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Optimal structural design of a morphing aircraft wing

Dissertation
Author: Smita Bharti
Abstract:
This work involves the development of design methodologies for a morphing aircraft wing. Morphing aircraft wings face conflicting design requirements of flexibility to accomplish the desired shape change, and stiffness to withstand aerodynamic loads. In this work, two design methodologies are developed. The first involves employing Genetic Algorithm wherein an attempt is made to design optimal wing topologies that meet these requirements. Non-linear Finite Element Analysis is used for function evaluation in order to account for the large deformation requirements of the problem. The solution methodology is applied to solve two wing-morphing problems with very different morphing requirements. Results from the two wing designs are presented. The second design methodology is based on development of an intuitive design to achieve the required wing morphing, followed by performing further analysis and calculation of design parameters. Such a scheme is useful in case of a two-dimensional wing shape change, where the means to achieve the required wing morphing is relatively easy to visualize. However developing an intuitive design for a three-dimensional problem might prove to be more difficult, in which case the scheme employing Genetic Algorithm might be used. Prototype development is presented as a proof of concept for employing cable actuation. The current dissertation presents the results from the two developed design methodologies, along with the design and prototype development of a section of a 10 lb aircraft wing. Details on the implemented Finite Element Algorithm, convergence issues, and minima finding are presented. Possible pitfalls of using a cable actuation mechanism are described, and suggestions for future work are made.

TABLE OF CONTENTS LIST OF FIGURES.....................................................................................vi

LIST OF TABLES.......................................................................................xi

ACKNOWLEDGEMENTS..............................................................................xiv

Chapter 1 I NTRODUCTION .................................................................1

1.1 Nomenclature...............................................................................2

1.2 The Wing Morphing Concept...........................................................3

Parameter.........................................................................................5

1.3 History of Morphing Aircraft Wing....................................................7

1.4 Recent Morphing Efforts.................................................................9

1.4.1 Robotic Design.....................................................................10

1.4.1.1 Entire Wing Rotation....................................................10

1.4.1.2 Segment Rotation........................................................11

1.4.2 Organic Design....................................................................12

1.4.2.1 Stretching Surfaces.....................................................12

1.4.2.2 Sliding Surfaces..........................................................15

1.5 Tendon-Actuated Internal Structure Approach...................................17

1.6 Previous Work on Cell Structures....................................................18

1.7 Classical and Evolutionary Algorithms..............................................21

1.7.1 Literature Review on Multi-Objective EA..................................26

1.8 Wing Design Considerations with Proposed Concept...........................31

Chapter 2 T EST P ROBLEMS AND S OLUTION A LGORITHMS .......32

2.1 Nomenclature...............................................................................33

2.2 Test Problems..............................................................................33

2.2.1 HECS Wing..........................................................................33

2.2.2 TSCh Wing..........................................................................35

2.3 Discrete GA..................................................................................37

2.4 NSGA II......................................................................................40

Chapter 3 N ON -L INEAR F INITE E LEMENT A NALYSIS .................46

3.1 Nomenclature...............................................................................47

3.2 Non-Linear Finite Element Analysis Equations...................................49

3.3 Verification of Implemented Algorithm.............................................53

3.4 Convergence of Non-Linear FEA......................................................55

3.5 Line Search and Backtracking.........................................................59

3.6 Multiple Minima............................................................................62

3.7 Comparison with ANSYS................................................................67

3.8 Discussion...................................................................................72

iv

Chapter 4 D ISCRETE G ENETIC A LGORITHM T EST C ASES AND R ESULTS .............................................................................74

4.1 Nomenclature...............................................................................75

4.2 Tendon-Actuated GA Approach.......................................................76

4.3 Problem Formulation.....................................................................79

4.4 Discrete Genetic Algorithm.............................................................83

4.4.1 Algorithm Implementation – Case I........................................83

4.4.2 Results – Case I...................................................................89

4.4.2.1 NASA HECS Wing........................................................89

4.4.2.2 Results – HECS Wing...................................................91

4.4.2.3 NextGen TSCh Wing....................................................92

4.4.2.4 Results – TSCh Wing....................................................94

4.4.3 GA Implementation – Case II.................................................96

4.4.3.1 Results – HECS Wing...................................................97

4.5 Discussion...................................................................................100

Chapter 5 NSGA II T RIAL P ROBLEMS AND R ESULTS ..............101

5.1 Nomenclature...............................................................................101

5.2 Discrete-Continuous Algorithm – NSGA II.........................................102

5.2.1 Algorithm Implementation – Case III......................................102

5.2.2 Parallel Implementation........................................................104

5.2.3 Validity Verification of the Non-Linear FEA...............................105

5.2.3.1 Results-HECS Wing......................................................106

5.2.3.2 Results-TSCh Wing......................................................121

5.3 Discussion...................................................................................134

Chapter 6 T ENDON -A CTUATED C ELL M ECHANISMS ...................136

6.1 Nomenclature...............................................................................138

6.2 TSCh Wing Morphing – Span-Sweep Change.....................................140

6.2.1 Kinematic Calculations for Cell Parameter Determination............142

6.2.2 Bending Moment Estimation..................................................145

6.2.3 Sizing Strut Cross-Section.....................................................147

6.2.4 Compliant Joints..................................................................149

6.3 Actuation Force Determination and Scaling.......................................154

6.4 Discussion...................................................................................159

Chapter 7 P ROTOTYPE D EVELOPMENT ...........................................160

7.1 Nomenclature...............................................................................160

7.2 Wing Specifications.......................................................................161

7.3 Cell Mechanism Design Details........................................................162

7.4 Construction Details......................................................................167

7.5 Actuation Mechanism....................................................................171

7.6 Discussion...................................................................................177

v

Chapter 8 C ONCLUSIONS ..................................................................178

8.1 Summary....................................................................................179

8.2 Contributions...............................................................................182

8.3 Future Directions..........................................................................183

Bibliography............................................................................................188

References on Flight Systems..............................................................188

References on Genetic Algorithm....................................................192

References on Cell Structures........................................................195

References on Skin Design............................................................196

Other References...................................................................197

Appendix A HECS W ING N ON -L INEAR FEA C ONVERGENCE ..198

Appendix B W ING L OAD C ALCULATIONS .......................................199

B.1 Nomenclature..............................................................................199

B.2 HECS Wing..................................................................................200

B.3 TSCh Wing..................................................................................201

∑ P 203

Appendix C HECS W ING - G EOMETRY AND L OADING D ATA ..205

Appendix D TSC H W ING - G EOMETRY AND L OADING D ATA ...209

Appendix E D ISCRETE GA W ALK T HROUGH ................................226

Appendix F NSGA II W ALK T HROUGH .........................................230

vi

LIST OF FIGURES Figure 1-1: Birds with (a) long distance soaring (Antarctic Giant-Petrel http://www.paulnoll.com) (b) High-speed swept wings (seagull) (http://www.crgrp.net/morphingsystems.htm) (c) Shape Changing wings (Falcon Ramrakhyani 2005).................................................................3

Figure 1-2: Single Mission Aircraft Wings (a) Global Hawk (www.is.northropgrumman.com ) (b) X-45 A (www.af.mil ).......................4

Figure 1-3: Sample wing shape changes......................................................4

Figure 1-4: Lockheed Martin Z Wing (http://www.newscientist.com/channel/mech-tech/aviation/dn4484)........6

Figure 1-5: NextGen Aeronautics Bat Wing (http://www.newscientist.com/channel/mech-tech/aviation/dn4484)........6

Figure 1-6: Parker Variable Camber Rib (Parker 1920)..................................8

Figure 1-7: Classification of Morphing Technologies (Jha et al. 2004)...............10

Figure 1-8: Cell Structures with Different Poisson’s Ratio (Gibson et al. 1988)..21

Figure 1-9: Classical Point-to-Point Optimization (Deb 2001)..........................22

Figure 1-10: Mapping from Decision space to function space (Deb 2001).........25

Figure 1-11: Non-Dominated Front (Deb 2001)............................................28

Figure 2-1: NASA HECS Wing Morphed Configuration (Courtsey NASA LaRC)....34

Figure 2-2: HECS Wing (a) Isometric (b) Top (c) Span View...........................34

Figure 2-3: TSCh Aircraft Wing Morphing.....................................................35

Figure 2-4: TSCh wing (a) Isometric (b) Front View......................................36

Figure 2-5: TSCh Wing Airload Distribution..................................................36

Figure 2-6: Two-Point Crossover................................................................37

Figure 2-7: Proportionate Selection analogous to Roulette Wheel (Deb 2001)...39

Figure 2-8: NSGA II Algorithm...................................................................41

Figure 2-9: Constrain-Dominated Sorting (Deb 2001)....................................42

Figure 2-10: Crowding Distance (Deb 2001)................................................43

vii

Figure 3-1: Newton-Raphson Iterations for Force Equilibrium.........................52

Figure 3-2: Crisfield Problem 1.1................................................................53

Figure 3-3: Newton-Raphson with initial x close to solution - Quadratic Convergence.....................................................................................56

Figure 3-4: Possible failures in Newton-Raphson Implementation (Press et al. 2002)...............................................................................................57

Figure 3-5: HECS Wing Topology-Sample Problem........................................61

Figure 3-6: Comparison of Ordinary Newton-Raphson Method and Newton- Raphson with Line-search....................................................................62

Figure 3-7: Different solutions for different starting U values..........................63

Figure 3-8: Different solutions for different starting U values – N-R with line search..............................................................................................64

Figure 3-9: 2 DOF Problem solved using non-linear FEA algorithm and ANSYS..67

Figure 3-10: Potential Energy vs. iteration – 2 DOF.......................................69

Figure 3-11: 6 DOF Problem......................................................................70

Figure 3-12: Potential Energy vs. Iteration – 6 DOF......................................72

Figure 3-13: Representation of Norm vs. U..................................................73

Figure 4-1: Discretized Wing Structure........................................................77

Figure 4-2: Sample Topology.....................................................................78

Figure 4-3: Stress Ratio Resizer.................................................................85

Figure 4-4: Stress Ratio Resizer – Sample Results........................................86

Figure 4-5: Discrete GA Flow Diagram.........................................................88

Figure 4-6: (a) HECS Wing in Deformed Configuration, (b) Initial Ground Structure for Bay 1 ............................................................................................90

Figure 4-7: Results – HECS Wing................................................................91

Figure 4-8: NextGen Aeronautics TSCh Wing (NextGen Aeronautics Inc.).........93

Figure 4-9: Results – TSCh Wing................................................................94

Figure 4-10: Linear vs. Non Linear Analysis.................................................97

viii

Figure 4-11: Topology from Linear and Non-linear Analysis............................99

Figure 5-1: Master Slave Implementation (Ramrakhyani 2005).......................104

Figure 5-2: GA Results from two different Initial Nodal Deflections..................106

Figure 5-3: Results from Trial 1..................................................................108

Figure 5-4: Results comparison from ramping up actuation forces...................111

Figure 5-5: Deflection comparison between same topology but ramped up actuation force...................................................................................111

Figure 5-6: Optimal Topology-wing under lift, drag and torsion.......................113

Figure 5-7: Results from Trial 2..................................................................114

Figure 5-8: Results comparison from ramping up actuation forces...................116

Figure 5-9: Final topology when using an F act multiplication factor = 5.............117

Figure 5-10: Optimal Topology-wing under lift, drag and torsion.....................117

Figure 5-11: Optimization Results – Trial III.................................................118

Figure 5-12: Final Topology using an Actuation Multiplication Factor of 4.8.......119

Figure 5-13: Wing under Lift, Drag and Torsion............................................120

Figure 5-14: Initial Ground Structure from previous TSCh run (Section 4.4.2.3)............................................................................................123

Figure 5-15: TSCh Wing – Initial GS– Same as the 1 st bay of Figure 5-14.........123

Figure 5-16: TSCh 3D results.....................................................................124

Figure 5-17: Optimal Topology – wing under lift, drag and torsion...................127

Figure 5-18: TSCh 2D Initial Ground Structure.............................................128

Figure 5-19: Trial II Results 1, 2 and 3........................................................129

Figure 5-20: Optimal Topology – Wing under lift, drag and torsion..................131

Figure 5-21: Trial III Results......................................................................132

Figure 5-22: Trial III optimal Topology – wing under lift, drag and torsion........133

Figure 6-1: Different Cell Shapes and Arrangement.......................................137

Figure 6-2: TSCh Wing – Unmorphed and Morphed Configuration...................141

ix

Figure 6-3: Alternate Cell Configuration.......................................................141

Figure 6-4: TSCh Wing – Cell Structure to achieve span and sweep changes....142

Figure 6-5: TSCh Wing – Cell Configuration.................................................143

Figure 6-6: TSCh Wing with additional rib....................................................144

Figure 6-7: Aircraft Wing Load Distribution – Front View................................145

Figure 6-8: Bending Moment Distribution along span (10 lb aircraft)...............146

Figure 6-9: Required strut thickness (and width) along the wingspan..............148

Figure 6-10: Plot of Wing Weight Fraction for different Aircraft Weights...........149

Figure 6-11: Compliant Joint......................................................................150

Figure 6-12: Strut Deflection and loading....................................................150

Figure 6-13: FBD of Strut Section...............................................................152

Figure 6-14: Joint Stress vs. Joint Position for different materials....................154

Figure 6-15: Cellular Mechanism for the TSCh Wing......................................155

Figure 6-16: Vector Loop Diagram of Cellular Mechanism...............................157

Figure 6-17: Actuation Scaling with Aircraft Weight.......................................158

Figure 6-18: Alternative to the TSCh Wing Design........................................160

Figure 7-1: Clark Y Profile.........................................................................161

Figure 7-2: 10 lb TSCh Wing sketched to scale.............................................162

Figure 7-3: TSCh Wing Morphed Configuration.............................................164

Figure 7-4: Airfoil Slots.............................................................................164

Figure 7-5: Slot requirement in the rib........................................................165

Figure 7-6: Modified Airfoil........................................................................166

Figure 7-7: Modified Link...........................................................................167

Figure 7-8: Manufactured Airfoil.................................................................168

Figure 7-9: Link.......................................................................................168

Figure 7-10: Templates for further machining..............................................169

x

Figure 7-11: Wing Configurations (a) Unmorphed (b) Morphed.......................170

Figure 7-12: Cell Mechanism with two cables...............................................171

Figure 7-13: Cable Lengths in unmorphed and morphed Configurations...........172

Figure 7-14: Change in lengths of the morphing (red) and unmorphing (blue) cables...............................................................................................173

Figure 7-15: Best Case scenario placement of Blue cable...............................174

Figure 7-16: Cable Actuation Mechanism.....................................................176

Figure 8-1: Functionally graded beam exhibiting Poisson-Curving Behavior (Lim 2002)........................................................................................184

Figure 8-2: Placement of Poisson-curving beam in the airfoil structure.............184

Figure 8-3: Force Distribution for Airfoil Shape Change..................................185

Figure 8-4: Hexagonal Cell – Span and Chord Coupled Motion........................185

Figure 8-5: Re-entrant Cell – Span and Chord Coupled Motion........................186

Figure 2-1: Aerodynamic Load Prediction for HECS Wing................................201

Figure 2-2: Chordwise and Spanwise Airload Distribution...............................202

xi

LIST OF TABLES Table 1-1: Effects of Wing Morphing on Aircraft Performance (Jha et al. 2004)..5

Table 3-1: Quadratic Convergence of Newton-Raphson..................................54

Table 3-2: Finite Difference Results............................................................55

Table 3-3: Sample results: % non convergent non-linear FEA from using different schemes...............................................................................59

Table 3-4: Leading Edge Nodal Deflections from the two Algorithm.................61

Table 3-5: Comparison of # iterations for convergence: N-R vs. N-R with line search..............................................................................................65

Table 3-6: Element Lengths – 2 DOF problem..............................................68

Table 3-7: Results from 2 dof Topology.......................................................68

Table 3-8: PE for different initial U .............................................................70

Table 3-9: Element Lengths: 6 DOF Problem................................................70

Table 3-10: U and PE: Case I, II, III and IV.................................................71

Table 4-1: Cable and Strut Material Properties (www.matls.com)....................87

Table 4-3: Morphing Achieved at Leading and Trailing Edges..........................91

Table 4-4: Morphing at Leading Edge Due to (1) Actuation without Air loads (2) Air loads without Actuation.............................................................92

Table 4-5: Morphing Achieved at Trailing Edge.............................................95

Table 4-6: Morphing at Trailing Edge Due to (1) Actuation without Air loads (2) Air loads without Actuation.............................................................95

Table 4-7: Fitness Values: Linear Vs. Non Linear Analysis..............................98

Table 4-9: Comparison of % Error in deflection for high actuation strain..........98

Table 4-10: Comparison of % (a 2 and a 3 together) in nodal co-ordinates at LE for high actuation strain......................................................................99

Table 5-1: Input Parameters......................................................................106

Table 5-2: Non-Convergent Non-Linear FEA.................................................107

Table 5-3: Fitness Values – Result 1, 2 and 3...............................................108

xii

Table 5-4: Comparison of number of cables, struts and voids for the three results..............................................................................................108

Table 5-5: Cable Strain.............................................................................109

Table 5-6: Leading Edge Nodal Deflections – Trial I.......................................109

Table 5-7: Objective function under different loading conditions.....................110

Table 5-8: Objective function under different loading conditions.....................112

Table 5-9: Fitness functions from Result 1, 2 and 3.......................................114

Table 5-10: Number of Cables, Struts and Voids in Results 1, 2 and 3.............115

Table 5-11: Cable Strain for Result 1, 2 and 3..............................................115

Table 5-12: Leading Edge Nodal Deflections – Trial II....................................115

Table 5-13: Objective Function under different loading cases..........................116

Table 5-14: Objective function under different loading conditions....................116

Table 5-15: Objective Function under different loading cases..........................119

Table 5-16: Leading Edge Nodal Deflections – Trial III...................................119

Table 5-17: Objective Function under different loading cases..........................120

Table 5-18: TSCh Wing Trials.....................................................................122

Table 5-19: Input Parameters....................................................................122

Table 5-20: Number of cables, struts and voids in Result 1, 2 and 3................124

Table 5-21: Fitness Values of the three results.............................................125

Table 5-22: Objective Functions under Different Loading Conditions................125

Table 5-23: TSCh 3D – Cable Strain...........................................................125

Table 5-24: Leading edge nodal deflections..................................................126

Table 5-25: Number of Cables, Struts and voids in Result 1, 2 and 3...............129

Table 5-26: Fitness Functions – Result 1, 2 and 3.........................................130

Table 5-27: Actuator Strain.......................................................................130

Table 5-28: Trial II wing morphing.............................................................130

xiii

Table 5-29: Objective Function under different loading conditions...................131

Table 5-30: Objective Function under different loading conditions...................132

Table 5-31: Trial III wing morphing............................................................133

Table 6-1: Parameters for a 10 lb aircraft....................................................146

Table 7-1: Initial and Final Cable Lengths....................................................174

Table 7-2: Prototype Deformation..............................................................177

Table 2-1: INPUT DATA.............................................................................202

Table 2-2: Chordwise Pressure Distribution..................................................203

Table 2-1: Sample Calculations for 5 span stations.......................................204

xiv

ACKNOWLEDGEMENTS This work would not have been possible encouragement from a number of people. I will take this opportunity to express my gratitude to them. The first is Dr. Mary Frecker, who I have now known for a number of years as my Master’s and later my PhD thesis advisor. I am thankful for the advice and encouragement that I received from her as I progressed in my career from a young, inexperienced student to a researcher. Dr. Frecker has been through my roller coaster graduate school life, and I appreciate her understanding very much. Working with her has been a great experience. I would next like to thank Dr. George Lesieutre for his advice and guidance as my co-advisor for the PhD thesis. He provided valuable insight during my thesis work. I would like to thank my committee members, Dr. Farhan Gandhi and Dr. Sommer for being on my committee and providing guidance. In addition, I would like to thank the reader of my Master’s thesis, Dr. Gary Koopmann for his valuable suggestions on my Master’s work. I would like to thank my professors for the valuable courses they taught me at Jawaharlal Nehru Technological University and at Penn State University. In addition to the subjects, they were also a big source of motivation in my work. I would like to thank people that have helped me in machining parts for my prototype. Larson Braid and the Teaching Assistants on the job were very helpful in providing useful suggestions as well as in aiding the machining. I would like to also thank Johan Zwart, my husband, for his guidance in my prototype building. On a personal level, I must thank my parents, Mrs. Asha Sinha and Mr. Bhishma Kumar for providing constant encouragement and guidance throughout my life. Without the motivation from them, this work would not have been possible. They have been my role models. I would like to thank my sister Sweta Bharati for her constant support and presence throughout my life. I would like to thank my friends, namely Anuja Jayaraman, Abhiroop Mukhopadhyay, Priya Unnikrishnan, Vijaya Krishnamoorthy, Chandrasekhar Subramaniam and Amalia Shaltiel for making my years at Penn State memorable. Finally, I would like to thank my husband Johan Zwart for his love, support and patience through these years.

Chapter 1

I NTRODUCTION

The goal of a wing morphing aircraft is to obtain high efficiency in flight and maximized performance under different flight conditions. Achieving maneuverability similar to birds by changing the shape of wings during flight is an important goal in aircraft research. Since the beginning of flight, various researches have been directed towards imitating the performance of birds in various environments and for different flight requirements. While aircraft designs have been successful in achieving high efficiency in single missions, designing a truly multi-mission aircraft is still a major challenge. Numerous morphing designs have been proposed in recent years and are being explored. In this work, a tendon-actuated wing design is explored. The designed wing is visualized to be composed of active tendons or cables, and passive struts. Different morphed wing shapes are possible depending on the layout of the struts and cables in the wing. The objective of the work is to find an optimal arrangement of cables and struts, such that the desired wing shape change is achieved when the cables are actuated. In addition to achieving the desired wing shape change under cable actuation, a second objective from the design is to provide stiffness when subjected to aerodynamic loads. Looking at these two objectives, one finds that they are conflicting in nature. The first objective seeks a flexible structure such that it can change shape with the least possible actuation effort. The second objective seeks a structure that is stiff to bear the aerodynamic loads. The current research aims to develop a design methodology for designing cable actuated, load bearing aircraft wing structures. Thus the aim is to develop a general design tool, which can be used to obtain a wing configuration that gives the desired morphing. Although it is very interesting to have such a design tool, it is usually very difficult and not beneficial to have a solve-all type of an algorithm. Recognizing this, two different solution methodologies have been proposed and explored: wing design using Genetic Algorithm, and design of tendon actuated cell structures that can be used to achieve two-dimensional coupled shape changes. While the first method is mainly mathematical in nature, the second method relies on

2

intuitive reasoning before carrying out analysis. It must be noted that the current research aims to achieve very large wing shape changes, with upto 60% change in span and 43° wing sweep. The current dissertation is broadly classified into two categories – optimal design of cable-actuated structures using Genetic Algorithm (GA), and cellular design to achieve coupled two dimensional shape changes. Chapter 2, Chapter 3, Chapter 4 and Chapter 5 discuss design using Genetic Algorithm. Chapter 2 discusses the two wing design problems that have been used as example problems throughout this work. In addition, Chapter 2 gives details on the two Genetic Algorithms used in this work, namely the discrete GA and NSGA II. In the GA, non-linear Finite Element Analysis (FEA) is used to account for the large deformation requirement of the problem. The challenges and issues in using the non-linear FEA are discussed in Chapter 3. Chapter 4 gives results from the wing design that were obtained from using the discrete GA. Chapter 5 presents the results from NSGA II. Cellular design is covered in Chapter 6 and Chapter 7. Chapter 6 gives the design details. Chapter 7 explains prototype development and physical actuation. Chapter 8 concludes with a discussion, contributions of the current research to the field, and suggestions for future work. Appendix A gives results from the non-linear FEA. Appendix B gives wing loading information. Appendix C gives load data from example problem 1 (HECS Wing) while Appendix D gives load data from example problem 1 (TSCh Wing). Appendices E and F give a walkthrough of Algorithms Discrete GA and NSGA II respectively. In this work, vectors are denoted in bold and scalars in normal typeface.

1.1 Nomenclature F (i)

: Fitness of individual i .

(f d ) m (i)

: Objective vector calculated from the dominant genotype

(f r ) m (i)

: Objective vector calculated from the recessive genotype m : Number of steps for selection

F : Gibb’s Free Energy

3

E

: Mean Energy

H : Entropy

T : Temperature of System

1.2 The Wing Morphing Concept Numerous examples can be found in nature where birds use different wing configurations for flight conditions such long distance soaring (Figure 1-1 (a)) and high-speed dash (Figure 1-1 (b)). Figure 1-1 (c) shows the wing shape change of a falcon flying at different speeds.

Inspired by bird wing shapes and from basic concepts of flight, fixed aircraft wings have been designed for optimal mission-specific performance, such as the Global Hawk with its high aspect ratio wings for high-altitude, high endurance surveillance and the X-45A with its backward swept wings for high-speed attack.

Figure 1-1: Birds with (a) long distance soaring (Antarctic Giant-Petrel http://www.paulnoll.com) (b) High-speed swept wings (seagull) (http://www.crgrp.net/morphingsystems.htm) (c) Shape Changing wings (Falcon Ramrakhyani 2005)

4

However, in order for an aircraft to possess true multi-mission capability, dramatic wing shape changes are required. Some of these wing-morphing requirements from conceptual wings are shown in Figure 1-3. The NASA’s Hyper Elliptic Cambered Section (HECS) wing is shown in its morphed configuration in Figure 1-3 (a). The HECS wing morphs from a planar configuration to the non-planar elliptical configuration shown in the Figure. The planar configuration is utilized at low speed cruise in order to minimize induced drag, while the non-planar configuration is useful for efficient maneuvering. The non-planar configuration minimizes the wing root bending moment and maximizes obtainable roll rate (Wiggins et al. 2004). The TSCh wing from NextGen Aeronautics Inc. (Figure 1-3 b) morphs its configuration from high aspect ratio cruise to the low aspect ratio backward swept dash. Most modern day commercial aircraft use discrete surfaces for achieving wing shape changes. Flaps, slats, ailerons, spoilers etc are some of the discrete control

(a) Global Hawk (b) X-45 A Figure 1-2: Single Mission Aircraft Wings (a) Global Hawk (www.is.northropgrumman.com ) (b) X-45 A (www.af.mil )

(a) HECS Wing (Courtesy: NASA LaRC)

(b) TSCh Wing (Courtesy: NextGen Aeronautics Inc.)

Figure 1-3: Sample wing shape changes

5

surfaces that are used today. These discrete surfaces are either necessary enablers to achieve controlled flight, or contributors to improved aerodynamic performance of the aircraft. However, they do not provide a means for a single aircraft to perform different mission tasks efficiently. Jha et al. (2004) summarize the effects of different wing shape changes on the capability of the aircraft. This summary is given in Table 1-1. Table 1-1: Effects of Wing Morphing on Aircraft Performance (Jha et al. 2004) Parameter Effect (All other Parameters unchanged) Wing Plan Area ↑ ↓ Increased lift, load factor capability Decreased parasitic drag Wing Aspect Ratio ↑

↓ Increased L/D, loiter time, cruise distance, turn rates. Decreased engine requirements Increase maximum speed; Decreased parasitic drag Wing Dihedral ↑ ↓ Increased Rolling moment capability, lateral stability Increased maximum speed Wing Sweep ↑

↓ Increased critical mach no., dihedral effect. Decreased high- speed drag Increased C Lmax

Wing Taper Ratio Wing Efficiency (spanwise lift distribution); induced drag Wing Twist Distribution Prevents tip stall behavior; Spanwise lift distribution Airfoil Camber Zero-lift angle of attack, airfoil efficiency, separation behavior Airfoil Thickness/ Chord Ratio ↑ ↓ Improved low-speed airfoil performance Improved high-speed airfoil performance Leading Edge Radius ↑ ↓ Improved low-speed airfoil performance Improved high-speed airfoil performance Airfoil Thickness Distribution Airfoil Characteristics, laminar/turbulent transition

6

Table 1-1 gives an overview of benefits from morphing, and most of the current research directions are focused on one or more of these aspects of wing morphing. As has been mentioned in Blondeau et al. (2004), in the innovative research proposal on Morphing Aircraft Structures (September 2001), DARPA defined the following specific goals: 200% change in aspect ratio, 50% change in wing area, 5° change in wing twist and 20° change in wing sweep. Two recent aircraft wing configurations under development stand out in terms of the large amount of morphing achieved. These are the Lockheed Martin’s Z wing and the NextGen Aeronautics’ Bat Wing. These are shown in Figure 1-4 and Figure 1- 5.

The Z wing transitions from a fully extended wing for cruising to a small folded and swept wing positioned above the fuselage for combat. In its extended configuration, the maximum L/D is 16, compared to a value of 11.1 in its folded configuration. It has a semi-span (for wind tunnel testing) of 2.9 m when unfolded, and 1.8 m in folded configuration. The Bat Wing morphs from a backward swept wing for dash to high aspect ratio cruise wing. Its span changes from 3 m to 2.2 m. Initial prototypes of these designs have been developed. Most current wing morphing schemes utilize techniques such as folding, telescoping, expanding or contracting a wing as shown above. In the following section, a review of past and current research in the field of aircraft wing morphing is performed. Due to the large available body of literature, an effort is made to categorize the recent and ongoing work in the field into specific groups depending on

Figure 1-4: Lockheed Martin Z Wing (http://www.newscientist.com/channel/mech- tech/aviation/dn4484)

Figure 1-5: NextGen Aeronautics Bat Wing (http://www.newscientist.com/channel/mech-tech/aviation/dn4484)

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the type of morphing sought. The review is limited to morphing of fixed wing aircrafts. Rotorcrafts have been excluded for the sake of brevity.

1.3 History of Morphing Aircraft Wing Researchers have flirted with the idea of wing morphing ever since the beginning of flight. The earliest wing shape change was achieved in the first successful controlled flight of the Wright flyer by the Wright Brothers. They achieved lateral control by what they called the “wing warping”. They observed that if the trailing edge of the wings were twisted in opposite directions, a differential lift would occur, causing the plane to bank. This twist was achieved using a series of tethers and pulleys connecting the wings to a shoulder harness worn by the pilot. If a sudden gust of wind blew from the right, the pilot would instinctively roll his right shoulder down causing the right wing to lose some of its lift. With less lift, the right wing would settle down for level flight. Ailerons are now used for achieving a similar functionality (www.pbs.org ). The Parker Variable Camber wing developed by Parker in 1920 was one of the first efforts toward wing shape change for improved performance. He attempted to address the problem of increasing the speed range of the aircrafts of the time. His suggestions for the problem were to use one of the following strategies:

1. Variable angle of incidence. 2. Variable surface. 3. Variable camber.

The variable camber was determined to be the only practicable solution with advantage greater than the variable angle of incidence, and less than the variable surface morphing. Figure 1-6 (Parker 1920) shows Parker’s Variable Camber Wing. Two spars were placed in the wing; one at the leading edge and the other at two- third chord distance. The portion between the spars was made flexible, and the portion behind the second spar rigid. The rib was allowed to slide over the rear spar. On increasing the angle of attack of the plane, unbalanced forces would act on the

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wing, tending to deform it upward. It was expected that this unbalance of forces would cause the portion between the spars to automatically be deformed upwards, and the rigid portion to move downwards, resulting in an increased camber. Although it was later found that the automatic operation was not as expected, the paper is insightful in terms of suggested morphing ideas. The following two paragraphs mention some of the early morphing concepts. A comprehensive study on these concepts was published by Jha et al. (2004) and has been reviewed in brief here. A variable camber wing designed by V. J. Burnelli was used in the GX-3 in 1929. In addition to wing camber, the wing also changed its area by moving its leading and trailing edge portions outwards and downwards, while the middle portion was held rigid. A telescopic wing concept was developed by G. I. Bakashaev of Russia in 1937 (RK) and modified in 1941 (RK-1). The idea was to use telescopic wing sections in tandem wings. The telescopic section was operated using an electric motor. The wing from RK-1 was able to change the wing area by 135%. The first variable incidence wing was designed for aircraft XF-91 in 1949. This was a supersonic aircraft, which used a high angle of attack for takeoff and landing and a low angle of attack for high-speed flight. The range of angle of incidence was -2° to 5.65°. In 1955 another variable incidence wing was designed for the F-8 Crusader. The wing could rotate about its rear spar by 7°. The first variable sweep wing was

Figure 1-6: Parker Variable Camber Rib (Parker 1920)

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developed for P-1101 in 1944. This wing could change the sweep angle from 35° to 45° only while the aircraft was on ground. In-flight sweep angle change was achieved in X-5 by Bell Aircraft Company. The wing could change the sweep angle from 20° to 60° in 20 sec. Other notable swing wing aircrafts were Grumman’s XF10F-1 and General Dynamics’ F-111 Aardvark. More recently, swing-wing designs have also been incorporated in high performance aircrafts such as Mig-23 (USSR 1967), Grumman F-14 Tomcat (1970) and Rockwell B-1B Lancer (1983). An oblique wing (AD-1) developed in 1979 was designed to rotate on its center pivot in order to reduce drag. Wing dihedral change was first achieved in Russian MiG 105-11. The wing was designed for stabilizing the aircraft by setting it 25° above horizontal during take-off and horizontal in subsonic flight. Small planform changes were developed to function as control surfaces. A tailless plane aircraft developed in 1953 by Short Brothers and Harland Ltd. had moving wing tips which possessed more control power than ailerons. The pivoted wingtips acted as elevators for pitch control as well as aileron for roll control. Camber control using leading edge flaps was achieved in F-16 fighting falcon. The wings have a set of flaperons to combine the effects of flaps and ailerons. These act as conventional ailerons during conventional flight and flaps hanging down by 20° during takeoff and landing.

Full document contains 250 pages
Abstract: This work involves the development of design methodologies for a morphing aircraft wing. Morphing aircraft wings face conflicting design requirements of flexibility to accomplish the desired shape change, and stiffness to withstand aerodynamic loads. In this work, two design methodologies are developed. The first involves employing Genetic Algorithm wherein an attempt is made to design optimal wing topologies that meet these requirements. Non-linear Finite Element Analysis is used for function evaluation in order to account for the large deformation requirements of the problem. The solution methodology is applied to solve two wing-morphing problems with very different morphing requirements. Results from the two wing designs are presented. The second design methodology is based on development of an intuitive design to achieve the required wing morphing, followed by performing further analysis and calculation of design parameters. Such a scheme is useful in case of a two-dimensional wing shape change, where the means to achieve the required wing morphing is relatively easy to visualize. However developing an intuitive design for a three-dimensional problem might prove to be more difficult, in which case the scheme employing Genetic Algorithm might be used. Prototype development is presented as a proof of concept for employing cable actuation. The current dissertation presents the results from the two developed design methodologies, along with the design and prototype development of a section of a 10 lb aircraft wing. Details on the implemented Finite Element Algorithm, convergence issues, and minima finding are presented. Possible pitfalls of using a cable actuation mechanism are described, and suggestions for future work are made.