonstrates the tool used as a design tool to develop a complete rotorcraft configuration. This configuration is larger than the base Proxflyer with the flapping feedback rotors desbribed in section 7.7. Each of the design studies highlights a different area of the analysis tool, showing the flexibility and usability of the tool. In particular showing that it can be used as a tool within a complete rotorcraft design process. This shows that the original objective, to develop an analysis tool that can be used for both specific configuration analysis and for developing new configurations, has been acheived.
8.2 Design Study Goals
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Design Study Goals
There are two goals which this chapter aims to fulfill. Firstly, to conduct design studies to display that the analysis tool developed can also be used as a design tool. And secondly, to show the flexibility of the Proxflyer type rotorcraft; the object of this thesis. As a result a variety of design characteristics are examined, which are described below with respect to each design study. Compared with other small rotorcraft the Proxflyer has increased inherent stability, thus the extent of these characteristics must be ascertained. This increased stability is linked directly to the flapping of the rotors. Specifically, any external disturbances which the rotorcraft experiences (ie. gusts) need to be absorbed or rejected. The Proxflyer absorbs gusts by allowing the rotors to make large flapping motions, which otherwise would cause a destabilising moment. By flapping, the rotors reduce the severity of the destabilising rotational moment. A comparison with conventional rotorcraft is shown in figure 8.1. This figure shows the horizontal component rotor force (red) reduces when flapping, thus reducing the overall moment. One of the most limiting features of the base Proxflyer design is the lack of control authority. The original platform only has an upward facing propeller on the tail to provide pitch control. Although this type of control may be adequate for smaller rotorcraft it may be inadequate for larger platforms. Larger rotorcraft have a much higher inertia, and therefore require larger controlling moment. Thus, trying to control a larger rotorcraft with a tail mounted propeller will be difficult. To overcome this limitation, direct control on the rotors is proposed. By controlling the rotors directly the rotorcraft will have higher control authority. As a result the rotorcraft can be controlled about pitch and roll axes rather than relying on a smaller pitch control only. A comparison of these control authorities is shown
(a) No Rotor Flapping
(b) Rotor Flapping
Figure 8.1 – Comparison of destabilising moments caused by wind gust.
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(a) Tail Control
(b) Rotor Control
Figure 8.2 – Comparison of control force available with tail control and rotor control. in figure 8.2, which shows a larger resulting magnitude pitch moment provided by rotor control. Efficiency is extremely important for any aircraft configuration. This is especially important if the rotorcraft is to be powered by electric motors. Electric motors require batteries for power, which have a lower energy density than conventional liquid fuel. Therefore any increase in efficiency allows electric rotorcraft to remain in flight for a longer time, for a set power-source size. These factors make rotorcraft efficiency an extremely important design characteristic; and as such needs to be included within the analysis and design tool. Examining each of these areas allows both the flexibility of the proposed platform and that of the design/analysis tool is displayed. The tests and analysis which are used to illustrate the developed design tool are outlined in the next section (8.3). As well as describing each of the analysis tests, the method for quantifying the results and implementing the test is also discussed.
8.3
Analysis Tests
Tests which can give quantifiable results are used to characterise a given rotorcraft configuration. In the case of the Proxflyer configuration, the tests used focus on three main areas: Efficiency, Stability and Controllability. Tests for each of these characteristics are detailed in the following sections (8.3.1-8.3.3). In these sections each design goal is linked to a quantifiable test, and thus linked to an output measurement. In addition to this this, the implementation of each test within the analysis tool itself is shown.
8.3 Analysis Tests
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Efficiency
Helicopter efficiency is often characterised by examining the power required to give a certain lifting capacity. For helicopters this is usually implemented by looking at the nondimensional thrust and toque coefficients. However, with the analysis developed, only dimensional outputs are determined. So, for convenience, the power required to lift a given mass is used as a measure of a configuration’s efficiency. To test any configuration the rotorcraft is first trimmed, and is is implemented with a simple trimming procedure at the beginning of an analysis process. The given configuration is trimmed to a certain rotor speed (equal on both rotors) which produces the lift. In this case a simple root finding method is used. From this trim position, the total power requirement is the sum of the two rotors’ power. As a wider performance check the surrounding thrust and power requirements are also examined by sweeping the surrounding rotor speeds. A sample of a speed sweep is shown in figure 7.13. A sweep of the surrounding rotor collective settings is also made, and is shown in Figure 7.14. The data from these figures has been repeated below as figures 8.3 and 8.4. When combined, these two plots can be used as a measure to determine if the configuration is close optimal.
8.3.2
Stability
As discussed previously the stability of a Proxflyer type rotorcraft is derived by the flapping rotors. The majority of destabilising effects on the platform are caused by a gust striking the rotorcraft from the side. To characterise the rotorcraft stability a test gust is applied from the side (along the X or Y rotorcraft body axis) of the rotors. This gust enables the flapping characteristics of any configuration to be tested, and in turn the rotorcraft stability performance. A pulse gust with ramped sides, as shown in figure 8.5, is used to test the stability. This gust strikes the rotorcraft at a given time after the simulation begins, and then the free response (or flapping feedback modified response) is examined. Performance of the rotorcraft is then be measured by examining the destabilising moment that the rotorcraft experiences. An example of this moment response is shown in figure 8.6. It can be seen that for a given gust input, a smaller maximum moment magnitude which the CG experiences indicates a more favourable stability response.
8.3 Analysis Tests
Figure 8.3 – Example plot of the results produced by a Rotor Speed Sweep.
Figure 8.4 – Example plot of the results produced by an Rotor Collective Sweep.
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Figure 8.5 – Gust input used to test the stability of an rotorcraft configuration.
Figure 8.6 – Example CG Moments experienced as a result of test gust input.
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Figure 8.7 – Cyclic input used to test the controllability of an rotorcraft configuration.
8.3.3
Controllability
Measuring the controllability of a rotorcraft configuration is completed in much the same way as for the stability. A characteristic control actuation is made, and the resulting rotorcraft response is examined. In particular the resulting forces which are applied to the rotorcraft CG are examined. For a Proxflyer rotorcraft the rotors flap to cause force rather than moment. The control actuation used to characterise the rotorcraft response is a step cyclic input, as shown in figure 8.7. To implement the controllability analysis a characteristic step input of cyclic is made, with the resulting rotorcraft response examined. In particular the CG force response is examined to determine the direct control authority available, as shown in the example in figure 8.8. This figure shows that the control response eventually settles out into a steady-state forces. The steady-state force is then a convenient measure used to examine the rotorcraft control authority. This allows different rotorcraft configurations to be compared by examining the force produced for a configuration with the same mass.
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Figure 8.8 – Example CG Forces experiences as a result of a test control input. Note that the thick lines occur as a result of the forces produced by the high frequency vibration of the blades.
8.4
Design Parameters
A number of different rotorcraft characteristics are examined. This allows a range of platform design parameters to be examined. The range of variables available to the designer is broken up into a number of different areas, these are: blade geometry, rotor geometry, rotorcraft configuration and control configuration. Each of these areas are discussed in the following sections (8.4.1 - 8.4.4), and the design parameters which they control are also discussed.
8.4.1
Blade Geometry
As would be expected, blade geometry is one of the major components which influence a rotorcraft’ performance. For the simple analysis performed within this thesis a linear representation of the blade geometry is used. By defining parameters at the root and tip of the blade, all radial locations are then be found by interpolating between these values. Defining the blade geometry has been reduced to eight key variables. The starting point for
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Figure 8.9 – Geometry of rotor blade which is able to be controlled for design and analysis. the blade geometry definition is the root and tip radii with respect to the rotor hub, which also defines the blade length. To complete the planform definition the root and tip chords must also be defined. And finally the twist with respect to the disc plane at the root and tip are also defined. These parameters allow a complete physical outline of the blade layout to be made. There are, in fact, two more variables which have not been defined. The aerofoil section of the blade needs to be chosen. This variable influences the blade’s aerodynamic characteristics, which are an important governing factor within the rotor analysis. As well as the aerofoil shape, the final controlling parameter is the blade mass. For this analysis, the blade mass is assumed to be distributed evenly along the length. Therefore, the blade mass only needs to be specified as a single parameter. A general geometric planform of the rotor blade is shown in Figure 8.9. This shows all the parameters discussed above, except for the aerofoil section and mass. All information required to model the blade within the analysis tool are thus defined, allowing complete analysis to be conducted. Varying these parameters allows any configuration to be examined.
8.4.2
Rotor Geometry
The assumptions made within the analysis tool limit variations to the rotor geometry. The assumptions require that each rotor have four blades, with fixed locations at 90◦ intervals. The blades are also locked to flap in pairs, which are on opposite sides of the rotor. For the analysis performed within these design studies changes to the geometry of the rotor are not considered. The tool may be adapted to account for different rotor configuration geometry,
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but is currently outside the immediate scope of this investigation.
8.4.3
Rotorcraft Configuration
The layout of the rotorcraft is locked to have two rotors with the same sizing, rotating in opposite directions. However, the position of the rotors with respect to each other and with respect to the CG can be varied. Generally there are three configurations which can be considered: both above; both below; and above and below. The structural and functional design difficulties imposed by the second and third configurations are not considered within this thesis. Each of these configurations gives differing characteristics in terms of stability and controllability. Tied to the three configurations, listed above, is the distance between the rotors and the rotorcraft CG. The three different configurations are show in figure 8.10. These distances are another two design paraments which can be controlled within the design analysis. As well as the positions of the rotors, the final design parameter is the rotorcraft mass. The mass is set to be constant because only a single rotorcraft concept is analysed, either new or existing. Either way, it is not necessarily a factor which can be varied easily.
8.4.4
Control Configuration
As described in the previous chapter (7), complete control may be placed on each of the two rotors. The three conventional rotorcraft controls of: Collective, Cyclic and Rotor Speed; are used. To be able to implement these controls, linkages from the rotor blades to the servo mechanisms are required. Due to this connection, an additional design feature is introduced. As discussed in the previous section (7.21), this feature has been defined as Flapping Feedback. With the introduction of Flapping Feedback and control, extra design variables are introduced into the analysis. By changing the linkage ratios of the controls, the Flapping Feedback characteristics will also change. Figure 7.21, in the previous section, shows the linkage lengths as l1 and l2 , and their respective connection to the blade. Thus these control linkage lengths become two additional design variables.
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(a) Both Above
(b) Both Below
(c) Above and Below
Figure 8.10 – Rotor position options with respect to the rotorcraft CG.
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Table 8.1 – Summary of the design variables available to be controlled. Parameter Root Radius Tip Radius Root Chord Tip Chord Root Twist Tip Twist Aerofoil Section Blade Mass Upper Rotor Position Lower Rotor Position Rotorcraft Mass Control Linkage Length 1 Control Linkage Length 2
8.4.5
Symbol rRoot rT ip cRoot cT ip θRoot θT ip — mB hU pper hLower m l1 l2
Design Variable Summary
From the discussion in the previous three sub-sections, the following table (8.1) shows all design variables that are able to be varied throughout any design analysis of this rotorcraft configuration. There are thirteen design variables which can be controlled directly within the analysis. These variables contribute to the performance of the rotorcraft as a whole, and can be kept constant or varied as necessary within either a design study or single analysis.
8.5
Design Study 1
The first of the two design studies examines a platform with similar sizing to an existing Proxflyer rotorcraft. And is used to show the applicability of the analysis tool to potentially improve this existing configuration. This function is displayed by improving the original platform configuration, by improving its performance characteristics. By benchmarking the existing configuration and then manipulating various parameters, the existing design is improved. Although this is only a brief study, the flexibility and utility of the analysis tool is illustrated. The platform examined for this study has been previously examined in a paper by this
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Figure 8.11 – Mosquito rotorcraft manufactured by Proxflyer. Photo courtesy Proxflyer [7]. thesis’ author [52]. Figure 8.11 shows the Mosquito platform produced by Proxflyer, which is similar to the configuration used as a starting point. The original rotorcraft has no rotor control, thus control analysis is not taken into account. The base geometry used for this analysis is shown in table 8.2. No changes to the rotor radii are allowed, only changes to the physical rotor blade planform geometry are considered, including chord and twist.
8.5.1
Goals
As control is not considered within this study, the criteria for improving the rotorcraft is reduced. Accordingly the design flexibility is also limited. Therefore, the goal of this analysis is to improve the performance of the configuration. The purpose of this study is to produce a platform which has excellent hover performance. Thus, the key performance characteristics for this rotorcraft are hover efficiency and gust tolerance. Tests for each of these factors are used to determine is a candidate configuration improves upon the original design. Section 8.3 described the tests which are to be used to conduct this process.
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Table 8.2 – Geometry of the basic rotorcraft used for the first design study. Parameter Root Radius Tip Radius Root Chord Tip Chord Root Twist Tip Twist Aerofoil Section Blade Mass Upper Rotor Position Lower Rotor Position Rotorcraft Mass
Symbol rRoot rT ip cRoot cT ip θRoot θT ip — mB hU pper hLower m
Value 45 mm 145 mm 25 mm 15 mm 35◦ 28◦ Cambered Flat Plate 1.9 g -100 mm -50 mm 100 g
Table 8.3 – Baseline rotorcraft performance for the first design study. Performance Component Hover Power Maximum Mx Maximum My
8.5.2
Value 5.2326 W 0.00262203 Nm 0.0123356 Nm
Analysis
To begin the analysis a benchmark for this platform is made. In the original configuration tests for hover efficiency and gust tolerance are made. Firstly, the rotorcraft is trimmed and then the hover power requirement is measured to examine hover efficiency. Then secondly, gust tolerance is tested using a characteristic gust is applied to the trimmed rotorcraft. For the base rotorcraft configuration the CG moment response to the gust is shown in figure 8.12. The maximum component of moment seen at the CG is used as a measure of gust sensitivity. A summary of the baseline rotorcraft performance is shown in table 8.3. Similar tests are applied to candidate designs and then compared to the original configuration. In this case, only changes to the blade planform are considered. Variations to chord and twist are based on the initial configuration, and are summarised in table 8.4. The range of changes explore all the design variables. From this process a basic manual optimisation is made to help find the design trends which dominate the rotorcraft’s performance. Each of the designs listed have been analysed and the performance criteria generated, and
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Figure 8.12 – Baseline gust response of rotorcraft for Design Study 1.
Table 8.4 – Design variations which has been analysed to explore the performance changes around the initial design configuration. Design Name Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Design 7 Design 8 Design 9 Design 10 Design 11
cRoot 35 mm 20 mm 25 mm 25 mm 25 mm 25 mm 25 mm 35 mm 20 mm 20 mm 20 mm
cT ip 15 mm 15 mm 15 mm 15 mm 20 mm 10 mm 15 mm 15 mm 10 mm 15 mm 20 mm
θRoot 35◦ 35◦ 35◦ 35◦ 35◦ 35◦ 40◦ 30◦ 25◦ 20◦ 20◦
θT ip 28◦ 28◦ 20◦ 35◦ 28◦ 28◦ 28◦ 28◦ 15◦ 15◦ 15◦
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Table 8.5 – Performance results for each of the design variations. Design Name Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Design 7 Design 8 Design 9 Design 10 Design 11
Hover Power (W) 4.8795 5.5227 4.5995 5.8994 4.9471 5.5629 5.5674 5.046 3.5997 3.4885 3.393
Mx (Nm) 0.002600 0.002700 0.002900 0.002000 0.002200 0.002000 0.002800 0.001500 0.000669 0.000948 0.000874
My (Nm) 0.016000 0.010900 0.012800 0.013100 0.014200 0.011100 0.013000 0.013400 0.007500 0.006400 0.007000
is summarised in table 8.5. The corresponding performance responses are included within appendix D, as Figures D.1-D.11. Figure 8.13 shows performance metrics from table 8.5 plotted with body Y axis moment versus hover power. Within Figure 8.13, the designs bounded by the green square show significant performance improvement. Although a full optimisation in this way is difficult, this study shows that the analysis tool performs well as a design tool.
8.5.3
Summary
From the table (8.5) and the plot (8.13) presented in the previous section the variation in performance over the design range can be noted. By bounding the first eight design variations in the red box, it can be seen that the performance does not change markedly. These analyses allow an individual design variable’s affect on performance to be found. This then allows a decision to be made as to how the design variables should be changed to improve the configurations total performance. The final three designs, bounded in the green box, show configurations with all variables changed. By changing the planform of the rotor blades as a whole the aerodynamic characteristics of the blade are significantly altered. It can be seen that these designs have an approximate improvement of 30% in power consumption, and 40% in gust reaction. Thus the total performance of the rotorcraft configuration is improved dramatically. Improvement in gust reaction is due to the twist of the blade being reduced. This reduction causes less drag on the blades as the gust strikes, and in turn less side force and pitching
8.5 Design Study 1
Figure 8.13 – Performance plot of all designs within Design Study 1.
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moment. The reduction in hover power is also due to the reduction in blade twist. As the twist is reduced, the total drag on each blade is reduced. This drag reduction causes a power reduction greater than the increase caused by the additional rotor speed required to maintain hover. This design study shows that the analysis tool can be implemented to analyse a complete configuration design. Not only can the tool be used for individual analysis, but it can also be used to optimise an existing rotorcraft design. However, this is not the only design process that the analysis tool may be used for. The design study in the following section (8.6) shows how the tool can be used to take a configuration concept, and use the analysis tool to find a design which can be used as a concept demonstrator.
8.6
Design Study 2
In comparison to the first design study, which focused on improving an existing design, this study focuses on designing a new rotorcraft. The configuration considered in this design study is significantly different to the Proxflyer rotorcraft. In addition to Proxflyer stabilising rotors two design features are introduced to enhance the base Proxflyer’s performance, which are: full rotor control and flapping feedback. With the introduction of the control and flapping feedback the new design will retain the Proxflyer stability, but introduce larger control authority. A number of configuration design choices are used to further limit the design scope. The rotors are to be positioned above and below the fuselage, rather than both above. This configuration separates the two rotors control linkages, thus reducing mechanical complexity of control two rotors above the fuselage. By placing the rotors in this configuration the rotorcraft can perform different maneuvers, including: translation without rotation; and rotation without translation. These maneuvering mechanisms are discussed by the thesis author [55], and are shown in appendix E. Despite the added maneuver ability there may be difficulty with placement of payload and location of undercarriage. However, these complications are not considered within this design study. For clarity the control scheme for the proposed configuration are outlined here. Vertical Control The rotorcraft is controlled about the Z axis in the same way as a normal coaxial helicopter. To translate along the Z axis uses either combined rotor speed and/or
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collective pitch changes. While rotate uses differential changes in either of these controls. Horizontal Control The main difference in control for this configuration is the mechanism for control about either the X or Y axis. As the rotorcraft is symmetric about the X-Z and Y-Z planes, control is similar for both the X and Y axes. In isolation, applying a cyclic control to a single rotor will cause a steady state flapping deflection (discussed in chapter 6). This feature is exploited for horizontal control for the new rotorcraft configuration. To translate the rotorcraft cyclic control is actuated on both rotors, which causes steady state flapping with rotor thrust pointed in the same direction. This applies a net force in the desired translation direction, as shown in figure 8.14. To rotate the rotorcraft cyclic control is applied in opposite direction on the two rotors. This forms a couple, which in turn applies a rotational moment as shown in figure 8.15. In addition to the first translation method, there is an alternate translation option which is similar to a conventional helicopter. Firstly the rotorcraft is rotated in the desired direction. Then secondly, the rotorcraft is balanced at the desired tilt angle, which causes the entire rotorcraft thrust to be directed in the desired translation direction. This then causes the rotorcraft to translate at a faster rate, and is shown in figure 8.16.
8.6.1
Goals
There is no firm starting point for the design process as a new configuration is being examined. The goal of this study is to produce a rotorcraft design which includes the features discussed in the previous section 8.6. Analysis of the design seeks to find a configuration which gives the best performance in terms of efficiency, stability and controllability. The first two of these measurements are used in the previous design study and do not need to be explained again. However, the test for controllability needs to be outlined. As discussed in the previous section (8.3.3) the controllability of a rotorcraft is tested with a characteristic control input. In this case a 5◦ cyclic pitch actuation is used. This test is used to maximise the translational control force which can be generated by the standard input. Therefore, the steady-state side force which is generated is used to characterise the control effectiveness. To find an optimal rotorcraft configuration, the best balance between efficiency, controllability and stability must be reached. Therefore the power required to drive the rotorcraft
8.6 Design Study 2
Figure 8.14 – Translation mechanism of the proposed new rotorcraft configuration.
Figure 8.15 – Rotation mechanism of the proposed new rotorcraft configuration.
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Figure 8.16 – Fast translation mechanism of the proposed new rotorcraft configuration.
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Table 8.6 – Fixed rotorcraft geometry used for the second design study. Parameter Root Radius Tip Radius Root Chord Tip Chord Aerofoil Section Blade Mass Rotorcraft Mass Control Linkage Length 1
Symbol rRoot rT ip cRoot cT ip — mB m l1
Value 75 mm 375 mm 35 mm 35 mm NACA 0012 28 g 2.5 kg 50 mm
must be minimised. The moment applied to the rotorcraft due to a characteristic gust must also be minimised. And finally the control authority must be maximised. An ”A to B” analysis is used to isolate the design variables which benefit these features the most. A number of limitations have been placed on this design study. Firstly, a single off-theshelf blade design has been chosen, shown in figure 8.17. Thus, only the constant twist angle of the rotor blade can be varied. This is analogous to varying the hover collective angle for both rotors. Secondly, the same distance between the CG and the rotor is used for both rotors. Therefore, the separation distance from the CG is a single controlling variable. Thirdly, as flapping feedback is used on this platform, the linkage lengths can also be changed. However, as the blade is at a fixed radius, only the second length, l2 (shown in figure 7.21), can be altered. And finally, the rotorcraft mass is set to 2.5kg. Table 8.6 shows the geometry of the rotorcraft which is fixed for this design study, leaving only: blade twist, rotor separation and linkage length 2 (l2 ) as design variables.
Figure 8.17 – Rotor blade used for the second design study example. Pictured is a carbon fibre replacement blade for the Thunder Tiger Mini-Titan RC rotorcraft [102].
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Table 8.7 – Design variations which has been analysed to explore the performance changes around the initial design configuration. Design Name D01 D02 D03 D04 D05 D06 D07 D08 D09 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20
8.6.2
Base Collective (◦ ) 8 10 12 14 16 18 12 12 12 12 12 12 12 12 12 12 12 12 12 12
Linkage Length (mm) 50 50 50 50 50 50 10 20 30 40 60 70 80 -50 50 50 50 50 50 50
Rotor CG Separation (mm) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 25 50 75 125 150 175
Analysis
A range of geometries are used to test the design variables that can be changed. Each of the resulting configurations are shown in table 8.7. These configurations have been chosen to test the effect each of the design variables has on rotorcraft performance both in isolation and in combination. Although only a number of configurations are tested, the trends which these variables have on rotorcraft performance are found. As an example, results for the first candidate design (D01) are shown here. Figure 8.18 shows the power and thrust for variation of rotor speed. While figure 8.19 shows the rotorcraft CG moment response for the stability gust test. And figure 8.20 shows the force response of the rotorcraft to the controllability test. Although this design study does not have a starting configuration, this analysis is used as a starting point. From here, the remaining candidate designs are tested and compared. This allows the design variables that have the most effect to be found.
8.6 Design Study 2
Figure 8.18 – Example plot of Power and Thrust change with variation of RPM, for Design Study 2.
Figure 8.19 – Example plot of CG Moment response for Stability test, for Design Study 2.
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Figure 8.20 – Example plot of CG Force response for Controllability test, for Design Study 2. Each design configurations is now tested and examined in more detail to establish the effect of each design variable. Once the effect of each design variable is established, recommendations as to an optimal configuration are made. Analysis results for each of the twenty configurations are summarised in table 8.8. Figures showing the performance plots for each configuration are shown in appendix D, as figures D.12 to D.31. The design configurations are arranged to allow examination of each design variable. Table 8.7 shows that designs D01-D06 have variation in collective pitch angle only; designs D07D14 have changes in control linkage length only; and designs D15-D20 have changes in rotor separation only. The performance of the candidate designs are plotted in two figures. Figure 8.21 shows the performance of stability versus hover power, and figure 8.22 shows comparison between controllability and hover power. Each of the design parameters have been highlighted in figures 8.21 and 8.22. Blade collective pitch highlighted as black (small solid); linkage length as red (medium dotted); and rotor separation as green (large dashed). These plots highlight each of the design variables, and allow the trends which are favourable to this rotorcraft design to be identified. Firstly, increasing collective gives a favourable reduction in hover power as well as slightly
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Table 8.8 – Analysis results for design criteria for each design configuration. Design Name D01 D02 D03 D04 D05 D06 D07 D08 D09 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20
Hover Power (W ) 194.60 156.83 140.15 131.22 126.43 123.96 140.15 140.15 140.15 140.15 140.15 140.15 140.15 140.15 152.87 146.73 144.34 137.30 131.63 125.62
Max. My Gust Moment (Nm) -0.2754 -0.2945 -0.2961 -0.3133 -0.3185 -0.3236 -0.4565 0.5148 -0.3802 -0.3363 -0.2639 -0.2425 -0.2207 0.3262 -0.2538 -0.2633 -0.2917 -0.2881 -0.2917 -0.2686
Steady-State Fy Control Force (N) 0.7226 0.9037 1.0052 1.0703 1.1075 1.1269 0.2852 0.5329 0.7418 0.9012 1.0668 1.0917 1.0952 -0.9073 1.2488 1.1705 1.0963 0.9263 0.8558 0.8133
increasing control authority. Secondly, the performance of both control force and gust sensitivity is improved with increasing control linkage length. This change does not alter hover power. Finally, increasing rotor separation decreases hover power, but also reduces control authority. Each of these design trends is used to propose a rotorcraft design with better performance characteristics.
8.6.3
Summary
Each of the designs analysed are used to establish trends that can be used to identify beneficial design variables. These design variables are then joined to produce a configuration which has an optimal design configuration. A detailed design process is outside the scope of this design study. However this analysis illustrates the process for initially developing a complete rotorcraft configuration. As a result of this study, figure 8.23 shows a sketch of the proposed rotorcraft configuration.
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Figure 8.21 – Comparison of Power vs Stability for each of the design configurations. Design parameter trends have been highlighted. This design study shows how the analysis tool developed within this thesis can be used to investigate new rotorcraft configurations. For a completely new configuration, candidate designs are compared to determine beneficial design variables. This allows a rotorcraft configuration with optimal performance to be proposed before being designed in detail. By continuing the design process, a rotorcraft configuration for use as a concept demonstrator can be developed. Overall this design study has shown that the developed analysis tool performs well as a design tool.
8.7
Conclusion
This chapter has demonstrated the utility of the developed analysis method, and its usefulness as a design tool. The important features to note are the flexibility and user-friendliness of the the method. By using simple but robust base analysis theories, as discussed in previ-
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Figure 8.22 – Comparison of Power vs Controllability for each of the design configurations. Design parameter trends have been highlighted. ous chapters, the computational expense has been minimised and utility maximised. Two separate design studies highlighted most of these features as a design tool. By conducting a design study that centred on improving an existing platform, the tool was shown to perform well as a detailed analysis method used for design. A small 100g platform based on an original Proxflyer type rotorcraft has been used to illustrate this. It was shown that the platform may be improved in hover efficiency by approximately 30%, while also improving the gust sensitivity by approximately 40%. This showed that the design tool can be used to highlight design flaws and explore better design configurations to solve these problems. The second of the two design studies focused on using the design tool to explore a new rotorcraft configuration. By taking a new rotorcraft concept, the tool created a summary of the design features. These features were then processed to find and propose an optimal
8.7 Conclusion
Figure 8.23 – General configuration model which illustrates design features.
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configuration from the candidates. The design tool provides enough detail to take the resulting design and produce a concept demonstrator platform from the optimal configurations investigated. These two investigations have provided results which illustrate the flexibility, usability, accuracy and robust nature of the developed analysis and design tool. The fidelity of the tool is more than enough to propose a rotorcraft platform with good performance characteristics. In addition new design features, which increase the Proxflyer’s possible range of use have been introduced. As a whole, the analysis methods and design tool perform well Proxflyer type rotorcraft, and with little change may be used for other base configurations.
Chapter 9
Conclusion 9.1
Project Summary
This project has explored the possibilities for use of a coaxial rotorcraft as an urban mission UAV. The variety configurations which may be used as a Rotary-Wing Unmanned Aerial Vehicles (RWUAVs) within an urban environment is vast. To optimally meet the range of requirements, a rotorcraft must have its conceptual design tailored to meet this environments unique demands. In addition to performance constraints, UAVs often have limited resources allocated to their development. The costs of Research, Design, Test and Evaluation (RTDE) often makes up 95% of the complete life cycle costs for an aircraft (discussed by Roskam [103]). To ensure that the RDTE portion of the life cycle cost is not wasted, analyses must be performed to ensure that the rotorcraft’s performance meets its mission requirements. For this entire project focus has been placed on the Proxflyer rotorcraft configuration. This rotorcraft type uses coaxial rotors with unique free flapping rotors. These rotors absorb disturbances which the rotorcraft experiences. To enhance this rotorcraft’s ability to cope with gusty and windy conditions detailed design configuration analysis needs to be used. Once an understanding of its inherent stability is known, improvements to its controllability and stability can be made. And will significantly extend the platforms operational region. The analysis methods developed for the Proxflyer allow variations to the base configurations to be examined. Analysing smaller rotorcraft configurations with complex analysis tech-
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niques is often unfeasible. Thus for small coaxial rotorcraft analysis needs to be developed specifically for the general configuration to ensure analysis efficiency. Three of the major developments and features that have been introduced into the analysis methods are listed below:
• Individual Blade Analysis; • Blade Flapping; and • Rotor Interaction.
The developed analysis has allow the Proxflyer configuration to be investigated around its most common flight region, hover. In addition to exploration of the base configuration, changes to the base platform have also been investigated. To increase the command authority, control within the rotors themselves has been considered. The inclusion of control on the Proxflyer rotors introduces a secondary effect of flapping feedback. Modelling of this effect has also been included as an additional design change. The development of a comprehensive, yet simple, analysis tool has allowed investigation of the performance of the base Proxflyer and additional design features. The additional design features may allow the Proxflyer rotorcraft to be used in a wider range of flight conditions. Proxflyer rotorcraft are predominately operated around hover and are dominated by rotor loading and blade dynamics. Thus, using a full flight model of the rotorcraft for dynamic simulations has not been considered. Each of these major developments, and other major milestones are summarised in more detail in the next section (9.2).
9.2
Major Developments
The major developments of this project have been briefly mentioned in the previous section. The following sections (9.2.1-9.2.6) summarise each of these areas in more detail.
9.2 Major Developments
9.2.1
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Rotor Analysis
Examining blade loading and motion dynamics forms the basis of any rotorcraft analysis. For this project, rotor analysis examines the loading and dynamic performance of the rotor blades. Rotor loading analysis techniques range from complex detailed analysis to simple first order theory. Blade Element Momentum Theory is used as the basis for all rotor analysis. BEMT analysis is based on sound physical principles, and is implemented numerically with a great deal of ease. For the level of complexity the computational accuracy of this method performs well assuming accurate sectional aerodynamic data is available. In addition to excellent performance, BEMT is a favourable choice due to its flexibility. The formulation of the numerical method allows for various external influences to easily be included. This flexibility allows for various additions to the method to be included, which have become integral to this project. Due to this flexibility individual blade analysis; blade flapping; rotor interaction; and control modelling are included. Each of these factors are outlined in the following sections (9.2.2-9.2.6).
9.2.2
Individual Blade Analysis
For BEMT to analyse either dynamics (aircraft or blade) or external effects blades must be analysed individually. Blades are analysed individually by altering the BEMT algorithm to analyse one quarter (or one nth ) of the rotor disc. Both aerodynamic and momentum analysis, used within the complete method, are altered to reflect individual blade examination. Aerodynamic analysis is altered to not analyse all blades together by not multiplying by the number of blades. And momentum analysis is changed likewise by dividing by the number of blades. These changes are highlighted within section 3.4 in equations 3.16, 3.17 and 3.18. Comparison between individual and multiple blade analysis shows that the total load produced and the induced velocity accurately reflect the change to individual blades.
9.2.3
Blade Flapping Analysis
The basis of the Proxyfler’s unique design and inherent stability is caused by its unique highly flapping rotors. A Proxflyer type rotors’ blades flap in pairs on opposite sides of the rotor, often up to 30◦ . The blade pairs are fully articulated, and each pair rotates about the
9.2 Major Developments
226
centre of the rotor hub. To simplify the modelling, and allow for a variety of effects to be included, simple rotational equations of motion are used. To acurately represent the blade flapping the blade load; rotational inertia; and gravity loads are included. This is shown in sections 6.3 and 6.4. Comparison against steady-state flap deflection is shown to compare well with experiment, as shown in the paper by the author [52]. This shows that the blade flap model performs well and fits within the analysis framework.
9.2.4
Rotor Interaction
A critical problem with BEMT analysis is that it offers no solution to account for the interaction between coaxial rotors. To account for this problem a method for modelling the interaction between the rotors was developed. The method which has been developed fits within BEMT analysis in the same way as blade flapping or other external effects. By applying an additional velocity term within the aerodynamic analysis the effect from one rotor to the other is modelled. This is shown in figure 4.6. The concept of using a velocity component to model influence between rotors is simple. However, implementation of this technique is not. A geometric mapping is used to determine the interaction between rotors. The geometric mapping is based on streamtube geometry of each rotor. The influence also uses the development of the streamtube to determine the final influence magnitude. Section 4.7 summarises the method to determine the influencing components. Modelling of the rotor interaction is not completed with a single BEMT evaluation. To determine a stable rotor loading, convergence on a stable induced velocity distribution over both rotors is found. This ensures that the loading distribution of both rotors includes the influence between the rotors. To ensure that this method performs well, comparison against experimental tests was conducted (section 5), and shows good agreement.
9.2.5
Control Analysis
The Proxflyer rotorcraft does not have either collective or cyclic control. Control is only provided by an upward facing tail rotor to pitch the platform, and differential rotor power to yaw. To improve the control authority of the aircraft direct control of the rotor blades
9.3 Conclusions
227
is proposed. This is similar to the control of a conventional helicopter. By introducing collective and cyclic control to the rotors, a great deal of additional control authority is gained. Control analysis is added to BEMT through the addition of an additional control term that is added to the blades geometric pitch. This term models the combined effect of collective and cyclic, and allows control to not only be analysed statically but also dynamically. This in turn allows for the analysis of aircraft control authority.
9.2.6
Flapping Feedback
When control is introduced to the rotors, an additional effect called flapping feedback is seen. This is discussed in section 7.5.3. Blade pitch will change when the blades flap with a restrained control lever. This gives a feedback effect, which will change the amount of lift which the blade produces depending on the flapping angle. The magnitude of feedback will change depending on the geometric setup of the control linkages. This effect is used to augment the performance of the rotor under given circumstances. The feedback pitch change due to flapping is calculated, and then applied to the rotor’s BEMT analysis as a geometric angle increment or decrement. This is a new design feature that has been introduced and found to be beneficial to rotorcraft performance.
9.3
Conclusions
To improve existing and design new rotorcraft configurations a specific methodology is needed. By choosing analysis methods which are simple yet robust, the performance of the developed analysis tool is powerful. The advances which have been outlined within this thesis contribute to a niche area of coaxial rotorcraft analysis. However, they do not only apply to the Proxflyer aircraft type. If required they may be modified for use with other rotorcraft. These developments allow rotorcraft analysis to be conducted accurately with lower computational overhead than many existing tools. The most significant single advancement of this project is the method developed to analyse interaction between coaxial rotors with BEMT. This theory is not limited to the modelling
9.4 Further Work
228
of coaxial rotors, it can also be used for analysing coaxial propellers or overlapping rotors. Although this is outside the scope of this thesis. However, use in these areas would require only minor changes. Characterisation of the performance of the Proxflyer rotorcraft has shown that although the base rotorcraft performs well, significant improvements can be made. It was shown that while maintaining stability, improvements to both efficiency and control authority can be made. The combination of the analysis developed allows these flight performance characteristics to be examined over a range of platform configurations. Of particular note is the development of a Proxflyer style rotorcraft, including cyclic and collective control as well as flapping feedback. Analysis and design this configuration has shown that new platform configurations can be developed with the simple yet robust analysis tool that has been developed.
9.4
Further Work
This project investigated many aspects associated with the analysis of MAV rotorcraft. The theory and implementations which have been shown outline advances into analysis of this rotorcraft category. However, there are several areas in which further work could be conducted, and include:
• Multi Rotor Interaction; • Low Reynolds Number Aerodynamics; • Dynamic Rotor Verification; and • Full Aircraft Dynamic Analysis.
These four issues highlight some of the areas which were outside the scope of this investigation. Further investigation of these areas will allow development of more flexible, accurate and robust analysis. Coaxial rotor interaction modelling using simple analysis methods provides flexibility. However, the simple nature of this method restricts the scope in which the theory can be used.
9.4 Further Work
229
The base theory of applying influence between coaxial rotor by using induced velocity mapping is sound. To expand the useability, additional theory to enable modelling influence between multiple rotors, possibly in an offset configuration, is needed. Once this has been completed, the base convergence method could be used to analyse anything from a Chinook to a quadrotor aircraft. The main drawback of Blade Element Momentum Theory is the fidelity being dependant on the sectional aerodynamic data used. For conventional sized helicopters there has been significant testing and modelling to determine accurate data. Whereas for smaller rotorcraft the Reynolds number in which the blades operate is orders of magnitude below conventional rotorcraft. This thesis has shown that the techniques developed function very well. However, to further reduce the scale of investigation lower Reynolds number aerodynamic data is required. Of particular interest is verification of the rotor interaction theory and blade flapping theory. The tested steady-state rotor loading and flapping angles have been shown to agree well with computational results. However, the dynamic response of these theories has not been tested. To further refine these theories, dynamic verification needs to be conducted. To characterise the flight performance of Proxflyer rotorcraft in more detail requires that a full flight model be used. The development of this model is outside the scope of this investigation. However the analysis developed within this project may be used within a full flight model. Analysis using a full flight dynamics model will allow additional facets of the Proxflyer type to be understood, and will allow further refined configurations to be designed.
Appendix A
Rotary Wing Definitions The definitions within this appendix apply to the analysis of any general rotary-wing aircraft. Alterations to the standard axis system are made throughout this thesis and noted where necessary.
Rotary Wing Definitions
231 Aircraft Axis Definition
Figure A.1 – Conventional RC helicopter with broad aircraft axis system overlaid. Original phot courtesy Mike Lehmann [104].
Rotary Wing Definitions
Figure A.2 – Conventional helicopter axis system wire-frame drawing.
232
Rotary Wing Definitions
Figure A.3 – Coaxial helicopter with broad aircraft axis system overlaid.
233
Rotary Wing Definitions
Figure A.4 – Coaxial helicopter axis system wire-frame drawing.
234
Rotary Wing Definitions
235 Rotor Axis Definition
Figure A.5 – Four bladed rotor with general axis system overlaid.
Rotary Wing Definitions
Figure A.6 – Four bladed rotor general axis system wire-frame drawing.
236
Rotary Wing Definitions
237 Blade Axis Definition
Figure A.7 – Rotor blade with general axis system overlaid.
Rotary Wing Definitions
Figure A.8 – Rotor blade general axis system wire-frame drawing.
238
Appendix B
Interaction Model Verification Appendix This appendix displays the processed results from the rotor interaction model verification process. The first three tables show the processed performance data, and the following plots show various manipulations of the data.
Interaction Model Verification Appendix
240
Experimental Results - 50mm Separation Table B.1 – Verification results for rotors with 50mm separation. Rotor Separation mm 50
Upper Rotor Speed RPM 0
50
500
50
1000
50
1500
50
2000
Lower Rotor Speed RPM 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000
Experimental Thrust N 0 0.33863 1.339 2.9488 5.2729 0.29619 0.50033 1.4841 3.0949 5.3271 1.1263 1.1117 2.0943 3.5809 5.6889 2.6201 2.4001 2.8622 4.3764 6.4104 4.643 4.5179 4.6035 5.6166 7.3854
Experimental Standard Deviation N 0 0.020416 0.01959 0.02664 0.071491 0.019714 0.028724 0.052465 0.049985 0.046533 0.02128 0.023767 0.039788 0.028632 0.052393 0.031806 0.025253 0.026492 0.036798 0.037859 0.184 0.045932 0.061719 0.060223 0.14467
Code Thrust with Interaction N 0 0.28302 1.1321 2.5472 4.5284 0.27051 0.44709 1.2112 2.3485 4.3508 1.082 1.0103 1.7885 3.0648 4.8446 2.4345 2.2952 2.4979 4.0243 5.7528 4.3281 4.0282 4.0413 5.0574 7.154
Code Thrust without Interaction N 0 0.29207 1.1683 2.6286 4.6731 0.29207 0.58414 1.4603 2.9207 4.9652 1.1683 1.4603 2.3365 3.7969 5.8414 2.6286 2.9207 3.7969 5.2572 7.3017 4.6731 4.9652 5.8414 7.3017 9.3462
Interaction Model Verification Appendix
241
Experimental Results - 100mm Separation Table B.2 – Verification results for rotors with 100mm separation. Rotor Separation mm 100
Upper Rotor Speed RPM 0
100
500
100
1000
100
1500
100
2000
Lower Rotor Speed RPM 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000
Experimental Thrust N 0 0.34056 1.3187 2.966 5.2188 0.27991 0.53426 1.501 3.0852 5.3308 1.1044 1.0643 1.8907 3.5357 5.7387 2.5309 2.2884 2.702 4.2253 6.3647 4.4572 4.2297 4.3503 5.3738 7.2035
Experimental Standard Deviation N 0 0.031397 0.026871 0.028999 0.026286 0.025244 0.026857 0.02224 0.023246 0.047529 0.02213 0.024819 0.016576 0.01642 0.022756 0.024859 0.020841 0.025628 0.048232 0.025297 0.06006 0.052457 0.041762 0.057145 0.10756
Code Thrust with Interaction N 0 0.28713 1.1485 2.5842 4.5941 0.26543 0.44099 1.2681 2.6065 4.3914 1.0617 1.0857 1.764 3.1402 5.0725 2.3889 2.2755 2.6063 3.9689 5.9278 4.2469 4.0344 4.343 4.9014 7.0558
Code Thrust without Interaction N 0 0.29207 1.1683 2.6286 4.6731 0.29207 0.58414 1.4603 2.9207 4.9652 1.1683 1.4603 2.3365 3.7969 5.8414 2.6286 2.9207 3.7969 5.2572 7.3017 4.6731 4.9652 5.8414 7.3017 9.3462
Interaction Model Verification Appendix
242
Experimental Results - 150mm Separation Table B.3 – Verification results for rotors with 150mm separation. Rotor Separation mm 150
Upper Rotor Speed RPM 0
150
500
150
1000
150
1500
150
2000
Lower Rotor Speed RPM 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000 0 500 1000 1500 2000
Experimental Thrust N 0 0.3127 1.3194 2.9696 5.3876 0.29077 0.54266 1.4904 3.0711 5.4917 1.1085 1.0239 1.9245 3.5595 5.9203 2.3908 2.1476 2.5627 4.2021 6.4139 4.2697 3.9113 3.9951 5.0972 7.0388
Experimental Standard Deviation N 0 0.021599 0.016927 0.029979 0.038746 0.046688 0.050848 0.024341 0.036295 0.037791 0.021718 0.030472 0.030037 0.021631 0.12247 0.029277 0.021388 0.026095 0.031532 0.035511 0.045889 0.042436 0.029007 0.021278 0.088729
Code Thrust with Interaction N 0 0.2895 1.158 2.6055 4.632 0.26337 0.44291 1.2977 2.7137 4.6798 1.0535 1.1273 1.7716 3.2494 5.1909 2.3703 2.3475 2.8814 3.9861 6.095 4.2138 4.1353 4.509 5.5662 7.0865
Code Thrust without Interaction N 0 0.29207 1.1683 2.6286 4.6731 0.29207 0.58414 1.4603 2.9207 4.9652 1.1683 1.4603 2.3365 3.7969 5.8414 2.6286 2.9207 3.7969 5.2572 7.3017 4.6731 4.9652 5.8414 7.3017 9.3462
Interaction Model Verification Appendix
243
50mm Separation - Constant Upper Rotor Speed
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.1 – Plot of rotor thrust verification with 50mm separation and Upper rotor held constant with varying lower rotor speed.
Interaction Model Verification Appendix
244
100mm Separation - Constant Upper Rotor Speed
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.2 – Plot of rotor thrust verification with 100mm separation and Upper rotor held constant with varying lower rotor speed.
Interaction Model Verification Appendix
245
150mm Separation - Constant Upper Rotor Speed
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.3 – Plot of rotor thrust verification with 150mm separation and Upper rotor held constant with varying lower rotor speed.
Interaction Model Verification Appendix
246
50mm Separation - Constant Lower Rotor Speed
(a) Lower Rotor 0RPM
(b) Lower Rotor 500RPM
(c) Lower Rotor 1000RPM
(d) Lower Rotor 1500RPM
(e) Lower Rotor 2000RPM
Figure B.4 – Plot of rotor thrust verification with 50mm separation and Lower rotor held constant with varying upper rotor speed.
Interaction Model Verification Appendix
247
100mm Separation - Constant Lower Rotor Speed
(a) Lower Rotor 0RPM
(b) Lower Rotor 500RPM
(c) Lower Rotor 1000RPM
(d) Lower Rotor 1500RPM
(e) Lower Rotor 2000RPM
Figure B.5 – Plot of rotor thrust verification with 100mm separation and Lower rotor held constant with varying upper rotor speed.
Interaction Model Verification Appendix
248
150mm Separation - Constant Lower Rotor Speed
(a) Lower Rotor 0RPM
(b) Lower Rotor 500RPM
(c) Lower Rotor 1000RPM
(d) Lower Rotor 1500RPM
(e) Lower Rotor 2000RPM
Figure B.6 – Plot of rotor thrust verification with 150mm separation and Lower rotor held constant with varying upper rotor speed.
Interaction Model Verification Appendix
249
Varying Separation - Lower Rotor 0RPM
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.7 – Plot of rotor thrust verification with varying rotor separation and Lower rotor held constant at 0RPM and varying upper rotor speed.
Interaction Model Verification Appendix
250
Varying Separation - Lower Rotor 500RPM
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.8 – Plot of rotor thrust verification with varying rotor separation and Lower rotor held constant at 500RPM and varying upper rotor speed.
Interaction Model Verification Appendix
251
Varying Separation - Lower Rotor 1000RPM
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.9 – Plot of rotor thrust verification with varying rotor separation and Lower rotor held constant at 1000RPM and varying upper rotor speed.
Interaction Model Verification Appendix
252
Varying Separation - Lower Rotor 1500RPM
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.10 – Plot of rotor thrust verification with varying rotor separation and Lower rotor held constant at 1500RPM and varying upper rotor speed.
Interaction Model Verification Appendix
253
Varying Separation - Lower Rotor 2000RPM
(a) Upper Rotor 0RPM
(b) Upper Rotor 500RPM
(c) Upper Rotor 1000RPM
(d) Upper Rotor 1500RPM
(e) Upper Rotor 2000RPM
Figure B.11 – Plot of rotor thrust verification with varying rotor separation and Lower rotor held constant at 2000RPM and varying upper rotor speed.
Appendix C
Blade Flapping Appendix This Appendix contains the full results of the test implementation of the flapping theory. It contains the Blade and Rotor flapping responses for the full gust spectrum described in Section 6.
Blade Flapping Appendix
255 0.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.1 – Plots of raw and processed flapping response for a 0ms−1 horizontal gust.
Blade Flapping Appendix
256 1.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.2 – Plots of raw and processed flapping response for a 1ms−1 horizontal gust.
Blade Flapping Appendix
257 2.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.3 – Plots of raw and processed flapping response for a 2ms−1 horizontal gust.
Blade Flapping Appendix
258 3.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.4 – Plots of raw and processed flapping response for a 3ms−1 horizontal gust.
Blade Flapping Appendix
259 4.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.5 – Plots of raw and processed flapping response for a 4ms−1 horizontal gust.
Blade Flapping Appendix
260 5.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.6 – Plots of raw and processed flapping response for a 5ms−1 horizontal gust.
Blade Flapping Appendix
261 6.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.7 – Plots of raw and processed flapping response for a 6ms−1 horizontal gust.
Blade Flapping Appendix
262 7.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.8 – Plots of raw and processed flapping response for a 7ms−1 horizontal gust.
Blade Flapping Appendix
263 8.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.9 – Plots of raw and processed flapping response for a 8ms−1 horizontal gust.
Blade Flapping Appendix
264 9.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.10 – Plots of raw and processed flapping response for a 9ms−1 horizontal gust.
Blade Flapping Appendix
265 10.0ms−1 Gust Input
(a) Blade Response
(b) Rotor Response
Figure C.11 – Plots of raw and processed flapping response for a 10ms−1 horizontal gust.
Appendix D
Design Study Appendix This appendix shows the resultant performance plots from each of the configuration variations within the two design studies.
Design Study 1 - Design 1
Figure D.1 – Design 1 gust response of aircraft for Design Study 1.
Design Study Appendix
267 Design Study 1 - Design 2
Figure D.2 – Design 2 gust response of aircraft for Design Study 1. Design Study 1 - Design 3
Figure D.3 – Design 3 gust response of aircraft for Design Study 1.
Design Study Appendix
268 Design Study 1 - Design 4
Figure D.4 – Design 4 gust response of aircraft for Design Study 1. Design Study 1 - Design 5
Figure D.5 – Design 5 gust response of aircraft for Design Study 1.
Design Study Appendix
269 Design Study 1 - Design 6
Figure D.6 – Design 6 gust response of aircraft for Design Study 1. Design Study 1 - Design 7
Figure D.7 – Design 7 gust response of aircraft for Design Study 1.
Design Study Appendix
270 Design Study 1 - Design 8
Figure D.8 – Design 8 gust response of aircraft for Design Study 1. Design Study 1 - Design 9
Figure D.9 – Design 9 gust response of aircraft for Design Study 1.
Design Study Appendix
271 Design Study 1 - Design 10
Figure D.10 – Design 10 gust response of aircraft for Design Study 1. Design Study 1 - Design 11
Figure D.11 – Design 11 gust response of aircraft for Design Study 1.
Design Study Appendix
272
Design Study 2 - Design 1
Design Study 2 - Design 2
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.12 – Design Study 2, Design Configuration 1 - Performance Plots.
Figure D.13 – Design Study 2, Design Configuration 2 - Performance Plots.
Design Study Appendix
273
Design Study 2 - Design 3
Design Study 2 - Design 4
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.14 – Design Study 2, Design Configuration 3 - Performance Plots.
Figure D.15 – Design Study 2, Design Configuration 4 - Performance Plots.
Design Study Appendix
274
Design Study 2 - Design 5
Design Study 2 - Design 6
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.16 – Design Study 2, Design Configuration 5 - Performance Plots.
Figure D.17 – Design Study 2, Design Configuration 6 - Performance Plots.
Design Study Appendix
275
Design Study 2 - Design 7
Design Study 2 - Design 8
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.18 – Design Study 2, Design Configuration 7 - Performance Plots.
Figure D.19 – Design Study 2, Design Configuration 8 - Performance Plots.
Design Study Appendix
276
Design Study 2 - Design 9
Design Study 2 - Design 10
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.20 – Design Study 2, Design Configuration 9 - Performance Plots.
Figure D.21 – Design Study 2, Design Configuration 10 - Performance Plots.
Design Study Appendix
277
Design Study 2 - Design 11
Design Study 2 - Design 12
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.22 – Design Study 2, Design Configuration 11 - Performance Plots.
Figure D.23 – Design Study 2, Design Configuration 12 - Performance Plots.
Design Study Appendix
278
Design Study 2 - Design 13
Design Study 2 - Design 14
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.24 – Design Study 2, Design Configuration 13 - Performance Plots.
Figure D.25 – Design Study 2, Design Configuration 14 - Performance Plots.
Design Study Appendix
279
Design Study 2 - Design 15
Design Study 2 - Design 16
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.26 – Design Study 2, Design Configuration 15 - Performance Plots.
Figure D.27 – Design Study 2, Design Configuration 16 - Performance Plots.
Design Study Appendix
280
Design Study 2 - Design 17
Design Study 2 - Design 18
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.28 – Design Study 2, Design Configuration 17 - Performance Plots.
Figure D.29 – Design Study 2, Design Configuration 18 - Performance Plots.
Design Study Appendix
281
Design Study 2 - Design 19
Design Study 2 - Design 20
(a) Efficiency RPM Sweep
(a) Efficiency RPM Sweep
(b) Stability CG Moments
(b) Stability CG Moments
(c) Controllability CG Forces
(c) Controllability CG Forces
Figure D.30 – Design Study 2, Design Configuration 19 - Performance Plots.
Figure D.31 – Design Study 2, Design Configuration 20 - Performance Plots.
Appendix E
Author’s Publications This appendix shows each of the papers which has been published throughout the duration of this project. The papers are shown in full, in reverse chronological order.
Hall, A., Wong, K.C. and Auld, D., “Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory”, Proceedings of the 7th Australian Pacific Vertiflite Conference on Helicopter Technology, Melbourne, Australia, 9 - 12 March, 2009 *Received best paper award.
Hall, A. and Wong K.C., “Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors”, Proceedings of the 3rd Australasian Unmanned Air Vehicles Conference, Melbourne, Australia, 9 - 12 March, 2009 Hall, A., Wong, K.C. and Auld, D., “Analysis and Conceptual Design of a Novel MAV Rotorcraft”, Proceedings of the 34th European Rotorcraft Forum, Liverpool, England, 2008 Hall, A., Wong, K.C. and Auld, D., “Coaxial Aero-Mechanical Analysis of MAV Rotorcraft with Rotor Interaction for Optimisation”, Proceedings of the 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, Canada, 2008 Hall, A. and Wong, K.C., “Development of an Analysis Package for Increased Stability Rotary-Wing Micro Air Vehicles”, Proceedings of the 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, Victoria, March 19-22, 2007 Hall, A., Wong, K.C. and Auld, D., “Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation”, Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA-2006-7076
Author’s Publications
283
7th Australian Pacific Vertiflite Conference on Helicopter Technology, 9 - 12 March, 2009
Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory Alexander P. K. Hall PhD Research Student School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney Sydney, NSW, Australia Phone: +61 – 2 – 90367152 Email:
[email protected] KC Wong, Doug Auld Senior Lecturer School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney Sydney, NSW, Australia Abstract This paper presents a new method for the analysis of the interaction between coaxial helicopter rotors. By using Blade Element Momentum Theory as a base analysis tool the computational expense is minimised. To account for the effect of one rotor on the other, an Augmenting Velocity is utilised. Through a geometric mapping process a distribution of influence parameters is defined from the existing distribution of BEMT induced velocities. As the influence is calculated from the current velocity estimate, a second outer convergence loop is placed around the BEM loop. This ensures that the overall distribution has converged. Along with the explanation of the new method an experimental verification has been performed. This verification shows the performance of the method is excellent for its overall computational expense. Keywords: Coaxial Rotor Interaction, Blade Element Momentum Theory, Experimental Verification
Introduction In recent years the coaxial rotor configuration has been increasingly considered for helicopters, particularly for non-conventional flight performance or unique applications (eg. Sikorsky X2 or Kamov Ka-50). This is particularly so for VTOL mini-AV designs for urban missions (eg. Proxflyer or AirScooter UAV). Benefits of this platform type range from elimination of the need for a tail rotor and the compactness of overall platform size, to the utilisation of increased stability rotor designs (eg Proxflyer, shown in Figure 1). These benefits would suggest broader use of this configuration for helicopter designs, but inherent mechanical design complications often deter designers from this choice. Specifically, the aerodynamic flow interactions between coaxial rotors have always been difficult to analyse. Often, only empirical methods or rules of thumb have been used to size rotors. In the past, computational methods have been extremely complex, difficult to implement, and computationally expensive. All of these aspects have limited the use of numerical tools within the design process. Although empirical methods allow a quick analysis with reasonable accuracy of the overall rotor loading, it often does not allow the distribution of loads to be found over the rotor. To be able to examine the rotor loading distribution is extremely important as
Presented at the 7th Australian Pacific Vertiflite Conference on Helicopter Technology, Melbourne, 9 - 12 March, 2009. Copyright © 2009 by the American Helicopter Society International, Inc. All rights reserved.
Figure 1: Proxflyer type aircraft. (Courtesy www.proxflyer.com [1]) it allows a more detailed performance analysis and design process to be followed. Blade Element Momentum Theory (BEMT) is an often used analysis technique for analysis of rotors and propellers. It is easy to use, computationally inexpensive, and simple to modify. This paper examines the development and implementation of an analysis technique which uses BEMT as a basis for analysis of coaxial rotor aerodynamic performance. The background, development and experimental verification of the technique as well as recommendation for further development are presented.
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Background Although the analysis of coaxial rotor (and propeller) aerodynamics is complex and often difficult to implement, there have been a range of investigations conducted. These cover both experimental and numerical analysis. Developing a new analysis technique which models the aerodynamics of coaxial rotors with BEMT requires that previous investigations be examined. The next three sections cover a basic outline of notable investigations into coaxial performance. This is only a brief outline of some of the previous work, but covers experimental investigations as well as both complex and simple numerical analysis techniques.
great deal of detail. This level of detail is more than is required for the analysis that is intended for design configuration optimisation work being discussed here. However, the results from this analysis type can give a range of data which is useful in quantifying the performance of various coaxial rotor configurations. Krothapalli et al.[4] used vortex tube theory to analyse dynamic inflow within manoeuvring flight. Griffiths & Leishman[5] also use a vortex based method for analysing dual rotor interference and performance within ground effect. Theodore & Celi[6][7] have also used this method for a more general coaxial rotor analysis. Finally, Anikin[8] shows the complexity of the flow fields involved in coaxial rotor analysis.
Empirical Relations Applying an empirical relation to the performance of coaxial rotors is often achieved by a simple relation. This relation will be based on experimental data and will take the form of a simple scaling of an isolated rotors performance. Specifically it would involve scaling the thrust and torque coefficient data by an experimentally derived knock-down factor. This will model the overall performance change easily. However, it will not allow any detailed analysis of the distribution of the rotor performance. Although the global performance of this method will be good, it relies heavily on the experimental data which is used to generate the relation.
All of these investigations show that this method is, more often than not, used for detailed analysis and improvement of an existing design. Therefore they are often better used for tweaking of final designs rather than for initial configuration investigation and design. The accuracy provided by vortex methods can easily become overwhelmed by the complexity and computational expense of the method. Thus, this type of analysis is not suitable for use within the analysis technique discussed here because of the computational expense. Also, this method would be difficult to introduce within the existing analysis developed for BEMT.
Wainauski & Vaczy[2] and Harrington[3] present experimental data gathered from a range of tests. Wainauski & Vaczy present experimental data from a counter rotating propeller rather than specifically a rotor. This data, although not directly linked to helicopter performance, can still be used to develop empirical relations. Alternately, Harrington examines the performance of a large (150 inch radius) two bladed rotor. This is excellent in terms of giving relations, but the scales of the tests are not directly comparable to smaller helicopter UAV rotors.
Other Methods In contrast to the more complex analysis methods there are analysis methods which offer an alternative in terms of complexity and computational expense. These less commonly used methods offer a different approach to that of vortex or empirical methods. By using these methods, computational overhead is reduced whilst maintaining accuracy and allowing loading distributions to be examined. The accuracy of these analysis methods is good, especially for the computational expense. Therefore, any of these methods can be used to start developing a specific analysis method for use with BEMT.
For empirical relations to always perform well, a large volume of test data is required. This is especially important if the scale and particularly the Reynolds number is to be varied over a large range. Thus, empirical relations can work very well if enough test data is gathered. But once again, this type of analysis will only give global performance alterations rather than more detailed rotor performance distributions. For this level of detailed a more in depth numerical analysis needs to be used. Vortex Methods An area of analysis which is commonly used for both conventional and coaxial rotor aerodynamic analysis is vortex methods. There are many different types of analysis within this area which can be applied to helicopter rotors. The range of application in which vortex methods can be used is also large. However, this is a complex method which analyses the rotor flow in a
By using strip theory and Euler equations, Colehour et. al.[9] developed an analysis tool for use with counterrotating propellers. Within this method a coefficient matrix of the effect between the rotors is used to influence each rotor directly. Although this method shows much promise, it is still too complicated to combine with the blade element method directly. Cho & Williams[10] used a frequency domain panel method to investigate the interaction between propellers. The pressure differential over the propeller blade was used to generate a coefficient to inturn calculate an influencing velocity for the opposing propeller. By applying influence with a velocity directly, Cho & Williams show a method which could be applied directly to BEMT. Given that BEMT does not allow the pressures over the disc to be found easily, another method must be found to generate the
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory influencing velocity. Although this is the case, this method is still the most closely aligned with the blade element method. Thus, the concept of applying an influencing velocity will be used as a basis for developing the interaction model for BEMT.
Blade Element Momentum Theory As the Blade Element Momentum Theory (BEMT) has been chosen to act as the base rotor loading analysis technique, it needs to be briefly discussed. BEMT is an analysis method which has been used for long time as a quick, reasonably accuracte analysis method. It is often overlooked as an option for both rotor and propeller analysis. As a result of the simple analysis methods it maintains an extremely low computational expense. In its most simple form, BEMT breaks the rotor into radial elements which are analysed in isolation. Thus, without any relation between the radial elements, the method can be kept as simple or complex as needed. The explanation here is summarised from Johnson[11], and then expanded upon to include coaxial rotor effects. Basic blade element momentum theory uses two separate analysis methods to analyse the loading distribution over the disc. The first of these is analysing each element with Momentum Theory to examine the broad streamtube based characteristics of the rotor. Although based on simple momentum theory, BEMT uses a slightly modified theory to allow the radial elements to be examined separately. In contrast to the global view provided by momentum theory, aerodynamic characteristics of a local blade section are examined using Aerodynamic theory. Each blade element is treated as a separate aerodynamic element and analysed as such. Figure 2 shows the basic aerodynamic vector diagram for a single element which is used for both momentum and aerodynamic theory. In this diagram, it can be seen that this theory models the increase in energy caused by the rotor as an induced velocity, ν. This induced velocity is found by using a convergence procedure for each element. Thus, allowing the distribution over the entire rotor to be found. The basic implementation of BEMT analyses all the blades as if they are acting together, which is not strictly correct. For any dynamic or control analysis this needs to be modified. By slightly changing the original
Figure 2: Aerodynamic diagram used to describe BEMT element flow.
Figure 3: Multiple blade breakup of streamtube for BEMT. analysis, BEMT can be expanded to include many other effects. To do this, each of the blades are modelled as contributing to a proportion of the overall streamtube. Or more simply, the entire rotor is analysed as if there are B number of streamtubes, as shown in Figure 3. By altering the analysis as described, the analysis can now include effects which are external to the streamtube itself. Blade motion such as flapping or lagging can then be analysed. Aircraft motion including translation or rotation can also be modelled. Likewise, the effect of external constant wind or wind gusts can also be included within the analysis model. BEMT analysis is based on the formulation of an aerodynamic vector diagram for each element. Therefore, including any of these external effects is as simple as adding an appropriate extra component to this diagram which reflects the effect desired. These external effects are either modelled as a vertical or horizontal velocity component with respect to the rotor disc plane. Adding additional effects of both vertical and horizontal components to the analysis is shown in Figure 4. In this way representation of the interaction caused by coaxial rotors can also be included within the analysis.
Interaction Model A general rule of thumb or knockdown factor can be used for coaxial rotor analysis if only overall changes in thrust and torque coefficients are required. However, if a more detailed distribution of the thrust and torque over the rotor are required, a more thourough analysis is needed. The method presented here has been developed to work with the Blade Element Method. As the standard BEMT does not have any inclusion for such
Figure 4: BEMT aerodynamic diagram including translation effects.
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Figure 5: Coaxial rotor influence between rotors. interactions, the goal was to introduce this modelling with minimal increase of computational expense. BEMT uses an induced velocity to represent the increase in energy transmitted to the flow as it passes the rotor. This provides a convenient way of modelling the effect between rotors. As discussed in the previous section, BEMT can allow extra effect to be analysed by adding an additional velocity term to the aerodynamic diagram. Therefore, an additional term can be added to represent the effect of one rotor onto a given blade element on the other rotor. This component is called the influence velocity and is represented by νinf. Due to this parameter being added to the analysis, the method has been named Velocity Augmentation. Velocity Augmentation uses a function to determine an influencing velocity component from the opposing rotor applied to the influenced rotor. In its basic form, this would entail an element directly above a rotor influencing a given element. This is shown in Figure 5. To apply the effect of coaxial interaction onto either rotor, a function to map the opposing rotors distribution is used. As BEMT uses a convergence procedure to find a stable solution for its induced velocity, the influence velocity cannot be applied from a single evaluation. This is
Figure 6: Influence convergence error for a single element.
Figure 7: Influence convergence procedure. because each evaluation of the induced velocity distribution uses the distribution from a previous evaluation. Therefore a second outer convergence loop needs to be applied to ensure that the induced velocity distribution for each rotor stabilises with the influence included. The variation of induced velocity for a given section with global convergence is shown in Figure 6. And the procedure to implement this is shown in Figure 7. Determining the function to apply the influence between rotors is easy if there is no flow change between the rotors (ie straight flow). But the real flow through a rotor changes on both sides rather than the discrete change modelled in BEMT. This effect needs to be included within the interaction model. To simplify the process of determining the influence effect function, the following assumptions have been made. Flow remains perpendicular to the rotor even under rotor flapping and transverse craft translation and gusts Contraction of the rotor flow about the rotor is linear Steady State Flow Between Rotors No rotation of the flow between the rotors These assumptions simplify an otherwise extremely complex geometry, shown in Figure 8, which makes up the flow between the rotors. However, even with the simplified geometry there is a multiple stage process to determine where each rotor element is receiving its influence from. The geometric definition is broken up into the calculation of the following key parameters, which are subsequently explained. Flap Angles Radial Location Stream Contraction Angle Vertical Separation and Influence Strength Radial and Azimuth Interpolation
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory Flap Angles Because the streamtube is assumed to remain perpendicular to the rotor plane, the direction of the streamtube is governed by the angles that the rotor flaps from horizontal. This is shown in Figure 9. Thus, the location at which a given blade receives its influence from is effected by the flapping angle of the blade. The flow between the rotors is assumed to be steady-state at a given time step. Therefore, the effective flap angle vertically in line with the influenced blade is needed. To determine this angle, the location of the rotors with respect to each other is needed, as shown in Figure 10. From this relation the effective angle between the rotors can be found, and the flap angle can be interpolated between the known flap angles of the surrounding blades.
Figure 8: Streamtube geometry assumptions of linear contraction and perpendicularity to rotor
Radial Location The magnitude of the influence is strongly effected by the correct radial influence location. The influencing radial location is governed by the rotor flap angles, rotor separation, element radial location and angle of the flow contraction. Figure 11 shows the complexity of the geometric relation of the influences. This figure shows a general geometric relation for the lower rotor influencing the upper. Although it may seem as if this can be solved easily, it is in fact very difficult to resolve. This is in no small part because the contraction angle that is being seen at any location is governed by the radial location. This then changes the influence location and so on. Therefore the influencing radial location is found by converging in on the radial location with the following Equation 1. For the reverse arrangement, upper influencing lower, the equations differ slightly, but are not shown here.
0 YL YU rU sin U rL sin L Figure 9: Streamtube geometry assumptions of linear contraction and perpendicularity to rotor
Figure 10: Calculation of rotor overlapping
rU cos U rL cos L
(1)
r tan L L 2 R
Figure 11: Radial position interpolation of lower rotor influencing upper rotor.
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ru rd 2d
tan 1
Figure 12: Rotor contraction angle.
Vertical Separation and Influence Strength The strength that the influencing location has of the analysed element is heavily dependant on the separation distance between the rotors. Vertical separation is found by subbing the radial influence location into the geometric relations used in this section. This vertical separation distance is shown previously in Figure 10. With the vertical separation, d, found the intensity of the influence can be found. Development of the flow past the rotor is governed by the axial distance from the rotor. This intensity can be illustrated as the effect which causes the stream to contract (as shown in Figure 12). Following on from this a scaling factor is found which represents how developed the flow is either in front or behind the rotor. A relation for finding this scaling factor is shown in Equation 3. This can then be applied directly to the induced velocity at the influence location to determine the influence velocity.
dP
k aug 1 Stream Contraction Angle Determining the radial influence location requires that the stream contraction angle of the influencing rotor is known. This needs to be calculated before the radial location is found. As the contraction of the streamtube is assumed to be linear about the rotors, the process is made significantly easier. Theory presented by McCormick[12] is used to find the radius of the streamtube at equal distances on either side of the rotor. This is then used to determine the contraction angle of the rotor at the disc plane, as shown in Figure 12 and Equation 2.
d R2 2 P
(3)
Radial and Azimuth Interpolation As stated previously, the location of the influence position may not align with either the rotor blades or an element location. Thus an estimate for the influencing velocity must be found from the position found. Interpolation is carried out between the surrounding blades and surrounding blade elements. Firstly, a linear interpolation is carried out between the bounding elements with respect to the azimuth location. This is shown in Figure 13 and Equations 4-6. Once the element bounding values are found at the influencing azimuth location, these can then be interpolated in a radial direction. Again a linear interpolation is used, thus giving the induced velocity which is scaled to the influencing velocity.
2 1 rInf r1 r2 r1
Inf 1
1 I Inf 1 1 1I 2 I 2 I 1I 1 1O 2 O 1O Inf 1 2 O 1O
Figure 13: Parameter interpolation.
(2)
(4)
(5)
(6)
Implementation To use the analysis method which has been developed, an overall procedure which combines all aspects needs to be used. The procedure has been designed to obtain a stable distribution of induced velocities over both rotors which include coaxial influence. This procedure to be
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory Table 1. Interaction Verification Geometry Parameter B rroot rtip croot ctip θroot θtip Blade Section Rotor Separation
Value 4 50 mm 225 mm 32 mm 18 mm 15° 6° Curved Flat Plate 100 mm
speeds and separations the widest range of data can be produced. This data will then be compared against performance results which have been generated with the coded analysis. Only thrust measurements will be examined because it is difficult to measure individual rotor torques and BEMT is not as accurate at predicting torque. Figure 14: Complete implementation diagram of Influence modelling within BEMT. used is shown in the following list, and is pictured in Figure 14. 1. Load in Helicopter States, Rates and Controls 2. Calculate geometric parameters required for Influence Calculation 3. Define initial guess for Induced Velocities 4. Loop to converge on Induced Velocity distribution a. Loop through Rotors, Blades and Sections i. Calculate influence component, νinf ii. Converge on Induced Velocity for element A. Aerodynamic Calculation B. Momentum Calculation C. Exit if converged b. Check for stable distributions 5. Stable Induced Velocity distribution reached 6. Calculate Rotor Loading Distributions 7. Calculate Craft Forcing
A rotor which reflects the size and Reynolds number requirements was selected and constructed for testing. The sizing of this rotor and the physical parameters which describe the overall test rig are listed in Table 1, and is shown in Figure 15. Although the test rig is able to produce a continuous range of rotor speeds, only a discrete number of speeds were used. This testing schedule was chosen to practically manage the overall number of sample points. To gain confidence and reduce scatter in the test results, each test configuration was run up to thirty times. Each of the thrust measurements from these tests was then averaged to give a thrust for the given setup. Exactly the same configurations were run in the coded analysis tool for comparison. This allows verification of the results and
A coded analysis package has been produced which implements this procedure within a rotor dynamics simulation. This program is able to perform a wide variety of analyses including static performance analysis.
Verification To ensure that the developed interaction analysis method performs as well as possible, benchmark verification needs to be conducted. Because of the limitations which existing experimental data provides, a complete set of new experimental data needs to be generated. This is especially the case because the method which has been developed is targeted at smaller rotors which operate at low Reynolds numbers. Most data available has been produced for rotors operating at much higher Reynolds numbers. By constructing a test apparatus which drives a set of test rotors at a variety of
Figure 15: Test Rig used for verification..
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory can illustrate the effectiveness and drawback of the analysis method developed. With all the test data compiled and compared to the results from the analysis tool, it was found that the tests match well. This can easily be seen when the results of the tests are plotted and compared to the coded results. By examining the variation of thrust with rotor speed when one rotor is held at a constant speed the trend of the data can be observed. Figure 16 shows the upper rotor being held at 1500RPM and the lower rotor being varied. While Figure 17 shows the lower rotor being held at the same speed and the upper being varied. The general trend between the two sets of data is shown to match very well in these figures. This is supported further when the variation from experiment is examined in Figure 18 (upper constant) and Figure 19 (lower constant). For this rotor separation of 100mm, the variation is always less than 20% and closer to 10% for the entire range.
The above comparison only takes into account a single rotor separation. However, variation of the rotor separation is an important factor to consider. Separation can be examined by plotting the thrust produced with constant rotor speeds (upper and lower) and varying the rotor separation. Figure 20 shows variation of separation with an upper speed of 1500RPM and lower of 1500RPM. Likewise Figure 21 shows the same, with an upper speed of 2000RPM and lower of 2000RPM. Although the performance of trend match with variation of separation is not as good as rotor speed, the magnitude compares well. However, both variation or rotor speed and separation need to be discussed further.
Discussion Performance of the coaxial interaction analysis method developed, although good, is not consistent across all data ranges. Within certain parameter ranges, the consistency is excellent, but across others, the performance drops. The consistency across all the data ranges is not an issue which affects the overall analysis
Figure 16: Verification result distribution. Upper rotor held at 1500RPM.
Figure 18: Variation from experimental results, with Upper rotor held at constant speed.
Figure 17: Verification result distribution. Lower rotor held at 1500RPM.
Figure 19: Variation from experimental results, with Lower rotor held at constant speed.
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory are small, therefore the tip speeds generally only range up to about 70ms-1. There is more chance that this theory would be applied to a larger rotor or a rotor operating at higher speeds, thus negating the error seen at lower speeds.
Figure 20: Variation of Thrust with Separation. Upper Rotor: 1500RPM, Lower Rotor: 1500RPM
Tailoring the analysis range to suit the method developed is a problem which can be solved. However, a second and more isolated problem is that of the aerodynamic data. Within this verification process the aerodynamic data used is not 100% accurate for the test region. Although cambered plate aerodynamic data was used, the Reynolds number for the data did not match that of the tests. At maximum speed, the blade tips were operating at an approximate Reynolds number of 40,000. However, the data taken from Pelletier and Mueller[13] only reaches a minimum Reynolds number of 60,000. This difference in Reynolds number may contribute a significant amount to the difference between the two sets of data. Problems of this type would be seen within any BEMT analysis as well. Although there are two areas within the testing and code analysis which have caused errors, the analysis method still performs very well. Should these two areas of error be eliminated, or minimised, the analysis method will perform even better.
Conclusion
Figure 21: Variation of Thrust with Separation. Upper Rotor: 2000RPM, Lower Rotor: 2000RPM operation. Error between experimental and code analysis is lower at higher rotor speeds. At higher rotor speeds the disc loading of each rotor is larger, thus producing an increased influence effect. Thus, the developed method performs much better at higher rotor speeds, where the disc loading is higher. This indicates that disc loading and Reynolds number may be important factors. When the data is examined with variation of rotor speed it can be seen that the variation between code and experiment is lower at higher rotor speeds. In these regions the rotor disc is more highly loaded. Therefore, the influence between the rotors can be though of as more ‘positive’ effect. Increased rotor speed or disc loading will therefore cause the interaction model to perform better. Having the method be more accurate at higher rotor speeds is not necessarily a problem. This is because the test which have been conducted cover a range of rotor speeds which would normally not be analysed. This is especially the case because the rotors
Although there are existing methods for analysis of coaxial rotor aerodynamics, they either do not contain enough fidelity or they are too computationally expensive. To counter the problem of complexity versus fidelity a method has been developed which aims to keep fidelity high whilst minimising computational expense. To do this Blade element momentum theory has been used as a base. By combing extra methodology to map influence between rotor, the goals of this analysis tool have been met. Flow between coaxial rotors is extremely complicated which introduces computational expense into any analysis tool. To simplify the analysis assumptions have been made which reduce the complexity without eliminating too much detail. The method developed uses a velocity component to augment the flow applied to each coaxial rotor. By doing this a realistic representation of the flow occurring on one rotor is seen at the second without the need for complex mathematics and analytical derivation. Subsequently the method has been coded into a functional analysis tool which can be used for a variety of analysis. The analysis too has been tested against experimental data to check its accuracy. Within reason, the analysis technique performs very well and does not deviated too far from expected results. Although the tool does not match experiment exactly, it is generally within a reasonable variation level from the experimental results. Also, it is extremely good at displaying the performance trends which are seen in experiment for a given rotor configuration.
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Coaxial Rotor Interaction Modelling Using Blade Element Momentum Theory Overall, the analysis technique developed is simple, easy to implement, computationally inexpensive and performs with very good accuracy. Further work is required to allow analysis with tighter tolerances. However, this is not within the scope of work presented here and would require further investigation and development for future presentation.
12. Book: McCormick, B. W. (1999), Aerodynamics of V/STOL Flight, Dover. 13. Periodical: Pelletier, A. & Mueller, T. J. (2000), `Low reynolds number aerodynamics of lowaspect ratio, thin/at/cambered-plate wings', Journal of Aircraft 37(5), 825{832.
References 1.
Webpage: Proxflyer Website, www.proxflyer.com, Accessed: October 2008
2.
Periodical: Wainauski, H. S. & Vaczy, C. M. (1986), Aerodynamic peroformance of a counter rotating prop-fan, in “22nd ASME, SAE, and ASEE Joint Propulsion Conference”, AIAA.
3.
Periodical: Harrington, R. D. (1951), Full-scaletunnel investigation of the static-thrust performance of a coaxial helicopter rotor, Technical Report NACA TN 2318, National advisory Committee for Aeronautics, Washington USA.
4.
Periodical: Krothapalli, K. R., Prasad, J. V. R. & Peters, D. A. (2001), `Helicopter rotor dynamic inflow modeling for maneuvering ight', Journal of The American Helicopter Society 46(2), 129-139.
5.
Periodical: Griffiths, D. A. & Leishman, J. G. (2002), A study of dual-rotor interference and ground effect using a free-vortex wake model, in `58th Annual Forum and Technology Display of the American Helicopter Society', The American Helicotper Society.
6.
Periodical: Theodore, C. & Celi, R. (1998), Flight dynamic simulation of hingeless rotor helicopters including a maneuvering free wake model, in `54th Annual Forum of the American Helicopter Society', The American Helicopter Society, The American Helicopter Society.
7.
Periodical: Theodore, C. R. & Celi, R. (2000), Flight dynamic simulation with refined aerodynamics and flexible blade modeling, in `56th Annual Forum of the American Helicopter Society', The American Helicopter Society, The American Helicopter Society, Virginia Beach, Virginia.
8.
Periodical: Anikin, V. A. (1991), “Aerodynamic features of a coaxial rotor helicopter”, in `17th European Rotorcraft Forum'.
9.
Periodical: Colehour, J. L., Davenport, F. J. & Sokhey, J. S. (1985), “Analysis of counter-rotating propeller performance”, in `AIAA 23rd Aerospace Sciences Meeting', AIAA.
10. Periodical: Cho, J. & Williams, M. H. (1990), “Counter-rotating propeller analysis using a frequency domain panel method”, Journal of Propulsion 6(4), 426-433. 11. Book: Johnson, W., Helicopter Theory, Princeton University Press, New Jersey, 1980, pp. 45-58 7th Australian Pacific Vertiflite Conference on Helicopter Technology, 9 - 12 March, 2009
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3rd Australasian Unmanned Air Vehicles Conference, 9 - 12 March, 2009
Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors Alexander P. K. Hall PhD Research Student School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney Sydney, NSW, Australia Phone: +61 – 2 – 90367152 Email:
[email protected] KC Wong Senior Lecturer School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney Sydney, NSW, Australia Abstract This paper presents a new helicopter configuration for use as an Unmanned Aerial Vehicle. The goal of this new configuration is to provide an aircraft which performs well when operating within cluttered urban environments. Thus it is designed to operate around hover with increased stability and controllability. By proposing a new configuration and then analysing various design configurations, parameters which contribute to the design goals are identified. This is then used to show design trends and the design region which the aircraft design should be located. Finally, a basic CAD model of the possible design is shown to illustrate the conceptual design in further detail. Keywords: Novel Aircraft Concept, UAV Design, Coaxial Helicopter, Increased Stability. Biography: Alexander Hall graduated from The University of Sydney with a Bachelor of Engineering in Aeronautical Engineering in 2004. He began his PhD studies in 2005 at Sydney Uni with a focus on the aeromechanics of small coaxial helicopter platforms for use as Unmanned Aerial Vehicles. During this time he has developed analysis tools for modelling the aeromechanics of the rotors for this type of helicopter. He has combined a method for analysing the interaction between coaxial rotors within this work. Using these analysis methods Alexander has developed new helicopter conceptual designs for use as UAVs.
Introduction Helicopters used as Unmanned Aerial Vehicles (UAVs) have become an attractive platform configuration. This is especially so for coaxial helicopters which until recently were mainly used for manned or ship based operations. Recently, there has been resurgence in both larger coaxial helicopters (Sikorsky X2 or Kamov KA50) and smaller unmanned platforms (Proxflyer or AirScooter). Larger aircraft can be used for high speed flight, whilst the smaller platforms have stability and size benefits for operating in cluttered urban environments. By designing the smaller platforms well, a balance can be reached between stability and controllability which makes this platform type an obvious choice as a UAV. This type of UAV development is even more prevalent as Mini Air Vehicle (MAV). The benefits of the coaxial platform, used as an MAV, extend far beyond the obvious operational and mission benefits. MAVs are allotted less development time and budget during their development. Thus, any platform type which can reduce the complexity within the development cycle is excellent, and should be pursued as a basis for an MAV.
This paper discusses the development of a new MAV helicopter platform conceptual design, specifically designed for use within urban or cluttered environments. Urban environments require higher levels of stability to overcome strong sharp gusts, and larger control authority to perform required manoeuvres around the many dynamic obstacles. Current UAV helicopters operate within these environments, although at a suboptimal level. This is especially the case when the scale of the aircraft is reduced from UAV to MAV scale. Within this environment there are two main factors which greatly affect the success or failure of a platform: Stability and Controllability. From a platform designers point of view these factors are hard to combine into a single rotorcraft platform. Ensuring that the platform meets these criteria as best as possible will allow the aircraft to perform well in its mission area.
Background Many current rotary wing UAV designs are very simple; and employ design and control techniques very similar to large manned helicopters. Coaxial helicopters used as UAVs often use two rotors placed above the fuselage with only one being controlled. However, various other configurations are also used. This includes the Proxflyer (Figure 1) which has no rotor control and the AirScooter (Figure 2) aircraft which has collective on both rotors
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors perform better at that task. By designing specifically for a given task design features which directly benefit the task can be incorporated in the design. This is opposed to including more general features which will not perform as well under a specific mission. The difficulty of including features which benefit a mission directly is not great so long as these features can be readily identified. Thus, the challenge for the concept design is to define appropriate design features rather than the specifics of the design.
Concept Overview Figure 1: Proxflyer type aircraft. (Courtesy www.proxflyer.com [1])
Figure 2: AirScooter G70 UAV. Courtesy AirScooter Corporation [2] and cyclic on the top. Often the rotors are of a design which only uses two blades. This configuration is often directly developed from existing radio controlled platforms. Although they may perform well for hobbyists as entertainment, they have not been designed specifically for the mission in which they are often used as UAVs/MAVs. Existing UAV or MAV helicopters are often only controlled from one of the two rotors, usually the bottom. This design choice is made to simplify the design and manufacturing process. However, it reduces the control authority which would be available should both rotors be utilised for control. Typically only larger manned aircraft, such as the Kamov KA-50 (Figure 3), have full control implemented on both rotors. Although as mentioned above the AirScooter uses a range of control on both rotors. This choice is made because the control authority required is larger and the budget for development is also larger. By only employing control on a single rotor, the aircraft produced has sub-optimal control characteristics. Obviously, an aircraft which has been designed specifically for the requirements of its mission will
To meet the broad requirements to operate within an urban environment a new conceptual design for a UAV helicopter has to be defined. The basis of the mission requirements is to develop a small helicopter platform which performs well in cluttered urban environments. Most of the operation of this vehicle will be centred on hover to facilitate surveillance operations. A configuration for this aircraft has been developed to ensure that a maximal balance between stability and controllability is achieved. Whilst maintaining high efficiency within its size constraints. Thus, the design requirements of this helicopter are: Stability, Controllability, Efficiency and Size Constraints. Proxflyer type rotors are fully articulated flapping rotors which help to absorb disturbances. In contrast an conventional helicopter rotor has rigid rotors which do not flap and thus are more susceptible to gusts. The conceptual design proposed has its roots in both conventional coaxial helicopters and the Proxflyer type aircraft. Rotors from a Proxflyer type platform and control from a conventional rotor. However, features from both of these aircraft types are taken and merged to produce an aircraft with a more applicable set of characteristics. The main features which this aircraft uses in its’ design are listed below. Top and Bottom Configuration Fully Controlled Rotors Fully Flapping Rotors Flapping Feedback Motion Control To more fully explain the aircraft configuration each of these characteristics are defined in the follow sections.
Figure 3: The Kamov Ka-50, manned coaxial rotorcraft. Courtesy www.wikipedia.org [3]
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors control, and the aircraft has six, the aircraft is over controlled. Although this may seem to introduce unnecessary complication into the design it is actually favourable. By outnumbering the degrees of freedom of the aircraft, the controls can provide various configurations for achieving the same outcome. It also can allow degrees of freedom to be controlled directly. This gives a finer control over the aircraft. These factors help to reduce the complexity of the control implementation and also help to reduce the complexity of any control law required. Figure 4: Above and Below Rotor Configuration. Top and Bottom Configuration The proposed configuration uses two fully controlled flapping rotors which are placed above and below the fuselage, as shown above in Figure 4. By placing the rotors in this position the mechanical problems associated with running concentric shafts at high speeds are avoided. The above and below configuration also reduces the complexities of arranging control linkages to both rotors above the fuselage. This configuration essentially creates a conventional rotor placed on either side of the fuselage. Thus, the control layout can be made the same for both rotors. If a typical coaxial configuration was chosen, control for the upper rotor could have been placed above the lower rotor. However, this would have involved introducing a requirement to channel control cables through the centre of the two rotating shafts. This would introduce difficulties in channelling the control cables in this way. Overall placing the rotors in top and bottom locations is a much better option rather than placing both on a single side. In terms of static stability, a typical coaxial configuration is unstable. Thus placing the rotors on either side will improve the static stability as well. Finally, as the rotors are placed on opposite sides, the distance between the rotors and the CG is maximised; therefore maximising the control authority for any rotational control. Fully Controlled Rotors An increase in control authority allows any aircraft to perform better in its controllability requirements. To increase the control authority in the aircraft, control is implemented on both of the rotors. As with a conventional helicopter this includes: Rotational Speed, Collective and Cyclic. Each rotor is powered from a separate motor. This increases the aircrafts performance by allowing each rotor to be operated at a motor speed closer to its optimal setting. Furthermore, torque balance and differential control can be achieved by balancing the torque between the two rotors. By controlling each rotor separately the control workload is distributed between the two. This allows any reduction of thrust when controlling the aircraft to be minimised. Control usage for the aircraft is also changed because the number of available controls is increased from 4 on a standard helicopter to 8 with this configuration. Because there are now eight degrees of freedom in
Fully Flapping Rotors The flapping rotor design of the Proxflyer aircraft has been incorporated to help increase the inherent stability of the aircraft. This will help to alleviate the effects of the turbulent urban environment. Fully flapping rotors contribute to the goal of increasing stability whilst maintaining controllability. By using this design, the challenge is now to implement control on this rotor type, rather than keeping them as passive rotors as seen on the original Proxflyer aircraft. Increased inherent stability provided by this design allows the aircraft to rely less on a complex control system, and more on its own dynamics for stability. By flapping freely, or mostly freely, the rotors are able to absorb a great deal of the energy from a gust. This avoids any major destabilising moments to be passed to the aircraft as a whole. Side forces will be produced rather than destabilising moments, which can then be rectified with control actuation in the opposite direction. Overall the flapping rotors provide a feature which helps to increase its inherent stability. Flapping Feedback By using full control with fully flapping rotors an interesting effect of flapping feedback within the rotors occurs. Flapping feedback is introduced to the rotors when control linkages are connected to the blades. When a blade pair flaps, the control linkage attached to the blade does not move with it. Thus, the flapping will add an additional component of blade pitch which augments the blade loading. Depending on the geometric layout of the control linkages, as shown in Figure 5, different feedback effects can be created. The additional component of
Figure 5: Flapping Feeback Configuration.
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors blade pitch can either increase or decrease the flapping of the blade. This in turn affects the dynamic properties of the rotor and the aircraft. It turns out that when used carefully, this feature can help to absorb a gust experienced by the aircraft. This also increases the flapping angle of the rotor due to control application, helping to increase control authority. These two features, although not directly intended, help to make the development of this aircraft design worthwhile. Motion Control The combination of the features discussed above allows the aircraft to be controlled in a different manner to a conventional helicopter. Rather than using the rotor disc to tilt the aircraft and thus moving the aircraft, the discs themselves are tilted in isolation. By using flapping feedback with cyclic control, the flapping angle of the rotors can be maintained without tilting the aircraft. This allows the thrust vector of either or both of the rotors to be controlled. As a result this gives a high level of control authority and fidelity. This control mechanism has been outlined previously by the authors[4]. Control about the vertical axis of the aircraft is implemented through differential control for Yaw, or net control for Climb/Descent. This is similar to a conventional helicopter. However, to translate the aircraft both rotors are controlled in cyclic at the same time. By tilting both rotors towards the same dirctions a portion of the aircraft thrust is directed in the commanded direction. This motion is shown in Figure 6. Likewise to control the rotation of the aircraft in either Pitch or Roll both rotors are tilted simultaneously. However, in this case they are tilted in opposite directions, causing a couple which rotates the aircraft, as shown in Figure 7. There is a second method for controlling the translation of the aircraft. This method is more similar to the control of a conventional helicopter. The aircraft is firstly tilted to Roll or Pitch the aircraft. In its rotated state it is then trimmed, to hold this angle. Thus the global aircraft lift vector is tilted causing a much larger control force. The larger control force will then cause the aircraft to translate at a higher speed. The two stage process to complete this control is shown in Figure 8.
Analysis
Figure 8: AircraftFast Translation Concept.
To determine the best overall sizing and configuration for this configuration, aerodynamic and rotor dynamics analysis needs to be performed. Detailed analysis of the aircraft can be used to design blade size, shape and aerodynamics properties, as well as determining the configuration of the rotors and control linkages. Specifically, any analysis is used to determine an overall configuration for the following features listed below. Blade Design Overall Configuration Layout Control Linkage Design
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors Rotor Speed Rotor Separation These are not an exhaustive list of design parameters; they are rather a list of the major parameter areas which can be controlled. The development of an analysis tool to examine aircraft of this type has been constructed in a number of parts. However, this was conducted throughout with a single goal to maintain low computational expense with good accuracy. There has been much previous explanation of the working of the analysis tool by the author [5][6][7]. Therefore, it is not discussed in detail here. The major areas included within the analysis tool are listed below. Each of these is discussed briefly in the following sections. Rotor Loading Coaxial Rotor Interaction Rotor Dynamics Rotor Loading Although there are many methods available for modelling the loading of a rotor, perhaps the simplest is the Blade Element Momentum Theory (BEMT). BEMT analyses the rotor with two separate theories, Aerodynamic and Momentum. By breaking the rotor into many individual elements BEMT allows not only the global performance of the rotor to be found, but also allows the distribution of the rotor performance to be analysed. This allows its use for analysis of other parameters. One of the benefits, besides its lower computation expense, is that it allows external effects outside the rotor to be included. This includes: Aircraft Motion, Rotor Dynamics and Rotor Interaction. Coaxial Rotor Interaction Although BEMT gives excellent fidelity for computation expense, it has no means for directly modelling coaxial rotor interaction. In any coaxial rotorcraft, the proximity of the rotors obviously affects the overall performance. However, the flexibility of the Blade Element Method allows introduction of coaxial rotor modelling with little additional effort. The method developed to model these effects uses the induced velocity from one rotor to apply an effect to the opposite rotor. This is shown in Figure 9. Thus, this performs a velocity augmentation which represents the performance change due to the coaxial influence. To implement this method a second outer convergence procedure is used. This ensures that not only is each blade element converged, but the entire distribution including coaxial influence is also converged. Rotor Dynamics To adequately model the flapping dynamics seen on the Proxflyer rotors, simple rotational equations of motion are used. The blades on this rotor type flap in two pairs. This is modelled by grouping effects seen on both blades together into the same dynamic model. By adopting this model, external disturbances can be
Figure 9: Coaxial rotor influence between rotors. represented by applying aerodynamic or control changes to the loading model. This is then transmitted to the flapping dynamics directly. Analysing dynamics in this manner can accurately represent the flapping caused by external gust loadings as well as controls and flapping feedback. Overall, this provides an excellent method for assessing the control authority as well as the inherent stability.
Helicopter Design To demonstrate both the conceptual design of the new helicopter, and also the analysis tool in action, a helicopter design process has been developed. The goal for this design process is to create an aircraft design which uses the features discussed above and performs well. For this configuration design, the only global feature which has been restricted is the mass of the aircraft to 2.5kg. Apart from the broad restriction on mass, another design restriction is that the rotor blades are taken from off-theshelf products. This restriction is made to ease the manufacturing process if a concept demonstrator is to be constructed. In this case, the blades have been chosen from an existing electric helicopter, the Thunder Tiger Mini Titan. With blades having specifications shown in Table 1. By restricting the rotor blades, the outcome of the design process comes down to finding the best combination of the following characteristics. Blade Collective Flapping Feedback Linkage Lengths Rotor Separation Although this may seem restrictive, there are more than enough parameters for manual optimisation. Features which are used to gauge the performance of the aircraft within the design process are listed below. Power Requirements Control power Gust rejection Each of these features has a differing effect on the requirements of the aircraft. Thus, the overall aircraft will be an amalgamation of each of these performance characteristics.
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors
Table 1. Rotor Blade Dimensions Parameter Root Radius Tip Radius Root Chord Tip Chord Mass Aerodynamic Section
Value 75mm 375mm 35mm 35mm 28g NACA0012
Configuration Analysis To examine the possible configurations, a number of tests have been developed to characterise a given configurations performance. Firstly, hover performance is examined by looking at the blade collective angle and rotor speed requirements. For any of the proposed aircraft configurations the aircraft is trimmed to give a stable hover. The power required to achieve this hover can be used as a measure of the hover performance. Figure 10 shows variation of the thrust and power produced by the aircraft for a range of rotor speeds set around the trim position. Stability will be gauged by the aircrafts’ response to a characteristic gust. The flapping rotors absorb gusts applied to the aircraft by flapping; however this flapping causes a destabilising moment to be seen at the CG. This makes a vast improvement over a conventional helicopter which does not have flapping rotors to help absorb the gust. Thus, to gauge the effectiveness of a configuration against gusts, the maximum CG moment during the applied gust is used as a measure. Figure 11 shows a sample CG moment response to the characteristic gust. Finally, control authority will be examined by looking at the side force produced by a standard cyclic application to the rotors. The flapping of the rotors causes a side force to be applied to the aircrafts CG. A
Figure 10: Sample Hover Efficiency Plot.
Figure 11: Sample Stability Plot. sample plot of the control response is shown in Figure 12. Obviously the goal will be to maximise this control force. Design Optimisation To illustrate various design configurations, the performance of a number of designs will be examined. This study will serve as a basic first cut Design Optimisation. Although not a full design optimisation, trends will be established as to how each of the design variables effects performance. From this trend analysis a final optimal design can be found in the future. However in the meantime, any of the better performing designs can be used to produce a concept demonstrator aircraft. To begin, the design analysis process a number of design configurations have been chosen to be tested. Each of these designs can be grouped into three subsets, grouped by the design variable which is varied. These subsets are broken up by variation of Collective, Rotor
Figure 12: Sample Controllability Plot.
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Coaxial Helicopter with Fully Controlled Flapping Feedback Rotors
Table 2: Design Configurations Tested Design
Collective
Rotor Separation
Control Length
D01 D02 D03 D04 D05 D06 D07 D08 D09 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20
(degrees) 8 10 12 14 16 18 12 12 12 12 12 12 12 12 12 12 12 12 12 12
(mm) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 25 50 75 125 150 175
(mm) 50 50 50 50 50 50 10 20 30 40 60 70 80 -50 50 50 50 50 50 50
Separation and Control Length. Table 2 shows a summary of each of the design configurations. Collective defines the blade setting around which the configuration is trimmed. Rotor Separation is each rotors vertical distance from the CG. And Control Length is the control linage length extending outward from the blade ( l 2 ). Each of the design which has been proposed has been analysed using the analysis tool and procedure described previously. Measured performance of each configuration in terms of its hover performance, gust sensitivity and control authority has been summarised into Table 3. This table shows the wide variety of performance which configurations can experience with small changes. Two plots summarising the performance of the configurations are shown in Figures 13 and 14. Figure 13 shows the hover power plotted against the gust stability. While Figure 14 shows hover power plotted against control force. Within each of these figures the variation of the three design parameters has been sorted by colour. The black solid line shows the variation of Collective; the red dotted line showing variation of Control Length; and the green dashed line shows the variation of Rotor Separation. From each of these trends the effect of each parameter on the aircraft performance can be noted. It can be clearly seen that increasing collective angle gives a reduction in power as well as an increase in control force. Increasing the control length, therefore decreasing
Table 3: Design Performance Results Design
D01 D02 D03 D04 D05 D06 D07 D08 D09 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20
Hover Power (W) 194.60 156.83 140.15 131.22 126.43 123.96 140.15 140.15 140.15 140.15 140.15 140.15 140.15 140.15 152.87 146.73 144.34 137.30 131.63 125.62
Max Gust Moment (Nm) -0.2754 -0.2945 -0.2961 -0.3133 -0.3185 -0.3236 -0.4565 0.5148 -0.3802 -0.3363 -0.2639 -0.2425 -0.2207 0.3262 -0.2538 -0.2633 -0.2917 -0.2881 -0.2917 -0.2686
Steady State Control Force (N) 0.7226 0.9037 1.0052 1.0703 1.1075 1.1269 0.2852 0.5329 0.7418 0.9012 1.0668 1.0917 1.0952 -0.9073 1.2488 1.1705 1.0963 0.9263 0.8558 0.8133
feedback, improves both the performance of control force and gust sensitivity which does not change hover power. Finally, increasing rotor separation decreases hover power, but also reduce control force. From this analysis, it can be seen that the aircraft configuration which is desired should have the following design characteristics. Higher Collective Higher Control Length Moderate Rotor Separation Within the plots it is seen that the design which would be chosen would be design D06. While not being the overall optimum configuration, this design has all the features listed above. And as a concept demonstrator this configuration should perform very well. Proposed Aircraft Configuration Despite none of the configurations having been yet built to date, a more general aircraft configuration has been designed which can be adapted to any given configuration. A CAD model of this aircraft is shown in Figure 15. The layout presented here is a general configuration which illustrates all the major design parameters. This design shows all characteristics which have been discussed previously. However some more intricate design details have been omitted for clarity. There is intention to construct and test-fly this platform configuration as a concept demonstrator.
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Figure 13: Configuration Performance Summary, Hover Power vs Gust Stability.
Figure 14: Configuration Performance Summary, Hover Power vs Control Force.
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Figure 15: Aircraft Conceptual Design Configuration.
Conclusion This paper has discussed the need for and benefits of developing a new conceptual design for a rotary-wing UAV. The design shows that new concepts and design configurations can be developed with simple, yet efficient analysis tools. To do this well, analysis of the new aircraft concepts needs to be performed where appropriate. In this case, the analysis of this aircraft type has been performed with a custom developed analysis tool. Although the custom tool does not perform analysis on the entire flight dynamics of the aircraft, it examines a wide enough array of analysis to perform configuration design for this aircraft type. The various analysis techniques used within this tool have been chosen specifically for their respective features and applicability to coaxial helicopter analysis. Perhaps most importantly, a method which predicts the performance characteristics of coaxial rotors has been developed. This allows a better estimate of the aircraft characteristics to be made, as opposed to analysis with modelling only a single rotor. As a result of the conceptual design process and aircraft analysis, various platform configurations have been examined. Testing of various configurations has allowed a desirable configuration to be found. Although not the absolute optimum configuration, the performance characteristics identified show promise. From this, the conceptual design configuration has been transformed into a CAD model. This model shows all major design features, and will allow an aircraft to be produced and flight tested.
References 1.
Webpage: Proxflyer Website, www.proxflyer.com, Accessed: October 2008
2.
Webpage: AirScooter Corporation Webpage, www.airscooter.net, AirScooter Corporation, Accessed: October 2008
3.
Webpage: Kamov Ka-50 Wikipedia Entry, http://en.wikipedia.org/wiki/Kamov_Ka-50, Accessed: October 2008
4.
Periodical: Hall, A., Wong, K.C. and Auld, D., “Analysis and Conceptual Design of a Novel MAV Rotorcraft”, 34th European Rotorcraft Forum, Liverpool, England, 2008
5.
Periodical: Hall, A., Wong, K.C. and Auld, D., “Coaxial Aero-Mechanical Analysis of MAV Rotorcraft with Rotor Interaction for AIAA/ISSMO Optimisation”, 12th Multidisciplinary Analysis and Optimization Conference, Victoria, Canada, 2008
6.
Periodical: Hall, A. and Wong, K.C., “Development of an Analysis Package for Increased Stability Rotary-Wing Micro Air Vehicles”, 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, Victoria, March 19-22, 2007
7.
Periodical: Hall, A., Wong, K.C. and Auld, D., “Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation”, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA2006-7076
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Analysis and Conceptual Design of a Novel MAV Rotorcraft Alexander Hall Postgraduate Student K.C. Wong Senior Lecturer
Doug Auld Senior Lecturer
School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney, Sydney, Australia Abstract This paper examines the development of an analysis package for use within the design process of small coaxial MAV rotorcraft. The analysis tool has been formulated to analyse the rotor dynamics and performance of a Proxflyer type rotorcraft. The analysis tool has been benchmarked against the base Proxflyer vehicle, and is therefore suitable for use with this platform type. Subsequently, a new platform configuration has been proposed which will provide better stability and controllability. The new design utilises the base elements of the original platform as well as a novel flapping feedback mechanism. This mechanism allows conventional rotor control as well as the Proxflyer rotor flapping. And in turn provides a much better method for controlling this platform type. Due to the flexibility of the design tool and the general design concept any sized platform can be designed. protecting the pilot. Although this reasoning only applies for larger aircraft, the use of UAVs in smaller application has always been a natural choice. Use of UAVs has now been well bedded within the aircraft industry for both large and small craft1, such as the Global Hawk or Predator. However UAV design has reached a point by which only small performance gains can be made redevelopment of conventional aircraft designs. Now the focus of UAV development must be firmly placed on optimising existing designs, as with manned aircraft, as well as developing novel platform concepts. One area in which the development of novel platform concepts has developed quickly is within smaller Mini Air Vehicles (MAVs). An MAV is generally classified as an aircraft which normally has a major dimension no bigger than 450mm. The size of these platforms allows trial of various concepts which would be difficult to implement on a larger platforms. Tail sitter VTOL vehicles such as the Bidule2 and TWing3,4 from the University of Sydney display a similar concept difficult to implement on a larger vehicle. In addition to fixed-wing platforms, rotary-wing MAV platforms provide an extremely effective autonomous aircraft configuration. This platform type can also be used as a basis for a variety of new ideas to be trialled.
Symbols B c CL CD dT F, f J M r VH VV W
-
-
number of rotor blades chord of blade section coefficient of lift coefficient of drag elemental thrust component Prandtl Tip Loss Factor rotational moment of inertia moment about rotor hub radial location horizontal velocity component horizontal velocity component resultant section velocity angle of attack inflow angle geometric angle flap angle induced velocity air density rotor rotational velocity rotor azimuth location
Introduction Unmanned Aerial Vehicles (UAVs) are a much preferred choice where a pilot would be placed in danger, or the length of the mission would strain the pilot both physically and mentally. Removing the requirement of a pilot from the design process places the emphasis on carrying out the mission rather than
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As the design of MAVs is generally a smaller overall project than a UAV or manned aircraft, they often suffer as a result of the smaller project size. A large number of these platforms are developed from existing radio controlled aircraft. By relying on the design of an existing platforms rather than developing one from scratch, the platform is never a completely optimal design for its given mission. This can give problems with systems integration and more importantly flight performance. By approaching the platform design as a process which is seamlessly integrated with the ultimate mission goal, a more optimal platform can be produced. This design methodology is well established within manned aircraft design, and should be transferred to the design of UAVs and MAVs. This paper presents work on the Concept, Analysis and Design of a novel rotary-wing platform. Design of this platform is benchmarked against similar existing vehicle concept which performs well. However, the existing vehicle can be improved upon by approaching the design process from a mission oriented stance. An analysis tool which models the base platform well has been developed. By using this analysis tool, the process of developing the platform from concept to design is stepped through showing the benefits of the Novel Platform Concept.
an MAV extra effort needs to be placed upon the control system, which needs to provide smooth motion for onboard sensors. Although this design provides excellent stability, its control authority and translation does not perform as well. To provide more control authority direct control over the rotor motion is needed. This can be achieved by changing the configuration to include control in the form of incorporating both collective and cyclic control to both rotors. If this platform concept can be altered to allow better control over the platform motion, whilst maintaining its stability, an overall better performing aircraft can be made. Analysis Tool Developing a novel rotorcraft concept based on the basic Proxflyer requires that an analysis model of the basic platform be used. By developing such a tool, the analysis of the basic design can be performed, as well as modifying the analysis to include new design concepts. The motion of this type of platform is almost entirely dominated by the loading and motion of its rotors. Thus new designs can only be adequately analysed if the dynamic motion and loading of the rotors can be adequately modelled. Being able to model flight performance changes of new design concepts would allow comparison to the baseline design thus allowing more optimal designs to be developed. To reduce the complexity of the analysis, only the dynamics of the rotor motion and its loading are modelled. The coupling between the dynamics of the vehicle and that of the rotors can be ignored, allowing the focus to remain on accurately modelling the rotor motion. To model the dynamic motion and loading of a Proxflyer type rotor, separate analysis methods for both dynamics and loading need to be used. Blade Element Momentum Theory (BEMT) is used to model the rotor loading; and Rotational Equations of Motion (REoM) are used to model rotor flapping dynamics. To refine the model further, tip losses are modelled with a Prandtl tip loss factor, and a model for coaxial rotor interaction is used. These analysis techniques have been outlined in previous papers by the author7,8 and are briefly discussed in the following sections.
Platform Type Background A new rotary-wing concept which showed potential to be used as an autonomous platform is the Proxflyer5 type platform, shown in Fig. 1. By using the flapping hub design and coaxial rotors the Proxflyer has excellent stability can easily maintain a steady hover within a relatively gust-free atmosphere. However, its control is provided only through an external tail rotor which tilts the aircraft. This control method results in translation which pendulums and does not provide a smooth motion. Should this platform type be used as
Blade Element Momentum Theory Blade Element Momentum Theory is a commonly used technique to accurately analyse rotor and propeller loading9. By breaking the rotor up into radial elements,
Figure 1. Proxflyer Type Vehicle6
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Rotational Equations of Motion By studying the rotor response of a Proxflyer type craft to external disturbances, it can be seen that the rotor flaps as two blade pairs, shown in Fig. 3. To model this motion simple Rotational Equations of Motion (REoM) have been chosen. REoM can easily be utilised to model the free and forced response of the rotor blade pairs to external inputs through a simple relation shown in Equation 3. As there is no spring or damper acting on the rotation of the blades, their response is governed by the moments applied to them. This equation can then be integrated to map the rotational response of the rotor blades.
Figure 2. Element Aerodynamic Diagram BEMT can determine a distributed loading over the entire rotor. Each element is analysed separately by Momentum and Aerodynamic theory used to determine an induced velocity flow, ν, over the element. This is shown in Fig. 2 with rotational, horizontal and vertical velocity components. Momentum and Aerodynamic theories are used to converge upon an elements induced velocity. Aerodynamic theory uses an estimate for the induced velocity to calculate a corresponding estimate of the elements thrust, shown in Equation 1. Momentum theory is then used to model the flow over the element as a continuous streamtube, and the thrust produced by the elemental section is found with Equation 2. This equation is then rearranged to form a quadratic which can be solved to find a new estimate for the elemental induced velocity. From the converged induced velocity, aerodynamic theory is then used again to find the Lift, Drag and Pitching Moment of the element.
dT C L dT
1 W 2 cdr 2
4rdr V Z B
J M
(3)
Prandtl Tip Loss Modelling BEMT models the load across a rotor blade as a continuously increasing load from root to tip. In its basic form, it has no account for losses that are expected at the blade tip. Accounting for this loss in lift is especially important when constructing the rotational forcing moment. If it is not taken into account there will be a notable over-prediction of the forcing moment. To account for this, Prandtl Tip Loss Modelling can be used which is an empirical fit to the loading data which accounts for losses experienced at the tip. To implement this method a simple scaling factor, F, is generated and applied to the aerodynamic calculations10,11. These are generated with Equations 4 and 5.
F
(1)
f
(2)
2
cos 1 (e f )
B Rr 2 r sin( )
(4) (5)
Coaxial Rotor Interaction Model Two rotors or propellers in close proximity will have an effect on each other. BEMT does not take this into account in its simplest form. A method for modelling the interaction between
Figure 3. Blade Pair Breakup
Figure 4. Influenced Element Aerodynamic Diagram
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two rotors with BEMT has to be developed. This model applies a second induced velocity, νinf, to a blade element to account for the counter-rotating rotors influence. Figure 4 shows the influence velocity within the aerodynamic diagram. A mapping function is used to geometrically map the induced velocity from an element on the opposing rotor onto the analysed rotor. This parameter is transformed to account for stream development and applied directly within the BEMT process. This additional velocity component will have an effect on the convergence of any element, therefore a second outer convergence loop is used to ensure that the entire coaxial rotor setup has converged.
Table 1. Platform Geometry Parameter Value B 4 rroot 0.045 m rtip 0.145 m croot 0.025 m ctip 0.015 m θroot 35° θtip 25° Blade Mass 2g Platform Mass 100 g Section per Blade 10 Blade Section Cambered Plate Rotor Speed ~1000 RPM Gust Magnitude 3ms-1 Gust Duration 0.1s pulse gust input. Each rotor disc responds to the gust by pitching up to meet the gust. Furthermore, in preparation to meet the gust the advancing side of the disc rises. The two rotors are rotating in opposite directions, thus the roll response is also in opposite directions. It can be seen that the response of each rotor is different due to the interaction modelling within the analysis. Differences in the magnitude and damping of the rotor response show that the upper rotor is receiving less of an influence due to the interaction. This is due to the upper rotor being upstream if its influencing rotor, whereas the lower rotor is downstream of its influencing rotor, where the flow is more developed.
Implementation and Results The analysis techniques described above have been combined into a total analysis package. This analysis package can be used to model the rotor dynamic response of Proxflyer type platform as required. A more detailed explanation of the implementation of the tool is shown in other papers by the author7,8. To demonstrate the analysis tool, a test case was developed in which a Proxflyer type rotorcraft is subjected to a wind gust. The geometry of the platform and gust data are shown in Table 1. While Fig. 5 shows the craft rotor response in disc pitch and roll to the
Figure 5. Rotor Response to Test Gust
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Novel Platform – Concept Proxflyer type rotorcraft exhibit favourable stability characteristics around hover, when flying in still air. However they lack any real ability to control the motion of the platform. Forward control is provided by applying a pitching moment to the platform through the tip of the tail boom. This method of control only allows very slow translation, and provides little authority over the attitude of the platform. Although this does provide a certain degree of control, it does not provide enough authority to make the platform useful. A rotorcraft which displays similar stability characteristics, as shown in Fig. 5, and also features good control authority would provide a platform with much better flight characteristics. In contrast to the Proxflyer, rotorcraft with higher control authority (either manned or unmanned) use changes of the rotor itself to control the aircraft. UAV coaxial rotorcraft such as the AirScooter12 (shown in Fig. 6), use conventional rotors with cyclic and collective controls. This method of control provides a higher degree of control authority for the aircraft, which in turn allows better overall flight characteristics. Having full control of a Proxflyer style rotor, with collective, and more importantly cyclic, produces a platform with much better stability and controllability. From observation of the rotors of a Proxflyer under an external disturbance, the rotor-planes adopt a steady deflected flapping state. If direct control over the pitch angle of the blades is used, control over the flapping of the rotor can be subsequently actuated. Actuation of the rotor flapping angle can then be used to translate and rotate the platform. By varying the level of control authority over the rotors, a balance between stability and controllability of the platform can be reached. The balance between these factors can be varied to suit particular in-flight conditions or overall platform configurations. Actuation of the change in blade pitch will generally require use of external control through use of a swashplate. Externally controlling the blade pitch is simple for a conventional rotor however, when the blades experience a large range of flapping angles control of the blades differ. As the blades flap and the control rod remains stationary, the actual pitch of the blade will change proportionally with the flap angle. At first this may seem to be counter-intuitive, but if implemented correctly this can be beneficial to controlling the flapping motion. The addition of ‘Flapping Feedback’ to the rotors can increase the ability of the rotors to maintain a rotor disc
Figure 6. AirScooter G70 UAV13 plane flap angle when actuated by control. In contrast it can also help to reduce the magnitude of the flap response to an external disturbance. Overall benefits of developing a platform with fully controlled flapping rotors can be seen in general terms, through the addition of direct control. However specifics of how this manifests itself within the response of the platform need to be defined. Motion Control Pitching and rolling the rotor disc will change the orientation of the lift vector, thus applying forces to the platform. The combination of two rotors can lead to a very effective platform control mechanism which also has the benefit of inherent stability. To control the flapping of the rotors, conventional control of RPM, Collective and Cyclic is used. This gives a total of four controls per rotor, and eight controls for the platform. As the number of platform controls exceeds the six degrees of platform freedom, the platform can then be directly controlled about all axes. Controlling each of the six degrees of freedom directly requires an explanation on how it is implemented. Controlling the platform motion in the Z direction is as simple as changing the collective on both rotors simultaneously, while keeping the rotor speed constant. The change in collective on both rotors will change the lift produced, and thus will change the crafts Z
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Figure 7. X or Y Craft Translation
Figure 8. Pitch or Roll Craft Rotation rotors’ thrust as well as the torque of the rotor. Therefore, the reduction of thrust on one rotor must be balanced by an equal increase in thrust on the opposing rotor. To rotate the platform about either the X or Y axis, a combination of rotor flapping is also used. Similar to the slow translation motion described above, manipulation of the rotor flapping can apply a moment about the platform. Figure 8 shows the top and bottom rotors flapping in opposite directions to offset the thrust components in opposite directions. This produces a moment about the X or Y axis causing rotation. The opposite flapping directions will also produce subsequent flapping out of phase with the desired flapping direction. However, in this case they will both be in the same direction, thus causing platform translation rather than rotation. This must also be remove by applying an opposite cyclic control. A second type of platform translation is which produces a faster platform response by increasing the force in the required direction of travel. Instead of deflecting the rotors in a similar direction, the platform is firstly rotated about the appropriate axis then the whole platform thrust is used to direct a force in the direction of travel. This procedure is shown in Fig. 9. Platform motion can then be controlled further through manipulation of the rotors as described above.
position. To affect this both rotors will also need to have a constant speed maintained, as with conventional helicopter designs. Z control can be also effected by using only speed control, should collective be unavailable. This is similar to many existing helicopters. To translate the platform in either the X or the Y direction, a combination of cyclic commands on both rotors is used. By actuating each rotor to either Pitch or Roll in the same direction, both of the rotors’ thrust vectors are tilted in the same direction. This will then apply a net force on the platform in the direction of tilt, as shown in Fig. 7, thus producing platform motion in the desired direction. However, when each rotor is flapped in a given direction there will be subsequent flap residue 90° out of phase. This can then be simply cancelled by applying cyclic to the opposite control direction. Applying control in this manner will allow the platform to be translated in the direction required with little or no platform tilt. As a consequence, this will only produce a slow translation in the desired direction and generally this is not how a normal rotorcraft translates. As with conventional coaxial rotorcraft, a yawing motion is performed by applying differential collective. This will apply different torque reactions about the rotor mast, therefore applying a moment about the Z axis. Changing the collective also changes the
Figure 9. Fast Craft Translation from Craft Rotation
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to ensure that the platform still remains gust tolerant, the rotors are subjected to a characteristic gust. This allows the overall rotor response to be examined. Example profiles of the cyclic and gust inputs are shown in Fig. 10. To make changes to the performance of this helicopter type, variations in blade design and control linkage system can be considered. Blade variations can be made through changes of either aerodynamic or mass properties. Aerodynamics changes are carried out by varying the Tip and Root values for Radial Location, Chord and Twist. A plot of a base geometric blade distribution of the Proxflyer is shown in Fig. 11. As well as the blade geometric design, the blade mass can be changed. As the total blade mass is assumed to be evenly distributed across all blade elements, thus a simple change in total blade mass applies evenly to the entire blade. Blade configuration and mass distribution changes are not considered within this paper. As flapping feedback is included within the simulation, variations in control linkage configuration locations are made, which changes the gain of the flapping feedback. A schematic of the control linkages are shown in Fig. 12. Variations in l1 and l2 allow the gain in the flapping feedback system to be varied, and thus have an effect on the rotor motion. The above tests are used to define the
Novel Platform – Analysis The goal of any rotorcraft design process is to develop a platform which has favourable flight characteristics. It has clearly been shown through an earlier section that the basic Proxflyer design has favourable stability characteristics. The concept described within this paper builds on this basic inherent stability by providing significantly better control characteristics. To verify the addition of beneficial control characteristics, the original design must be compared to the new concept. Specifically, tests must be performed to ensure that the stability (Gust Response), control authority (Control Response) and overall efficiency of the new platform outperforms the original platform. Once the new concept has been proven to meet these tests, a more detailed design process can begin. For a given platform mass, a trim algorithm is run to obtain the rotor speeds required to maintain steady hover. Efficiency can be gauged by examining the relative power requirements of each configuration. The control of collective and rotor speed can be tested by making a sweep about the trim condition. To test the cyclic control authority, a standard control input is commanded and the rotor flapping response is then found. Finally,
Figure 10. Gust and Control Test Simulation Inputs
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Figure 11. Base Proxflyer Blade Chord and Twist Distribution concept is made. This analysis requires that the geometry of the base platform be defined, which has been modelled from a Proxflyer type platform approximately the size of the Bladerunner6. The geometry of the test platform is similar to the geometry used to illustrate the analysis tool, shown in Table 1. Benchmarking the new platform concept against the base design allows benefits of the new design to become immediately apparent. A standard set of analyses is used as a benchmark between the original platform and the platform with new design features. The standard set of analyses is generated from the analysis suggested above, and is summarised below.
performance of new designs with respect to the existing design. Therefore a base platform configuration, such as a 200g platform, must be used. This initial platform design is designed to have exactly the same design as a basic Proxflyer platform. Following an initial analysis, differing combinations of the new designs are applied to the analysis model. Results from these analyses allow a better performing platform to be produced. Novel Platform – Design To demonstrate the benefit of the new platform, an initial analysis of that design
1. Trim platform for steady hover at given platform mass. 2. Perform RPM sweep around hover condition. 3. Perform Collective sweep about hover RPM. 4. Simulate Rotor Response to 3ms-1 Wind pulse input. 5. Simulate Rotor Response to 5° Cyclic Control input.
Figure 12. Control Linkage and Flapping Feedback Schematic
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Table 2. Base Craft Geometry Parameter Value B 4 rroot 45 mm rtip 145 mm croot 25 mm ctip 15 mm θroot 33° θtip 15° Blade Mass 2.0 g Craft Mass 200 g Elements per Blade 10 Blade Section Cambered Flat Plate
Table 3. Trim Configuration Parameter Value Upper Rotor Speed 1479 RPM Upper Rotor Power 5.16 W Lower Rotor Speed 1479 RPM Lower Rotor Power 4.99 W Residual Torque 0.001012 Nm the base craft are summarised in Table 3. These trim values are also the same for any of the new craft as no blade changes are being considered. Using this trim configuration as a base, Fig. 13 shows the variation of output thrust, and total required power, with rotor speed about the trim condition. As would be expected, the total thrust and power vary proportionally with rotor speed. However if Fig. 14 is examined, the variation of thrust and power with rotor Collective, it can be seen that the blades are operating near blade. Thus, a small increase in collective, or any other angle change, can cause the blades to stall giving sub-optimal performance. To compare the base design to the new platform configuration, dynamic performance of the rotor is examined. The performance of the base vehicles rotors with respect to gusts needs to be found. A standard gust profile shown in Fig. 10 is used to generate the
Of the five tests described above, only the first four tests will be performed on the base platform design, as no rotor control is present. As well as the gust simulation testing new designs against the base platform, a cyclic input simulation is used to gauge the control authority of new designs with respect to each other. Table 2 shows the geometry and analysis parameters of the base platform configuration. To begin, the base configuration must be examined to set a baseline for further comparison. As with any set of tests, the base configuration is firstly trimmed to define a hover rotor speed. The trimmed conditions for
Figure 13. Base Craft – Rotor Speed Sweep
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Figure 14. Base Craft – Rotor Collective Sweep 17 show a flapping feedback rotors response to a gust and control input simulation. This rotor exhibits gust response characteristics which are comparable to, or better than, the base configuration. Control authority of this craft is shown through the steady-state flapping angle which the rotor adopts. In this case, the control response that the platform provides will be able to actuate platform motion. Table 4 shows a summary of the gust and control simulation flapping response magnitudes for varying combinations of control linkage lengths. For comparison of these configurations, gust response is gauged by the maximum rotor deflection, while control
required response to external disturbances. Figure 15 shows the rotor flapping response in pitch and roll as a response to the gust disturbance. As the gust strikes the rotor, it responds through a large initial disturbance in the pitch direction. Following the cessation of the gust, the rotors return to there steady-state positions. The deflection magnitude reflects the gust energy, thus can be used as a measure of the rotors stability performance. A lower deflection showing the rotor is better at absorbing a gust, and will place less force onto the platform itself. Once control of the platforms rotor is used, both the gust response and control response can be used as a benchmark. Figures 16 and Parameter
Lower Rotor
Upper Rotor
l1 l2 Max Pitch Max Roll SS Pitch SS Roll Max Pitch Max Roll SS Pitch SS Roll
Table 4. Analysis Results Feedback 1 Feedback 2 25 15
Units mm
Base Craft -
mm
-
15
° ° ° ° ° ° ° °
-5.64 0.35 -5.55 0.38 -
-5.03 2.82 1.39 -2.53 -4.32 3.16 0.86 -2.32
10
Feedback 3 25
Feedback 4 15
Feedback 5 15
25
-15
-25
15
-5.53 1.12 3.87 -2.26 -5.21 1.76 2.74 -2.76
-5.65 -1.59 2.51 1.86 -5.61 -1.79 3.34 2.61
-5.40 -3.23 0.93 1.91 -5.11 -3.76 1.04 2.32
-5.40 1.86 2.73 -2.82 -4.93 2.47 1.67 -2.83
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Figure 15. Feedback Craft – Rotor Gust Response
Figure 16. Feedback Craft – Rotor Control Response
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flight characteristics. This future design study will include changes to the blade configuration, as compared to keeping it consistent with the base design. Allowing both the blade design and the flapping feedback mechanism to be varied will provides an analysis which contains a larger range of possible configurations. This versatility will allow a global optimisation of the platform configuration to be performed, and result in an efficient rotorcraft platform which can be designed around any takeoff weight and mission specifications.
response is gauged be steady-state flapping deflection. The gust and control response of the rotor varies widely with variation of the control lengths. When the ratio of the control linkage lengths ( l1 and l2 ) is large, the change in blade pitch with flapping angle is also large. Thus, as the blades are already operating near stall they can easily reach stall. This will manifest as a degradation of the overall rotor performance, as can be seen by the lower magnitudes in the Feedback 1 and 3 configurations. To ensure that the rotor remains below stall, a low change in pitch angle and thus low linkage ratio is required. The results of a lower linkage ratio are shown on the Feedback 2, 4 and 5 configurations. Each of these configurations has a gust response which is comparable to the base design, while also displaying excellent control authority. The performance of a platform design around the base configuration can be improved by applying a flapping feedback control configuration with a control linkage ratio less than 1. By providing control authority as well as the base stability, a new platform which far surpasses the original can be designed.
References 1. US Department of Defence. Unmanned Systems Roadmap 2007-2032, US DoD, Washington, USA, 2007 2. Wong, K.C., Guerrero, J.A., Lara, D. and R. Lozano, Attitude Stabilization in Hover Flight of a Mini Tail-Sitter UAV with Variable Pitch Propeller, Proceedings of the International Conference on Intelligent Robots and Systems – IROS 2007, San Diego, CA, USA, 29 October – 2 November 2007. 3. Stone, R.H., Aerodynamic Modeling of the Wing–Propeller Interaction for a Tail-Sitter Unmanned Air Vehicle, Journal of Aircraft, January-February 2008, Vol. 45, No. 1, pp 198210 4. Stone, R.H. et al., Flight Testing of the T-Wing Tail-Sitter Unmanned Air Vehicle, Journal of Aircraft, April-March 2008, Vol. 45, No. 2, pp 673-685 5. Muren, P., Passively Stable Micro VTOL UAV, Proxflyer AS, Norway, 2004 6. Proxflyer Website, http://www.proxflyer.com, Accessed May 2008 7. Hall, A.P.K, Wong, K.C. and Auld, D., Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA-2006-7076 8. Hall, A. and Wong, K.C., Development of an Analysis Package for Increased Stability RotaryWing Micro Air Vehicles, 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, Australia, 2007 9. Johnson, W., Helicopter Theory, Princeton University Press, Princeton, N.J., 1980 10. Moriarty, P. J. and Hansen, A. C., AeroDyn Theory Manual, National Renewable Energy Laboratory, NREL/TP-500-36881, Golden, Colorado, U.S.A., 2005. 11. Leishman, J. G., Principles of Helicopter Aerodynamics., Cambridge University Press, New York, N.Y., 2000, 12. Airscooter Website, http://www.airscooter.com, AirScooter Corporation, Accessed May 2008 13. Airscooter G70 UAV, http://www.airscooter.net/assets/G70_uav.jpg, AirScooter Corporation, Accessed May 2008
Conclusion An analysis tool which accurately models the rotor dynamics and performance of a platform with similar configuration to the Proxflyer has been developed. This tool allows the rotor flapping dynamics as well as its performance to be examined for a wide range of rotor and blade configurations. In addition, it also allows new configurations to be created and tested with special attention paid to the effect on rotor dynamics. In particular it has allowed the conceptual design of a new platform. Analysis of the base and flapping feedback platform configurations shows that the new design exhibits excellent stability and controllability characteristics. Flapping feedback augments the blade pitch angles as a function of the flapping angle, resulting in gusts being absorbed more efficiently. As well as displaying positive stability characteristics, use of flapping feedback allows direct control of the rotors. Direct rotor control provides significantly better control authority than the base Proxflyer configuration. For this base configuration, a basic flapping feedback design has been presented which shows the benefits of using this design feature. Further analysis of these design features will result in a platform configuration with better
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Coaxial Aero-Mechanical Analysis of MAV Rotorcraft with Rotor Interaction for Optimisation Alexander P. K. Hall * The University of Sydney, Sydney, New South Wales, Australia, 2006 K. C. Wong † , Doug Auld ‡ The University of Sydney, Sydney, New South Wales, Australia, 2006
This paper outlines extensions which have been made to an analysis package for use with Coaxial MAV Rotorcraft. Of greatest note is the change which provides a method for analysing the interaction between coaxial rotors. The method which allows the interaction of coaxial rotors is outlined to display the underlying principles. It is then benchmarked against experimental data to show the validity of the method. An implementation of the interaction method is then shown as through the Aero-Mechanical analysis of a set of coaxial rotors. By developing the already proven analysis techniques to include performance changes provided by the coaxial rotors a more refined analysis tool has been created. Thus, as the analysis tool now better models coaxial rotor dynamics, it can be more reliably used to perform aircraft configuration design optimisation.
Nomenclature B c CL dr dT F, f J MAERO MGRAVITY MINERTIA r R VH, VZ
v
inf , ,
U
= = = = = = = = = = = = = = =
number of rotor blades chord of blade section coefficient of lift of blade section span of blade section thrust component of blade section Prandtl Tip Loss Factor and Intermediate Factor rotational moment of inertia aerodynamic forcing moment gravity forcing moment inertial forcing moment radial location of blade section radius of rotor horizontal and vertical velocity components induced inflow over blade section influence velocity over blade section
= flap angle, velocity and acceleration = air density = local flow angle
I.
Introduction
NMANNED Aerial Vehicles (UAVs) have become a highly utilised aircraft type. The variety of applications is as varied as the platforms types used. Initially, UAVs were the domain of fixed wing aircraft. However, there is an ever increasing trend for UAVs to be utilised for intra-urban environments. Therefore, this trend has increased the requirement for helicopters and other rotorcraft to meet these roles as UAVs. Furthermore, a large range of aircraft
*
Postgraduate Student, AMME, The University of Sydney, Student Member AIAA Senior Lecturer, AMME, The University of Sydney, Senior Member AIAA. ‡ Senior Lecturer, AMME, The University of Sydney †
1 American Institute of Aeronautics and Astronautics
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configurations can be used to meet these developing requirements. UAVs allow unusual designs to be investigated for use to meet specialised mission applications1. Accurate and realistic performance analysis tools are essential for the design of any aircraft. The degree of complexity of the tool is highly dependant on the type of aircraft being designed and the level of detail required. This is especially true when looking at helicopter design and even more pertinent when coaxial rotors are being analysed. For the design of UAVs, accuracy must be maintained even though a smaller computational budget is often assigned. The design of a coaxial rotorcraft UAVs requires unique design tools to analyse the performance and suitability of a range of designs. One particular coaxial rotorcraft design which shows promising stability characteristics is the Proxflyer© type craft1. This design type employs a unique fully flapping rotor that helps to increase the aircrafts’ stability when subjected to external disturbances. The combination of fully flapping rotors, and the proximity of the coaxial rotors makes the analysis of this craft difficult. However, the benefits of this aircraft seen in-flight indicate the advantages of this design. To improve upon the promising characteristics displayed, a more detailed analysis of this design must be made. This paper presents work undertaken to develop a simple analysis package into a more detailed design tool. Previously, only simple blade dynamics have been considered within the analysis of this craft type. The analyses from previous papers8,9 were based on Blade Element Momentum Theory (BEMT), Prandtl Tip Loss Modelling and Simple Rotational Equations of Motion. To gain a more realistic estimate of the performance of the coaxial rotors, modelling which represents the interaction between the rotors has been included. Subsequently, a more detailed implementation of the original analysis has been made, including interaction modelling. Thus, a design tool has been created to analyse the performance of the Proxflyer© type rotors, and allow further design studies to be carried out.
II.
Previous Work
One of the earliest analysis techniques use to analyse helicopter rotor loading is the Blade Element Method. First used for propellers3 it now has a variety of uses for helicopter rotors. Comprehensive analysis packages such as CAMRAD II4 and 2GCHAS5 have been developed to conduct a detailed analysis of an entire helicopter. These comprehensive tools perform extremely well as an in depth analysis of an existing or final design. However, a more general tool is required for design or optimisation. Tools for Wind Turbine analysis, such as AERFORCE6 and AeroDyn7 show much promise for crossing over to rotorcraft design. Previous work by the author8,9 discusses a simple method for the analysis of highly dynamic coaxial rotors, as seen on the Proxflyer. In these papers it has been shown that this analysis method performs well when modelling the behaviour of Proxflyer type rotors. However, while the actual rotor dynamics are modelled well, the method does not allow for any mutual interaction between rotors. As helicopter performance is dominated by the performance of rotors, any factors which adversely affect the accurate analysis of rotor performance need to be improved. This is especially important when coaxial rotor performance is being analysed. Results from these first implementations show promise as a starting point. Leading to the developing an analysis package which can be utilised as a design tool. However, a method for modelling the coaxial rotor interaction must be developed and included. Coaxial rotorcraft design is generally approached in much the same way as a conventional helicopter. However, more focus needs to be placed on the aerodynamics surrounding the rotors. Extension of existing analysis techniques to account for rotor interaction can be made through various methods. Generally the simplest method for taking interaction into account is by applying an empirically derived augmentation to the forcing of each rotor. To do this, experimental data must be used to find the augmenting factor to apply to the rotors. Sources such as Wainauski & Vaczy10 and Harrington11 provide a convenient range of data to produce such a relationship. Applying an augmentation factor will provide a good representation for the overall change in performance. However, it will not allow the changes to the distribution of forces and moments over the disc to be seen. Having an accurate loading distribution is important when studying rotor dynamics. To account for this, a method which combines with the overall analysis method must be used. A common technique used to analyse helicopter rotors is Vortex methods. As such, a wide variety of methods for adapting this method to coaxial rotors has been made. Krothapalli et al.12, Theodore & Celi13,14, Anikin15 and Griffiths & Leishman16 all discuss the use vortex methods to analyse the performance of coaxial rotorcraft. The implementation of these methods is too complex to be used in a simple analysis tool. These interaction methods also cannot be used as they are based on Vortex analysis rather than blade element momentum theory. To develop a technique which can be combined with BEMT, methods which use direct flow characteristics must be examined. Colehour et. al.17 use a method which determines a set of influence coefficient matrices from the flow pressures around the rotors. These are then used to apply influence to the rotor. Similarly, Cho and Williams18 use a 2 American Institute of Aeronautics and Astronautics
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panel method to calculate an influence velocity factor to model the influence between the rotors. These two methods provide a convenient starting point to develop an influence modelling method for use with BEMT. Specifically, calculation of an influence velocity from the BEMT flow model will be used to apply the effect of the rotors on each other.
III.
Approach
By limiting the analysis to the aero-mechanical behaviour of the rotors of the Proxflyer©; the overall implementation will be simplified. As the main flight region of these aircraft is centred around hover and slow translation, limiting the analysis to these conditions is appropriate. Simple analysis techniques will also be used to ensure that the overall complexity of the analysis code is kept to a minimum. To help keep the complexity of the code to a minimum, a number of assumptions have been made. These assumptions are based on those used in the previous work by the author. These are summarised below
Rotor blades are modelled as rigid beams connected rigidly to the hubs. Each blade pair experiences the same deflection. Platform flight region is hover, thus no craft dynamics are modelled.
Aside from those listed above, a number of other assumptions have been made to simplify inclusion of the rotor interaction. As the interaction model is based upon the mapping of the geometry of each streamtube, simplifications to this geometry are made, and are listed below.
Streamtubes remain perpendicular to the rotor plane Streamtubes act independently Flow between rotors at any given time is steady-state Incompressible Inviscid flow
By applying these assumptions the model of the streamtube is greatly simplified. This allows the interaction model to be formulated with a greater degree of ease, and the computational overhead for this analysis being reduced significantly. The analysis tool developed models the dynamic behaviour of Proxflyer© type rotors excited by external disturbances. As a result accurate hover region performance data can be generated. Thus the performance of these aircraft can be generated for any number of differing design configurations. By using this type of tool, the design of this type of small rotorcraft UAV can be optimised around stability, controllability and performance.
IV.
Description of Analysis
Three main analysis areas have been combined to produce an overall tool which analyses coaxial helicopter aero-mechanics. Each of these techniques has been chosen to ensure simplicity within both analysis methods and the tool coding. By adhering to simple analysis techniques, the computational expense of the tool is minimised. The three analysis areas are: Rotor Loading Analysis, Rotor Dynamics Modelling and Rotor Interaction Modelling. Both the Rotor Loading Analysis and the Rotor Dynamics Modelling have been discussed in detail within previous papers by the author8,9. Therefore, only a brief overview of each is presented here, with the focus remaining on the rotor interaction method. Each of these is discussed in the following sections below. A. Rotor Loading Analysis Blade Element Momentum Theory (BEMT) has been chosen as the base method to determine the loading distribution over each rotor. BEMT is an iterative method which converges on an induced velocity, . This induced velocity represents the energy increase over the disc, and thus the rotors effect on the stream. To converge on a stable velocity distribution the following two equations (Equations 1 and 2) are used.
dT
4rdr (VZ v )v B
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(1)
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dT C L
2 1 VH 2 VZ 2 cdr 2
(2)
The BEMT method does not account for losses at the blade tips, therefore Prandtl Tip Loss Theory is used to account for this. As outlined by Leishman2, the formulae for this method are shown in equations 3 and 4.
F
2
f
cos 1 (e f )
B Rr 2 r sin( )
(3)
(4)
B. Rotor Dynamics Modelling Simple rotational equations of motion are used to model the flapping of each of the blade pairs. By using a simple method for modelling the blade flapping, all major effects can be easily included. The equation used to model the flapping is shown in Equation 5. Each of the two rotors are broken down into two distinct rotor pairs onto which the rotation equations of motion are applied.
J M AERO M INERTIA M GRAVITY
(5)
C. Rotor Interaction Modelling To account for the effect of two rotors operating in close proximity, a model which represents the rotor interaction must be developed. For this analysis a method which can be described as ‘Velocity Augmentation’ has been developed. As the flow from a rotor is present both up and downstream of the disc plane, a velocity component caused by the rotor will be seen at any point. Although this effect will be small upstream, and have an upper limit downstream, the development of the rotor effect is easy to model. As such, the rotors effect on the stream at the opposing rotors axial location will be used to augment the opposing rotors performance. From Figure 1 it can be seen that at any instant each rotor will have an effect on the other. In this case it is represented by the induced velocity from one rotor having an effect on the other. The Blade Element Method uses a convergence method to find the induced velocity over a blade section. Therefore, the interaction effect will not be correctly represented until both rotors have reached equilibrium simultaneously. This is because the mapped effect from one rotor is used to determine the induced velocity on the other rotor. The inclusion of this effect is shown in Figure 2 as inf . As the stability of the entire solution depends on both rotors reaching convergence, modification of the original blade element method is made. To add the effect of rotor interaction into the blade element method, a second outer convergence loop is used. The outer convergence loop which contains the original BEMT procedure within itself is shown in Figure 3. This diagram shows that at each stage of the outer convergence loop, a new estimate for rotor interaction is made. Estimates for the rotor interaction are calculated from the induced velocity distribution itself. This allows rotor interaction to be introduced into the solution without the need for an additional degree of freedom. By approaching the method in this way, the goal of lower computational expense is maintained.
Figure 1. Velocity Augmentation between rotors. 4 American Institute of Aeronautics and Astronautics
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Determining the value of the influence velocity, νinf, is completed by a process of geometric flow mapping. Contraction of the streamtube flow between rotors is assumed to be constantly linear because the rotor pair are within a diameter of each other. By also assuming that there is negligible rotational effect placed on the stream, mapping of the flow can be reduced to a two dimensional flow section. The two dimensional linear contraction of the streamtubes about the rotor planes is shown in Figure 4. It can be seen that determining the location of an elements influence is now a simple Figure 2. BEMT Velocity diagram with Influence. geometric task. Thus the induced velocity used is also a simple task. The magnitude of the influence effect will only be equal to the influencing induced velocity if the separation between the planes is zero. Therefore, a scaling effect needs to be placed onto the induced velocity to change the induced velocity into an augmenting velocity. By using the stream development factor, k d , the scaling to the influence can be made as shown in Equation 6 (taken from McCormick19). The resulting value is then included within the BEMT calculations, and combined with the outer convergence loop rotor interaction is now included within the rotor loading model.
kd 1
Figure 3. Rotor Interaction Outer Convergence Loop
s s R2 2
(6)
Figure 4. Rotor Streamtube Contraction with Rotor Flapping
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V.
Results
To demonstrate the validity and versatility of the developed analysis method a set of results has been generated. As the base analysis method has been tested previously, only the new elements of the analysis tool will be tested. This includes verification of the interaction method through an experimental test, and display of the complete analysis tool to illustrate its’ use. These two areas are discussed independently in the following sections. A. Rotor Interaction Verification To verify the rotor interaction model, a given rotor Table 1. Interaction Verification Geometry configuration can be analysed and then verified through Parameter Value experiment. In this case the set of rotors used was custom built with an approximate diameter of 450mm; exact B 4 dimensions of the rotor are shown in Table 1. The rroot 50 mm experimental setup involves placing the rotors with their 225 mm rtip gearbox on top of a 6-axis load cell and measuring the 32 mm croot loads produced at varying rotor speeds. This setup is 18 mm ctip shown in Figure 5. 15° θroot Each of the rotors was run through a range of speeds 6° θtip from 0 to 2000 RPM with 500 RPM intervals. This Blade Section Curved Flat Plate provides a range of data to benchmark the coded method Rotor Separation 100 mm against. At each combination of rotor speeds, the rotor is repeatedly run in the following pattern: 0 RPM → TEST RPM → 0 RPM. This allows a number of test points to be gathered and thus the mean and standard deviation of the test data can be found. By completing this test schedule for the given configuration, the variation of the lower rotors speed for a constant upper rotor speed can be derived, and compared to the analysis tool. Figure 6 shows the thrust produced for variation of the lower rotor with an upper rotor speed of 1500 RPM. It can be seen that although the code predicted results are not exactly the same as the experimental data, the trend matches well. It can also been seen that analysis with rotor interaction far outperforms analysis without interaction. A similar trend is seen for the full range of upper rotor speeds, thus showing that the analysis tool performs well over the entire range of rotor speeds. It has been shown above that although the trend of the code is similar to experiment, the absolute thrusts do not match. Figure 7 shows the percentage variation from experiment which is seen between the coded method and experiment across the entire rotor speed range. Although the range of errors up to approximately 20% may seem Figure 5. Rotor Experimental Setup. large, it is within the expected range. The major reason this variation occurs is due discrepancies in the 2D sectional aerodynamic data. For the coded implementation aerodynamic data with a Reynolds number of 60,000 was used, whereas within the experiment the rotors always operate at or below 45,000. In this region it is difficult to obtain accurate aerodynamic data, and therefore a larger error than usual is expected.
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Figure 6. Thrust Produced for Upper Rotor at 1500 RPM; Experimental, Code with Interaction and Code without Interaction
Figure 7. Thrust Variation between Experiment and Code with Interaction
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B. Analysis Tool Results To display the workings of the developed design tool, a sample set of analysis results has been generated. The analysis results pictured here are for a Proxflyer© type platforms with a larger rotor diameter than any of the existing Proxflyer© designs. The geometry and parameters of the aircraft configuration to be analysed are shown in Table 2. This rotor geometry has been analysed for cases with and without interaction and show distinctly different results. A summary of the results from each of the analysis cases are shown in Table 3. While Figures 8 to 11 show the rotor response to an external pulse gust input of 5ms-1 and an RPM sweep about the hover rotor speeds. The difference in both the rotor performance in terms of hover speed, power requirements and dynamic motion can easily be seen. This shows the effect that the interaction modelling has on the overall aeromechanical analysis of a given rotor configuration. From this set of data it can be seen that the analysis tool can readily be used to perform overall platform configuration analysis. And as a result, it can be used to perform design optimisation to find the best configuration for a given set of platform performance goals.
Table 2. Results Craft Geometry Parameter Value B 4 rroot 50 mm 300 mm rtip 25 mm croot 15 mm ctip 20° θroot 10° θtip Blade Mass 20 g Craft Mass 500 g Section per Blade 50 Blade Section NACA0012 Rotor Separation 150 mm Table 2. Analysis Results Parameter With Without Interaction Interaction Total Thrust (N) 4.905 4.905 Rotor Speed (RPM) 1027.3 935.5 Power – Upper (W) 7.874 5.937 Power – Lower (W) 6.943 5.937 Residual Torque (Nm) 0.00866 0.0
Figure 9. Gust response without Interaction Modeling.
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Figure 9. Gust response with Interaction Modeling.
Figure 10. RPM Sweep without Interaction Modeling. 9 American Institute of Aeronautics and Astronautics
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Figure 11. RPM Sweep with Interaction Modeling.
VI.
Summary
A fully functional analysis tool has been developed which can be used to analyse the dynamic rotor performance of a Proxflyer© type craft. This tool is able to be used to analyse any given rotor configuration under a variety of external inputs. To further refine the accuracy of this tool, an analysis method which models the interaction between coaxial rotors has also been formulated and implemented. The interaction modelling method was benchmarked against experimental test data and matched well. By combining this method into the original analysis tool, performance of coaxial rotorcraft can be reliably analysed under various conditions.
References 1
US Department of Defence. “Unmanned Systems Roadmap 2007-2032”, US DoD, Washington, USA, 2007 2 Proxflyer AS, “Proxflyer Website”, Proxflyer Website., URL: http://www.proxflyer.com/ [cited 2 February 2008] 3 Leishman, J. G., “Principles of Helicopter Aerodynamics”., Cambridge University Press, New York, N.Y., 2000, pp. 78 4 Johnson, W., “CAMRAD II, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dyanmcis.”, Johnson Aeronautics, Palo Alto, California, 1992-1997. 5 Rutkowski, M. J., Ruzicka, G. C., et al., “Comprehensive Aeromechanics Analysis of Complex Rotorcraft Using 2GCHAS.”, Journal of the American Helicopter Society, Vol. 40, No. 4, 1995, pp. 3-17. 6 Björk, A., “AERFORCE: Subroutine Package for unsteady Blade-Element Momentum Calculations.”, FFA, TN 2000-07, Bromma, Sweden, 2000. 7 Moriarty, P. J. and Hansen, A. C., “AeroDyn Theory Manual.”, National Renewable Energy Laboratory, NREL/TP-50036881, Golden, Colorado, U.S.A., 2005. 8 Hall, A., Wong, K.C. and Auld, D., “Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation”, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA-2006-7076 9 Hall, A. and Wong, K.C., “Development of an Analysis Package for Increased Stability Rotary-Wing Micro Air Vehicles”, 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, Australia, 2007 10 Wainauski, H. S. & Vaczy, C. M. (1986), “Aerodynamic peroformance of a counter rotating prop-fan”, in ‘22nd ASME, SAE, and ASEE Joint Propulsion Conference’, AIAA.
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11 Harrington, R. D. (1951), “Full-scale-tunnel investigation of the static-thrust performance of a coaxial helicopter rotor”, Technical Report NACA TN 2318, National advisory Committee for Aeronautics, Washington USA. 12 Krothapalli, K. R., Prasad, J. V. R. & Peters, D. A. (2001), “Helicopter rotor dynamic inflow modeling for maneuvering flight”, Journal of The American Helicopter Society 46(2), 129–139. 13 Theodore, C. & Celi, R. (1998), Flight dynamic simulation of hingeless rotor helicopters including a maneuvering free wake model, in “54th Annual Forum of the American Helicopter Society”, The American Helicopter Society, The American Helicopter Society. 14 Theodore, C. R. & Celi, R. (2000), Flight dynamic simulation with refined aerodynamics and flexible blade modeling, in “56th Annual Forum of the American Helicopter Society”, The American Helicopter Society, The American Helicopter Society, Virginia Beach, Virginia. 15 Anikin, V. A., “Aerodynamic Features of a Coaxial Helicopter.”, 17th European Rotorcraft Forum, Berlin, Germany, 1991. 16 Griffiths, D. A. & Leishman, J. G. (2002), A study of dual-rotor interference and ground effect using a free-vortex wake model, in “58th Annual Forum and Technology Display of the American Helicopter Society”, The American Helicotper Society. 17 Colehour, J. L., Davenport, F. J. and Sokhey, J. S., “Analysis of Counter-Rotating Propeller Performance.”, AIAA 23rd Aerospace Sciences Meeting, AIAA, Reno, Nevada, U.S.A., 1985. 18 Cho, J. and Williams, M. H., “Counter-Rotating Propeller Analysis Using a Frequency Domain Panel Method.”, Journal of Propulsion, Vol. 6, No. 4, 1989, pp. 426-433 19 McCormick, B. W., “Aerodynamics of V/STOL Flight” ,Dover, Mineola, New York, 1999
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Development of an Analysis Package for Increased Stability Rotary-Wing Micro Air Vehicles Alexander P. K. Hall*, K. C. Wong+ * Postgraduate Student, School of Aerospace, Mechanical and Mechatronic Engineering (AMME), The University of Sydney, NSW 2006,
[email protected] + Senior Lecturer, AMME, The University of Sydney, NSW 2006,
[email protected]
ABSTRACT Recently, the advent of new electronic technologies has allowed the miniaturisation of many electronic components commonly used in Aerospace applications. This advent of these technologies gives rise to the need for new generations of small autonomous platforms in many Aerospace applications. In particular, the need for new platform designs to support operations within urban environments has risen dramatically. One platform type that is suited well to operations within urban environments are RotaryWing platforms. Design optimisation provides a tool that is ideally suited for increasing inherent stability of a Rotary-Wing Micro Air Vehicles (MAVs). However, to use such a design tool an analysis package suited to the task is required. This paper discusses the current research being undertaken into the development of analysis package for Rotary-Wing Micro Air Vehicles (MAVs). The analysis package in question has been specifically formulated for analysis of Rotary-Wing MAVs for use with optimisation. The type of platform in used as a basis for the development of the analysis package is the Proxflyer© type craft. This craft uses a Co-Axial Contra-Rotating rotor system with a free-flapping/teetering hub design. Increased inherent stability characteristics, both dynamic and static, are displayed by this platform design. As such, this provides both a grounding model for the development of the analysis package, as well as a starting point for the optimisation process.
Notation B c CL CD CM dT F f J C K R r dr VH VM VT VV VZ W
Number of Rotor Blades Blade Section Chord Coefficient of Lift Coefficient of Drag Coefficient of Pitching Moment Elemental Thrust Prandtl Tip Loss Factor Pradntl Intermediate Factor Rotational Moment of Inertia Rotational Damping Constant Rotational Spring Constant Rotor Radius Elemental Radial Location Elemental Width Horizontal Velocity Motion Velocity Tangential Velocity Vertical Velocity Vertical Motion Velocity Resultant Velocity Element Angle of Attack Flap Angle
m N kgm2 Nms Nm m m m ms-1 ms-1 ms-1 ms-1 ms-1 ms-1 rad rad
Flap Rate
rad s-1
Flap Acceleration
rad s-2
Inflow Angle
rad
Geometric Blade Angle Inflow Velocity Air Density Local Inflow Angle Rotor Rotation Velocity
rad ms-1 kgm-3 rad rad s-1
Introduction Recent trends in the aerospace industry are tending to focus more on the use of Unmanned Aerial Vehicles (UAVs). As such, a number mission profiles that are traditionally assigned to manned aircraft are now being re-developed for use with UAVs. Unmanned craft have significant benefits over manned craft due in no small part by not having to accommodate a pilot. Without the need for a pilot, the aircraft design process can be centered around the mission rather than the safety of the pilot. This helps to reduce the design, manufacture and testing programme duration. With these benefits UAVs have become more prevalent within the aerospace industry. The range of mission profiles which UAVs can be used for is ever expanding. From military surveillance and combat to civilian weather observations and aerial photography, UAVs can be used for a wide variety of applications. Within both
Presented at the 6th Australian Vertiflite Conference on Helicopter Technology, Melbourne, VIC, March 19-22, 2007. Copyright © 2007 by the American Helicopter Society International, Inc. All rights reserved.
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military and civilian operations, mission profiles are heavily dominated by the urban environmental. However, urban environments provide challenging to all platform types. Cluttered environment, wind gusts and dynamic obstacles are just a few of the obstacles UAVs face when operating within these environments. While fixed-wing craft can operate at higher altitude above these regions, rotary-craft can navigate closer to the obstacles; thus proving more useful for profiles which require operation in close quarter operations. Development of rotary-wing UAVs has followed that of their fixed-wing UAV counterparts much similar to manned aircraft. In comparison to fixedwing UAVs, the development of rotary-wing craft has lagged for a number of reasons. METTLER, DEVER and FERON1 state that a benefit of rotarywing UAVs is their ability to adopt steady hover and direct motion about all axes. However, they suffer from extensive stability issues. Similar stability issues are seen in full size rotary-wing craft; however manifest themselves more with reduction in scale to UAV size. A commonly used option for countering these instabilities is to augment the craft stability with a control system. Stability augmentation, through the use of a control system reaps extremely good results. However, with limited space and often development budget, a rotary-wing Micro Aerial Vehicle (MAV) has limited practicable use for a stability control system. An option that has great potential for rotary-wing MAVs is to develop a craft that has increased inherent stability. By using a craft design which has increased stability characteristics within the physical design itself, a stability augmentation system can be eliminated. The Proxflyer©2 concept, shown in Figure 1, has shown itself to possess increased inherent stability without augmentation. Using this craft design as a starting point, a craft that has further increased stability and controllability can be developed. To design this craft, an analysis package needs to be developed which accurately models the stability and control characteristics of the Proxflyer© type craft. Subsequently, this tool can then be used to optimise the craft design for more favourable stability and control characteristics. This paper presents work that has been conducted into the conceptual development of an analysis package that models the Proxflyer© flight characteristics. By using simple analysis techniques, assumptions and appropriate implementation, the development of an analysis tool can be made. This tool used in conjunction with a design optimisation scheme can be used to find a global craft designed optimised for stability and controllability.
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Figure 1. Proxflyer© Craft2
Background Developing new rotary-wing aircraft designs which attempt to increase stability is not a new research area. It is common knowledge that helicopter and rotary-wing platforms have a distinct set of instabilities which pose difficulties to their operation. As stated previously, a common method for solving this problem is to place a control system which augments the state response of the aircraft. This can be achieved through the use of a pilot, or for more challenging environments an electronic control system. However, the use of a control system is not the optimal solution for a small-scale rotary-wing platform design point of view. The designers’ approach would be to improve upon the stability through the aeromechanical design of the craft. Traditionally the rotary-wing designer would tend to use a trial and error method for improving upon stability characteristics. With the advent of ever increasing computational power, the designer can now make use of analytical and numerical analysis tools within the design process. Further to the use of these analysis techniques is the more recent introduction of design optimisation. Design optimisation allows an analysis package to be used to develop a globally optimised solution to a given problem. This type of process requires that the analysis package display properties that are beneficial to the optimisation process. These properties include but are not limited to Accuracy, Usability and Stability. Many analysis packages already exist for analysis of rotary-wing aircraft, many of these tools display characteristics that are beneficial for design optimisation. However, if design optimisation is to be used with a genetic algorithm a large number of function evaluations need to be made. Thus, many of the more computationally expensive packages become unsuitable; such as CAMRAD II3 or 2GCHAS4. Alternate to these types of analysis packages, less computationally expensive packages can be used; such as AERODYN5 or AERFORCE6. These packages are more modular and require the use of other packages to run effectively. Despite these dependencies, modular tools have all the
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characteristics required by design optimisation and they also have lower a computational expense. Analysis and design optimisation conducted on a Proxflyer© type platform begins at a reasonably unknown point. This is due to the uncertainty of the internal working of the aeromechanical design of the craft. Given this uncertainty, a lower level of accuracy within the analysis tool must be accepted and accounted for. A modular analysis tool that has a lower computational expense is ideally suited for use with the analysis of a Proxflyer© type craft. Lower computational expense also allows for a greater number of function evaluations to be made, which may be required to reach global optima. To begin the design optimisation process, an analysis tool which models the characteristics of a Proxflyer© type craft must be developed.
Figure 2a. Proxflyer ‘Picoflyer’7
Increased Inherent Stability Craft The Proxflyer© type craft is a concept for rotarywing aircraft which displays increased inherent stability flight characteristics. This concept for increased stability craft has been applied to a number of different scales of craft. Craft sizes range from the tiny ‘Picoflyer’7 weighing in at 3.3g; to the largest craft, ‘Mosquito’8, weighing in at 110g with a 360mm rotor diameter. Both of these craft are pictured in Fig 2a,b. Proxflyer© has developed a number of craft sizes, which are summarised in Table 1 below. These craft achieve their unique increased inherent stability through the use of a number of different design features. The majority of these design features are centered on the rotor hubs, which contribute significantly to its improvements in stability. The rotor hubs are arranged in such a way to allow the four bladed rotors to act as if they has two distinct blade pairs (Figure 3). These blade pairs are created through the use of a hub which allows two perpendicular flapping motions. By separating and joining the two blade pairs (pictured in Figure 4) each pair is allowed to flap independently. The second major design feature which contributes to increased stability is the counter-rotating rotors. This counter-rotation eliminates the differential torque effect and combines with the independent flapping hubs to help reject external perturbations.
Figure 2b. Proxflyer ‘Mosquito’8
Figure 3. Increased Stability Hub
Longitudinal Pair
Table 1. Proxflyer© Craft Geometry2
Craft Picoflyer Nanoflyer Microflyer Blade Runner Mosquito Mosquito Twin-Tail
Rotor Diameter (mm) 60 85 128 290 360 360
Mass (g) 3.3 2.7 7.8 50 110 130
Lateral Pair
Figure 4. Blade Pair Breakup
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Development Goals Successful outcomes from this project require that the overall goals for each stage of the project to be defined. The goal of this project is to develop a rotary-wing UAV which has increased inherent stability. However as stated previously, this overall goal needs to be split into subset goals. One of the key goals for the entire project, and specifically for this paper, is to develop a framework for analysis of a Proxflyer© type craft. Analysis of the Proxflyer© type craft needs to be set out in such a way as to allow easy integration with an optimisation scheme. For success Salas and Townsend9 suggest that a framework for the analysis tool as well as that for the optimisation scheme be used. They go onto suggest that the framework for analysis tools should follow the same path as that for the optimiser itself. The key bases for this framework are: Architectural Design, Problem Formulation Construction, Problem Execution and Information Access. By following this framework, the goals for the analysis tool can be met more easily. For successful integration and use with an optimisation package, the analysis tool needs to follow the suggested framework. However, a distinct set of goals should also be adopted for the development of the analysis tool itself. These goals contribute to decisions made whilst formulation to the direction of the overall tool. Analysis of small rotary-wing UAV platforms should include the follow goals: Accuracy Simple Techniques Easy Implementation Quick Run Times Should all of these properties be followed, optimisation towards a global optimum can be reached more easily. By combining these goals for the analysis tool with the framework required by Salas and Townsend, a tool which performs well under optimisation can be developed.
Analysis Tool Development Design optimisation process is heavily dependent on the appropriate development and use of the analysis tool or tools used. Therefore the techniques on which the analysis tool is based upon and how they are used is of especial importance. There are three major components of the development process which contribute to this development and thus need to be discussed in detail. These components used are: Assumptions
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Analysis Techniques Implementation Each of these contributing factors to the overall development of the analysis tool are outlined in detail in the following sections. Assumptions Use of simple analysis techniques within the development of this analysis tool already lends itself to reduced computational expense. However, to achieve realistic function evaluation times, a further reduction in computational expense must be made. This is of foremost importance for use with rotary-wing craft due to the complex nature of the system dynamics. Analysis of a Proxflyer© type craft lends itself to making a number of assumptions which allow the level of complexity to be reduced whilst maintaining a reasonable level of accuracy. Maintained levels of accuracy continue in line with reduced levels of accuracy required by high a high number of function evaluations. As further detailed analysis on the globally optimal craft configuration will be performed once this configuration is reached. Base craft configuration parameters of the Proxflyer© type craft include a number of features which can be easily replicated within analysis with a number of simple assumptions. First and foremost is the isolated teetering hub design, which is most likely key to its increased stability. Assuming that the rotor blades can be modeled as rigid beams which are rigidly fixed to the rotor hub allows the rotors to act in an isolated manner (described above). This rigidity within the blades themselves, as well as in relation to the rotor hubs will accurately model their isolated flapping motion. To strengthen the modeling of the rotors as acting independently, the hub can be broken into two separate flapping pairs. These blade pairs then act as a single oscillating beam which allows the actual rotor flapping to be modeled simply. An important initial assumption which has been made is that each of the rotors does not have any aerodynamic influence upon each other. This assumption is made to reduce the initial implementation complexity of the analysis tool. However, this assumption can be easily reversed once a working tool has been developed. Thus, allowing a factor which will be important to the accurate modeling of the craft to be introduced at a later date. A summary of the assumptions made are listed below: Rotor blades are modeled as rigid beams Rotor blades are rigidly connected to hub Isolated flapping of blade sets Isolated rotor aerodynamics
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Techniques Each of the following three sections describes the development, implementation and use of the major analysis techniques used. Analysis performed on this type of craft is heavily reliant on the forcing that is applied to the body of the craft. To model the forcing experienced by each of the rotor blades, and thus the craft as a whole, Blade Element Momentum Theory (BEMT) is used. As aerodynamic losses at the blade tips are not accounted by this theory, Prandtl Tip Loss Theory is applied to the blade loading. The dynamics of the rotor system can be modeled through the use of Rotational Equations of Motion with major forcing supplied by the blade loads. These major analysis techniques account for the most variability within the system dynamics. And thus, will allow dynamic modeling of the entire craft to be eventually conducted. Blade Element Momentum Theory As mentioned above, the most important subset of analysis techniques is the use of Blade Element Momentum Theory to model blade loads. BEMT is an analysis technique which easily allows the aerodynamic loads on a rotor or propeller to be determined. As its name suggests BEMT uses two distinct first principle analysis methods to determine the blade loading; these being Aerodynamic Theory and Momentum Theory. To begin BEMT analysis, the continuous geometry of the rotor blades must be split into a discrete number of blade sections. Each of these blade elements then has a set of known geometric properties which then allows individual analysis. When the given geometric properties are known and combined with its flow properties, the elemental properties can pictured as shown in Figure 5. As pictured in this diagram, an aerodynamic inflow velocity, υ, is induced over the blade section. This inflow velocity needs to be found to be able to determine the aerodynamic loading of the blade element. By using
ν
VZ VM VT
W
Ωr
Figure 5. Element Aerodynamic Diagram
aerodynamic and momentum theory, a convergence loop can be set up to find the inflow velocity. The convergence on inflow is conducted as set out by Johnson10 and summarised below: Determine an estimate for elemental thrust from aerodynamic theory using Equations 1 to 6. 1 dT C L W 2 cdr 2 (1) C L f ( ) (2) W VV2 V H2 V tan V VH 1
(3)
VV V M V Z V H VT r
(4) (5)
(6) Use the above found estimate of thrust and momentum theory, Equations 7 and 8 to solve the quadratic equation for an improved estimate of inflow velocity. 4rdr V Z dT B (7) 2 rdrVZ dT 0 B B (8) Use the first estimate from Step 1 and the new estimate from Step 2 to find a new estimate for the next iteration using Equation 9 next current new 2 (9) Repeat steps 1-3 until the next estimate is within tolerance of the next estimate. Once a converged value for inflow velocity has been found, predictions for the entire element loading can be found from Eq 10-12. 2 1 dL C L VV2 VH2 cdrF 2 (10) 2 1 2 2 dD C D VV VH cdrF 2 (11) 2 1 dM C M VV2 VH2 c 2 drF 2 (12) Prandtl Tip Loss Theory
Blade Element Momentum Theory predicts a continuous blade load distribution from root to tip. BEMT does not have any adjustment for losses that are experienced at the blade tips. Initially this does not seem to cause a large error to the overall lift, drag and pitching moment distributions. However, when the flapping moment applied at the blade hub is calculated a larger influence is seen. A simple numerical adjustment can be applied to the loading distributions after calculation with BEMT through the use of Prandtl Tip Loss Theory.
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Prandlt Tip Loss Theory was developed from experimental observation by Prandtl and turned into a simple relation. This relation is implemented in the form of an adjustment factor, F, which is applied directly to the loading distributions. Two equations shown below, Equations 13 and 14 (sourced from the AeroDyn Theory Manual11 and Leishman12), are used to find the adjustment factor:
F
2
cos 1 (e f )
B Rr f 2 r sin( )
(13) (14)
Rotational Equations of Motion Rotational Equation of Motion are used to model the flap dynamics of the rotors themselves. This is in line with the assumptions made that the rotors act as teetering type rotors which act freely. As stated in the assumptions, this modeling of the teetering is achieved through the use of two distinct sets of equations for each rotor. By modeling each rotor as two beams oscillating about the hub, the physical model of the craft is adhered to. In its raw for Rotational Equations of Motion have spring and damping included within the dynamics. However, there is no external physical spring or damping acting on the system. Therefore, the spring and damping constants can be removed from the equation of motion, as shown in Equations 15 and 16 displayed below. J C K M (15) J M (16) The use of simple rotational equations of motion leads directly to the choice to use Runge-Kutta integration. Runge-Kutta integration performs well when used to model dynamic systems. The
Implementation
Maintaining low computational cost with reasonable accuracy is of utmost importance for this analysis tool. This must not only be reflected in the analysis techniques used, it must also be kept in mind when developing and coding the implementation method. By keeping this goal in mind, a simple yet effective analysis tool implementation can be used to run the entire craft dynamics analysis. The implementation scheme for this tool is pictured below in Figure 6. This layout of analysis technique is essentially what would be expected for any dynamic analysis tool. As such, it follows well documented methods for its implementation and is known to be effective.
Analysis Tool Test Implementation To test the implementation and analysis tool methodology, a set of codes which implements the analysis tool described above has been made. This test implementation has been made to test the feasibility of the analysis tool as a tool to be used with optimisation. Beneficial properties for optimisation have been discussed in previous sections; as such these properties are to be examined with this implementation. Results for this test implementation have been developed in a previous paper by HALL et. al13. This paper describes a more detailed procedure for development of the analysis tool, as well as the actual code implementation. Within this paper results have been generated for a range of craft trim conditions. However, for the current
Get Loads
Input
Trim
increased computational cost, over other Euler Integration, also pays for itself with accuracy generated within the system, leading to accurate answers for a reasonable computational cost.
Current State
Get Rates
Integrate
Figure 6. Analysis Implementation
New State
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Table 2. Craft Geometry
Parameter B rroot rtip croot ctip θroot θtip Blade Mass Craft Mass Section per Blade Blade Section Rotor Speed
Value 4 0.045 m 0.145 m 0.025 m 0.015 m 35° 28° 1.9 g 100 g 50 NACA0012 1000 RPM
implementation example uses these code results to demonstrate the usability of the analysis tool. Craft geometry used for this implementation as well as the transverse wind application speeds are shown in Tables 2 and 3 respectively. The transverse wind speeds shown in Table 2 describe the wind perturbation velocity that is applied to the craft in a trim state. The range of results that have been generated for this craft are only for a single rotor in isolation, as there is no rotor interaction modelled. Raw results for a single wind speed are shown in Figure 7 which describes the flapping
Table 3. Test Wind Velocity
Wind Component XWnd (ms-1) YWnd (ms-1) ZWnd (ms-1)
Initial Value 0 0 0
Final Value 5 0 0
Variation 0.125 -
oscillation of the rotor blade pairs after the wind gust has struck the aircraft. Figure 8 shows these results after post-processing to give the flap deflections with respect to craft fixed axes (described in HALL et. al13). Finally, Figure 9 shows the steady state craft fixed flap deflections for the entire range of wind speeds. These results show how well this analysis tool performs with coded implementation. The run time for each function evaluation is approximately 90 seconds for 2.5 seconds of rotor simulation. This function evaluation run time will be further reduced with more efficient coded implementation of the analysis techniques which have been described. However, this implementation shows that the overall performance of the analysis technique once implemented as an analysis tool is very good, and shows significant promise as a tool for use with design optimisation.
Figure 7. Raw Results - 2ms-1 Transverse Wind Velocity
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Figure 8. Processed Results - 2ms-1 Transverse Wind Velocity
Figure 9. Steady-State Rotor Pitch and Roll Deflections
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Conclusions This paper has summarised the conceptual design process that has taken place to develop an analysis package for increased inherent stability rotary-wing UAVs. By taking into account the project goal of using design optimisation to achieve this improved craft design a number of restrictions have been placed on the development. However, these restrictions have served to help with implementation of first principle analysis techniques. By using these first principle analysis techniques, the analysis tool has been made as simple as possible for a maximum of accuracy. This paper primarily covers the conceptual development of the analysis tool, subsequent development of a coded implementation needs to be finalised. However, the test implementation that has been used to demonstrate the viability of the coded analysis technique shows that an implementation is relatively simple. Further code implementation will be completed using the C++ coding environment to ensure that quick function times are maintained throughout. Both pre and post processing will be required to implement each function evaluation. This is beneficial so as to maintain correct analysis and interpretation of results.
References 1
Mettler, B., Dever, C. and Feron, E., “Scaling Effects and Dynamic Characteristics of Miniature Rotorcraft.”, Journal of Guidance, Control and Dynamics, Vol. 27, No. 3, 2004, pp. 466-478.
2
Proxflyer AS, “Proxflyer Website”, Proxflyer Website., URL: http://www.proxflyer.com [cited 30 October 2006]
3
Johnson, W., “CAMRAD II, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dyanmcis.”, Johnson Aeronautics, Palo Alto, California, 1992-1997.
4
Rutkowski, M. J., Ruzicka, G. C., et al., “Comprehensive Aeromechanics Analysis of Complex Rotorcraft Using 2GCHAS.”, Journal of the American Helicopter Society, Vol. 40, No. 4, 1995, pp. 3-17.
5
Laino, D.J., and Hansen, A. C., “User’s Guide to the Wind Turbine Aerodynamics Computer Software AeroDyn.”, Windward Engineering, Salt Lake City, Utah, U.S.A., 2002.
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6 Björk, A., “AERFORCE: Subroutine Package for unsteady Blade-Element Momentum Calculations.”, FFA, TN 2000-07, Bromma, Sweden, 2000. 7
Proxflyer AS, “Proxflyer Website - Picoflyer”, Proxflyer Website., URL: http://www.proxflyer.com/pi_meny.htm [cited 30 October 2006]
8
Proxflyer AS, “Proxflyer Website - Mosquito”, Proxflyer Website., URL: http://www.proxflyer.com/pf_meny.htm [cited 30 October 2006]
9
Salas, A. O. and Townsend, J. C., “Framework Requirements For MDO Application Development.”, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimisation, AIAA, St Louis, Missouri, 1998, AIAA-98-4740
10
Johnson, W., Helicopter Theory., Princeton University Press, Princeton, N.J., 1980, pp. 37-40, 49-56.
11 Moriarty, P. J. and Hansen, A. C., “AeroDyn Theory Manual.”, National Renewable Energy Laboratory, NREL/TP-500-36881, Golden, Colorado, U.S.A., 2005. 12
Leishman, J. G., Principles of Helicopter Aerodynamics., Cambridge University Press, New York, N.Y., 2000, pp. 102
13
Hall, A., Wong, K.C. and Auld, D., “Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation”, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006, AIAA2006-7076
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Simple Rotor Dynamics Analysis of MAV Rotorcraft for Optimisation Alexander P. K. Hall * The University of Sydney, Sydney, New South Wales, Australia, 2006 K. C. Wong †, Doug Auld ‡ The University of Sydney, Sydney, New South Wales, Australia, 2006
This paper presents the initial work that has been conducted towards the development of a MAV rotorcraft analysis tool for use with optimisation. By using simple first principle techniques, a tool for analysis of increased inherent stability rotors has been developed. Specifically, this is the first step in the development of a complete analysis tool for use with analysis of stability and controllability of MAV rotorcraft. Development of the analysis methods used is discussed in conjunction with the techniques used for implementation of these techniques. Following development of the method, results are shown to illustrate the application of the method. These results are shown to be within reasonable margins of physical results, supporting the validity of using simple analysis techniques for use with analysis of MAV rotorcraft stability for optimisation.
Nomenclature B c CL, CD, CM da, A dT, T F, f J, C, K M P R, r, dr VH, VM, VT, VV, VZ W , , , ,
,
S
= = = = = = = = = = = = =
number of rotor blades chord of blade section coefficient of lift, drag and pitching moment of blade section annulus area and disc area thrust component of blade section and total rotor thrust Prandtl Tip Loss Factor and intermediate function rotational moment of inertia, damping and spring constant moment about rotor hub pressure radius of rotor, radial location of section and blade section span horizontal, motion, tangential, vertical and vertical motion velocity components resultant section velocity blade section angle of attack, inflow angle and geometric angle
= = = = = =
flap angle, velocity and acceleration induced velocity and mean induced inflow over disc air density local flow angle rotor azimuth location rotor rotational velocity
I.
Introduction
INCE the inception of the aviation industry (a period of little more than a century), the range of mission profiles that have been developed for aerial vehicles has been expanded immensely. Those mission profiles suited to
*
Postgraduate Student, School of Aerospace, Mechanical and Mechatronic Engineering (AMME), The University of Sydney, Student Member AIAA † Senior Lecturer, AMME, The University of Sydney, Senior Member AIAA. ‡ Senior Lecturer, AMME, The University of Sydney, Member AIAA. 1 American Institute of Aeronautics and Astronautics
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Unmanned Aerial Vehicles (UAVs) has grown correspondingly. Whilst primarily minimizing the risk to human operators, UAVs can also be a cost effective low risk solution to many of the traditional manned missions. Advances in electronics sensors and airframe materials have also supported this change with an emphasis towards UAVs. Traditionally, UAVs have been designed around a fixed-wing vehicle. It has been shown though that rotary-wing platforms can perform better in specific mission profiles which are now suited to UAVs. METTLER, DEVER and FERON1 argue that by being able to hover and move about all axes, small rotorcraft UAVs perform well in challenging environments. These vehicles, unfortunately, are inherently unstable and this instability becomes problematic when a further reduction in size is applied. Micro Air Vehicles (MAVs) are a subset of UAVs which are an order of magnitude smaller in size than current generation vehicles. The small size of MAVs allows them to conduct missions that would prove problematic for larger vehicles including missions such as hazardous agent detection and covert imaging (BOHORQUEZ et al.2). The smaller size of MAVs leaves little room for a complicated bulky electronic control system and as a result of this, vehicles which provide a larger degree of inherent dynamic stability would be more suited to operating as MAVs. The dynamic stability of a MAV rotorcraft platform is of extreme importance should the vehicle have a mission that incorporates a turbulent atmosphere. Of equal importance is the maneuverability and responsiveness of the vehicle. A method for ensuring that stability, maneuverability and control responsiveness are all within required bounds, is to develop a flight dynamics analysis model for use in conjunction with design optimisation methods. Design optimisation has become a well recognized tool for the development of globally optimal solutions to design problems. When applied to either manned or unmanned rotorcraft, design optimisation is a tool that can be used to simplify the design process (CELI3). LIM and CHOPRA4 explain that in recent years with the increased power of computers this especially has become the case. The use of design optimisation for the development of an increased inherent stability rotorcraft MAV shows potential that is difficult to achieve with other design methods. Developing a new set of analysis codes for use within design optimisation allows this process to be specially tailored to suit the methodology from the outset. Analysis tools for design optimisation should be developed around a similar framework to optimisation packages. Once a specific optimisation package structure has been chosen, coding of an analysis tool will follow a logical framework. SALAS and TOWNSEND5 discuss key framework criteria that should be taken into account when developing a design optimisation tool. The main suggested framework criteria are Architectural Design, Problem Formulation Construction, Problem Execution and Information Access. ISAACS et al.6 suggest that an analysis tool should follow the above framework criteria to ensure optimum communication between the optimisation and analysis packages. A well developed analysis tool should have optimal design, formulation, execution and information access as key features. By developing an analysis tool from first principle techniques, optimisation framework can be followed closely. This paper presents work that has been conducted to develop a simple dynamic analysis model of an increased inherent stability rotorcraft MAV. Currently, only the dynamics of the rotor and blades are being modeled. A set of codes that uses traditional analysis methods with a numerical approach has been developed. Blade Element Momentum Theory has been used for the core aerodynamic force calculations. Adjustments for tip losses, which are seen in all rotor aerodynamics, were performed using Prandtl Tip Loss Theory. Rotational equations of motion were used to analyse the dynamic response of the rotor. Results generated indicate that the set of codes developed produces an accurate model of the rotor dynamics. By using these traditional methods, accurate analysis can be conducted through numerical implementation.
II.
Previous Work
Much work has been has been centered around the development of analytical and numerical tools, to assist with the prediction of rotorcraft performance. Computational analysis tools such as 2GCHAS7 and CAMRAD II8 have been developed for use with full comprehensive analysis tasks. 2GCHAS is a multi-disciplinary tool used for predicting rotorcraft characteristics. CAMRAD II is another comprehensive computational package used for rotorcraft flight performance analysis. Both 2GCHAS and CAMRAD II have multi-disciplinary analysis approaches and as a result have a relatively high computational expense. A less computationally expensive approach to rotorcraft analysis can be achieved through the use of a modular approach. Wind Turbine aerodynamic analysis packages such as AERFORCE9 and AeroDyn10,11 use such a modular approach and show promise for use with rotorcraft. Wind Turbine aerodynamic analysis packages allow the components of analysis to be separated into different packages; allowing the dynamic analysis to be carried out by a
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third party analysis program such as MSC.Adams. By leaving the detailed dynamic analysis to a third party program more emphasis can be placed on the accuracy of the aerodynamic packages. Analysis completed through the use of either a comprehensive or modular approach can be used to model rotorcraft dynamics. Comprehensive analysis has been used on larger projects where computational expense is less of a problem. Modeling of the Apache helicopter by the U.S. Army used this type of analysis with CAMRAD II12. The 2GCHAS set of codes was correlated against experimental data for both the Chinook and Black Hawk13 helicopters, whereas, a modular approach was used to model Wind Turbine Dynamics by Ahlström14. Both methods show potential for modeling the dynamics of rotorcraft MAVs.
III.
Approach
The computational expense of analysis tools used for optimisation must be kept within limits for realistic run times to be achieved. Simple traditional analysis techniques implemented numerically have been used to simplify the overall complexity of the dynamic analysis. By combining these simple techniques with appropriate assumptions, the complexity of the analysis has been further reduced. Analysis has been chosen to be conducted on a Proxflyer© type vehicle (Fig. 1). The Proxflyer© concept shows attributes that are favorable for increasing inherent stability of rotorcraft. Having these characteristics, it has 15 been chosen as a starting point for further development in Figure 1. Proxflyer Type Vehicle this research area. This vehicle has four-bladed teetering hubs which are uncontrolled and free to flap about each blade-set axis. When this rotor design is set up in a co-axial contra-rotating configuration, the dynamic stability of the craft is increased. By using this type of design as a starting point, a set of codes that models the rotor motion has been developed. This allows an optimisation scheme to be used to find a balance between stability and maneuverability. The assumptions that have been made to reduce complexity are : Rotor blades are modeled as rigid beams Rotor blades are rigidly connected to hub Isolated flapping of blade sets Isolated rotor aerodynamics These assumptions allow focus to be placed on the accurate modeling of aerodynamics and dynamic motion. Future development into multi-disciplinary analysis including aeroelastic behavior of blades, coupling between blade sets, aerodynamic interaction between rotors and full craft dynamic motion analysis, will be introduced.
IV.
Description of Analysis
Simple traditional analysis techniques have been used to develop a set of codes to model the dynamic behavior of the rotors described above. Currently, three separate main analysis techniques have been chosen to be used in the dynamic modeling. As previously outlined, these techniques are: Simple Blade Element Momentum Theory, Prandtl Tip Loss Theory and Simple Rotational Equations of Motion. Each of theses techniques is discussed below as well as techniques used for analysis implementation and post-processing. A. Simple Blade Element Momentum Theory Aerodynamic load distribution over each blade is determined by using the Blade Element Momentum Theory (BEMT). This traditional analysis technique breaks each blades into a number of small elements. With geometry and overall flow properties around each of these elements known, an inflow past the element is found. As the name suggests, convergence on the
ν
VZ
W
VM VT
Ωr
Figure 2. Element Aerodynamic Diagram
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inflow over the section is achieved using Momentum and Aerodynamic theory. This allows the aerodynamic loads for each blade section determined. Derivation of the following theory has been adapted from theory presented by Johnson16. The aerodynamic sub-set of equations used within BEMT are developed from simple aerodynamic theory. For use within the convergence part of BEMT only an estimate for the thrust produced by the blade is used. By using basic aerodynamic theory and expanding this for use with BEMT, aerodynamic theory maintains its simplistic nature. This, allows for an efficient, simple implementation within the BEMT code. To determine the thrust produced by a single blade section Eq. (1) is used with components obtained through the use of Eq. (2-6). A graphical explanation of the element aerodynamic properties is shown in Fig. 2. dT C L
1 W 2 cdr 2
(1)
C L f ( )
(2)
W VV2 V H2
(3)
VV VH
(4)
VV V M V Z
(5)
V H VT r
(6)
tan 1
Momentum theory makes up the second sub-set of equations to used within the BEMT code. This part of the code makes use of the momentum theory to allow the iterative process to make the next approximation for the induced flow velocity. By taking standard momentum theory over an entire rotor disk, Eq. (7) and (8) are derived. By expanding Eq. (8) for a given radial location to make annular elements, an entire annulus is represented by Eq. (9). T Pda
(7)
T 2 AVZ
(8)
dT 4rdr V Z
(9)
By focusing the code set around modeling the dynamic motion of the rotor and blades, isolating momentum theory to account for a single blade is needed. This can be achieved by making a simple approximation that the contribution of a single blade is equal to a proportion of the total momentum effect. Thus, for this simple theory, the effect of a single blade can be modeled using a proportion of the total effect. By dividing the total momentum effect by the number of blades, the effect of a single is established and represented by Eq. (10). dT
4rdr V Z B
(10)
Once the inflow velocity, , has been converged upon, the loads which are normal and tangential to the disc plane and the pitching moment for that particular element can be found by using Eq. (11) to Eq. (13). dL C L
2 1 VV2 VH2 cdrF 2
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(11)
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dD C D dM C M
2 1 VV2 VH2 cdrF 2
(12)
2 1 VV2 VH2 c 2 drF 2
(13)
B. Prandtl Tip Loss Theory Uncorrected Blade Element Momentum Theory does not account for loses at the tips of rotor blades. Rotor tip loses significantly reduce the overall lift distribution used to calculate hub moments. A correction factor is needed to adjust for the tip loses. Prandtl Tip Loss Theory has been used to adjust for this correction. The tip loss theory outlined by Prandtl can be expressed through the use of two equations, Eq. (14) and Eq. (15), as outlined in the AeroDyn Theory Manual11 and by Leishman17, and shown below.
F
2
f
cos 1 (e f )
(14)
B Rr 2 r sin( )
(15)
These equations are used to alter the Lift, Drag and Pitching Moment distributions over each of the blades once the convergence on the induced velocity has been completed. For ease of implementation within the BEMT code, the Prandtl Tip Loss Factor (PTLF) is found following the convergence on inflow velocity. This is then applied directly to the equations used to find the Lift, Drag and Pitching Moment, shown in Eq. (11) to Eq. (13). C. Simple Rotational Equations of Motion Flapping of the rotor is modeled by firstly breaking up the rotor into two different flap axes. These flap axes coincide with the two sets of blades, thus allowing easier construction of two sets of equations. This axis breakup is shown in Fig. 3. A simple dynamics model is used to show the rotor motion. This model is implemented by using a set of simple rotational equations of motion, Eq. (16). As a direct consequence of the rotor having no hub spring or damping, is that the equations of motion become even simpler. The final equation used is shown below as Eq. (17). J C K M
(16)
J M
(17)
Longitudinal Pair
Lateral Pair
Figure 3. Blade Pair Breakup
The implementation of the two sets of Rotation Equations of Motion is a simple dynamic motion integration scheme. This integration scheme uses either Euler (for simple first order approximations) or Runge-Kutta (for more dynamically accurate models) integrations methods. D. Analysis Implementation Simple analysis techniques and implementation is of high priority in the development of this set of codes. To ensure that the simple first order analysis techniques are used appropriately, and computational expense is kept to a minimum, a simple implementation scheme needs to be developed. The method used needs to encapsulate all the techniques mentioned above, in an appropriate manner to ensure simplicity. The global analysis run scheme for this set of codes is shown below in Fig. 4.
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Get Loads
Input
Current State
Trim
Get Rates
New State
Integrate
Figure 4. Analysis Implementation E. Post Processing Results produced by the analysis process come out as raw data which displays the pitch and roll flap deflections for the blade pairs fixed to the rotational axis. From this a sinusoidal relationship between the flap deflections and the rotor position is expected. To make either a qualitative or quantitative analysis of the dynamic motion of the rotor, it is desirable to have the rotor flap deflections with respect to the craft axes. The translation between rotor deflections and the craft axis deflections is pictured in Fig. 5. To carry out this translation the relations are shown in Eq. (18) and Eq. (19).
CraftP P cos R cos
2
R
Craft Pitch
(18)
P
CraftR
P cos R cos 2
(19)
V.
Craft Roll
Figure 5. Axis Translation
Results
Proxflyer© type craft are typically operated indoors, adopting flight regimes which centre around a trimmed hover flight condition. To test the initial implementation of the simple analysis code-set, the geometry of the Proxflyer© type craft pictured in Fig. 1 has been used. The geometric properties of this craft are listed in Table 1. A simplified model of this craft has been used to allow Table 1. Craft Geometry the test implementation of the code to run faster. A Parameter Value single rotor model is a valid simplification to make, B 4 because no rotor interactions have been modeled rroot 0.045 m within the code. This assumption will reduce the 0.145 m rtip overall computational expense of each run. 0.025 m croot Assuming a linear variation, from root to tip, of the 0.015 m ctip Blade Chord (c) and Twist (θ) with Radius (r), 35° θroot further reduces the complexity of the model 28° θtip analsyed. Fifty elements have been used to allow Blade Mass 1.9 g accurate results without increasing the Craft Mass 100 g computational expense. This arrangement gives Section per Blade 50 typical analysis run times of approximately 150 Blade Section NACA0012 seconds. Rotor Speed 1000 RPM The test range for implementation is set to a small range of transverse wind velocities. This is 6 American Institute of Aeronautics and Astronautics
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based upon the trimmed flight condition being assumed to be centered on hover. Further limitations of test wind velocities are imposed due to a breakdown of the current implementation of the Blade Element Momentum Theory. By limiting the velocity range to 5ms-1, failure of the BEMT method and thus failure of the program has been avoided. The ranges of wind velocities that have been used for the test range are shown in Table 2. These transverse wind velocities are modeled as a step input of the transverse wind velocity striking the aircraft. This velocity range allows test Table 2. Test Wind Velocity analysis to be conducted over a Wind Component Initial Value Final Value Variation range of velocities that a MAV XWnd (ms-1) 0 5 0.125 rotorcraft may experience around a YWnd (ms-1) 0 0 trimmed hover flight condition. 0 0 ZWnd (ms-1) Analysis runs have been performed for the range of wind velocities and craft geometry described above. Raw results for this analysis have been recorded and then post-processed. This not only allows for further analysis to be performed after the initial analysis run has been completed, but also reduces the computational expense over the analysis run. As analysis of dynamic motion of rotors is the objective of this paper and not the overall dynamic motion of the craft, post-processing involves only the translation of rotor-fixed axes pitch and roll, to pitch and roll about the craft axes. Methods for this post-processing are discussed in previous sections (Eq. (18) and Eq. (19)). Rotor-fixed pitch and roll data produced by these analysis runs has a characteristic sinusoidal look, which qualitatively matches with expected results for rotating devices. A plot of this raw pitch and roll data for a transverse wind velocity of 2ms-1 is shown in Fig. 6. Following the post processing the roll and pitch data are transformed to craft-fixed axes and this data is shown in Fig. 7. This figure also shows the steady-state rotor pitch and roll deflections.
Figure 6. Raw Data - 2ms-1 Transverse Wind Velocity
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Figure 7. Processed Data - 2ms-1 Transverse Wind Velocity By determining the steady-state rotor deflection in the pitch and roll direction, a quantitative value for the effect of the transverse wind velocity can be evaluated. Figure 8 shows the steady-state rotor pitch and roll deflections plotted over the full transverse wind velocity test range.
Figure 8. Steady-State Rotor Pitch and Roll Deflections
VI.
Discussion
Results generated and presented in the previous section show analysis runs that have been conducted for testing of the analysis codes. This implementation of the simple technique has been conducted as the first in a number of steps of the development of a full craft motion analysis package. The purpose of this implementation and testing has 8 American Institute of Aeronautics and Astronautics
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been to establish the potential of the technique for use within the full analysis package. Should analysis of increased inherent stability rotor dynamics in this manner be completed correctly, a solid basis for further development is needed. However to achieve this, the validity of the package needs to be checked. Initial implementations of the analysis technique being developed makes results uncertain. To check and verify these results in strict detail would be costly and unnecessary. This implementation is only a rough first coding of the technique, and the goal of the analysis tool is to develop a package with reasonable accuracy at a low cost to the user. Spending great time and detail to verify the first stage of development would be counter-intuitive. To determine the validity of the analysis technique, checks with physical implementation have been undertaken. A good test for this type of analysis implementation, at this stage of development, is to ensure that the results are of the order of magnitude of physical results. To test the results to this type of level, basic wind tunnel testing has been carried out on an increased inherent stability MAV rotorcraft design. The setup of the wind tunnel testing has been based on the craft geometry that was used to generate the results displayed in the previous section. A craft from which the geometry has been taken was modified to use a single rotor to match the setup modeled. Rotor speed and transverse wind speed were also matched with the analysed configuration. The craft was restrained from its base to ensure minimal interference effects were experienced. Comparisons with the steady-state rotor flap deflections can be made through comparison with photos taken of the rotor, once transient effects have settled out. Lateral and longitudinal steady-state rotor flap deflections are shown in Figures 9 and 10 respectively. By measuring the steady-state flap deflections, displayed in Table 3, it can be seen that Figure 9. Lateral Flap Deflection analysis results correlate with physical results. Rotorcraft analysis packages that are suited to analyzing increased inherent stability craft come in a number of different forms. Two main categories of analysis packages exist: Comprehensive Packages and Modular Packages. The analysis package that is discussed and used, fits loosely into the modular package category. However, when this type of package is compared with comprehensive packages it does not always perform as well as might be hoped. As would be expected, a comprehensive package has no problem obtaining the accuracy required to perform the analysis required. It does, however, often fall short in terms of the computational expense that needed to achieve a greater level of accuracy. Typically comprehensive packages require a Figure 10. Longitudinal Flap Deflection large volume of computing resources to perform the desired task. Computational resources of this size are normally not considered exhaustive when used for single runs on large projects. However when the resources available to a project are small, the computational expense of an analysis package becomes of high priority. This is especially so when the goal of the package is to create a craft design that is globally optimized. With projects of this type, the number Table 3. Steady State Flap Deflections of analysis iterations can be several orders of magnitude Wind Tunnel Code Value larger than that of analysis of an existing craft. Thus, this Lateral (º) -2.0 -2.9 makes the use of a comprehensive package to find a global Longitudinal (º) -11.0 -13.6 maxima or minima unfeasible. Hence, the use of a modular type package for the attainment of an optimised design becomes more attractive. Ease of use and accuracy are of high importance when creating an analysis package specifically designed for use with optimisation packages. This analysis package shows high potential for use with optimisation for a number of reasons. Firstly, the analysis package has short run times, and secondly, as stated previously, the accuracy of the results obtained is good for the low computational expense. Both these factors are favorable, and show that this method and implementation are suited to optimisation. However, a most favorable point is that this package has 9 American Institute of Aeronautics and Astronautics
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been developed with an optimisation framework in mind. As a result, implementation into an optimisation scheme becomes a simple process with the development of pre and post process to obtain the parameters required.
VII.
Conclusions
The analysis methods that have been presented within this paper show that a quick simple method for rotor dynamics has been develop from first order methods. Accuracy of this method has been shown to be sufficient for use as a basis for an analysis tool within a design optimisation scheme. By basing the analysis model closely on the increased inherent stability Proxfler© type craft, results shown are within an order of magnitude to physical results. With a small number of refinements, this analysis technique should be very useful as the basis of a full dynamic motion analysis tool. The analysis technique that is used has been coded in a method that allows further development into a full dynamic motion analysis tool. Initial development has followed a framework that is suited for use with design optimisation techniques. As such, the coding has been shown to perform in such a way that it will support pre and post processing. This will allow for ease of implementation with optimisation packages. Completion of the full craft dynamic motion analysis package must include work on a number of areas. Development of the Blade Element Momentum Theory method must be completed to ensure stability over a wider range of working velocities. Following on from a more reliable implementation of BEMT is to model aerodynamic interaction of the rotors. Correct coding of the full craft equations of motion must also be undertaken to ensure a simple, yet accurate analysis suite. To finalize the analysis suite, a pre and post processing package must also be developed to allow quick interaction with a given optimisation package.
References 1
Mettler, B., Dever, C. and Feron, E., “Scaling Effects and Dynamic Characteristics of Miniature Rotorcraft.”, Journal of Guidance, Control and Dynamics, Vol. 27, No. 3, 2004, pp. 466-478. 2 Bohorquez, F., Samuel, P., et al., “Design, Analysis and Hover Performance of a Rotary Wing Micro Air Vehicle.”, Journal of the American Helicopter Society, Vol. 48, No. 2, 2003, pp. 80-90. 3 Celi, R., “Recent Applications of Design Optimization to Rotorcraft – A Survey.”, Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 176-189 4 Lim, J. W. and Chopra, I., “Aeroelastic Optimization of a Helicopter Rotor Using an Efficient Sensitivity Analysis.”, Journal of Aircraft, Vol. 28, No. 1, 1991, pp. 29-37 5 Salas, A. O. and Townsend, J. C., “Framework Requirements For MDO Application Development.”, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimisation, AIAA, St Louis, Missouri, 1998, AIAA-98-4740 6 Isaacs, A., Sudhakar, K. and Mujumdar, P. M., “Design and Development of MDO Framework.”, MSO-DMES 2003 Conference Paper No. 78, Goa, India, 2003 7 Rutkowski, M. J., Ruzicka, G. C., et al., “Comprehensive Aeromechanics Analysis of Complex Rotorcraft Using 2GCHAS.”, Journal of the American Helicopter Society, Vol. 40, No. 4, 1995, pp. 3-17. 8 Johnson, W., “CAMRAD II, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dyanmcis.”, Johnson Aeronautics, Palo Alto, California, 1992-1997. 9 Björk, A., “AERFORCE: Subroutine Package for unsteady Blade-Element Momentum Calculations.”, FFA, TN 2000-07, Bromma, Sweden, 2000. 10 Laino, D.J., and Hansen, A. C., “User’s Guide to the Wind Turbine Aerodynamics Computer Software AeroDyn.”, Windward Engineering, Salt Lake City, Utah, U.S.A., 2002. 11 Moriarty, P. J. and Hansen, A. C., “AeroDyn Theory Manual.”, National Renewable Energy Laboratory, NREL/TP-50036881, Golden, Colorado, U.S.A., 2005. 12 Jones, H. E. and Hunz, D. L., “Comprehensive Modeling of the Apache in CAMRAD II.”, American Helicopter Society Structure Specialists Meeting., AHS, Williamsburg, Virginia, U.S.A., 2001. 13 Lim, J. W. and Anastassiades, T., “Correlation of 2GCHAS Analysis with Experimental Data.”, American Helicopter Society Aeromechanical Specialists Conference, AHS, San Francisco, California, U.S.A., 1994. 14 Ahlström, A., “Aeroelastic Simulation of Wind Turbine Dynamics.”, Ph.D. Dissertation, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden, 2005. 15 Proxflyer AS, “Mosquito Picture”, Proxflyer Website., URL: http://www.proxflyer.com/pf_meny.htm [cited 26 January 2006] 16 Johnson, W., Helicopter Theory., Princeton University Press, Princeton, N.J., 1980, pp. 37-40, 49-56. 17 Leishman, J. G., Principles of Helicopter Aerodynamics., Cambridge University Press, New York, N.Y., 2000, pp. 102
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References [1] Christian Bermes, Kevin Sartori, Dario Schafroth, Samir Bouabdallah, and Roland Siegwart. Control of a coaxial helicopter with center of gravity steering. In International conference on SIMULATION, MODELING and PROGRAMMING for AUTONOMOUS ROBOTS, pages 492–500, Venice, Italy, November 2008. [2] Samir Bouabdallah, Roland Siegwart, and Gilles Caprari. Design and control of an indoor coaxial helicopter. In Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, October 9 - 15 2006. IEEE. [3] Wikipedia. S-64 skycrane wikipedia webpage. http://en.wikipedia.org/wiki/S-64 Skycrane, March 2009. [4] Lance A. Morgan. The bell 47 helicopter. http://www.bell47.net/, January 2009. [5] Schiebel Corporation. Schiebel - camcopter s-100. http://www.schiebel.net/, January 2009. [6] Kamov. Kamov webpage. http://www.kamov.ru/, November 2008. [7] Proxflyer. Proxflyer webpage. http://www.proxflyer.com/, October 2008. [8] Wikipedia. Ch-47 chinook wikipedia webpage. http://en.wikipedia.org/wiki/CH-47 Chinook, January 2009. [9] Boeing. Boeing: Integrated defense systems - v-22 osprey. http://www.boeing.com/rotorcraft/military/v22/index.htm, January 2009. [10] Kaman helicopters webpage. http://www.kamanaero.com/helicopters/kmax.html, February 2009. [11] Gabriel M. Hoffmann, Haomiao Huang, Steven L. Waslander, and Claire J. Tomlin. Quadrotor helicopter flight dynamics and control: Theory and experiment. In AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, South Carolina, USA, 20-23 August 2007. AIAA. [12] Yamaha Motor. Yamaha autonomous-flight unmanned helicopter deployed for observation illegal dumping around mt. fuji. http://www.yamaha-motor.co.jp/global/news/2002/02/06/sky.html, January 2009.
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