Master's thesis of Engineering: Aerodynamic performance comparison of a conventional UAV wing and a FishBAC morphing wing

Aerodynamic Performance Comparison of a Conventional UAV Wing and a FishBAC Morphing Wing

A thesis submitted in fulfilment of the requirements for the degree of Master of Engineering

Arthur Wong

School of Engineering

College of Science, Technology, Engineering and Maths

RMIT University

June 2021

Bachelor of Engineering (Aerospace Engineering) (Honours), RMIT University

Declaration I certify that except where due acknowledgement has been made, the work is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics procedures and guidelines have been followed. I acknowledge the support I have received for my research through the provision of an Australian Government Research Training Program Scholarship. Signed Arthur Wong 08 June 2021

Acknowledgments

I would like to take this opportunity to thank all those who have supported me during this program. I thank RMIT University for allowing me to continue my development in the masters by research program. I would like to thank my senior supervisors Professor Cees Bil and Dr Matthew Marino for looking over my growth and providing guidance to me completing the program. I thank the technical staff team particularly Gil Atkin and Paul Muscat for assisting me in getting from a concept and design to a prototype of the morphing wing and a compliant morphing skin providing guidance, advice, teaching composite lay-up techniques necessary to reach the end goal. Additionally I thank Nhu Huynh, my long-time girlfriend for her endless encouragement and support during the program as well as my friends and family for their support.

Table of Contents Declaration ............................................................................................................................................... i

1 Introduction ......................................................................................................................................... 2

2 Literature Review ................................................................................................................................. 5

2.1 Types of Morphing Wings ............................................................................................................. 7

2.1.1 Planform Morphing ................................................................................................................ 8

2.1.2 Out-of-Plane Morphing ........................................................................................................ 11

2.1.3 Airfoil Adjustment ................................................................................................................ 13

2.2 Morphing Wing Actuation .......................................................................................................... 14

2.2.1 Internal Mechanisms ........................................................................................................... 14

2.2.2 Piezoelectric Actuators ........................................................................................................ 15

2.2.3 Shape Memory Alloys .......................................................................................................... 15

2.3 Examples of Morphing Structures .............................................................................................. 15

2.3.1 Fish Bone Active Camber (FishBAC) ..................................................................................... 15

2.3.2 Zig-Zag Wingbox ................................................................................................................... 18

2.3.3 GNAT Spar ............................................................................................................................ 19

2.4 Morphing Wings in Industry ....................................................................................................... 20

2.5 Morphing Wing Concept Selection ............................................................................................. 21

2.6 Literature Review on Morphing Skins ......................................................................................... 22

2.6.1 Honeycomb and Honeycomb Variants ................................................................................ 24

2.6.2 Corrugated structures .......................................................................................................... 25

2.6.3 Flexible Matrix Composites (FMC) ....................................................................................... 26

2.6.4 Concept Selection ................................................................................................................ 27

2.6.5 Further Investigation into Flexible Matrix Composites (FMC) ............................................. 27

3 Motivations and Past Research .......................................................................................................... 28

3.1 Wing Concept and Conceptual Design ........................................................................................ 28

3.1.1 Morphing Wing Actuation Method ...................................................................................... 32

3.2 Wing Design ................................................................................................................................ 34

4 Research Questions............................................................................................................................ 35

4.1 Project Scope .............................................................................................................................. 35

5 Research Methodology ...................................................................................................................... 36

5.1 Airfoil Development .................................................................................................................... 36

5.2 Simulations .................................................................................................................................. 37

5.2.1 XFLR5 .................................................................................................................................... 37

iii

5.2.2 Tornado ................................................................................................................................ 45

5.2.3 Wind tunnel Testing ............................................................................................................. 48

6 Building the Morphing Wing .............................................................................................................. 49

6.1 Morphing Skin Concept ............................................................................................................... 50

6.3 Evolution of the Morphing Skin .................................................................................................. 51

6.3.1 Morphing Skin Manufacturing Process ................................................................................ 54

6.4 Summary of the Morphing Wing Design ..................................................................................... 55

7 Results ................................................................................................................................................ 57

7.1 Flow Visualization ....................................................................................................................... 57

7.1.2 Summary of Flow Visualization Behaviour........................................................................... 57

7.2 Wind Tunnel Data Post Processing ............................................................................................. 59

7.3 Experimental Results and Discussion .......................................................................................... 60

7.3.1 Conventional T240 Wind Tunnel Results ............................................................................. 61

7.3.2 Morphing Wing Wind Tunnel Results .................................................................................. 66

7.3.3 Roll Results ........................................................................................................................... 76

7.3.4 Discussion of Results ............................................................................................................ 82

7.3.5 Summary of Comparison – Conventional T240 vs Morphing Wing ..................................... 84

8 Conclusions ........................................................................................................................................ 90

8.1 Recommendations/Further research .......................................................................................... 91

References ............................................................................................................................................ 92

APPENDIX A – Wind tunnel Calibration .............................................................................................. 100

APPENDIX B – Assembly of the Wing and Preparation of the Wing ................................................... 109

APPENDIX C – Flow Visualization for Various Morphing Deflections ................................................. 117

APPENDIX D – Experimental Results ................................................................................................... 137

APPENDIX E – Comparison between Wind Tunnel Test and Simulation ............................................ 151

APPENDIX F – XFLR5 Convergence ...................................................................................................... 159

APPENDIX G – Further Information on the Vortex Lattice Method .................................................... 163

List of Figures

Figure 1 Principles of aircraft drag polar affected by airfoil camber variation in steady cruise flight [10]. ................................................................................................................................................................ 3 Figure 2 Precedent T240 aircraft and its wing’s dimensions in plan view. ............................................. 4 Figure 3 Morphing wing dimensions in plan view. ................................................................................. 5 Figure 4 Makhonine Mak-10 aircraft [4]. ................................................................................................ 6 Figure 5 Examples of variable sweep wings [4]. ..................................................................................... 6 Figure 6 Span morphing wing via telescopic wing [28]. ........................................................................ 10 Figure 7 Planform alteration types [2]. ................................................................................................. 11 Figure 8 Camber morphing concept visualization [2]. .......................................................................... 11 Figure 9 Span-wise bending morphing concept [2]. ............................................................................. 12 Figure 10 Wing twisting concept seen in the 1899 Wright Kite [36]. ................................................... 13 Figure 11 Airfoil adjustment morphing concept visualization [2]. ....................................................... 14 Figure 12 Airfoil adjustment via actuators inside the wing [37]. .......................................................... 14 Figure 13 A SMA spring actuator recovering its original shape after heating [47]. .............................. 15 Figure 14 FishBAC rib design [23]. ........................................................................................................ 16 Figure 15 FishBAC utilized as a morphing trailing edge and model parameters [49]. .......................... 17 Figure 16 Top-view of the zig-zag wingbox concept [25]. .................................................................... 18 Figure 17 Schematic of GNATSpar concept [24]. .................................................................................. 19 Figure 18 Rack and pinion actuation system for GNATSpar [6]. ........................................................... 20 Figure 19 Flexsys' Flexfoil deflected [22]. ............................................................................................. 21 Figure 20 Composite Cellular Material Morphing Wing [56]. ............................................................... 21 Figure 21 FishBAC and corrugated morphing trailing edge concept [60]. ........................................... 25 Figure 22 FMC fibre orientation for a) span morphing and b) for camber morphing [52]. .................. 26 Figure 23 Three-view of the initial rib design that connects to the trailing edge [69]. ........................ 28 Figure 24 Colour coded isometric view of morphing wing concept [69]. ............................................. 29 Figure 25 Revised rib design and its assembly [69]. ............................................................................. 29 Figure 26 Revised rib displacements [19]. ........................................................................................... 30 Figure 27 Velcro strips on revised rib [69]. ........................................................................................... 31 Figure 28 Step by step assembly of the wing [69]. ............................................................................... 31 Figure 29 Four view of the fuselage wingbox without the covering panel........................................... 32 Figure 30 Assembled fuselage wingbox. ............................................................................................... 33 Figure 31 Proposed servo locations in the fuselage wingbox and morphing wing. ............................. 33 Figure 32 CAD model of wing design (without stringers attached) [70]............................................... 34 Figure 33 Complete CAD model of 2nd wing design [70]. ...................................................................... 35 Figure 34 Construction of the T240 airfoil. ........................................................................................... 36 Figure 35 Morphing wing airfoil construction. ..................................................................................... 37 Figure 36 XFLR5 simulation process for wing aerodynamic analysis. ................................................... 38 Figure 37 T240 airfoil in XFLR5. ............................................................................................................. 39 Figure 38 T240 airfoil with flap deflections in XFLR5. ........................................................................... 39 Figure 39 2D analysis results of T240 airfoil with Flaps applied at various Reynolds numbers in XFLR5. .............................................................................................................................................................. 42 Figure 40 XFLR5 Analysis for 𝑪𝑳 vs 𝜶 at various Reynolds numbers. ................................................... 45 Figure 41 Tornado simulation process. ................................................................................................. 46

Figure 42 TORNADO Analysis for 𝑪𝑳 vs 𝜶 at various Reynolds numbers. ............................................ 47 Figure 43 Schematic of the industrial wind tunnel at RMIT University. ............................................... 48 Figure 44 Electronic turntable aft of the contraction point in the wind tunnel. .................................. 48 Figure 45 Isometric view of the Morphing Wing. ................................................................................. 50 Figure 46 2D Morphing Wing splines from XFLR5. ............................................................................... 50 Figure 47 Initial morphing skin design A to morphing skin design C. ................................................... 51 Figure 48 Morphing skin design D to morphing skin design E. ............................................................. 52 Figure 49 Morphing skin F to Morphing skin G. .................................................................................... 53 Figure 50 Morphing skin H to the Final Skin. ........................................................................................ 54 Figure 51 Compliant morphing skin demonstration. ............................................................................ 54 Figure 52 Exploded isometric view of the Morphing Wing. ................................................................. 56 Figure 53 Conventional T240 Wing results for 𝑪𝑳 vs 𝜶 at various Reynolds numbers. ....................... 63 Figure 54 Conventional T240 Wing Wind Tunnel results for 𝑪𝑫 vs 𝜶 at various Reynolds numbers. . 65 Figure 55 Morphing Wing results for 𝑪𝑳 vs 𝜶 at various Reynold numbers. ....................................... 68 Figure 56 Morphing Wing Experimental results for 𝑪𝑫 vs 𝜶 at various Reynold numbers. ................ 71 Figure 57 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing. ............................................................................................................................... 74 Figure 58 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing with flaps. .............................................................................................................. 75 Figure 59 TORNADO and wind tunnel results for 𝑪𝒍 vs 𝜹 at various Reynolds number. ...................... 78 Figure 60 𝑪𝑳 comparison for the Conventional T240 and Morphing wing at various Reynolds numbers. .............................................................................................................................................................. 79 Figure 61 Difference in TORNADO and wind tunnel testing for 𝒑 vs 𝜹 at various Reynolds numbers. 80 Figure 62 𝒑 comparison between Conventional T240 and Morphing Wing at various Reynolds numbers. ............................................................................................................................................... 81 Figure 63 𝒑 comparison between Conventional T240 and Morphing Wing at various Reynolds numbers. ............................................................................................................................................... 82 Figure 64 Calibration setup in the y-axis (drag axis) of the JR3 Load cell, measured at z= 1 m above the load cell. .............................................................................................................................................. 100 Figure 65 Calibration curve for the Lift axis of the JR3 load cell – “Lift” Force output vs “Lift” Force input. ................................................................................................................................................... 102 Figure 66 Calibration curve for the phantom outputs of the JR3 load cell – “Drag” Force output vs “Rolling” Moment output. .................................................................................................................. 102 Figure 67 Calibration curve for the Drag axis of the JR3 load cell – “Drag” Force output vs “Drag” Force input. ................................................................................................................................................... 103 Figure 68 Calibration curve for the Drag axis of the JR3 load cell – “Drag” Force output vs “Yawing” Moment input. .................................................................................................................................... 104 Figure 69 Calibration of the JR3 load cell by applying pure moments in the Yaw axis, at x= -0.3m via T- beam. .................................................................................................................................................. 104 Figure 70 Calibration of the JR3 load cell by applying pure moments in the Yaw axis, at x= 0.3m via T- beam. .................................................................................................................................................. 105 Figure 71 Pure Yaw moment configuration calibration in the Drag axis of the JR3 load cell. ............ 106 Figure 72 Pure Yaw moment configuration calibration in the Drag axis of the JR3 load cell. ............ 106 Figure 73 Using calibration data from Yaw moment calibration, calibration curve for the Drag axis of the JR3 load cell. ................................................................................................................................. 107

Figure 74 Calibration of the JR3 load cell by applying pure moments in the Roll axis, at y= -0.3m via T- beam. .................................................................................................................................................. 108 Figure 75 Using calibration data from Rolling moment calibration, calibration curve for the Lift axis of the JR3 load cell. ................................................................................................................................. 108 Figure 76 Using calibration data from Rolling moment calibration, calibration curve for the Lift axis of the JR3 load cell. ................................................................................................................................. 109 Figure 77 Layout of Leading edge and Spar to be bonded. ................................................................ 110 Figure 78 Bonding Ribs to the Leading edge. ...................................................................................... 111 Figure 79 Bonding Ribs to the Trailing edge. ...................................................................................... 111 Figure 80 Bonding the thin Al sheet to the Wing................................................................................ 112 Figure 81 Bonding the thin Al sleeve to the Trailing edge. ................................................................. 112 Figure 82 Bonding reinforcing L shape carbon fibre angles to the ribs. ............................................. 112 Figure 83 Assembled morphing wing minus the wingtip.................................................................... 113 Figure 84 Isometric view of Wing tip post modifications; removal of spar box and addition of thin Al strips. ................................................................................................................................................... 113 Figure 85 Bottom view of Wing tip post modifications; removal of spar box and addition of thin Al strips. ................................................................................................................................................... 114 Figure 86 Isometric view of the Bonding of the wingtip cover to the wingtip. ................................. 114 Figure 87 Top view of the Bonding of the wingtip cover to the wingtip. ........................................... 115 Figure 88 Curing of the Epoxy resin applied to the foam components of the Morphing wing and wingtip. ............................................................................................................................................... 115 Figure 89 Morphing wing spray painted. ............................................................................................ 116 Figure 90 Wingtip spray painted. ........................................................................................................ 116 Figure 91 Morphing wing - post cure of the spray paint. ................................................................... 116 Figure 92 Flow visualization for 𝜹𝒎 = 0°. ........................................................................................... 118 Figure 93 Flow visualization for 𝜹𝒎 = 2°. .......................................................................................... 120 Figure 94 Flow visualization for 𝜹𝒎 = 3°. ........................................................................................... 121 Figure 95 Flow visualization for 𝜹𝒎 = 5°. ........................................................................................... 123 Figure 96 Flow visualization for 𝜹𝒎 = 10°. ......................................................................................... 125 Figure 97 Flow visualization for 𝜹𝒎 = 15°. ......................................................................................... 127 Figure 98 Flow visualization for 𝜹𝒎 = 20°. ........................................................................................ 128 Figure 99 Flow visualization for 𝜹𝒎 = 25°. ......................................................................................... 130 Figure 100 Flow visualization for 𝜹𝒎 = 30°. ....................................................................................... 132 Figure 101 Flow visualization for 𝜹𝒎 = 35°. ....................................................................................... 134 Figure 102 Flow visualization for 𝜹𝒎 = 40°. ....................................................................................... 136 Figure 103 Conventional T240 Wing Experimental results for 𝑪𝑳 vs 𝜶 and 𝑪𝑫 vs 𝜶 at Re 202000 and Re 269000. .......................................................................................................................................... 138 Figure 104 Morphing Wing Experimental results for 𝑪𝑳 vs 𝜶 and 𝑪𝑫 vs 𝜶 at Re 202000 and Re 269000. ............................................................................................................................................................ 140 Figure 105 Experimental results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers with error bars. ......... 143 Figure 106 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing with flaps and error bars. .................................................................................... 145 Figure 107 𝑳/𝑫 vs 𝑪𝑳 comparison of the ideal morphing deflection and conventional wing with flaps and error bars (using the agreeable data). ......................................................................................... 146

vii

List of Tables

Figure 108 TORNADO and wind tunnel testing results for𝑪𝒍 vs 𝜹 and 𝒑 vs 𝜹 at Re 202000 and Re 269000. ............................................................................................................................................... 147 Figure 109 XFLR5 Analysis for 𝑪𝑳 vs 𝜶 at Re 202000 and Re 269000. ............................................... 148 Figure 110 TORNADO Analysis for 𝑪𝑳 vs 𝜶 at Re 202000 and Re 269000. ........................................ 148 Figure 111 𝑪𝑳 and 𝒑 comparison between Conventional T240 and Morphing Wing at Re 202000 and Re 269000. .......................................................................................................................................... 149 Figure 112 𝒑 comparison between Conventional T240 and Morphing Wing at various Reynolds Numbers. ............................................................................................................................................. 151 Figure 113 Morphing Wing performance comparisons at 𝜹𝒎 = 0° to 𝜹𝒎 = 40° at various Reynolds numbers .............................................................................................................................................. 159 Figure 114 Lifting lines in both spanwise and chordwise directions superimposed onto a wing [33, 89] ............................................................................................................................................................ 163 Figure 115 Velocity (the direction is coming out of the paper) induced at point P by the infinitesimal segment of the lifting surface[33]. ..................................................................................................... 164 Figure 116 Single horseshoe to a system of horseshoe vortices (Vortex lattice) on a finite wing [33]. ............................................................................................................................................................ 166 Figure 117 Nomenclature for calculating induced velocity by a finite length vortex segment [89]. . 167 Figure 118 A typical horseshoe vortex [89]. ....................................................................................... 168 Figure 119 Vector elements for the calculation of induced velocities [89]. ....................................... 169 Figure 120 Nomenclature for tangency condition: (a) normal to element of mean camber surface, (b) section AA, (c) section BB [89] ............................................................................................................ 171 Figure 121 Dihedral angle [89]. ........................................................................................................... 171

Table 1 Morphing Skin Concepts. ......................................................................................................... 22 Table 2 Material combinations tested by Kirn [66]. ............................................................................. 27 Table 3 Summation of flow visualisation behaviour ............................................................................. 58 Table 4 Difference in results for XFLR5 and TORNADO to experimental results. ................................. 83 Table 5 High-lift device comparison of the conventional T240 and the morphing wing at Re 168000. .............................................................................................................................................................. 85 Table 6 Comparison of the roll performance between the conventional T240 wing and the morphing wing at Re 337000. ............................................................................................................................... 86 Table 7 Comparison of conventional T240 and morphing wing in cruise condition at Re 337000 ...... 87 Table 8 Experimental results of similar morphing concepts in literature [34, 49, 51, 76, 86]. ............ 88 Table 9 Load results for the calibration of the JR3 load cell in the x-axis (Lift axis). .......................... 101 Table 10 Load results for the calibration of the JR3 load cell in the y-axis (Drag axis). ...................... 103 Table 11 Pure moment Yaw results for the calibration of the JR3 load cell in the y-axis (Drag axis). 104 Table 12 Pure moment Roll results for the calibration of the JR3 load cell in the x-axis (Lift axis). ... 107 Table 13 List of non-converged conditions in XFLR5 .......................................................................... 159

viii

Nomenclature

b Wingspan, in 𝑚

c Chord, in 𝑚

Coefficient of Lift 𝐶𝐿

Section Lift coefficient 𝐶𝐿𝑙𝑜𝑐𝑎𝑙

Coefficient of Drag 𝐶𝐷

Induced Drag 𝐶𝐷𝑖

Parasite Drag 𝐶𝐷0

Rolling moment coefficient 𝐶𝑙

Lift-curve slope 𝐶𝐿𝛼

Aileron effectiveness 𝐶𝑙𝛿

Coefficient of Pressure 𝑐𝑝

Specific fuel consumption 𝑐𝜏

Drag, in N 𝐷

Oswald efficiency factor 𝑒

Fuel consumption, in 𝑘𝑔/ℎ 𝐹

Frequency, in ℎ𝑧 𝑓

Mass moment of Inertia about x-axis, in 𝑘𝑔/𝑚2 𝐼𝑥𝑥

Lift, in N 𝐿

Roll Moment, in Nm L

Lift to Drag ratio 𝐿/𝐷

Moment, in Nm 𝑀

Roll rate, in 𝑑𝑒𝑔/𝑠 𝑝

𝑝̇ Roll rate acceleration, in 𝑑𝑒𝑔/𝑠2

𝑞 Dynamic pressure, 1/2𝜌𝑉2

S Wing area, in 𝑚2

𝜌∞𝑉∞𝑑 𝜇∞

Re Reynolds number,

Aircraft Weight, in N 𝑊

Airspeed, in 𝑚/𝑠 𝑉

Stall Airspeed, in 𝑚/𝑠 𝑉𝑠𝑡𝑎𝑙𝑙

Angle of attack, in 𝑑𝑒𝑔 𝛼

Angle of attack at which stall occurs, in 𝑑𝑒𝑔 𝛼𝑠𝑡𝑎𝑙𝑙

Rotation angle of load cell, in 𝑑𝑒𝑔 𝛽

Deflection angle, in 𝑑𝑒𝑔 𝛿

Morphing wing deflection angle, in 𝑑𝑒𝑔 𝛿𝑚

Flap deflection angle, in 𝑑𝑒𝑔 𝛿𝑓

Aileron deflection angle, in 𝑑𝑒𝑔 𝛿𝑎

Angle, in 𝑑𝑒𝑔 𝜃

Control arm angle at zero deflection in the morphing wing, in 𝑑𝑒𝑔 𝜃𝑜𝑓𝑓𝑠𝑒𝑡

Recorded control arm angle at a deflected position for the morphing wing, in 𝑑𝑒𝑔 𝜃𝑟𝑒𝑐𝑜𝑟𝑑𝑒𝑑

Viscosity, in 𝑘𝑔/𝑚𝑠 𝜇

p Density, in 𝑘𝑔/𝑚3

Dihedral angle, in 𝑑𝑒𝑔 Γ

Change in (subscript) ∆

Sweep angle, in 𝑑𝑒𝑔 Λ

Subscripts

𝑚𝑎𝑥 Maximum

𝑚𝑖𝑛 Minimum

𝑥 About x-axis

𝑦 About y-axis

𝑧 About z-axis

𝑑𝑎𝑚𝑝𝑖𝑛𝑔 Due to damping

1/2𝑏 Half wing

𝑖 Initial

𝑟 Recorded

𝑀𝑊 Morphing Wing

𝑏𝑜𝑑𝑦 The Aircraft body without the wings

𝑜𝑢𝑡𝑝𝑢𝑡 Recorded output of JR3 load cell

𝑖𝑛𝑝𝑢𝑡 Recorded input for the JR3 load cell

𝑝ℎ𝑎𝑛𝑡𝑜𝑚 Non-physical occurrence in load cell

𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 When moment/force is linked to another parameter

𝑑𝑒𝑐𝑜𝑢𝑝𝑙𝑒𝑑 When a coupled moment/force is separated from the coupled parameter

Abstract

Morphing wings were once in the common in early aviation however due to a lack of strong and lightweight materials they were abandoned in favour of conventional wings. Due to the recent advances in smart technologies, morphing wings has become of interest in aviation. This paper proposes the use of internal mechanisms to promote morphing in a wing to increase aerodynamic performance as opposed to the smart technologies. To determine the aerodynamic superiority of the morphing wing it was compared to a conventional wing of the same geometry. The remote-control (RC) aircraft Precedent T240 was used as the basis of the wing design for the morphing wing. The FishBAC (Fish Bone Active Camber) morphing concept is used in this research, to design and prototype a morphing wing for the Precedent T240 RC model aircraft. The simplicity and cost effectiveness of the internal mechanisms will allow for a wider audience to adopt the morphing wing design. The conventional wing will be compared to a morphing wing of the same geometry through simulations and wind tunnel testing. The morphing wing required a compliant morphing skin suitable to facilitate the extension of the top surface and contraction of the lower surface of the wing. A FMC (Flexible Matrix Composite) skin was developed for facilitation of extension the top surface of the wing whilst the contraction of the bottom surface was bypassed through the usage of a thin aluminium plate. The morphing wing and the conventional wing performance were simulated using the TORNADO program and the XFOIL adapted XFLR5 and validated experimentally through wind tunnel testing. The wind tunnel experiments showed that the morphing wing had superior aerodynamic performance in comparison to the conventional wing, with the exception of stall speed due to the increased weight of the morphing wing. The theoretical results accurately predicted the performance of the morphing wing for low morphing deflections and angles of attack. The results have shown that the design of the morphing wing is acceptable as a simple and an affordable option. Due to the higher performance (in most areas) while considering the weight penalty due to the more increased complexity of a morphing wing system as opposed to a conventional wing system. Hence a FishBAC morphing wing is aerodynamically superior to its conventional counterpart.

Keywords: Morphing wing, FishBAC, wind tunnel testing, XFLR5, TORNADO, Flexible Matrix Composite

1 Introduction A morphing object is an object that undergoes a large change in form or shape [1], therefore a morphing wing is a wing which undergoes a continuous change in its wing geometry to adapt to its mission profile [2]. By altering the wing mid-flight, in theory the wing will be able to increase its aerodynamic performance with a small increase in drag. Although flaps, ailerons and other conventional control surfaces do change the wing geometry it is not considered as morphing the wing, since it causes a discontinuous profile.

There is an increasing pressure for aircraft designs to become quieter and more efficient due to regulations on noise pollution and carbon emissions [3, 4]. Reducing noise pollution and carbon emissions could both be achieved by implementing morphing wings into commercial aircraft [4]. With the emergence of advanced materials, further research into morphing wing design and their aerodynamic benefits can be explored.

While conventional rigid wings use hinged control surfaces which causes breaks in continuity of the curvature of the wing profile, hence increasing parasite drag. While an advantage of morphing wings are the smooth continuous gapless control surfaces which will reduce the drag [5]. Profile discontinuities, sharp edges and deflected surfaces cause the aircraft to be more prone to detection in both radar and acoustics [6].

Morphing wings provide various benefits for aircraft depending on the type of morphing wing the aircraft adopts, however there are general advantages that all morphing wings offer. Morphing wings improve the aerodynamic efficiency of the aircraft since they have smooth continuous profile [2, 7] (discontinuous profiles cause disrupted airflow) and can increase the lift coefficient for the same altitude through changes in wingspan, chord length, camber, and sweep. Implementing morphing wings can also lead to a reduction in noise due to the lack of control surfaces [8]. The improved aerodynamic performance of an aircraft results in less fuel consumption and results in improved range [7]. The lift-drag ratio is also improved due to the increase in lift from morphing deflection [7]. This is shown in equation 1 where fuel consumption (𝐹) is dependent on the specific fuel consumption, weight of the aircraft and the lift-drag ratio, 𝐿/𝐷 [9]. In general, the largest amount of time for a flight profile is spent in the cruise. During cruise at the recommended setting, fuel consumption is dependent on the specific fuel consumption 𝑐𝑇, lift-to drag ratio 𝐿/𝐷 and the weight of the aircraft, 𝑊.

𝐶𝐷 𝐶𝐿

𝑊 (1) 𝐹 = 𝑐𝑇

Decreasing the fuel consumption would increase the endurance of an aircraft. Decreasing 𝐹 could be done by decreasing engine specific fuel consumption, increasing the lift-drag ratio and/or decreasing the weight of the aircraft. A solution to increase the lift-drag ratio is to change the camber line of the wing by altering the shape of the airfoil [9].

Figure 1 Principles of aircraft drag polar affected by airfoil camber variation in steady cruise flight [10].

In Figure 1, the linear dashed line from the origin represents the maximum 𝐿/𝐷 written as 𝐶𝐿/𝐶𝐷. For a fixed airfoil section wing, as angle of attack, 𝛼 increases the 𝐿/𝐷 decreases. The lift coefficient, 𝐶𝐿 is not exclusively determined by 𝛼, by altering the airfoil profile through camber morphing 𝐶𝐿 can be increased. The objective of morphing the airfoil wing section is to follow the optimal 𝐶𝐿/𝐶𝐷 for any given 𝐶𝐿. Typically, the cruise phase of flight for an aircraft is the longest phase of flight for an aircraft. For unmanned aerial vehicles, UAVs this is emphasised since there is not a human component thereby the operation of the UAV is not limited to human stamina [9]. Hence morphing to maximise the lift- drag ratio during the entire cruise of the aircraft is the ideal outcome.

Due to their complexity, morphing wings are more difficult to design and are generally heavier than conventional wings [11, 12].

The objective of the research was to confirm the increase in aerodynamic performance that comes with camber morphing in comparison to the aerodynamic performance of a fixed airfoil wing. The specific aerodynamic performance examined in this study were lift coefficient, lift-drag ratio, rolling moment coefficient and the initial roll rate. A remote control, RC aircraft was used as the base of the research. The conventional fixed airfoil wing’s performance was compared to the morphing wing’s performance. The RC aircraft used was the Precedent T240 which is a scale model of the Cessna 180 aircraft, the design of the T240 wing illustrated in Figure 2. To compare the conventional T240 wing to the morphing configuration, the morphing wing must have geometry to the conventional wing so that it can be retrofitted to the T240 aircraft. As such the morphing wing was designed for the T240 aircraft, which is seen in Figure 3. In the morphing wing configuration, the ailerons and flaps were removed because the entire morphing section of the wing (aft of the spar) acts as the control surface as shown in Figure 3. The spar of the T240 ends at 30% chord. Hence 70% of the chord aft of the spar

was used for morphing. The T240 features two struts, to support the wing. The morphing wing removes the rear strut of the wing to allow for further morphing.

Figure 2 Precedent T240 aircraft and its wing’s dimensions in plan view.

Previous research was conducted on the camber morphing wing, seen in section 3 which concluded in a skeleton design of the morphing wing and an actuation system. To achieve the objective of aerodynamic analysis of the morphing wing, a suitable skin and a prototype of the morphing wing was required. Previous research did not achieve a skin that maintained a zero Poisson’s ratio and provided spanwise structural support. Hence in this study a morphing skin was designed and manufactured for the purpose of wind tunnel testing. The morphing skin design underwent many iterations before satisfying the spanwise support and achieving a zero Poisson’s ratio. Which was accomplished via a “dual” skin, where the upper and lower surfaces of the wing used different materials as a skin. The upper surface skin was a Fibre Matrix Composite, FMC where the matrix material was silicone and the fibre material was carbon fibre. The lower surface skin was a thin aluminium plate that bends when the morphing wing was deflected.

UAVs are the ideal test bed for morphing technologies, due to their small size, ability for autonomous navigation and control, are cheaper to build than full scale aircraft and lack of pilot making it safer than manned aircraft.

Figure 3 Morphing wing dimensions in plan view.

2 Literature Review The Morphing Aircraft Structures (MAS) program by Defense Advanced Research Projects Agency (DARPA) defines morphing aircraft as a multi-role platform that changes its state to adapt to changing environments providing superior system capability not possible without reconfiguration [13, 14]. Additionally, morphing aircraft uses designs that integrates innovative combinations of advanced materials, actuators, flow controllers and mechanisms to achieve the state change [13, 14].

The morphing wing concept was introduced before the first powered flight in 1903 [15]. However due to the technological limits at the time that is materials available during that time were not strong and flexible enough, the concept was abandoned in favour of rigid wings i.e. conventional wings.

Birds inspired early aviators to pursue flight which led to the pursuit of morphing vehicles. The smooth and continuous shape-changing capability that birds possess however was beyond what was technological capable at the time. Aviators turned to variable geometry designs using conventional hinges and pivots both of which were used for many years. Since the recent advances in aerodynamics, controls, materials and structures the interest in morphing vehicles have been reignited and bird-like flight that is smooth and continuous shape change for aircraft is now once again pursued [16].

Valasek mentioned that that the connection between bio-inspiration and aeronautical engineering is an important one [16]. As without birds (or bats) the concept of flight may have never occurred to early aviators. Otto Lilienthal a Prussian aviator who lived in the nineteenth century, was fascinated by bird flight which led him to become a designer. He insisted on using flapping wing tips instead of the conventional propeller due to his fascination of bird flight. From his observations of bird flight particularly their twist and camber distributions led to the development of his air-pressure tables and airfoil data. Several early pioneers recognized the value in morphing as a control effect [17].

The Wright brothers used wing warping for lateral control. The warping was accomplished by attaching wires to the pilot’s belt and controlled by the shifting body position. The Etrich Taube design series were completely bio-inspired except for the omission of flapping wings [16]. The Wright and Taube designs demonstrated that warping controls can be effective on aircraft with thin and flexible

wings. However, conventional hinged controls; ailerons and rudders, were more appropriate for aircraft with rigid structures. The technological state of materials at the time was not advanced enough to allow usable warping for high performance aircraft hence the conventional control surfaces were used. However, morphing was still achieved as the geometry of wings camber was actively altered via conventional hinges, pivots and rails [8, 16].

The design by the Wright brothers showed that warping controls can be effective on aircraft with thin and flexible wings. One of the first successful modern morphing flight was due to Ivan Makhonine, the aim was to improve cruise performance by reducing induced drag due to lift. Makhonine used in-flight wing planform area morphing to reduce the landing speed while providing a smaller wing for high- speed flight. He developed a telescoping wing planform which was used on the MAK-10 seen in Figure 4 [18, 19].

Figure 4 Makhonine Mak-10 aircraft [4].

In the 1950s variable geometry research sponsored by NASA led to experimental transonic designs such as the Bell X-5. The X-5 was the first full scale aircraft that was capable of wing sweep during flight, seen in Figure 5 at different sweep settings. Take-off and landing were improved when the wings were fully extended and at low speeds whilst high speed performance and drag was reduced when the wings were swept backwards. The wing could be swept to 20°, 45° and 60° during flight and were tested at both subsonic and transonic flight [18, 19, 20].

Figure 5 Examples of variable sweep wings [4].

The AFTI F-111 Mission Adaptive Wing (MAW), was intended to minimize the penalties for off-design flight conditions through smooth-skin variable camber and variable wing sweep angle. Since the MAW has variable camber surfaces it does not suffer from discontinuous surfaces or exposed mechanisms that conventional aircraft experience. Because of the smooth flexible upper surfaces and fully enclosed lower surfaces that can be actuated during flight to provide the desired camber. Due to the success of the program advancements to a fully morphing aircraft were made. The variable geometry concept found its way into commercial air transport, it was considered for various conceptual designs such as the Boeing 2707 Supersonic Transport in the 1960s. Due to the success of the variable geometry concept, bio-inspiration was overlooked or it was not considered promising enough during the period [8, 16].

Recent discoveries in bird flight mechanics and new insights of bio-inspired research resulted in the re-ignition of using flying animals as a design base for morphing aircraft. And the recent advances in materials, where materials are strong, lightweight and flexible also contribute to the re-ignition in morphing wing design research.

Research programs have appeared in the recent years bringing in most of the early morphing concepts including bio-inspiration, warping, shape changing, variable geometry, structures, materials, controls and aerodynamics. The NASA morphing aircraft project developed from the Langley Research Centre (LaRC), was program conducted from 1994-2004 [8].The program sponsored research across a wide range of technologies that included biotechnology, nanotechnology, biomaterials, adaptive structures, micro-flow control, biomimetic concepts, optimization and controls. The focus of this project was to bring together the NASA morphing unmanned air vehicle. The aircraft concept was made up of the various morphing concepts which include bio-inspiration, warping, shape changing, variable geometry [8, 16, 18, 19].

2.1 Types of Morphing Wings Early aircraft like the Wright flyer were bio-inspired from observing birds, for their wing warping capabilities [21]. Nature provides a rich source of inspiration for the new generation of morphing wings. During flight, animals perform active changes in wing shape that are associated with stability and manoeuvre control and those that are associated with the wingbeat cycle [7]. Biological wings i.e. wings of birds, bats and insects are of morphing designs with continuous variable planform, camber or twist. It can be said that morphing wings are the norm of small scale flying in nature whilst for engineers’ rigid wings have been the norm for all aircraft. The limitation to rigid wing design is due to a lack of material strength and flexibility. Due to recent developments of new materials, bio-inspired morphing wings are once again of interest to engineers [22].

Due to advances in technology, modern morphing systems use shape memory alloys, piezoelectric, magnetostrictive materials, magnetorheological fluids and electrorheological fluids into compliant structures activated by electric fields, temperature or magnetic fields [8]. Where a compliant structure could be a structure that is flexible and changes its shape through elastic deformation. Smart material based morphing wings will be covered in section 2.2.2 and 2.2.3.

Birds have been the main driving force for bio-inspiration among morphing structures for engineers. The fascination of birds led to the Wright brothers’ developing the wing-warping control system which eventually led them to undertake the first powered, manned and controlled flights. It should be noted that birds have a total of three morphing structures; two being the wings and the third being their

horizontal tail, the tail changes its shape similarly to the changes in the wings [16]. Birds can rapidly morph between different planforms [7]. The changes in wing area are possible due to the degree of overlap between feathers changes as the bird flexes, spreads its wings and tail. The feathers create the lifting surfaces of the wing, which comes from the follicles within the skin and which in the case of the flight feathers is attached by ligaments to wing bones. The flight feathers are large feathers that are responsible for most lift and thrust during flight. They are flexible structures, and the slight roughness may generate turbulence even when they lie flush to the wing surface [8, 16, 18, 19].

As for mammals only bats can fly (mammals that are capable of gliding such as the flying squirrel are not considered to be flying mammals). A bat’s wings must resist extensive load changes over the course of a wingbeat cycle, to accommodate this, their wings have evolved to sustain the forces associated with powered flight. Bat wings are composed of an elastic muscularized membrane that is stretched between the digits of their hands, hindlimbs and body, this enables high-order control of the wing. Bat wing bones experience torsional loads whereas bones of other mammals’ experience bending loads. The bones of bats are highly dense which correlates with strength and stiffness; therefore, the bones of the wing are relatively strong and heavy [16].

into three major groups: planform alternation, out-of-plane Morphing wings can be split transformation, and camber change. Planform alternation is when the wing is altered through a change in area or wing sweep adjustment. Out-of-plane transformation is when the wing is twisted or the chord or the span wise camber are adjusted. Airfoil adjustment is when the thickness of the airfoil is altered.

Planform alternation and out-of-plane transformation both have multiple methods of morphing. Planform alternation has three general methods of alteration; wingspan adjustment, change in chord length and change in sweep angle. Out-of-plane transformation also has three general methods of alteration: chord-wise bending, span-wise bending and wing twisting [2]. All these methods of alteration can be broken down into various methods.

There are various types of morphing structural arrangement some of these include: Fish Bone Active Camber (FishBAC), Compliant Spar, Zig-zag wingbox and Gear Driven Autonomous Twin Spar (GNATSpar) [6, 23, 24, 25].

Conventional control surfaces such flaps, slats and landing gears are discrete morphing [14]. The discontinuous structure caused by these control surfaces results in loss of aerodynamic efficiency. Whereas morphing structures provides continuous wing profile hence no loss in aerodynamic efficiency, due to their morphing nature the aerodynamic efficiency of the morphing wing is more efficient than the conventional wing.

Since morphing wings change their wing geometry, the skin of the wing is required to morph with the wing. These skins are called morphing skins, morphing skins are generally comprised of flexible rubber like material such as silicone, this is explored further in section 2.6.

2.1.1 Planform Morphing

2.1.1.1 Wingspan Wingspan is generally adjusted by using telescopic structures seen in Figure 6, where the span of the wing is increased. Another method of span alteration is to use a scissor like mechanism [26]. The

planform can also be altered by using extendable ribs and spars which enable independent changes in span and chord [27].

Low aspect ratio wings suffer from poor aerodynamic efficiency however they fly faster and are more manoeuvrable [24]. Hence the drag of the wing is reduced therefore the range/endurance of the aircraft is increased. Increasing the wingspan, leads to an increase in aspect ratio. Which has a major effect on aerodynamic performance as aspect ratio is relevant in many aerodynamic properties such as: lift therefore induced drag 𝐶𝐷𝑖, lift-drag ratio, range and endurance [28, 29, 30]. Hence in wingspan morphing designs, both wingspan contraction and extension should be utilized.

Increasing the wingspan leads to an increase in wing root bending moment [30]. Ajaj et al conducted analyses, which showed that by increasing the wingspan by 50% led to a 50% increase in wing root bending moment [6]. With increased wingspan, spanwise lift distributions and induced drag are decreased for the same lift [25, 30]. Neal et al found that increasing the wingspan results in a low drag for higher 𝐶𝐿 [29]. In Neal’s wind tunnel experiment, at zero span change, 𝐶𝐿 = 0.6 and at a 100% increase in wingspan 𝐶𝐿 ≈ 0.68 at both conditions 𝐶𝐷 = 0.15 [29]. Hence maintaining a low drag for higher 𝐶𝐿 also results in a higher lift-drag ratio. Using a telescopic wing design, Blondeau et al increased the aspect ratio of the wing by up to 114% [28]. Within the telescopic archetype of span morphing, there are two sub-archetypes. The first, features telescopic shells which has each subsequent shell being smaller than the previous one resulting in a step between each telescopic shell. Therefore, the chord progressively decreases between each shell, resulting in a slight tapering effect. The step between each of the shells results in the generation of parasite drag. The skin for this wing type is rigid. The second, uses an extendable spar mechanism, this type is covered by a compliant skin [14, 24]. Compliant skin or morphing skin will be covered in section 2.6.

Rolling moment generated by asymmetric span morphing is sensitive to angle of attack [24]. While conventional ailerons do not display this behaviour therefore morphing wing aircraft should not be operated in the same manner as conventional aircraft. Additional inertial terms are introduced in the roll equation of motion when using span morphing. Assuming the basic operating weight is kept, excess span morphing yields diminishing returns in endurance. A 35% increase in wingspan resulted in a 6.5% increase in endurance whilst a 22% increase in wingspan resulted in 6% increase in endurance [24]. A 22% increase in wingspan can reduce the take-off field length and landing distance by 28% and 10% respectively. Ajaj et al determined that span morphing becomes less effective as the weight of the aircraft increases and becomes detrimental if the weight of the morphing aircraft is 12.5% heavier than the conventional counterpart [24] .

Figure 6 Span morphing wing via telescopic wing [28].

2.1.1.2 Chord Length Changes Changes in chord length are usually achieved through the extension or retraction of leading edge or the trailing edge, by usage of actuation systems. Another method is to change the chord length without resizing any leading or trailing edge flaps using an interpenetrating rib mechanism through DC motors and lead screws [31]. A visualization of increasing chord is illustrated in Figure 7. By increasing the chord length, the wing area S, increases therefore increasing lift. Perkin et al achieved a chord length increase by using sliding ribs, they also considered telescopic ribs to increase chord length [32]. Chord length change can also be achieved by using extendable ribs and De costa used screws that when rotated would lengthen the chord size of the rib [27].

2.1.1.3 Sweep Sweep angle variation is usually achieved by pivoting the wings of the aircraft. However, sweep angle can also be actuated by two electromechanical, lead screw actuators [29]. Another wing sweep is based on bi-stable composite spars that are interconnected with a truss-rib structure [29]. A change in sweep concept is illustrated in Figure 7.

Sweep changes the aerodynamic centre and Centre of Gravity (CG) position, the change in position depends on the sweep angle, which in turn changes the aircraft stability. Hence affecting handling and control of the aircraft. Sweeping wings at high speeds can decrease the drag the wing generates [6, 30]. In their fully swept position Neal found that the both the maximum 𝐶𝐿 and minimum 𝐶𝐷 increases from the unswept case [29]. From Neals experiment, sweep also increases 𝛼𝑠𝑡𝑎𝑙𝑙, i.e. increases the angle at which stall occurs [29]

Sweep is generally suited for trans-sonic flight, As the wing is swept back it reduces the normal velocity component of the airflow to the leading edge. Which means that the normal velocity component of the airflow is smaller than the actual airspeed hence reducing compressibility effects, wave drag and lift. Siouris found that by sweeping the wings back generate an increase in lift-drag ratio by up to 80% by sweeping the wing from 20° to 40° for the same lift conditions [3]. The increase in lift-drag ratio was due to the decrease in wave drag. Siouris obtained a maximum lift-drag ratio at Λ = 40° for their given conditions [3]. Siouris found that sweeping the wings forwards had an adverse effect on lift-drag ratio [3].

Figure 7 Planform alteration types [2].

2.1.2 Out-of-Plane Morphing

2.1.2.1 Camber Morphing Camber morphing is usually achieved by bending the wing at any given point/s along the chord of the wing seen in Figure 8 this method is quite common in literature. Camber morphing can be conducted through multiple actuation methods such as the use of internal mechanisms, piezoelectric actuation and shape memory alloy actuation [2].

Figure 8 Camber morphing concept visualization [2].

This principle is like flaps however unlike flaps which are non-discrete and non-continuous, camber morphing features continuous surfaces and can be discrete geometrical changes in the airfoil section. Since the principle of camber morphing is like the flap, it features the same aerodynamic advantages with a smaller drag penalty than conventional flaps. Such as the lift is increased in comparison to the non-cambered counterpart of the wing, the zero-lift angle of attack becomes more negative [33].

Morphing camber designs have become compliance based over the years [23]. Camber morphing has been used in variety of applications such as helicopter rotors, ship rudders, submarines and hydrofoil boats [23]. Increasing camber leads to a shift in the drag polar of the airfoil and causes an increase in 𝐶𝐿 for a minimal drag penalty [9]. Which increases the lift-drag ratio of the aircraft, which can lead to an increase in endurance and range as both are dependent on lift-drag ratio. However, the increase is subject to the increased weight of the morphing wing system. Variable Cambered airfoils have higher stall angles and higher lift-drag ratio than rigid cambered airfoils [34] and by extension non-cambered airfoils.

2.1.2.2 Span-wise Bending Span-wise bending morphing is usually achieved by bending the wing at any given point/s along the span of the wing, seen in Figure 9. Span-wise bending morphing could also be morphing dihedral, this is seen in Figure 9. Span-wise bending morphing wings benefit from dihedral effects such as lateral and longitudinal control [12].

Figure 9 Span-wise bending morphing concept [2].

Span-wise bending wings can be applied to wing-in-ground-effect vehicles. When wing-in-ground- effect vehicles fly close to the surface, they benefit from an increase in lift and a reduction of drag. Applying variable dihedral morphing to wing-in-ground-effect vehicles can benefit in reduced drag and increased lift while in ground effect [12]. While at high altitude it can be used in the standard planar wing configuration i.e. the non-morphed condition. Therefore, span-wise bending morphing wings can benefit from the wing-in-ground-effect when flying close to the surface and transition to conventional planar wing configuration at higher altitudes.

Wiggins et al saw that as wingspan undergoes wingspan bending downwards, side force coefficient increases towards the wingtip this is due to the pressure force acting normal to the wing surface [12]. Wingspan bending also affects the distribution of lift and side forces generated by the angle of attack and camber of the airfoil changes. Span-wise bending morphing increases the Oswald efficiency factor, 𝑒, however the total induced drag also increases [12]. It should be noted that as span-wise bending morphing increases the projected wingspan of the wing decreases. This is seen in Wiggins et al study where in the fully morphed case, the projected wingspan decreased by 11% [12]. In the same case the drag of the fully deflected case was 10% larger than the drag of the non-deflected wing for the same lift.

2.1.2.3 Wing Twist Wing twisting (seen in Figure 10) is usually achieved by twisting the wing at any given point/s along the span and the chord of the wing. This method is similar to the chord wise morphing as the camber along the span does change but it is not uniform as the span before the twist remains the same. However, unlike camber morphing, the camber remains the same but the angle of attack of the wing changes instead. By wing twisting can obtain low-drag and high lift [30]. This morphing method is not as common in literature as others due to the complexity of the morphing method [35]. Wing twisting morphing can be used for roll control.

Figure 10 Wing twisting concept seen in the 1899 Wright Kite [36].

A disadvantage of the concept is that to enable the morphing, most of the inner space of the wing must be utilized to achieve morphing. Positive twist increases lift and drag however it also provides greater roll performance [35]. From their experiments, Rodrigue et al found that for 𝛼 ≤ 8° with wing twisting the coefficient of lift increased with minimal drag increase [35]. However, the drag had a major increase for 𝛼 > 6° and for 𝛼 = 10° the wing twisted wing had a similar coefficient of lift as the conventional configuration [35]. This shows that for wing twisting has diminishing returns at higher angles of attack. Rodrigue et al found that lift-drag ratio is also increased for wing twisting morphing for 𝛼 ≤ 6° [35]. Wing twisting sees the most gains in lift-drag ratio for lower angles of attack, where at 𝛼 = 2°, Rodrigue et al saw an increase of approximately 13% for lift-drag ratio [35].

2.1.3 Airfoil Adjustment Airfoil adjustment is when the airfoil shape is changed without majorly affecting the mean camber line, as shown in Figure 11. This could be done by changing the thickness distribution of the base airfoil using actuators, as shown in Figure 12. With this morphing method, the wing would be able to morph between its normal thickness to a desired thickness. Hence, the wing can alternate between thin or thick body aerodynamic properties depending on flight phase. Thin airfoils suffer from flow separation at lower angles of attack and a lower section lift coefficient, 𝑐𝑙 [33]. Thin airfoils however have lower drag characteristics and is much better suited for supersonic flow [33]. Thick airfoils suffer from higher drag coefficients however they provide higher maximum lift coefficient [33]. This means that thick airfoils also have a higher rate of climb than the thin airfoil counterparts [33]. Therefore, this method is not as popular as the other morphing methods since thin airfoil sections are better suited for supersonic flow. And most applications morphing is required for subsonic flow.

Figure 11 Airfoil adjustment morphing concept visualization [2].

Figure 12 Airfoil adjustment via actuators inside the wing [37].

2.2 Morphing Wing Actuation There are three general methods to morph a wing which are: morphing through internal mechanisms, piezoelectric actuation, and shape memory alloy actuation. Disadvantages of smart materials-based actuators are their limitations in achievable active strain, blocking stress or actuation frequency [38]. Actuation characteristics of smart materials are dependent on the physical principle they are based on. Currently there is no solution that can satisfy all three properties: strain, stress, and frequency [38]. Because of this there are not many concepts that have reached the wind tunnel testing or flight- testing phase. Since the response time of shape memory actuators tend to be slow, they are not suited for fast response situations in flight.

Smart material-based actuators can limit some of the structural properties of a wing, such as usage of smart material-based actuators as the part of the skin to be compliant with the morphing wing. Giulio found that in some cases the smart material-based actuators negatively impacted the aerodynamic properties which in turn nullified the lightweight advantage [38].

2.2.1 Internal Mechanisms Morphing is achieved through the alteration of the internal structure of the wing. Where rib deformation via hinges is the most common [2], there are various methods to achieve this such as the segmenting the ribs or by altering the leading edge and/or trailing edge by means of actuators [2]. This method can typically be used for airfoil adjustment, sweep and increase in span examples are shown in Figure 6, Figure 7 and Figure 12.

Internal mechanisms include linear actuators, servos, stepper motors and pneumatic actuators [26, 34, 39, 40, 41, 42, 43, 44, 45]. Hinges, joints and a combination of threaded nuts and bolts are often seen with the aforementioned internal mechanisms [26, 34, 39, 40, 41, 42, 43, 44, 45]. Compliant mechanisms can be used in tandem with the hinges and actuators as seen in Vasista et al and Yang et al [41, 46]. Variable geometry truss manipulators have also been used as a mechanism to achieve morphing [40].

Linear actuators and pneumatic actuators operate in a different manner from one another, but both use horizontal translation to achieve morphing in morphing wings. Where linear actuators and

pneumatic actuators use electrical and compressed air/gas respectively, to actuate. Linear actuators and pneumatic actuators were used in the works of Moosavian, Monner, Joo, Yang and Poonsong [26, 34, 40, 43, 45].

Rotational forces utilized by electric servos, stepper motors and threaded nuts and bolts (which use rotation to translate the mechanism) are another method of actuating morphing wings [39, 41, 42, 44].

Internal mechanisms have been used in the follow morphing configurations: Span and chord extension morphing, spanwise bending, camber and sweep [26, 34, 39, 40, 41, 42, 43, 44, 45]. Hence showing the versatility of internal mechanisms as the actuation method of a morphing wings.

2.2.2 Piezoelectric Actuators Morphing by piezoelectric actuation is achieved through the deformation through electrical current i.e. when the piezoelectric material experiences an electrical current the material deflects. Piezoelectric actuators are generally used in high frequency applications like rotary wing aircraft and controlling local flow, they also generally have small deflections that require high voltage [5].

2.2.3 Shape Memory Alloys Shape memory alloys (SMA) has the property of shape memory as the name implies can return to the initial shape after being deformed by a weight load that is activated by heat caused by an electrical current [47]. Morphing is achieved through the electrical current, the concept of the shape memory effect can be seen in Figure 13. The shape memory alloys can be woven with anisotropic fibres to be used as wires. Since SMA require heat to be maintain the desired shape, more energy is required by the system hence the system is less energy efficient. The actuation mechanism may interfere with other system components for example structural ribs [48]. SMA actuators can develop permanent strain throughout life due to the heat cycles this result in actuators becoming loose and their length must be adjusted.

Figure 13 A SMA spring actuator recovering its original shape after heating [47].

2.3 Examples of Morphing Structures

2.3.1 Fish Bone Active Camber (FishBAC) The structure of a FishBAC is generally made up of a rib that consists of thin chordwise bending beam spine with stringers branching off that are connected to a pre-tensioned elastomeric matric composite (EMC) skin surface, seen in Figure 14. Structural deformation occurs though compliance hence

mechanisms, linkages or sliding skins are required. The deformation of the FishBAC occurs through compliance, the bending deflections are caused by a high stiffness tendon system.

The design of the core and skin feature near-zero Poisson’s ratio in the spanwise direction. By pre- tensioning, the skin in the chordwise direction the out-of-plane stiffness is increased whilst also prevents lower surface skin buckling when morphing. The out-of-plane stiffness is increased by pre- tensioning the skin in the chordwise direction this also eliminates lower surface skin buckling when undertaking morphing. In Woods et al design actuators are mounted in the D-spar drive, a tendon spooling pulley through a non-backdrivable mechanism i.e. large loads are unable to displace the deflection of the system [23]. Since the tendon system is non-backdrivable, no actuation energy is required to hold the deflection position of the structure this also allows the stiffness of the tendons to contribute to load carrying (chordwise bending is experienced when under aerodynamic loads), without increasing the energy required to deflect the structure.

Figure 14 FishBAC rib design [23].

FishBAC is more aerodynamic efficient than traditional trailing edge flaps since there was a 25% in lift- drag ratio at equivalent lift conditions [23]. In Woods’ comparison with the flapped airfoil the 𝐶𝐿𝑚𝑎𝑥 was almost identical 𝐶𝐿𝑚𝑎𝑥 = 1.07 for the morphing condition and 𝐶𝐿𝑚𝑎𝑥 = 1.08 for the flapped condition [11]. The 𝐶𝐿𝑚𝑎𝑥 however did occur earlier by an angle of attack of 1.2°. Woods did not encounter a drop off in morphing benefit in their testing. Woods believes this means that the trailing edge separation phenomena was delayed [11].

Increasing camber deflection shifts the drag polars left for a 𝐶𝐷 vs 𝛼 plot, which means minimum drag becomes increasingly negative. Woods also found due to morphing there was an increase in lift and only a small increase in drag [11]. This is supported by Woods experimental data where the increase in zero lift drag coefficient from zero deflection to maximum deflection was 0.009, which was 59% of their minimum zero lift drag coefficient [11]. The FishBAC design has higher lift-drag ratio and can maintain it longer over a range of angles of attacks roughly a range of 9.05°, it does however plateau. While flaps have a smaller range of maximum lift-drag ratio, a range of 3.6° [11].

Further work conducted by Woods et al shows variation in the utilization of the FishBAC, where the FishBAC is utilized for the trailing edge [49] seen in Figure 15. Woods expected to see that increasing camber shifts the lift curve up and to the left, increasing lift at a given angle of attack but also lowering the angle at which stall occurs [49]. It was also noted that, the amount of additional lift ∆𝐶𝐿 generated for each deflection increment diminishes with increasing deflections [49]. From the wind tunnel testing woods confirmed that the FishBAC achieves a higher 𝐿/𝐷 ratio across the entire operating

envelope (-5° ≤ α ≤ 14°) when compared to the 𝐿/𝐷 ratio of the flapped airfoil across the entire operating envelope [49]. Woods saw significant increases in efficiency (𝐿/𝐷 ratio), from 160% for low α (0° ≤ α ≤ 5°) and 27% for high α (α > 10°). The minimum efficiency improvement was 16% at 𝐶𝐿 ≈ 0.5 and above 200% for higher 𝐶𝐿 [49].

Woods concluded that the FishBAC is more aerodynamically efficient than the flapped configuration at all angles of attack and lift coefficients [49].

Airfoil NACA 23012

Morphing type FishBAC trailing edge

1 𝑚 𝑏

270 𝑚𝑚 𝑐

Morphing coordinate start 0.75𝑐

Figure 15 FishBAC utilized as a morphing trailing edge and model parameters [49].

A possible disadvantage of this design is that it could be difficult to repair since the FishBAC rib would tend to be a single piece. It would also be difficult to gain access into the internal structure of the wing due to the skin as it is likely the skin would be bonded onto the wing surface. The bottom surface would require pre-tensioning to avoid buckling when undergoing deflection. There would also be limited empty space in the wing due to design. There are also some variations of the FishBAC design, the variations can be in the form of percentage amount of chord that utilizes the FishBAC design, the design of the spine and stringers [50, 51].

The large deflections and continuous compliant architecture of this design is applicable for fixed wing aircraft ranging from small UAV to commercial airliners. The design is also suitable for rotary wing applications such as helicopters, tilt rotors, wing turbines and tidal stream turbines.

2.3.2 Zig-Zag Wingbox The zig-zag wingbox is composed of two main parts a rigid part and a morphing part. The rigid part is near the wing root and is a semi-monocoque construction like the baseline wingbox of the UAV it consists of two straight spars running the spanwise direction with stressed covers (skin and stringers) and ribs are running chordwise. The rigid part contains the fuel tank and transfers loads to the morphing part of the fuselage. The morphing part consists of various morphing partitions where each partition consists of two spars located at the leading edge and trailing edge, each spar consists of two hinged beams that have rectangular cross sections. The angle between the beams can be varied during actuation which alters the span of the morphing elements. Rotation of the beams in each morphing partition with respect to the z-axis (as seen in Figure 16) of the wing allows the span or the length of the partition to be altered. The spars are hinged at its two end points and are attached to the adjacent ribs.

Figure 16 Top-view of the zig-zag wingbox concept [25].

The ribs transfer the loads experienced from the spars of one partition to the adjacent one which then transfers it to the next partition, until the load is transferred to the inboard rigid part which can then transfer loads to the bulkheads then to the fuselage. To avoid the deformation of the flexible skin, the skin is only connected to the ribs and not the spars.

The zig-zag wingbox allows 44% variation in wingspan that is a 22% in both extension and contraction, which corresponds with the ideal 22% increase in wingspan [25]. The weight of the zig-zag wingbox system was found to be 34% heavier than the conventional wingbox and ribs. Hence an increase in weight by approximately 5.7% compared to the conventional counterpart. Approximately a 5.5% increase in endurance without factoring the weight of the flexible skin, hinges, clamps and actuation components [25].

An advantage of this concept is the design of the flexible morphing skin. The flexible morphing skin is a sandwich panel skin which is comprised of tensioned elastomeric matrix composite covers that are

reinforced by a zero Poisson’s ratio core. The elastomeric matrix composite is usually made up of a silicone or polyurethane elastomer matrix and reinforced with carbon fibre [52]. This is similar to the Flexible Matrix Composite (FMC) concept which is covered in section 2.6. In short, the morphing skin has low stiffness in the direction where extension is desired and high stiffness in the other. Resulting in a near zero Poisson’s ratio when undergoing extension.

The zig-zag wingbox concept could be more successful on smaller UAVs since a lower number of morphing partitions and smaller structural deformation would be required. Ajaj et al also suggests coupling sweep and span for further benefits in the concept [25].

2.3.3 GNAT Spar Gear driven autonomous twin spar better known as GNATSpar is a spanwise morphing concept, seen in Figure 17 and Figure 18. The GNATSpar does not use telescopic structures to alter the length of the span but instead uses excess spar length to alter the length of wingspan. The spars are longer than the semi-span of the wing, the excess length of spar is stored in the opposite sides of the wing and in the wing-fuselage interface.

Figure 17 Schematic of GNATSpar concept [24].

The design allows for a uniform cross-section along the wing semi-span. The GNATSpar is a multifunctional morphing concept because it is the primary load carrying structure and it is also the actuation system to achieve span extension. The actuation system is located in the wing-fuselage interface, the actuation system consists of a pinon gear placed between two racks corresponding to each of the spars which produces a symmetrical movement on both spars, spur gear (which is mounted together with the pinion gear) and a DC (Direct Current) motor that drives the spur gear via a worm gear, the spur gear drives the pinion gear which in turn drives the racks.

The GNATSpar is covered by a flexible elastomeric skin, to allow span variations whilst still being able to maintain the aerodynamic profile of the wing. Some of the ribs are bonded to the flexible skin this allows the skin to deform uniformly when the spar alters its length. The GNATSpar is self-locking due to the low lead angle of the worm gear, this results in no actuation energy required to overcome the flexible elastic skin loads to keep the spar in its desired length.

GNATSpar allows up to 25% extension in wingspan, which reduces induced drag and increases flight endurance [6]. The GNATSpar is structurally superior to conventional telescopic spars. Due to the

additional wingspan being stored in the fuselage and other side of the wing. This means that the GNATSpar can withstand the increased wing root bending moment loads more than the traditional telescopic spar wing designs.

Figure 18 Rack and pinion actuation system for GNATSpar [6].

2.4 Morphing Wings in Industry Morphing wings have yet to be introduced into commercial use due to the low maturity level of the technology. Research and development projects have been conducted for example NASA’s Mission Adaptive Digital Composite Aerostructure Technologies (MADCAT) team in collaboration with various universities and Flexsys.

An advantage of this design is that the spar is not split for each wing resulting in a stiffer structure. A disadvantage of the design is the strict manufacturing tolerances in the joint of the GNATSpar. This issue was addressed, however a rotation of 5° of components could still occur at the joint [6]. Another issue is the large actuation force required for the flexible skin covered wing. The design also suffered from non-uniform airfoil across the wingspan when undergoing morphing. Which was due to the non- uniform expansion nature of the flexible skin due to Poisson’s contraction. Overall Ajaj et al, found that the design was both a simpler design and weighed less than a traditional telescopic spar design [6].

Flexsys has been testing and developing their flexfoil compliant wing to replace conventional non- continuous trailing edges. The flexfoil is capable of deflections from -9 to +40 degrees, span-wise twist and high response rate (50 degrees per second). The flexfoil can be retrofitted to existing aircraft, flaps and sub-flaps capable of ±10 degrees of camber deflection and span-wise twist. The flexfoil has been tested on a Gulfstream III business jet [53, 54].

In 2015 a wing morphing project by NASA in collaboration with the Air Force Research Laboratory (AFRL) and FlexSys Inc conducted successful flight testing with morphing wings. 22 test flights were conducted in six months with the experimental Adaptive Compliant Trailing Edge (ACTE) Control surfaces, seen in Figure 19.

Figure 19 Flexsys' Flexfoil deflected [22].

The ACTE offers significant improvements over conventional flaps, ACTE technology can be retrofitted or used in new designs, ACTE reduces wing structural weight, improve aerodynamic performance, improve fuel economy and generate less noise than conventional flaps [55]. The testing was conducted on large scale aircraft. The flight test consisted of setting control surfaces at flap angles from -2° to 30°. The tests were conducted at a single fixed setting to gather incremental data and to mitigate risk even though ACTE flaps are designed to morph throughout the entire range of motion.

In 2016 and ongoing, NASA’s MADCAT team have been developing a morphing wing, the wing as seen in Figure 20 is made of building-block units made of carbon fibre composite material. The building blocks are assembled into a lattice/arrangement of repeating structures; the way the blocks are assembled determines the way they flex. The wing morphs by using actuators and computers. The project is being funded by ARMD’s Transformative Aeronautics Concepts Program under Convergent Aeronautics Solutions project. The wing has been tested and further investigation is being conducted.

Figure 20 Composite Cellular Material Morphing Wing [56].

2.5 Morphing Wing Concept Selection From the observed literature, the two most common methods of morphing were camber morphing (specifically FishBAC camber morphing) and wingspan morphing. The advantages and disadvantages of the two methods were considered and were examined in sections 2.1.1.1 and section 2.1.2.1. Both methods share similarities with the other such as, increase in lift for a small decrease in drag, both can increase endurance and range of the aircraft and both can conduct a roll moment asymmetric

It is unlikely for morphing wings to be commonplace in the aviation industry soon, due to the low maturity level of the technology as ongoing research and development is still being conducted as well furthermore the technology must be able to pass the regulations set by the regulatory body (which is dependent on where the aircraft will be potentially manufactured and operated).

2.6 Literature Review on Morphing Skins There are various types of compliant morphing skins found in literature, common examples include: using an elastomer sheet and a combination of structural actuation components and an elastomer skin [57, 58, 59, 60, 61].

morphing. Although both methods share similarities, wingspan morphing does not seem to have as a large benefit on endurance and range as examined by Ajaj et al, where maximum increase of 6.5% of endurance was observed for 35% increase in wingspan [24]. This increase in endurance was likely to be less than the stated 6.5% when increased weight of the morphing system is considered. As of the time of this research was conducted, the endurance increases due to FishBAC morphing method has yet to be explored. Considering the studies conducted by Woods et al and Ajaj et al, the FishBAC seems to provide better lift-drag ratio performance than the wingspan morphing method. When other factors such as potential for increase in endurance, potential weight of the system and ease of manufacture and reliability, it further suggests that FishBAC morphing could be the better option.

Some examples of morphing skins, seen in literature are shown in Table 1:

Table 1 Morphing Skin Concepts.

Concept description Visualization

Honeycomb [57]

Honeycomb variant/Accordion [58, 59]

Corrugated skin [62]

composite SMA actuator [63]

Corrugated core with elastomer skin [64]

Elastomer foam [61]

Silicone matrix with pneumatic muscle fibres [65]

Saristu (silicone, foam with angles) aluminium [61]

From Table 1, three potential candidates were considered for the upper skin of the morphing wing they are corrugated core with elastomer skin, flexible matrix composite skin and the honeycomb.

2.6.1 Honeycomb and Honeycomb Variants The morphing wing skin concept involves a flexible honeycomb (or variations of honeycombs) accompanied by a flexible elastomer. The honeycomb allows for deformation in one direction i.e. has

low in plane stress whilst providing high out of plane stress. The flexible elastomer sheet assists in shear loads, keeping the aerodynamic profile and resists the strain experienced by the extension caused by morphing. This morphing wing concept is suitable for one dimensional morphing whether that be span, chord or camber morphing, some examples of honeycomb or accordion style are depicted in Table 1.

In general, if no constraints are placed on the honeycomb, it can be extended to experience a high Poisson’s ratio [58], showing high elasticity. Olympio proposed two possible solutions a hybrid cellular honeycomb and the accordion honeycomb concepts [58]. The hybrid cellular honeycomb concept essentially has alternating honeycomb cells where the first is a positive cell and the second being negative and so forth. When the hybrid cellular honeycomb undergoes deformation, the positive cells will contract in y-direction whilst the negative will match the expansion but, in the x-direction.

Whilst for the accordion honeycomb concept it behaves exactly like an accordion when undergoing deformation. When examined both concepts showed zero Poisson’s ratio meaning both are suitable for one dimensional morphing [58]. The accordion style honeycomb morphing skin was also adapted into a cosine honeycomb by Liu et al [59].

2.6.2 Corrugated structures Corrugated structures are in general structures that have a series of parallel ridges and furrows an example of this would be a corrugated panel or a corrugated cardboard box. Corrugated structures can be suitable for a morphing skin due to their anisotropic behaviour which allows for high stiffness in the transverse direction of corrugation and compliant in the corrugation direction [64].In the application of one-dimensional camber this means that the corrugated morphing skin would be stiff in the spanwise direction and flexible in the chordwise direction. The corrugated morphing skin would be a corrugated core material with elastomer face sheets sandwiching the corrugated core material.

The corrugated core material would provide the spanwise stiffness and chordwise compliance while the elastomer face sheets would provide a smooth aerodynamic surface. The corrugated core material could be manufactured via the use of a mould or rapid proto typing depending on the type of core material to be used. Dayyani et al used the concept alongside the FishBAC ribs as seen in Figure 21 [60].

Figure 21 FishBAC and corrugated morphing trailing edge concept [60].

2.6.3 Flexible Matrix Composites (FMC) Flexible matrix composites (FMC) like normal composites are constructed from two or more materials; one generally being an elastic material which is called the matrix material and the second being the rigid, strength providing fibre material which is simply the fibre material. An FMC allows for large strains and low in-plane stiffness in the matrix dominated direction whilst the fibre matrix dominated has high stiffness and improves out of plane load carrying capability.

Hence FMCs combine properties of two materials, therefore the strength of materials and rules of mixtures for composite can be used to determine the mechanical properties. Then elastic modulus for the FMC in the fibre dominated direction is,

𝐸𝑦 = 𝐸𝑓𝑉𝑓 + 𝐸𝑚(1 − 𝑉𝑓)

The elastic modulus for the FMC in the matrix dominated direction is,

𝐸𝑥 = 𝐸𝑓𝐸𝑚 (1 − 𝑉𝑓)𝐸𝑓 + 𝑉𝑓𝐸𝑚

And the Poisson’s ratio is,

𝑣𝑦𝑥 = 𝑣𝑓𝑉𝑓 + 𝑣𝑚(1 − 𝑉𝑓)

Note that 𝑣𝑚 is also another composite material in an aspect since the (fibre is generally hardened using epoxy) hence the Poisson’s ratio needs to be interpolated from the materials used.

Where, 𝐸𝑓 and 𝐸𝑚 is the elastic modulus of the fibre and matrix dominated direction respectively. Similarly, 𝑣𝑓 and 𝑣𝑚 is the Poisson’s ratio of the fibre and matrix material. And the fibre volume ratio is 𝑉𝑓.

This visualization of this concept can be seen in Figure 22Error! Reference source not found.. In comparison to regular composites FMC have a higher ratio of fibre/matrix however they use the same formulae for various mechanical properties for example elastic modulus and Poisson’s ratio [52].

Figure 22 FMC fibre orientation for a) span morphing and b) for camber morphing [52].

Matrix materials for FMC tend to typically be silicone, rubber and thermoplastic whilst fibre materials are typically fibreglass, carbon fibre and Kevlar [52, 66].

2.6.4 Concept Selection For a corrugated morphing skin, it would be difficult to implement when using a corrugated structure however it still has been done by Dayyani et al [67]. The appropriate angle for the ridges and furrows of the corrugated core would also need to be determined therefore adding additional level of complexity. In addition to this if the corresponding elastomer face sheet is not completely tight the corrugated core would a negative effect on the aerodynamics as Xia et al found a decrease in the lift curve slope due to bumps caused by the corrugated core material [68]. These two pitfalls could also be true for the honeycomb accordion or cellular honeycomb as the appropriate pattern and positive & negative cells would need to be determined as well as they are both similar concepts. Considering that part of the scope of the research is to have a simple design that can be utilized by a wider aerospace community that may lack resources to implement said design. A limitation of morphing skins is that they cannot withstand large aerodynamic loads because of the flexibility required for structural deformations [25]. The FMC skin concept was selected over the other concepts as it the simplest concept of the three yet still effective. The variables involved in manufacturing a FMC skin are the matrix material, fibre material and the fibre orientation, however it should be noted that the FMC skin was not required to be perfect as its purpose is to provide a smooth and streamline profile for the morphing wing. Due to the advancements in fibre materials, the FMC should allow for morphing skin to withstand aerodynamic loads without buckling.

2.6.5 Further Investigation into Flexible Matrix Composites (FMC) Like regular composites the mechanical properties of the FMC are determined by the mechanical properties of all the materials which make up the composite. In Kirn’s paper explores the feasibility of FMC through manufacturing and testing of many combinations and variations of the matrix material and fibre material seen in Table 2 [66].

Kirn found that pressure moulding is suitable manufacturing method for FMC however issues regarding misorientation of the fibres are apparent unless preventative measures are taken. Kirn secured the fibre orientation through clamping down the fibres whilst laying up the FMC to fix the orientation the carbon fibre as a result few fibres were disorientated. Kirn manufactured test specimens with fibre orientations of 0°, ±45° and 90° in the fibre direction related to the applied load and conducted tensile tests. The tensile tests determined that a 10% strain can be achieved and sustained for both ±45° and 90° specimens without failure. The failure modes seen for ±45° and 90° are delamination of the edges and cracks in the coupons, respectively.

Table 2 Material combinations tested by Kirn [66].

3 Motivations and Past Research The objective of this project is to compare the aerodynamic performance of a morphing wing as a direct replacement of a conventional wing of similar shape. For this study, the wing of a T240 Precedent RC model aircraft was used as a case study. This is a conventional, non-swept, constant chord wing with a single flap and ailerons the wing design is shown in Figure 2. The flap and ailerons are replaced by full-span morphing using asymmetric morphing for roll control.

With regards to the aerodynamic performance comparison, three aspects were compared:

1. Lift-drag ratio 2. Maximum lift 3. Roll rate

This aerodynamic study follows on from a previous design study that focused on the design of the morphing wing structure and actuation mechanism [18, 19, 69, 70].

3.1 Wing Concept and Conceptual Design The morphing wing design was proposed by Vivian et al [69] with further analysis by Scopelliti and Gou [18, 19]. Given the requirements that the morphing wing must be of simple design and low cost, the FishBAC design was selected (see Figure 23) and a simple mechanical torque-based actuation system was used. The complete morphing wing concept can be seen in Figure 24.

The motivation behind this project is for a morphing concept that is simple system and inexpensive to manufacture. As most research conducted tends to use complex systems using materials such as shape memory polymers and piezoelectric actuators that are expensive, not easily obtained and come with their own issues. This morphing wing research, if successful will produce a working morphing wing design that is simple, easily manufacturable, and affordable for small aircraft. Therefore, if the design is to be applied to UAVs then the systems will be far less complex and more affordable, this design can also be utilized by aircraft hobbyists due to the 3D printers being widespread and many hobbyists would be able to print out their own parts.

Figure 23 Three-view of the initial rib design that connects to the trailing edge [69].

The inherited morphing mechanism was manufactured by using affordable and simple materials such as balsa wood, aluminium, and polymers through rapid prototyping. Due to the simple design and

ease of manufacture since 3D printers are commonplace, this morphing wing can be manufactured and used by RC aircraft hobbyists.

Various analysis tasks were conducted during project including:

• Airfoil analysis using XFOIL software • Material selection and analysis • Wing design using CATIA software • Finite element analysis and modelling using ABAQUS software

Figure 24 Colour coded isometric view of morphing wing concept [69].

The material for the leading edge was balsa wood since it is lightweight and easily shape-able. However, the wing structure before the maximum thickness point, about 30% of the chord, must carry all the bending and torsion loads. An aluminium spar was added to assist the balsa wood leading edge in carrying the loads. The control arms are present to transfer the rotational loads which in-turn assists the deformation of the ribs. The trailing edge is to guarantee a uniform deflection of the ribs and supports the wing skin.

The analyses showed that the wing design was feasible and was sufficiently strong enough to handle loads experienced from normal operation conditions [18, 19].

Figure 25 Revised rib design and its assembly [69].

However, it was found that the initial rib was not strong enough to withstand the actuation stresses at maximum deflection [18]. Therefore, the initial rib design was refined into a three-section rib design i.e. bracket, fishbone and rib-end, shown in Figure 25, where the rib end and bracket would be

manufactured from the same material. Because of this the fishbone core can retain its flexible properties through the selected material.

Material testing was conducted to determine which materials to use from the selected: PolyLactic Acid plastic (PLA), ThermoPlastic Elastomers (TPE) and Acrylonitrile Butadiene Styrene (ABS). Material testing was conducted according to the standards ISO 527-1, ISO 527-2, ASTMD638 and ASTMD790 B.2 [69]. A FEM analysis was conducted to assist the material selection, and to achieve a deflection of 10° which translate into a 43mm deflection of the rib end a downwards force of 47.5N is needed. To achieve the maximum lift-drag ratio for a given angle of attack, the camber of the airfoil does not need a large increase hence a deflection of 10°. The deflections of the revised rib design are depicted in Figure 26.

The required force of 47.5N led to the decision that the rib design will be split into three and so that multiple materials can be used. The bracket, fishbone and rib end were manufactured from ABS, TPE and PLA respectively. The thickness of each component can vary and was optimized to 3mm, 10mm and 10mm for the bracket, fishbone and rib end respectively. The arm design was also refined as it was redesigned to have a honeycomb geometry which leads to a saving in time to manufacture and weight, yet it retains its stiff properties. PLA material was used to manufacture the arm. The wing skin was composed of 80% cotton and 20% spandex resulting in a fabric like that of swimming suits, hence it provided the required elasticity of the skin, and the skin was attached using Velcro strips mounted onto ribs and the wing. A prototype of the rib depicted in Figure 27.

Figure 26 Revised rib displacements [19].

Figure 27 Velcro strips on revised rib [69].

Figure 28 Step by step assembly of the wing [69].

The wing was manufactured using rapid prototyping in particular Fused Deposition Modelling (FDM) and Computer Numerical Control (CNC). FDM was used to manufacture elements of the wing, FDM was used since it is an inexpensive machine and the materials used are also inexpensive, there were no resins to cure and no chemical post processing was required with the method. The rib-end, brackets, arms, and fishbone core were manufactured using this method with their respective materials. The CNC was used to manufacture the leading edge which was separated into two parts; upper and lower parts so that the aluminium tube could be used. The wing assembly used for experimental tests is shown in Figure 28.

From this point further work was conducted on the rib and wing which is described in section 3.2.

3.1.1 Morphing Wing Actuation Method The actuation method of the morphing wing involves the torsion rod, control arm and the compliant design of the FishBAC morphing ribs. The torsion rod acts as both the rotation point and the means or source of deflection in the wing. The idea was to incorporate two servos, one located in the wing-box (the design can be seen in Figure 29 and Figure 30) near the wing-root and one located in the rigid wingtip which is shown in Figure 31. When actuated the servos would rotate the torsion rods through connected linkages, which would then cause the control rod to rotate and act as guides for the FishBAC ribs as they deflect across the wing. Due to the limitation of free space within the wingtip, the wingtip servo would be smaller hence a smaller rating than the servo housed in the wing-box.

Figure 29 Four view of the fuselage wingbox without the covering panel.

Figure 30 Assembled fuselage wingbox.

Figure 31 Proposed servo locations in the fuselage wingbox and morphing wing.

3.2 Wing Design The wing design is based off the FishBAC rib structure design. The morphing part of the design is centred on two plastic strips that run along the chord direction of the wing profile, the design is illustrated in Figure 32. The two plastic strips are very stiff in-plane but are very flexible in the direction of morphing. Stringers are attached to the plastic strips by sliding slots over the strips and adhering them into place. The fully assembled wing design is shown in Figure 33.

Figure 32 CAD model of wing design (without stringers attached) [70].

The wing was designed to be as light weight as possible whilst still being able to withstand the typical aerodynamic loads seen under normal operating conditions with a safety factor of 2g. The leading edge was manufactured from balsa wood as balsa wood is very light weight and easily shaped by CNC. The spar was manufactured from aluminium as it is light weight and sufficiently strong. The combination of the leading edge and spar manufactured from balsa wood and aluminium respectively should be able to withstand the aerodynamic loads under normal operating conditions. The morphing strips were manufactured from plastic, the stringers should be manufactured from a stiffer material. The ribs need to support the torsion bar; therefore carbon fibre reinforced plastic was chosen as the material for the ribs to ensure the maximum stiffness and support capability. Similarly, the arms are manufactured using carbon reinforced plastic as the arms need to be stiff due to the deformations from morphing will cause friction which requires the moments to deform the wing to increase. This wing design weighs 1.3kg, has a low cost of production, can be manufactured with relative ease and has high stiffness.

Figure 33 Complete CAD model of 2nd wing design [70].

4 Research Questions To date in literature there are not many studies that compare the aerodynamic performance of the morphing wing to a conventional wing. There are even fewer studies that compare the roll performance of both configurations. Also, the predecessors of this research did not verify the aerodynamic performance of the morphing wing, therefore this study delves into aerodynamic performance of the morphing wing and compares it to the conventional wing configuration.

The morphing wing concepts reviewed in the current literature are generally limited to a laboratory setting and have complex systems due to smart technologies; SMA, piezoelectric systems. The goal of the research is to show that is possible to use a simple morphing wing system on medium sized UAV and RC aircraft to do this a flyable morphing wing system for a Precedent T240 RC aircraft. With that in mind, in this stage of the research a simpler morphing wing system will be designed and prototyped using low cost and off the shelf readily available technologies.

The research questions of this study are:

• How does theoretical aerodynamic analysis of morphing wings compare to wind tunnel tests? • How does wing morphing perform in terms of roll control, i.e. asymmetric morphing, and as a

high-lift device for low-speed performance?

• How does the aerodynamic performance of a morphing wing compare to its conventional

4.1 Project Scope The study shall explore the aerodynamic performance for a FishBAC morphing wing through wind tunnel testing at normal operating flight conditions and compare it to conventional configuration. This project will not consider optimization of the wing profile as it is paramount to the project that a morphing wing is directly compared to a conventional wing for the same profile. The difference between the conventional T240 wing and the morphing wing is lack of ailerons and flaps instead the entire morphing section is a control surface. The aerodynamic performance of lift, drag, lift-drag ratio and roll rate will be compared. The research will also not consider the effect of the wing-body and fuselage on aerodynamic performance.

counterpart with the same geometry?

Due to the objective of having a simple morphing mechanism, the morphing concept shall be achievable through simple mechanisms specifically internal mechanism. The inherited wing design has been analysed structurally hence there is not much flexibility with design changes that can be made. The purpose of this part of the research is to manufacture a prototype of the morphing concept and determine the aerodynamic characteristics of the morphing concept.

The use of analytical tools such as XFLR5 and TORNADO were used to estimate the performance of both the conventional and morphing wing configurations.

5 Research Methodology The research methodology was briefly as follows:

The predecessors of this research did not reach a conclusion for a compliant morphing skin. Hence this study also carried out research to determine a suitable compliant morphing skin for the morphing wing.

• Examination of previous work • Airfoil development • Theoretical simulations via XFLR5 and TORNADO • Design and manufacture of the morphing wing • Wind tunnel testing

5.1 Airfoil Development To design and build a morphing wing, based off the conventional T240 wing, the wing dimensions must be known, as shown in Figure 2. Originally the wings are inserted into the fuselage via a tab on each wing. Once inserted the wings are held together via the spar. Comparing Figure 31 and Figure 2, in the morphing wing design the tab is removed and instead incorporates the fuselage wingbox mentioned in section 3.1.1.

XFLR5 and TORNADO are both aerodynamic analysis tools based on the XFOIL code, which will be explained in section 5.2.

To build a morphing wing with the same airfoil section, the airfoil section of the T240 had to be determined. The conventional T240 wing root was used to trace the airfoil and coordinates were mapped at intervals of 10mm chordwise on the upper and lower surface of the airfoil. The airfoil coordinates were transferred to CATIA-V5 for further modelling and smoothing, seen in Figure 34.

Figure 34 Construction of the T240 airfoil.

To achieve the splines for the morphing wing at various deflections, the predecessor’s morphing wing was deflected and traced over, seen in Figure 35. The required morphing angle was determined by using two points, the centre of the torsion rod and the centre of the rib end fasteners. The centre of

the torsion rod and the centre of the rib end fasteners are where the control arm begins and ends respectively illustrated in Figure 35. The initial angle of the control arm was taken when wing was not morphed and recorded this will be the initial control arm angle or offset angle i.e. 𝜃𝑜𝑓𝑓𝑠𝑒𝑡 therefore to determine the actual morphing angle, 𝛿𝑚, it will be the recorded angle, 𝜃𝑟𝑒𝑐𝑜𝑟𝑑𝑒𝑑 offset by the control arm angle ; 𝛿𝑚 = 𝜃𝑟𝑒𝑐𝑜𝑟𝑑𝑒𝑑 - 𝜃𝑜𝑓𝑓𝑠𝑒𝑡

The traced airfoils were then converted into coordinates and drawn and smoothened in CATIA before converting them to the appropriate .DAT file formats for both XFLR5 and TORNADO.

Figure 35 Morphing wing airfoil construction.

5.2 Simulations Simulations are used to predict the aerodynamic performance of the aircraft. However, the results from simulations need to be validated to determine its degree of accuracy which is conducted through wind tunnel testing. Hence both simulations and wind tunnel testing are required to determine aerodynamic performance. XFLR5 and TORNADO were both used to predict the performance of the conventional and morphing configurations. Both methods are used since, they complement each other where the other one fails. For example, XFLR5 was unable to perform a roll analysis while TORNADO over-predicts lift.

On a side note, due to the age of the T240 conventional wing, to avoid any damage that could have been done from high-speed testing the velocity of the wind tunnel was kept to a minimum. The test conditions seen in this section of the paper are taken directly from the wind tunnel testing section of this paper and will be further explained.

5.2.1 XFLR5 XFLR5 is a performance approximation tool based on the XFOIL airfoil tool, it is an accurate approximation tool for thin airfoils considering its resource cost [71, 72]. The calculation method of XFLR5 depends on the selected method. XFLR5 can perform both viscous and non-viscous aerodynamic analyses using any of the three methods: Lifting Line Theory (LLT), Vortex Lattice Method (VLM) and 3D panel methods [47]. In this study the VLM method was used and is discussed in section 7.2.1.3.

XFLR5 does have its limitations as it cannot capture flow separation at low Reynolds numbers (less than Re 25000) and it tends to overestimate results however the results are still generally acceptable [72]. XFLR5 does not consider the thickness of the airfoil as it takes a thin body principle i.e. it uses the mean camber line as the airfoil [47, 73]. Because XFLR5 does not consider the thickness of the airfoil, XFLR5 is mostly suited and accurate for thin airfoils [74]. XFLR5 is suited for low Re number analyses and for 𝛼 before stall as it fails to capture separation of the flow [75, 76, 77]. XFLR5 performs well for viscid 2D applications and with some limitations in 3D [78]. Since XFLR5 is best used for low Re number and low 𝛼 applications it is best used for small UAVs. XFLR5 tends to underestimate drag because it cannot determine viscous drag and that simulating the aircraft is a detriment [78].

Gryte found that deviations in the 2D and 3D results arises when the 3D geometry compared to the idealized 2D infinite wing, this is evident in the deviation of drag when compared to their experimental value [74]. They had determined that the drag is offset since viscous drag is not considered since XFLR5 is based on inviscid flow. XFLR5 cannot capture large rotational components accurately [74].

The process for using XFLR5 in wing aerodynamic analysis is shown Figure 36

Airfoil Creation 2D Analysis 3D Wing Creation 3D Analysis

Figure 36 XFLR5 simulation process for wing aerodynamic analysis.

To conduct the aerodynamic analysis of the wing, the airfoil was imported into XFLR5. Once imported, the airfoil was then edited to have 150 points, 150 points which yields more reliable results. The performance of infinite (2D) conventional wing can be simulated; the Reynolds number (determines the relationship between the velocity and viscous forces) and the angle of attack 𝛼 range were both inputted. The Reynolds number and 𝛼 range that are analysed for the infinite wing must be larger than that of the finite (3D) wing to prevent errors. Once that was done, the 3D wing needs was created to the desired geometry, which also was done for each desired control surface setting. From there the desired analysis method was chosen from: Lifting line theory (LLT), Vortex Lattice method (VLM) and the panel method. After which the desired range airspeed and 𝛼 were set.

5.2.1.1 2D Analysis of Conventional T240 Wing Following the process tree, the T240 airfoil was created for its various flight conditions including flap settings which can be seen in Figure 37 and Figure 38, using these airfoils a 2D analysis is performed. For the 2D analysis, the operating range of 𝛼 and Re needs to be larger than usual to avoid errors in the simulation where points do not solve properly and can yield the errors. This is because the value of a 2D value 𝐶𝐿 needs to be present for the 3D solution of 𝐶𝐿 to be determined. Because of this the 2D 𝛼 range will now be -10° ≤ 𝛼 ≤ 20° instead of -5° ≤ 𝛼 ≤ 15°. Some of the 2D results of the analyses are shown in Figure 39.

Figure 37 T240 airfoil in XFLR5.

Each individual flap and aileron setting were then applied to the airfoil. The flap and aileron deflections were set to a maximum of 28° for flaps (𝛿f𝑚𝑎𝑥= 28°) and a maximum/minimum of ±13° (𝛿a𝑚𝑎𝑥= 13°,𝛿a𝑚𝑖𝑛= -13°). Testing of the deflections of the flaps and ailerons were conducted at quarter intervals e.g. 𝛿𝑓=7°,𝛿𝑓= 14°,𝛿𝑓= 21°,𝛿𝑓= 28°.

Figure 38 T240 airfoil with flap deflections in XFLR5.

In Figure 39 the 2D results of the XFLR5 for both 𝐶𝐿 and 𝐶𝐷 are shown. From Figure 39 the lift prediction tracks well with normal lift behaviour as the stall angle of attack is reduced as the flap deflection increases. There is also linearity with the increase in lift as flap deflection increases. There are slight differences between Reynolds numbers, whereas Reynolds numbers increases the differences in lift between each flap deflection is more pronounced. The drag predictions in Figure 39, does not follow normal drag behaviour closely, as the drag curve does not exhibit smooth parabolic behaviour as there are two incidences of horizontal transition in the curve. The drag increase does match with the increases in lift since induced drag is proportional to lift. However, the drag increase does see a large increase from 𝛿𝑓 = 7° which continues to 𝛿𝑓 = 28°. Drag however does decrease as Reynolds number increases which could be due to flow becoming more stable as the Reynolds number increases.

Flap 14 degrees

Flap 07 degrees Flap 28 degrees

Flap 0 degrees Flap 21 degrees 2

Re 168000

1.5

0.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.5

Flap 14 degrees

Flap 0 degrees Flap 21 degrees

Flap 07 degrees Flap 28 degrees

Re 236000

1.5

0.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Flap 14 degrees

Flap 07 degrees Flap 28 degrees

Flap 0 degrees Flap 21 degrees 2

1.5

0.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.5

Re 337000

Flap 14 degrees

Flap 0 degrees Flap 21 degrees

Flap 07 degrees Flap 28 degrees

0.25

𝛼, Angle of Attack, in 𝑑𝑒𝑔

0.2

g a r D

0.15

0.1

f o t n e i c i f f e o C

0.05

𝐷 𝐶

-10

-5

Re 168000

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Flap 14 degrees

Flap 07 degrees Flap 28 degrees

Flap 0 degrees Flap 21 degrees 0.25

0.2

0.15

g a r D

0.1

0.05

f o t n e i c i f f e o C

𝐷 𝐶

-10

-5

Re 236000

Flap 14 degrees

Flap 07 degrees Flap 28 degrees

Flap 0 degrees Flap 21 degrees 0.25

𝛼, Angle of Attack, in 𝑑𝑒𝑔

0.2

g a r D

0.15

f o t n e i c i f f e o C

0.1

𝐷 𝐶

0.05

-10

-5 𝛼, Angle of Attack, in 𝑑𝑒𝑔

Re 337000

Figure 39 2D analysis results of T240 airfoil with Flaps applied at various Reynolds numbers in XFLR5.

5.2.1.2 3D Analysis of Conventional T240 Wing The desired flight (-5° ≤ 𝛼 ≤ 15° for Re 168000, Re 202000, Re 236000, Re 269000 and Re 337000) conditions were then be entered, and analyses were then run after the desired method was selected. The VLM analysis shows that as 𝛿𝑓 increases the 𝐶𝐿 increases. The increase in 𝐶𝐿 is linear and causes the aircraft to stall at a lower 𝛼, which is all expected behaviour for a normal plain flap.

XFLR5 does not consider the parasite drag when conducting a 3D analysis hence the drag polars given in XFLR5 only consists of induced drag. The results of the 3D analysis of the conventional wing are shown in Figure 40 and is discussed in section 7.3.1.

5.2.1.3 Limitations of Lifting Line Theory (LLT) in XFLR5 Wings that have a low aspect ratio and high sweep will are unlikely to yield accurate results. The wing planform is expected to be in the X-Y plane hence it is preferred for the wing to have low dihedral this is because sweep and dihedral are not considered in the calculation of the lift distribution in this method. Regarding the settings for an analysis using LLT, the relaxation factor should be roughly 20 (the relaxation factor must be greater than 1). A higher relaxation factor does not mean the results are more accurate it is the exact opposite; a higher relaxation factor should only be used for a wing with higher number of stations spanwise.

5.2.1.4 Limitations of Vortex Lattice Method (VLM) in XFLR5 VLM is a numerical method suited for thin lifting surfaces and small 𝛼, small sideslip angle applications [75]. VLM’s principle is to solve the incompressible flows around lifting surfaces with a finite span [75]. The lifting surfaces each have a grid of horseshoe vortices superimposed onto them and velocities are induced by each of the horseshoe vortices on any given point are calculated using the Biot-Savart law. The horseshoe vortex strength is calculated by summing of all the control points on the lifting surface, this leads to a set of equations which should satisfy the boundary condition of no flow through the surface. From there the pressure differentials are integrated to determine the total forces and moments [33, 75]. VLM calculates lift distribution, the induced angles and induced drag are inviscid and linear, meaning it is independent of speed and the viscosity of the air [78]. VLM is not affected by any wing geometry [78].

XFLR5 lacks a viscous interactive boundary layer loop, where the interactive boundary layer loop is a coupling method between potential flow and viscous flow on surfaces [79]. The purpose of the boundary layer is to modify the geometry of surfaces and to disturb the inviscid potential flow. Hence a loop is needed to reach a solution that satisfies the viscous model and the potential flow model. However, XFLR5 does not implement this loop in all of its methods [79]. Resulting in the lift acting linearly for all angles of attack and significant differences in lift coefficient predictions at low Re [79].

VLM results are linear therefore it does not consider the effects of stall hence it should not be used at angle around or beyond the stall angles [75, 77, 80]. The method also tends to underestimate drag [33, 74].

Classic (linear) LLT and VLM methods are derived from Inviscid (non-viscous) assumptions for fluid. Hence results for these methods ignore viscous drag and are independent of speed [81]. Due to sizing and speed of aircraft, viscous drag cannot be ignored [81]. The viscosity of the 2D analyses is extrapolated to 3D analysis.

The XFLR5 predictions shown in Figure 40 are expected to be accurate for the conventional T240 more so at lower flap deflections. However since XFLR5 uses inviscid methods it does not consider stall hence the stall angle of attack is not predicted. When flaps are deflected, stall occurs earlier in wings hence the predictions at higher flap deflections are unlikely accurate.

The results lift and drag predictions for the T240 wing are expected to be overestimated and underestimated, respectively and this is also expected for the morphing wing. It is expected that the predictions of XFLR5 will be more accurate for the conventional T240 wing than the morphing wing. In Figure 40, Figure 42 and Figure 46 Morphing Wing is referred to as “MW” followed by the deflection angle for example 𝛿𝑚 = 10°, is “MW10DEG”.

For further information on VLM theory please refer to APPENDIX G.

5.2.1.5 General Differences Between LLT and VLM Unlike LLT, the VLM calculates lift distribution, the induced angles and induced drag as inviscid and linear, meaning it is independent of speed and viscosity [79]. VLM is not affected by wing geometry. LLT should only be used if stall angles are examined and if the wing geometry fits the geometry limitations of the LLT, elsewise VLM should be used in all cases [78]. LLT in XFLR5 is a viscous method, which requires 2D polars in order to conduct a 3D analysis which makes the method dependent on the convergence of analyses. While VLM can utilise an inviscid 3D analysis which does not require a prior 2D analysis [79].

5.2.1.6 Convergence of 2D and 3D Analysis XFLR5 requires 2D analysis to be conducted first before a 3D analysis can be conducted. For non- converged flight conditions (Re, 𝛿𝑚 and 𝛼) refer to APPENDIX F for the tabulated flight conditions.

Observations for convergence of the 2D analysis for the desired Re, 𝛼 and 𝛿𝑚 was as follows:

Convergence for 𝛿𝑚 < 10° achieved for most 𝛼 and Re. For 10° < 𝛿𝑚 < 15°, there is nonconvergence for some 𝛼, however the behaviour of the curve can still be determined. For 𝛿𝑚 > 20°, depending on the Reynolds number, nonconvergence can occur for specific 𝛼. This is particularly noticeable for 𝛿𝑚 = 25°, where for most Re and 𝛼, results are not converged. The lack of convergence could be due to limitations of 2D approximation for the viscous drag [81]. Another issue that persists throughout all 𝛿𝑚 where for low Re (168000 and 202000), there is a step-in result, where 𝐶𝐿 and 𝐶𝐷 would be lower than the rest of the data points for 𝛼 < 0°.

However, as noted in the XFLR5 notes (section 5.2.1.4), a 3D inviscid VLM analysis does not require polars, i.e. a 2D analysis to be performed first and viscous characteristics are set to zero.

Hence, the lack of convergence for the 2D analysis did not affect the results of the 3D analysis. This was further confirmed by conducting a viscous VLM analysis, which required the 2D polars. Although not shown here, the converged results were identical to that of the non-viscous analysis. In the viscous analysis, low 𝛿𝑚 and low 𝛼 conditions resulted in converged results like that of the 2D analysis, however for higher 𝛿𝑚 and 𝛼, results were unconverged. Therefore, the non-viscous VLM analysis method was used over the viscous VLM since results were identical for the same test conditions.

Figure 40 XFLR5 Analysis for 𝑪𝑳 vs 𝜶 at various Reynolds numbers.

5.2.2 Tornado TORNADO is a VLM-based solver that is written in MATLAB [82]. TORNADO can solve for aerodynamics coefficients using two methods; regular VLM which is based on fixed wake, or the TORNADO method

which has a free stream following the wake [83]. Because one of the methods TORNADO uses is VLM, TORNADO is best suited for pre-stall 𝛼 [82]. Hence TORNADO has a limiting range of angle of attack that can be analysed, specifically ~8°-10° [82, 84]. Pereira found that the variation of results in TORNADO tend to decrease as the number of panels assigned to the lifting surface increases [83]. TORNADO does not capture cambered wings performance well, since it treats the cambered wing as a flat thin wing approximation where the boundary conditions are shifted [82].

Melin found that a minimum of eight panels should be used, as it still gives good comparable results when compared to experimental data [82]. Like XFLR5, TORNADO is best suited for larger forces and not suited for viscous forces such as drag [82, 83].

Airfoil Creation Wing Modelling

3D Analysis

Figure 41 shows the process of how to conduct a TORNADO analysis.

Figure 41 Tornado simulation process.

To begin the Tornado analysis, the wing must first be created this was done by importing the airfoil data then following the geometry input prompts given by Tornado. Various wings were created one for each flap and aileron input variations where the flap and aileron inputs to Tornado are identical to the ones in XFLR5. Once that was completed the flight condition is then set, the flight conditions being identical to the ones conducted in XFLR5. The results of TORNADO are shown in Figure 42 and will be discussed in section 7.3.3.

TORNADO can generate good results with known experimental data by using at least eight panels per wing [82]. Computational time and accuracy are dependent on the number of panels. Considering this and the fact that TORNADO can generate good results with as little as eight panels [82], a panel distribution of 5x10 was used (5 panels chordwise and 10 panels spanwise) i.e. a total of 50 panels were used for the conventional T240 with zero flap input, 𝛿𝑓 = 0° and for all morphing wing conditions. While for the flap settings a denser 5x4 panel distribution was localized at the flap section in order to capture the non-uniformity of the flow due to flaps being deflected. For the rest of the wing a 4x3 panel distribution was used.

TORNADO predicts similar behaviour in the conventional T240 wing as XFLR5 does, this is likely possible due to the non-cambered shape of the airfoil. The differences between the two methods arises when the morphing wing is deflected. Since unlike XFLR5 which is not affected by wing geometry, TORNADO is not well suited for highly cambered wings. Hence, the predictions of TORNADO for the morphing wing are expected to be inaccurate from 𝛿𝑚 = 10°, as at this point flow separation is likely to occur in the morphing wing. Like XFLR5, TORNADO does not consider stall of the aircraft and is best suited for angles of attack before stall and for thin airfoils because of this, results for the

morphing wing are expected to become increasingly inaccurate as morphing deflection increases. This evident in Figure 42, where coefficients of lift exceed 2 and even reach a maximum of close to 10.

Figure 42 TORNADO Analysis for 𝑪𝑳 vs 𝜶 at various Reynolds numbers.

5.2.3 Wind tunnel Testing

Figure 43 Schematic of the industrial wind tunnel at RMIT University.

The wind tunnel testing was conducted in a sub-sonic closed return wind tunnel, the wind tunnel is located in-house at RMIT University. The schematic of which can be seen in Figure 43. Wind tunnel testing was conducted to validate the results of the simulations of XFLR5 and TORNADO. The testing is conducted on the electronic turntable which can rotate the setup with an accuracy of 𝜃 = 0.1°. The turntable is located immediately after the contraction point in the wind tunnel, seen in Figure 44.

Figure 44 Electronic turntable aft of the contraction point in the wind tunnel.

The wind tunnel testing was conducted with the aid of a reflection plane. The purpose of the reflection plane is to separate the wing from the testing instruments, separate the boundary layer of the wind

tunnel and prevent the transverse of flow from occurring. Since the testing is conducted immediately after the contraction point, the boundary layer for the wind tunnel would have just begun to form, hence it would not be very large. Because of this the wind tunnel floor itself can act as the reflection plane given that the gap between the wing root and the wind tunnel floor is not large.

The wind tunnel testing process is as follows; ensure the electronic turntable is set to 𝛼 = 0° and mount the desired wing configuration into the sleeve for the load cell which is mounted on the turntable. The wing is aligned using the marked indicators and is then secured to prevent any rotation. The wing was always initially aligned to 𝛼 = 0°, the turntable is then locked. The angle of the wing was always confirmed before conducting the initial testing at 𝛼 = 0°. After the initial testing conducted at 𝛼 = 0°, the locks of the turntable were disabled and the turntable is rotated to the next angle, locks were then engaged, tests were conducted, and results recorded. This step is repeated until all desired angles and airspeeds were completed, -5° ≤ 𝛼 ≤ 15° and 𝑉 = 25km/h, 30km/h, 35km/h, 40km/h and 50km/h (Re 168000, Re 202000, Re 236000, Re 269000 and Re 337000). The 𝛿𝑚 is then changed and the process is repeated until all desired configurations are tested.

In short this could be summed up as:

1. Set desired 𝛿𝑚 2. Aligned and secured the wing in the turntable for 𝛼 = 0°. 3. Engaged turntable locks and begin testing and record results for each airspeed. 4. Disengaged the locks, rotated the turntable to the desired 𝛼. 5. Repeated steps 3 & 4 until all the 𝛼 were tested. 6. Disengaged the locks and returned the turntable to 𝛼 = 0°, the wing was removed. 7. Steps 1 to 6 were repeated until all 𝛿𝑚 were completed.

The results were recorded using JR3 400N force balance and its accompanying recording software. Which has a maximum force rating of 400N (𝐹𝑥 = 400𝑁, 𝐹𝑦 = 400𝑁) and a maximum moment rating of 63Nm (𝑀𝑥, 𝑀𝑦, 𝑀𝑧 = 63𝑁𝑚). The results were determined over a ten second period where average result was taken. Before the testing was conducted, calibration of the force balance was conducted, and the offset yaw angle was determined which can be seen in the Appendix A. From the calibration it was discovered that in the force balance, moments around the 𝑥-axis was coupled with the force in the 𝑥-axis.

The offset yaw angle was determined to be approximately -1.3°, please note that this offset was not applied to the data set unless specified. Due to results only being recorded at 1° intervals, an offset of -1° was applied.

6 Building the Morphing Wing

The offset yaw angle is due to the tunnel inflow which is caused from the closed return design of the wind tunnel. The offset yaw angle was determined by mounting flat board in the wind tunnel in the same position as the wing then the angle of attack was changed until the lift generated by the configuration was approximately zero.

Figure 45 Isometric view of the Morphing Wing.

This section details the design, manufacturing and analysis of the morphing wing. The complete morphing wing shown in Figure 45.

Figure 46 2D Morphing Wing splines from XFLR5.

6.1 Morphing Skin Concept Since a suitable skin for the wing was not found in previous work, leaving the task to be completed in this study. A literature review was conducted to determine a suitable concept for the morphing wing, which is covered in section 2.6.

The skin for the wing will be a dual skin concept consisting of an upper and lower skin, the upper skin being the compliant morphing skin and the lower skin being a thin aluminium plate able to bend without plastic deformation. The morphing skin will need to have low out-of-plane stiffness that is being able to be deformed chordwise and so that it will not require a high actuation force whilst also possessing high in-plane stiffness that is being rigid in the spanwise direction. With the implementation of the thin aluminium plate, the bottom surface does not need to be pre-tensioned as opposed to the pre-tensioning required in Woods et al’s design [23] . The morphing skin will also require a zero Poisson’s ratio since the skin should not contract in the spanwise direction when the camber morphing occurs.

6.3 Evolution of the Morphing Skin This section will the detail process from the initial design of the morphing skin to the final skin. The initial FMC skin was to have unidirectional carbon fibre to be infused with silicone as seen in papers by Murray and Kirn [52, 66]. Small samples of the skin were manufactured using the unidirectional carbon fibre at various toe sizes to determine which toe size was suitable and which were not (Morphing skin A). If the fibres were not tensioned during the silicone pouring and curing process then the fibres would sink to the bottom of the flat plate seen in Figure 47.

In order to counteract this a tensioning rig was designed and built. To keep the fibres in place to allow for the silicone to flow through the fibre and to keep the fibres tensioned and in place so that they would not slack. The fibres were indeed tensioned and generally centred in the silicone matrix however there was an issue of distancing and orientation of the carbon fibre tows seen in Figure 47.

This worked at a smaller scale (Morphing skin C) however at the full scale of the tensioning provided by the rig was not enough to keep the fibres from slack, as the tensioning could not overcome gravitational forces as the fibres would begin to slack after being ~50mm away from the tension points (Morphing skin D). Therefore, the fibres would sink to the bottom and not be encased in silicone. Next the fibres were laid flat and straight and vacuum bagged before applying more silicone to get an equal distribution (Morphing skin E). The skin was also shown to slack in between each of the ribbed sections of the wing seen in Figure 48. A persisting issue from morphing skin A to E is that the carbon fibre would drift hence not being parallel and not equal distance apart from each other. Up to this point, the morphing skin design was unsuccessful which likely stems from the carbon fibre fabric being dry. However, lessons were learnt during the pursuit of that concept as various aspects of handling the silicone and its additives were noted during the endeavour.

Figure 47 Initial morphing skin design A to morphing skin design C.

Firstly, the silicone “Dragonskin 10” while extremely elastic does have an issue with having a high friction, i.e. it does not slide across surfaces easily hence an additive “Slide STD” to reduce the friction was obtained. However once Slide STD is added it increased the viscosity of the silicone which inhibits the silicone from infusing through the carbon fibre resulting in only one side being infused with silicone which is depicted in Figure 48. The viscosity was then decreased using the “silicone thinner”.

Figure 48 Morphing skin design D to morphing skin design E.

The issue with the initial concept is that it prioritized the flexibility of the skin which is why the carbon fibre in the silicone was not hardened via any resin. The next skin would use carbon fibre laminate instead of dry carbon fibre fabric a small sample was manufactured and tested (Morphing skin F and onward) seen in Figure 49. The skin will incorporate strips of carbon fibre to correspond to the lengths of the leading edge to the initial rib section of the wing, the width of the spine of the rib and the final rib to the trailing edge section of the wing with spacing in between for silicone.

The carbon fibre laminate infused with silicone did show slack in between each of the rib sections of the wing however the slack was less than that of what was seen with the initial skin. The slack was then further reduced by adding an aluminium angle at the end of the leading edge to the initial rib section of the wing and the final rib to rib end section, each angle length was equal to the spanwise length of the skin (Morphing skin G) seen in Figure 49. This further reduced the amount of slack observed and deemed an acceptable solution and in addition to further reduce the amount of slack observed additional ribs will be incorporated to the wing i.e. the distance between ribs will be reduced. Initially there were five ribs, the number of ribs was increased to nine. However, when the skin was stretched/deflected during deflection slack was observed at rib-less sections of the wing. The sections at which no slack was observed i.e. the sections of the wing where ribs were present were reinforced by the ribs hence zero slack.

Figure 49 Morphing skin F to Morphing skin G.

To counteract this slack, L shape carbon fibre angles were bonded to each of the ribs before the skin to act as ribs in sections of the wing that lack ribs to reinforce the skin and reduce the slack observed, seen in Figure 50. The crest outline of the surface was used to manufacture a mould for the carbon fibre laminate for the morphing skin, depicted in Figure 50. A thin aluminium sleeve was used to prevent the separation of the aluminium plate from the bottom of the wing. In morphing skin F to the final skin, the bond between the silicone and the carbon fibre laminates does have an issue where it is not bonded properly. However, it can be remedied by applying tape, which was done prior any testing.

The concept does increase the required actuation load however this was already considered when sizing the servos. A persisting issue that exists from the initial morphing skin to the final morphing skin is the voids left by escaping air. However, the voids can be filled by pouring additional silicone to fill the hole, this can also be done for tears in the skin. This means that the skin can be easily repaired given the damage is only localised to silicone components.

Figure 50 Morphing skin H to the Final Skin.

The bottom skin was a thin plate Al plate (2024 AL-CLAD T3) which was only bonded to the wing before the deformation part of the wing, this allowed the plate to freely deflect along with the deformation of the wing. To prevent any slack from the thin Al plate, a thin Al sleeve was bonded to the trailing edge preventing the thin Al plate from separating to the bottom of the wing. The morphing wing deflection and thin Al sleeve shown in Figure 51.

Figure 51 Compliant morphing skin demonstration.

It should be noted that the compliant morphing skin designed and manufactured during this study was for the purpose of wind tunnel testing. Therefore, the skin was not designed to undertake any form of flight testing.

6.3.1 Morphing Skin Manufacturing Process

The layup process of the morphing skin is briefly outline below.

1. Wet lay up two ply of carbon fibre at dimensions required whilst considering tolerance for a

CNC cutter and for extra material as tolerance. a. Enough for 11 strips and 1 trailing edge. b. Ensure it is on a larger and clean plate for vacuum bagging. i. Perforated peel ply -> peel ply->plastic bagging->breather->vacuum bag. c. Cured at roughly ~1bar. 2. Post cure of the ply it was cut into the required dimensions and number of components via CNC router. 3. The same was also done with the carbon fibre leading edge component of the leading-edge side of skin with some differences. a. The leading-edge side was placed on a mould that matches the curvature of the airfoil location that it will be placed on. b. Each layer of the laminate was placed individually on the mould to prevent any folding 4. Two L-shape aluminium angles were cut to size. a. Vertical components of the angle were removed at locations where they would contact the spines of the rib and the control arm. b. Sharp edges were smoothened. 5. Both the aluminium angles and the leading edge and trailing edge carbon fibre laminates were bonded using HUNSTMAN Araldite 420 a. After being lightly abraded and cleaned using 400grit sandpaper and ISOPROPYL alcohol wipes 6. Components laid out vertically and parallel at 4mm apart which allows for pretension at 0° morphing deflection. 7. Dragonskin silicone mixed up and applied to the laminates and cured at room temperature.

6.4 Summary of the Morphing Wing Design Design considerations:

a. Excess silicone is removed during the application process. b. Post cure excess silicone is removed. c. Any gaps were filled out with further silicone.

The weight of the wing was not considered as a major factor since the wing will only be undergoing wind tunnel tests. Since only the leading edge and spar carries torsional and bending loads, the strength of these two components were prioritised over reducing the weight of the design. The geometry of the morphing wing needed to match the conventional T240. The design considered the inclusion of the fuselage wingbox. A knife edge was required for the trailing edge therefore an exception was considered. The morphing profile must be smooth and continuous. The complete morphing wing design and its components is depicted in Figure 52.

Figure 52 Exploded isometric view of the Morphing Wing.

The leading edge and trailing edge are the solid and rigid components of the morphing wing. These two components do not morph. The leading edge contains slots across the span to allow for the brackets of the ribs and the spar to be inserted. There is also an indentation in the leading edge located immediately after the crest to incorporate the FMC skin. The thin aluminium plate is also considered as there is a small indentation located on the bottom surface of the leading edge. The trailing edge is designed in the same manner as the leading edge.

The rib design utilizes three components: bracket, FishBAC rib and rib end. Since only the middle section of the rib is deflected i.e. the FishBAC rib, the bracket and rib end are rigid components. The height of the rib was designed to consider the reinforcing brackets and the thickness of the FMC skin to ensure the airfoil shape was not compromised. The rib components are all connected via tabs and slots in each component, where the rib end and bracket are tabbed and the FishBAC rib is slotted. The bracket and rib end attach the rib to the spar and leading edge and the trailing edge respectively.

The morphing of the wing is actuated by rotation of a torsion rod. The morphing surface extends from the point of maximum thickness to the trailing edge. The ribs are allocated at equal distance along the entire span. The torsion rod induces a uniform deflection across the span. The rotation of the torsion rod also induces rotation in the control arms which guide the deflection of the FishBAC ribs. The control arms are parallel to ribs and positioned next to the ribs with an offset to avoid contact. The control arms determine the deflection shape of the FishBAC ribs.

The wing utilises a dual skin system, a compliant morphing skin for the top surface and a thin aluminium plate for the bottom surface. The FMC skin maintains a zero Poisson’s ratio during morphing which allows for the extension of the top surface of the wing during deflection. The thin aluminium plate bends during morphing which allows for contraction of the bottom surface.

The reinforcing brackets located along the spines of the FishBAC ribs prevent the FMC skin from slacking between the spines and non-ribbed areas. Since the reinforcing brackets are positioned above the spines of the FishBAC ribs, sections of the reinforcing brackets were cut to avoid contact with the ribs and control arms.

To prevent any separation of the thin aluminium plate from the wing, a thin aluminium sleeve was

7 Results

7.1 Flow Visualization Flow visualization was conducted for both the top and bottom surfaces of the morphing wing, shown in APPENDIX C, while a summation of the observed flow behaviour is in Table 3 for each morphing condition and flight condition.

bonded to the trailing edge to allow for the plate to freely slide in as necessary to prevent any separation from the wing. The wing tip was designed to house the servo that would induce morphing. Because of this the wingtip was designed in two parts: wing tip and wing tip cover.

The flow of the morphing wing was observed at intervals of 5°, using cotton tufts along the span and the chord on both the upper and lower surfaces of the wing, which can be seen in Figure 92 to Figure 102. From the figures the separation for the upper surface does not occur at lower angles of attack and lower angles of morphing as expected, separation of the flow does occur at roughly 𝛿𝑚 > 5° and for 𝛼 > 10°. Although this separation for higher angles of attack can be reattached if airspeed is increased. There are also particular sections which exhibit separation whilst others in the same chordwise or spanwise location does not show separation this could be due to interference from the cotton tufts. The lower surface does not show separation at most conditions, it does show some disturbance around the strut which is to be expected. However, flow aft of the strut returns to an attached condition. The speed of the flow has very little to no effect on the bottom surface.

Flow visualization was conducted for Re 168000, Re 236000, Re 269000 and Re 337000. There are noticeable differences on the top surface of the wing between Re 168000 and subsequent Reynold’s numbers. Re 168000 and Re 236000 are similar at certain conditions whilst Re 269000 and Re 337000 are similar at most conditions therefore only Re 168000 and Re 269000 of the top surfaces are displayed. The flow visualization for the bottom surface is almost identical for all conditions and only Re 269000 is displayed for the bottom surface.

7.1.2 Summary of Flow Visualization Behaviour The behaviour for the bottom surface remains the same for all morphing deflections and flight conditions. There are no discernible differences for the bottom surface for the observed angles of attack and Reynolds numbers.

Airspeed does affect the behaviour of the flow, particularly at Re 168000 at higher morphing deflections and angles of attack, flow is separated. When the airspeed is increased, flow can be reattached for some of the morphing deflections and angles of attack. The separation encountered at Re 168000 is likely due to the flow not having enough energy to remain attached.

At 𝛿𝑚 = 0° or the T240 base airfoil experiences separation at 𝛼 ≈ 15° from the silicone region to the trailing edge. This coincides with T240 as the stall angle of the T240 airfoil is 𝛼 ≈ 12°. Once 𝛿𝑚 > 0°, the behaviour of flow changes, being dependent on the airspeed, angle of attack and morphing deflection.

From 2° ≤ 𝛿𝑚 ≤ 10° separation of the trailing edge and rib end sections are dependent on the angle of attack. In those conditions the lowest airspeed (Re 168000) showed separation of the range of angles of attack than at airspeeds higher than Re 168000. Separation at the rib end is not apparent at 𝛿𝑚 =

2° for all flight conditions. From 𝛿𝑚 ≥ 15° separation of the trailing edge and rib end occurs at all angles of attack and airspeed. Tufts in the silicone section experiences disturbances at 𝛿𝑚 ≥ 2° however it is dependent on the angle of attack. Separation in the silicone section occurs higher angles of attack from 10° ≤ 𝛿𝑚 ≤ 15°.

Disturbances is seen at the crest from 𝛿𝑚 ≥ 2° at 𝛼 = 15° and separation occurs at 𝛿𝑚 ≥ 15° at 𝛼 = 15°. The leading-edge tufts experiences disturbances and separation at 𝛿𝑚 ≥ 15° at 𝛼 = 15°. Disturbances could be caused by the wing reaching turbulent flow due to a combination of the angle of attack and the morphing deflection. The frequency and behaviour of the disturbances are likely linked to the behaviour of turbulent flow. Hence it is advised that the morphing deflection should be kept low and at low angles of attack for cruise to avoid turbulent flow.

Table 3 Summation of flow visualisation behaviour

%𝑐 where separation to occurs 50 50 50 50 50 75 75

50 50 50 50 50 50 50 75 75

𝛿𝑚(in deg) 40 35 30 25 20 15 10 5 3 2 0 𝛼 (in deg) 0 10 10 10 10 35 35 35 50 50 50 75 15

Where %𝑐 corresponds to for wing section -5 10% 35% 50% 75% 10 10 10 10 35 35 35 75 75 75 75 5 10 Leading edge Crest Silicone Trailing edge

Comparing the flow visualizations with theoretically results of the morphing wing in Figure 40 and Figure 42 it is within expectations. That is that for low morphing deflections and low angles of attack the predictions of XFLR5 and TORNADO on appearance are in line with the flow visualization. This changes from 𝛿𝑚 = 15° where disturbances and separations begins occurring around the silicone region of the wing even at low angles of attack (𝛼 = 5°) where as both XFLR5 and TORNADO still show an increase in performance of 𝐶𝐿. In other words, the flow visualization is indicating turbulent/non- linear flow whilst XFLR5 and TORNADO still treats flow at 𝛿𝑚 = 15° as linear flow. This phenomenon continues to 𝛿𝑚= 40°, where in the flow visualization the disturbances and separation increases in magnitude and progress to even the crest of the wing. Both TORNADO and XFLR5 still assume the flow is attached up to this point.

However, XFLR5 does show a decrease in performance after 𝛿𝑚 = 25° until 𝛿𝑚 = 40°, this means that XFLR5 does recognize that the morphing wing does become less efficient if excessive morphing is conducted. Although the results show that flow is still attached, which is due to the inviscid method used. This does line up with flow visualization to an extent as flow is attached for low angles of attack

and lower morphing deflections. While at higher morphing deflections and at high angles of attack, disturbances and flow separation occurs across the upper surface of the wing.

TORNADO does not predict a general decrease in performance for the coefficient of lift as morphing deflection increases. There are two cases where this a decrease in lift coefficient occurs, being 𝛿𝑚 = 30° and 𝛿𝑚 = 40°. This could be due to the transformation that TORNADO applies to the airfoil sections since TORNADO assumes that the wings are thin bodies where in reality the wing profiles at these deflections are highly cambered which is not suitable for TORNADO. TORNADO does predict a drop in performance of coefficient of lift however it is limited to 𝛿𝑚 = 35° and 𝛿𝑚 = 40°, where the drop is only relative to the angle of attack for the same deflection. That is the 𝐶𝐿 of 𝛿𝑚 = 35° and 𝛿𝑚 = 40° is still higher than that of 𝛿𝑚 = 0°. Like XFLR5, this is due to the inviscid method which is best suited for pre stall angles of attack as well as non-highly cambered airfoils. The flow visualization does not show this as being true as at 𝛿𝑚 = 35° and 𝛿𝑚 = 40°, disturbances and separation occurs throughout the upper surface of the wing.

7.2 Wind Tunnel Data Post Processing Results obtained from the wind tunnel testing will be calibrated using the corrections/calibrated using equations in Appendix A. The lift and drag, 𝐹𝑥 and 𝐹𝑦 respectively must be changed to the wind axes from the body axes i.e. lift and drag must be converted using equations 2 and 3.

From these observations, the flow visualization can be used to determine at which morphing deflection and angles of attack the theoretical results are not reliable. Hence for the theoretical results of XFLR5 and TORANDO at 𝛿𝑚 ≥ 15° should be viewed critically, especially in the case of TORNADO results since no decrease in performance was predicted. The theoretical results for 𝛿𝑚 ≤ 10°, can be viewed as more reliable as separation and disturbances are not as apparent. the results for 𝛿𝑚 = 2° (for all angles of attack) and 𝛿𝑚 = 3° (until 𝛼 = 5°) could be viewed as most reliable as little to no disturbances and separation occurs at those conditions.

𝐿 = 𝐹𝑥 cos 𝛼 − 𝐹𝑦 sin 𝛼

(2)

𝐷 = 𝐹𝑦 cos 𝛼 + 𝐹𝑥 sin 𝛼

(3)

Then equations 4 & 5 were used to determine the 𝐶𝐿 & 𝐶𝐷. The dynamic pressure, 𝑞 used in equations 4 & 5 was the calibrated dynamic pressure from Appendix A. The dynamic pressure was calibrated by using a pitot static tube which was used to measure the difference in pressure at the wing and at the walls of the wind tunnel This method is also applied for flap input and morphing deflection i.e., to determine 𝐶𝐿 𝑚𝑎𝑥.

𝐶𝐿 =

𝐿 𝜌𝑉2𝑆

1 2

(4)

𝐶𝐷 =

𝐷 𝜌𝑉2𝑆

1 2

(5)

Rearranging equation 4 and substituting 𝐿 for the weight of the aircraft, 𝑉𝑠𝑡𝑎𝑙𝑙 was determined.

To determine the rolling moment, the offset of the wing and the centre of pressure for the wing must first be determined. The offset of the wing is made up of the half thickness of the load cell, the rod connecting the load cell to the sting and the sting board thickness.

The centre of pressure was determined by extracting the 𝐶𝐿𝑙𝑜𝑐𝑎𝑙 spanwise distribution from Tornado at 𝛼 = 0° with zero inputs and then conducting a trapezoidal integration method (equation 6) until a zero aerodynamic moment was achieved.

𝑏 ∫ 𝑓(𝑥) 𝑎

∆𝑥 2

𝑑𝑥 ≈ (𝑓(𝑥0) + 2𝑓(𝑥1) + 2𝑓(𝑥2) + 2𝑓(𝑥3) + ⋯ + 2𝑓(𝑥𝑛−1) + 𝑓(𝑥𝑛)) (6)

𝑏−𝑎 𝑛

Where ∆𝑥 = and 𝑥𝑖 = 𝑎 + 𝑖∆𝑥

An alternative is to determine the area of each strip and sum them up and split up the distribution curve into two major components with multiple strips in each component.

∑ 𝐴 =

(𝑦𝑛−1 + 𝑦𝑛)∆x

(𝑦1 + 𝑦2)∆x +

(𝑦2 + 𝑦3)∆x + where 𝐴 is the sum of all areas, 𝑦 are 𝐶𝐿 𝑙𝑜𝑐𝑎𝑙 values , ∆x is the width of the strip (interval size)

(7)

∑ 𝑀 = 𝐹𝑥

(8)

Following this method, the Centre of pressure was found to be at roughly 50% of the semispan (the distribution was slightly skewed to towards the tip of the semi-wing, 49-51 split), for 𝛿𝑓 = 0° at 𝛼 = 0°. This method was validated by using equation 6 with the results from the wind tunnel and the measured offsets of the load cell, rod and sting board. When using equation 6, the moment arm for each lifting surface, 𝑥 was the distance between the point of interest to the applied force. In this case the force is lift generated by the wing which acts at the centre of pressure of the wing. Solving equation 8, the centre of pressure of the wing is evaluated to be at 51.78% of the semispan hence showing both methods give similar results.

This approximation was also used for the Centre of pressure for the ailerons while they are deflected and the morphing wing. Due to the offset of the wing from the load cell the moments determined by experiment is not the true moment generated by the wing. Using the calibrated lift from the experimental data and the approximated centre of pressure of in the spanwise direction the wing, the true moments generated by the wing was determined. Which was done by using equation 8 where 𝑥 is the wing root to the centre of pressure of the wing.

𝑀

From here the rolling moment coefficient, 𝐶𝑙 can be determined from equation 9, like with equation 4 & 5 the calibrated dynamic pressure must be used.

𝐶𝑙 =

𝑞𝑆𝑏

(9)

The equations related to roll are shown in section 7.3.3.

7.3 Experimental Results and Discussion It should be noted that not all tests could be conducted on the same day hence varying temperatures and different ambient pressure. Because of this there would be differences in results for any same

All of which were conducted for each of the morphing deflections and flight conditions.

test conducted hence being a source of error. The effects of this are seen in Figure 53 and Figure 54, where the data points of 𝛿𝑓 = 28° and 𝛿𝑚 = 0° are offset. To account for this, a specific test was conducted multiple times throughout the testing period. The specific test was chosen (𝛿𝑚 = 3° at 𝛼 = 0°) which was tested at different times of the day, over multiple days. By testing the condition of 𝛿𝑚 = 3° at 𝛼 = 0° over several days and collecting data, error bars were generated which represents the standard deviation of the results that can occur.

7.3.1 Conventional T240 Wind Tunnel Results

1.6

Wind Tunnel

1.4

1.2

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.8

0.6

Re 168000

t f i L f o t n e i c i f f e o C

0.4

, 𝐿 𝐶

0.2

-10

-5

-0.2

This section covers the experimental results of conventional T240, the results are shown then discussed. The conventional T240 wing underwent tests in the normal condition (without any control surface input), various flap and aileron deflections. The parameters discussed in this section include 𝐶𝐿 and 𝐶𝐷, while other parameters such as 𝐿/𝐷 and 𝑝 will be discussed in section 7.3.2 and section 7.3.3 respectively.

𝛼, Angle of Attack, in 𝑑𝑒𝑔

1.6

Wind Tunnel

1.4

1.2

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.8

0.6

Re 236000

t f i L f o t n e i c i f f e o C

0.4

, 𝐿 𝐶

0.2

-10

-5

-0.2

-0.4

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Wind Tunnel

1.6

1.4

1.2

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.8

0.6

0.4

Re 337000

0.2

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.2

-0.4 𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 53 Conventional T240 Wing results for 𝑪𝑳 vs 𝜶 at various Reynolds numbers.

0.35

0.3

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.25

g a r D

0.2

0.15

f o t n e i c i f f e o C

0.1

Re 168000

𝐷 𝐶

0.05

-10

-5

0.35

0.3

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.25

g a r D

0.2

0.15

f o t n e i c i f f e o C

0.1

Re 236000

𝐷 𝐶

0.05

-10

-5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

0.35

0.3

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.25

g a r D

0.2

0.15

f o t n e i c i f f e o C

𝐷 𝐶

0.1

Re 337000

0.05

-10

-5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 54 Conventional T240 Wing Wind Tunnel results for 𝑪𝑫 vs 𝜶 at various Reynolds numbers.

Observations from the wind tunnel test for the conventional T240:

• Stall behaviour for the conventional T240 to begins at approximately 𝛼 = 10° • 𝐶𝐿𝑚𝑎𝑥 was achieved at 𝛿𝑓 = 28°, 𝛼 = 15° at Re 337000 • Additional input of flaps increases the 𝐶𝐿 and does not affect the lift curve slope as expected of traditional flaps.

• Coefficient of roll is largely linear with 𝛿𝑎

When comparing the experimental results of the T240 and the theoretical results of XFLR5 and TORNADO we can see that with no inputs the 𝐶𝐿 are all very similar, this starts to diverge as inputs are added. The divergence is expected since separation of flow around the plain flap roughly occurs at around 10° deflection [85] and since XFLR5 and TORNADO does not consider flow separation due to control surfaces and hence overpredict the 𝐶𝐿 and 𝐶𝑙 whilst underpredicting 𝐶𝐷. We can see that from zero inputs (𝛿𝑓 = 0°) to 𝛿𝑓 = 7°, 𝛿𝑓 = 14°, 𝛿𝑓 = 21° and 𝛿𝑓 = 28° the divergence of 𝐶𝐿 becomes larger and larger however the lift curve slope itself essentially is the same. The divergence is also apparent for ailerons, when 𝜃𝑎 > 3° in either direction flow becomes separated and there is a difference between the wind tunnel results and the results predicted by TORNADO.

𝐶𝐷 is underpredicted in both XFLR5 and TORNADO as they do not accurately predict parasite drag (𝐶𝐷0). Since 𝐶𝐷 = 𝐶𝐷𝑖 + 𝐶𝐷0, it is unreliable 𝐶𝐷 is recalculated by substituting 𝐶𝐷0 from the wind tunnel experiments into XFLR5 and TORNADO which now results in 𝐶𝐷 being larger than what is seen experimentally. Although this is an issue, this is also seen in the examined literature [11, 34, 51, 76, 86] and can be considered normal. Due to this consideration the predicted 𝐿/𝐷 for XFLR5 and TORNADO would be underpredicted.

Wind Tunnel

delta_m = 2 degrees delta_m = 5 degrees delta_m = 15 degrees delta_m = 25 degrees delta_m = 35 degrees

delta_m = 0 degrees delta_m = 3 degrees delta_m = 10 degrees delta_m = 20 degrees delta_m = 30 degrees delta_m = 40 degrees

1.5

0.5

t f i L f o t n e i c i f f e o C

Re 168000

, 𝐿 𝐶

-10

-5

-0.5

7.3.2 Morphing Wing Wind Tunnel Results This section covers the experimental results of morphing wing, the results are shown then discussed. The morphing wing underwent tests in each morphing deflection from: 𝛿𝑚 = 0°, 2°, 3°, 5°, 10°, 15°, 20°, 25°, 30°, 35° and 40°. The parameters discussed in this section include 𝐶𝐿, 𝐶𝐷 and 𝐿/𝐷, while 𝐶𝑙 and 𝑝 are discussed in this section 7.3.3.

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Wind Tunnel

delta_m = 2 degrees delta_m = 5 degrees delta_m = 15 degrees delta_m = 25 degrees delta_m = 35 degrees

delta_m = 0 degrees delta_m = 3 degrees delta_m = 10 degrees delta_m = 20 degrees delta_m = 30 degrees delta_m = 40 degrees

Re 236000

1.5

0.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

delta_m = 2 degrees delta_m = 5 degrees delta_m = 15 degrees delta_m = 25 degrees delta_m = 35 degrees

Wind Tunnel

delta_m = 0 degrees delta_m = 3 degrees delta_m = 10 degrees delta_m = 20 degrees delta_m = 30 degrees delta_m = 40 degrees 2

1.5

Re 337000

t f i L f o t n e i c i f f e o C

0.5

, 𝐿 𝐶

-10

-5

-0.5 𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 55 Morphing Wing results for 𝑪𝑳 vs 𝜶 at various Reynold numbers.

By observing the linearity of the 𝐶𝐿- 𝛼 curves of the morphing wing results, the 𝐶𝐿 behaviour of the morphing wing seems to be split into three behaviours. As 𝛿𝑚 increases, the stall 𝛼 decreases, which follows typical flap behaviour. For the analysed 0° ≤ 𝛿𝑚 ≤ 10°, in Figure 55 there is a linear increase in 𝐶𝐿 i.e. the lift curve slope is linear, meaning linear flow is occuring. The behaviour of the flow changes once 𝛿𝑚 = 15°, between 15° ≤ 𝛿𝑚 ≤ 25° the increase in 𝐶𝐿 at this point the wing could have already reached the stall condition, signifying non-linear flow and beginning of flow separation. While for 𝛿𝑚

≥ 20°, lift progressively decreases as morphing deflection increases. The increase in 𝐶𝐿 due to morphing stops at 𝛿𝑚 = 25°, morphing beyond 𝛿𝑚 = 25° has negative effects on 𝐶𝐿. This effect is seen, where at 𝛿𝑚 = 40° and at 𝛿𝑚 = 10° the 𝐶𝐿 is approximately the same. The decreases in 𝐶𝐿 for 𝛿𝑚 ≥ 25° is due to the increasing flow separation seen at the silicone region of the wing (located on the upper surface of the wing) which is apparent from Figure 98 to Figure 102.

From the flow visualization in Figure 99 to Figure 102, the flow of the bottom surface of the wing are still attached. It appears that the flow from the trailing edge, separated flow joins with the separated flow from the crest (seen in Figure 99 to Figure 102), creating a larger separated region of flow. Hence the reversed flow region for 𝛿𝑚 ≥ 25° is larger than the reversed flow regions of 𝛿𝑚 ≤ 25°, where the separation of the bottom surface from the trailing edge is not as significant at lower morphing deflections. Which could be the cause for the drop in lift coefficient. This goes in line with the flow visualization at the respective morphing deflections (seen in Figure 92 to Figure 97), where the upper surface begins to see flow separation at the rib-end section.

This also affects the rolling of the wing where if morphing is too large there would be a decrease in rolling moment resulting in a smaller roll rate. Therefore, any further morphing beyond 𝛿𝑚 = 25° is detrimental to 𝐶𝐿, 𝐶𝑙, and 𝑝̇. The dotted lines through each of the 𝛿𝑚 in Figure 55 approximates the linear conditions of the morphing wing. However, the most stable behaviour was taken in determining 𝐶𝐿 𝑚𝑎𝑥 therefore 𝐶𝐿 𝑚𝑎𝑥 occurs at 𝛿𝑚 = 5°.

Post wind tunnel testing, the lift and drag equations were used to generate Figure 53 to Figure 57. From Figure 53 and Figure 55 the 𝐶𝐿 𝑚𝑎𝑥 of the conventional T240 and the morphing wing is approximately 1.2 and 1.45 respectively, an increase of 20% due to morphing. Rearranging Equation 4 and substituting aircraft mass, 𝑊 for 𝐿 and solving for 𝑉, now stall speed, 𝑉𝑠𝑡𝑎𝑙𝑙. The mass of each aircraft configuration are as follows:

𝑚1/2𝑏 = 1.1 𝑚𝑏𝑜𝑑𝑦 = 5.45

T240 Single wing mass (𝒌𝒈) T240 aircraft weight (minus wings) (𝒌𝒈) Total aircraft weight (N) 𝑊 = 75 (7.65 𝑘𝑔) Morphing Wing Single wing mass (𝑘𝑔) 𝑚1/2𝑏 = 3.73 𝑚𝑏𝑜𝑑𝑦 = 5.45 T240 aircraft weight (minus wings) (𝑘𝑔) Total aircraft weight (N) 𝑊 = 127 (12.91 𝑘𝑔)

The stall speed, 𝑉𝑠𝑡𝑎𝑙𝑙 of the conventional T240 and the morphing wing is 10.9 m/s and 12.9 m/s respectively, an increase of 18%. If 𝐶𝐿 performance during turbulent flow is considered, then the morphing wing can increase the 𝐶𝐿 up to 23%, reducing the increase in stall speed. Stall speed is generally only relevant during take-off and landing. Therefore, a trade-off of in performance for take- off and landing for an increase in lift-drag ratio in cruise is required. The morphing wing prototype has yet to be optimised for weight therefore the single morphing wing mass of 3.73kg can be reduced. Because of this, the stall speed can be improved.

For the range of 𝛼 analysed as 𝛿𝑚 increases the 𝐶𝐷 increases, which is expected since induced drag increases due to the increase in lift, 𝐿 from morphing. The 𝐶𝐷 - 𝛼 curves follow typical parabolic drag behaviour except between 5° ≤ 𝛿𝑚 ≤ 10°. Between 10° ≤ 𝛿𝑚 ≤ 15°, 𝐶𝐷 - 𝛼 curves behave linearly. For 𝛿𝑚 > 15° the behaviour of the 𝐶𝐷- 𝛼 curves resemble typical drag behaviour. At 𝛿𝑚 = 30°, the drag polar behaves differently as a decrease in drag is observed. The 𝐶𝐷 at 𝛿𝑚 = 30° is smaller than 𝐶𝐷 at 𝛿𝑚 = 25°, This could be due to the stall characteristic of the airfoil profile. At 𝛿𝑚 = 40°, there is a large spike in 𝐶𝐷 at 𝛼 = 0°. This spike is seen at lower 𝛿𝑚 and even 𝛿𝑓 (for the conventional wing) which are

0.8

Re 168000

0.7

0.6

0.5

delta_m = 0 degrees delta_m = 2 degrees delta_m = 3 degrees delta_m = 5 degrees delta_m = 10 degrees delta_m = 15 degrees delta_m = 20 degrees delta_m = 25 degrees delta_m = 30 degrees delta_m = 35 degrees delta_m = 40 degrees

g a r D

0.4

0.3

0.2

f o t n e i c i f f e o C

𝐷 𝐶

0.1

-10

-5

5 𝛼, Angle of Attack, in

shown in Figure 54 and Figure 56. This behaviour could be due to the nature of the airfoil or the setup of the wing in the wind tunnel during experimentation. Another observation that can be made from examining Figure 56 is that linear flow occurs from 0° ≤ 𝛿𝑚 ≤ 5° as the 𝐶𝐷 curves of those morphing deflections all intersect at the zero-lift angle of attack which occurs at 𝛼 ≈ -3°. This means that the drag behaviour for the morphing wing for 0° ≤ 𝛿𝑚 ≤ 5°, is still predominately determined by induced 2, which can be determined by the parabolic nature of the 𝐶𝐷 curves. From 𝛿𝑚 = 10° drag i.e. 𝐶𝐷𝑖 ∝ 𝐶𝐿 there is a massive increase in drag hence the drag generated by the morphing wing is predominately pressure drag, that is drag caused by separation of increasing morphing deflections. This is evident since the 𝐶𝐷 curves do not follow normal drag behaviour, the drag seems to consist of more parasite drag than induced drag. The increasing drag seen from 𝛿𝑚 = 10°, could be due to the ever-increasing parasite drag which is caused by the continual increase of the morphing deflection. As morphing deflection increases, the camber of the wing continually increases which then increases the size of the separated region of flow to continually increase. As the flow passes the trailing edge of a highly cambered wing, the flow does not have the energy to reattach in the freestream direction after the trailing edge. Hence the massive increase in drag for 𝛿𝑚 ≥ 10°. This could also explain the drop in lift performance observed in Figure 55, as in the flow visualization the silicone region on the upper surface of the wing (in Figure 96) begins to show signs of disturbance and separation. Whereas for 𝛿𝑚 ≤ 10° the silicone region of the upper surface of the wing remains attached and undisturbed until about 𝛼 = 10° which is the stall angle of attack of the T240 airfoil.

0.8

0.7

Re 236000

0.6

0.5

g a r D

0.4

0.3

f o t n e i c i f f e o C

0.2

𝐷 𝐶

0.1

-10

-5

0.8

Re 337000

0.7

0.6

0.5

g a r D

0.4

0.3

0.2

f o t n e i c i f f e o C

𝐷 𝐶

0.1

-10

-5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 56 Morphing Wing Experimental results for 𝑪𝑫 vs 𝜶 at various Reynold numbers.

Figure 57 displays plots of 𝐿/𝐷 vs 𝐶𝐿, traditionally Figure 57 would be displayed as 𝐿/𝐷 vs 𝛼, however it is displayed as 𝐿/𝐷 vs 𝐶𝐿 to frame it in the design stage. Where the maximum lift-drag ratio is desired for a specific lift coefficient. In this framing it is easier to determine if the morphing wing is more

efficient in terms of lift-drag ratio than the conventional T240 wing as both would be compared at the same lift coefficient.

As 𝛿𝑚 increases, the pool of data points translates to the right and is lower in the plot this is due to the increase in 𝐶𝐿 and the decrease in 𝐿/𝐷 due to the increasing 𝐷. For the conventional wing, 𝐿 is a function of both 𝑉 and 𝛼. While for a camber morphing wing, 𝐿 is a function of both 𝑉, 𝛼 and 𝛿𝑚. Therefore if 𝑉 is kept consistent, then for any given 𝐶𝐿 there are various possible combinations of 𝛼 and 𝛿𝑚 to achieve said 𝐶𝐿. From the large pool of 𝐿/𝐷 for 𝐶𝐿 it would be ideal to cruise at the highest 𝐿/𝐷 for any given 𝐶𝐿. Therefore, during cruise a camber morphing wing aircraft should alter its 𝛼 and 𝛿𝑚 to achieve a maximum 𝐿/𝐷 for a given 𝐶𝐿, an example of this is shown in Figure 57. Hence during a cruise condition where a lower 𝐶𝐿 is required (0.2 ≤ 𝐶𝐿 ≤ 0.6) it would be ideal for to deflect the wing to 𝛿𝑚 =2, 3°, 5° (with the corresponding angle of attack) depending on the desired 𝐶𝐿. While for phases of flight that require a higher 𝐶𝐿 (𝐶𝐿 ≥ 0.8) such as take-off, landing or stall, it would be ideal for the morphing wing to deflect to 𝛿𝑚 = 10° (with the corresponding angle of attack).

By observing Figure 57 the base morphing wing outperforms the conventional T240. That is the 𝐿/𝐷 for a given 𝐶𝐿 for the morphing wing at 𝛿𝑚 = 0° is generally 20% larger than the conventional T240 wing at 𝛿𝑓 = 0°. Since the morphing wing is designed to be identical to the T240 wing it should have identical performance to the T240 wing. The only difference being that the morphing does not have discontinuous control surfaces such as flaps and ailerons and the components related to their actuation. The difference in performance could be due to several factors such as the lack of control surfaces, difference in geometry due to manufacturing and surface finish. Another possible factor for the discrepancy could be the extended trailing edge of the morphing wing which forms a knife edge. It could also be possible that the extra wingspan of the T240 for the insertion to the fuselage could reduce aerodynamic efficiency of the wing. The reduction could be due to the blunt profile and the tab, surrounding the area of the inserted portion of the T240 wing.

• 𝛿𝑚 = 2° : 14% • 𝛿𝑚 = 3° : 30% • 𝛿𝑚 = 5° : 41% • 𝛿𝑚 = 10° : 89%

The 20% offset in performance is ignored since the 𝐿/𝐷 for both wings should be identical. Hence the T240 wing at 𝛿𝑓 = 0° is treated as the morphing wing at 𝛿𝑚 = 0°. The morphing wing was at any morphing deflection was compared to itself at 𝛿𝑚 = 0°. Within the T240’s range of 𝐶𝐿, the morphing wing has larger 𝐿/𝐷 for a given 𝐶𝐿 than the T240 until 𝛿𝑚 = 20°. The median increase in the performance of the morphing wing for each applicable 𝛿𝑚, considering the range of 𝐶𝐿 and in relation to 𝛿𝑚 = 0°:

From Figure 57 it can be said that the morphing wing maintains a large lift-drag ratio (𝐿/𝐷 ≥ 12.75) over a large range of lift coefficients (0.3 ≤ 𝐶𝐿 ≤ 1.2). However, the morphing wing would need to transition to the appropriate morphing deflection to keep the high lift-drag ratio over the range of lift coefficients. Please note Figure 57 does not contain any error bars, the same figure with error bars can be found in APPENDIX D.

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal 20

Re 168000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

-10

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 236000

o i t a R g a r D o t t f i L ,

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

𝐷 / 𝐿

-5

-10

𝐶𝐿, Coefficient of Lift

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 337000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

-10

𝐶𝐿, Coefficient of Lift

Figure 57 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing.

T240 flap 0 degrees T240 flap 21 degrees

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

Re 168000

o i t a R

g a r D o t t f i L ,

𝐷 / 𝐿

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

𝐶𝐿, Coefficient of Lift

T240 flap 0 degrees T240 flap 21 degrees

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

Re 236000

o i t a R

g a r D o t t f i L ,

𝐷 / 𝐿

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

𝐶𝐿, Coefficient of Lift

T240 flap 0 degrees T240 flap 14 degrees

T240 flap 07 degrees T240 flap 21 degrees

Re 337000

o i t a R

g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

𝐶𝐿, Coefficient of Lift

Figure 58 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing with flaps.

In Figure 58, as 𝛿𝑓 is increased, the 𝐿/𝐷 ratio for the conventional T240 wing decreases and this is the case for all observed Reynolds numbers. Because of this behaviour, while flaps do indeed increase the lift generated by the wing, the increased drag, negatively effects the 𝐿/𝐷 ratio i.e. efficiency of the wing. Hence the flaps are predominately used for high lift scenarios such as take-off and landing. In comparison the 𝐿/𝐷 ratio of the morphing wing generally increases with morphing deflection. Hence

the morphing wing has greater 𝐿/𝐷 performance and aerodynamic efficiency over the conventional T240 wing.

7.3.3 Roll Results The roll motion of an aircraft is determined by the rolling moment generated by the wings of the aircraft, the counteracting damping due to the induced change in angle of attack of the bottom wing and the moments of inertia of the aircraft. Equation 10 is based on the roll motion equation seen in Abel’s work [87].

(10) 𝑀 − 𝑀𝑑𝑎𝑚𝑝𝑖𝑛𝑔 = 𝐼𝑥𝑥𝑝̇

To determine the initial roll acceleration of the wing, imagine at the start of the roll motion, the damping moment due to induced change in angle of attack has not occurred. Hence the 𝑀𝑑𝑎𝑚𝑝𝑖𝑛𝑔 = 0. Hence equation 11 can be derived from equation 10 as at the beginning of the roll motion, damping has not yet occurred. Equation 11 is used to determine the approximate initial roll acceleration of the wing.

𝑝̇ ≅

𝑀 𝐼𝑥𝑥

(11)

The roll rate of wing which is how quickly that the wing can complete a rotation, can be determined assuming a steady state roll motion, i.e. 𝑝̇ = 0 meaning the wing has reached a constant roll rate. Hence equation 10 can now be written as:

(12) 𝑀 = 𝑀𝑑𝑎𝑚𝑝𝑖𝑛𝑔

Where the rolling moments are determined the lift generated by the wings, efficiency of the ailerons/morphing wing and the airfoil. While the moment generated by the downward moving wing i.e. the damping wing generates a downforce due to the change in angle of attack of the wing. The downward force can be approximated to act at half-way across the span of one wing. The upwards moving wing would contribute little to no damping therefore it is assumed that it does not contribute to damping. Since only one wing contributes to damping then half of the total wing area is used and the downward force can be assumed to act at a quarter of the wingspan. Therefore equation 12 can be written as:

) 𝑞 ( ) ( 𝑏) 𝐶𝑙𝛿𝛿𝑞𝑆𝑏 = 𝐶𝐿𝛼 ( 𝑝𝑏 4𝑉 𝑆 2 1 4

32𝑉

𝑝 =

𝛿

𝐶𝑙𝛿𝛿 = 𝐶𝐿𝛼 𝑝𝑏 𝑉

𝑏

𝐶𝑙𝛿 𝐶𝐿𝛼

(13)

TORNADO does not consider separation as both XFLR5 and TORNADO use the linear VLM. Due to this TORNADO results for higher angles of morphing are likely to be unreliable as the VLM code is best

suited to thin and lightly cambered airfoils. Because of this XFLR5 was not used for roll analysis whilst TORNADO was used however results at higher morphing deflections and at high angles of attack were viewed critically. In Figure 42 where 𝐶𝐿 > 2 is unlikely to occur considering performance of the base airfoil of the morphing wing and more separation occurring at higher angles of morphing are not accounted for in the code. Because of this result from 0° ≤ 𝛿𝑚 ≤ 5° are likely to be somewhat accurate since flow separation would be low in that range. This will likely affect roll results as well, which is evident when compared to the experimental data seen in Figure 59 to Figure 63.

Note that for roll motion of the conventional T240, a roll moment occurs via deflections of both ailerons in opposite directions. Whilst for the morphing wing a roll moment occurs via asymmetric morphing i.e. a single wing being deflected whilst the other wing remains undeflected. From Figure 60 the roll motions conducted by the morphing wing outperformed the conventional T240 wing from 𝛿𝑚 = 3°, where the difference in performance increases until around 𝛿𝑚 = 15°, at 𝛿𝑚 = 20° the benefits of morphing wing for begins to taper off.

From this observation, the morphing wing generally has a larger 𝐶𝑙 for most 𝛿 than the conventional T240. This behaviour is likely due to several factors. Remembering the differences between the morphing configuration and the conventional T240 configuration is asymmetric and symmetric rolling, respectively. For the morphing configuration, the entire span of the wing is used however only one wing is used for the roll motion. While the conventional T240 wing configuration uses ailerons for roll control, where the length of the ailerons was half the wingspan. Although the total effective span of the control surfaces that contribute to rolling motion are the same in both configurations. The conventional configuration has the advantage of symmetric morphing, meaning that it has the advantage of coupling moments. However, the morphing wing still produces larger rolling moment. The chord length of the “control surface” could be a contributing factor. 70% of chord length of the morphing wing is deflected and the deflection is continuous whilst the conventional T240 uses approximately 30% of the chord length, and the deflection is discontinuous and sharp, seen in Figure 2 and Figure 3.

It can be concluded that the morphing wing has a better roll performance than that of the conventional T240 wing however roll rate acceleration (𝑝̇) and roll rate (𝑝) must be considered. From equation 11, we can see that roll rate acceleration (𝑝̇) is highly dependent on mass moment of inertia about the 𝑥-axis, 𝐼𝑥𝑥 and rolling moment generated by the wing. From Figure 59 and Figure 60 that the morphing wing generates more rolling moment than the conventional wing at an equivalent deflection. So, if the morphing wing has the same 𝐼𝑥𝑥 as the conventional wing then the 𝑝̇ of the morphing wing would be greater than that of the conventional wing. Because of the wing is retrofitted on the aircraft, therefore only 𝐼𝑥𝑥 of the wings was considered for equation 11, since 𝐼𝑥𝑥 of the rest of the aircraft would be the same as the conventional T240 wing setup. Equation 11 uses mass moments of inertia about the 𝑥-axis, 𝐼𝑥𝑥 for the entire wing, for each configuration is:

Morphing Wing Conventional T240 wing

𝐼𝑥𝑥 = 2.752 𝑘𝑔𝑚2 𝐼𝑥𝑥 = 1.238 𝑘𝑔𝑚2

By examining the 𝑝̇ of both wings seen in Figure 61 and Figure 62, the conventional T240 and the morphing wing have similar 𝑝̇ for all 𝛿 at most Reynolds numbers. The similarity between the results increases as airspeed increases, which can be seen in Figure 62.

This however does not disprove the notion that morphing wing outperforms conventional T240 wing as the morphing wing has not yet been optimised for weight. Therefore, weight reductions can be made, and the internal layout of the morphing wing could be altered which would reduce the 𝐼𝑥𝑥 of the morphing wing setup, hence increasing 𝑝̇.

To increase the 𝑝̇, one could increase the rolling moments generated by the wing or decrease the 𝐼𝑥𝑥 of the aircraft. Since the rolling moment has already been increased through morphing of the wing, the most logical step would be to decrease the 𝐼𝑥𝑥 of the wing.

Figure 59 TORNADO and wind tunnel results for 𝑪𝒍 vs 𝜹 at various Reynolds number.

As predicted 𝐶𝑙 decreases if 𝛿𝑚 too large this would in turn lead to a drop in rolling moment which in turn would decrease the 𝑝̇, roll acceleration. Therefore, morphing beyond 𝛿𝑚 = 25° is detrimental to 𝐶𝐿, 𝐶𝑙, and 𝑝̇. Due to the static nature of the test roll damping was ignored and changes to lift and drag were also ignored. Therefore, the determined roll acceleration of the configuration should be considered as the initial roll acceleration of the respective setups. The roll acceleration would likely change during an actual roll motion because of changes in angle of attack of the wing which would lead to changes in lift, drag and moments and the damping of the aircraft would affect the roll motion as well.

It should be noted that the roll analysis was not conducted in XFLR5 due to an issue that was encountered during the roll analysis. From Figure 60, it is evident that the morphing wing has a higher coefficient of rolling moment than the conventional T240 at equivalent deflection, for example at 𝛿𝑚 = 3°, the morphing wing has a larger rolling coefficient than the conventional T240. This means that if a specific rolling moment coefficient is required then the morphing wing can achieve it at a lower deflection than the conventional T240 wing.

This is evident when the slopes for the linear region of the graphs in Figure 60 are determined. The slope or the aileron/morphing effectiveness (𝐶𝑙𝛿), for the morphing wing is approximately two times (depending on the Reynolds number) that of the conventional wing. Which at Re 337000 is 𝐶𝑙𝛿 = 0.0098 and 𝐶𝑙𝛿 = 0.005 for the morphing wing and conventional T240 wing, respectively. Rolling moment coefficient does tend to decrease as morphing is increased beyond 𝛿𝑚 = 20° however this is not unexpected nor is it significant as 𝛿𝑚 = 20° would likely be unnecessary in a non-combat scenario and it would also be harder to control the roll motion of the aircraft at said deflection or higher.

Figure 60 𝑪𝑳 comparison for the Conventional T240 and Morphing wing at various Reynolds numbers.

In Figure 60, the linear behaviour of the morphing wing ceases after 𝛿𝑚 > 10°, this implies separated flow. Hence in Figure 59, the similarity in results between the experimental and TORNADO diverges from one another. However, for 𝛿 ≤ 10°, the results are similar for both conventional T240 and the morphing wing. This is again due to the TORNADO not being able to give accurate results for conditions after stall since it does not consider flow separation because of the usage of the inviscid method. Since VLM is only good for attached flow, which extends to TORNADO as it uses a modified VLM code. The breakdown in accuracy can be seen in Figure 59 when 𝛿𝑚 = 20°, (where from the flow

visualization and the lift coefficient plot), that flow is separated and further solidifies that TORNADO is not suited for high angles of attack and highly cambered airfoils.

Figure 61 Difference in TORNADO and wind tunnel testing for 𝒑̇ vs 𝜹 at various Reynolds numbers.

Figure 62 𝒑̇ comparison between Conventional T240 and Morphing Wing at various Reynolds numbers.

Another key parameter to examine for the roll performance of an aircraft is the roll rate (𝑝). Which in a steady state roll condition where the roll acceleration ceases and the roll rate reaches maximum, roll rate is independent of roll acceleration hence roll rate is independent of 𝐼𝑥𝑥 in a steady state roll condition. Using equation 13, the roll rate was determined for both conventional T240 and morphing wing shown in Figure 63. It is evident that the morphing wing has a larger roll rate than the conventional T240. In Figure 63, for a given roll rate the morphing wing achieves it earlier than the conventional T240. For example, to achieve 𝑝 = 105 deg/s at Re 236000, the morphing wing would need 𝛿𝑚 = 5° whilst the conventional T240 requires 𝛿𝑎 = 9°. The observed maximum roll rate for the conventional T240 and the morphing wing is 𝑝 = 152 deg/s and 𝑝 = 341 deg/s. Like in the case of lift, excessive morphing has a detrimental effect on roll rate, as 𝛿𝑚 > 15° roll rate decreases. This is likely due to stalled flow due to the large morphing deflection which would affect the rolling efficiency of the morphing wing (𝐶𝑙𝛿).

From observing the rolling behaviour of the morphing wing and the conventional T240 wing, it can be said the morphing wing has better rolling performance to the conventional T240 wing. Which is due to the increased 𝐶𝑙, 𝑝 and equivalent 𝑝̇. However, recalling that the morphing wing prototype has not been optimised for weight, the 𝐼𝑥𝑥 can see reductions leading to an increase in 𝑝̇ performance. Which if fulfilled then the roll performance of the morphing wing would be superior to the conventional T240 for all 𝐶𝑙, 𝑝 and 𝑝̇. However, it should be noted that due to the increase in performance from the morphing wing, the handling qualities of the roll motion would be more difficult to control than that of the conventional wing.

Figure 63 𝒑 comparison between Conventional T240 and Morphing Wing at various Reynolds numbers.

7.3.4 Discussion of Results The theoretical and experimental behaviour of the morphing wing was analysed and compared. The theoretical analyses were conducted using XFLR5 and TORNADO. XFLR5 and TORNADO both use inviscid methods to predict performance of the morphing wing. There are slight differences between the pair, where XFLR5 uses the VLM and TORNADO uses a modified VLM method. Both methods are best suited for flight conditions before stall, i.e. low angles of attack and low control surface deflection angles. Therefore, both tend to overpredict lift and under predict drag. Hence this limitation affected the morphing wing analysis particularly at higher angles of morphing where impractical values for 𝐶𝐿 were obtained.

The lift-drag ratio observed in the XFLR5 and TORNADO analyses comes to similar conclusions as seen in literature where the most efficient lift-drag ratio is obtained in the 0° ≤ 𝛼 ≤ 5°. It also is observed that at 𝛿𝑚 > 5° that the lift-drag ratio begins to flatten and become linear from -5° ≤ 𝛼 ≤ 15°, this could be due to the increased camber of the wing.

In the lift-drag ratio curves, we can see that the typical curve for lift-drag ratio begins to lose shape as soon as 𝛿𝑚 > 1° and loses it shape completely by 𝛿𝑚 > 10°. This makes sense, as 𝛿𝑚 increases so does drag as the increase in camber and lift generated which also increases 𝐶𝐷𝑖. This could probably be seen in the flow visualization where disturbances and separation began to occur as soon as 𝛿𝑚 > 1° as there is separation from the rib end section of the wing to the trailing edge of the wing.

The results of both methods are very similar for 𝛿𝑚 = 0° and results begin to increasingly diverge from 𝛿𝑚 > 0°. This is expected as the methods used by XFLR5 and TORNADO are not identical. TORNADO and XFLR5 continually predict an increase 𝐶𝐿 as 𝛿𝑚 increases until 𝛿𝑚 > 30° where XFLR5 predicts a

drop in 𝐶𝐿. Which is unlikely as eventually an increase in 𝛿𝑚 would cause flow separation and would no longer result an increase lift-drag ratio and would only result in an increase in drag.

As 𝛿𝑚 increases the similarity between XFLR5 and the experimental results increase, while the similarity between XFLR5 and TORNADO and by extension experimental results decrease. When 3° ≤ 𝛿𝑚 ≤ 10° the differences between XFLR5 and experimental results have a median similarity of approximately 10%. The similarity between XFLR5 and the experimental results are within 5% for 𝛿𝑚 = 10° and 𝛿𝑚 = 15° at 𝛼 = 4° and 𝛼 = 3° respectively. The divergence after these points could be due to stall occurring, where XFLR5 and TORNADO do not consider stall characteristic and are preferably for low 𝛼. Overall, the average median difference for XFLR5 and TORNADO from the experimental results for 𝛿𝑚 as follows when considering airspeed is displayed in Table 4:

Table 4 Difference in results for XFLR5 and TORNADO to experimental results.

Deflection XFLR5 TORNADO

25% 31% 𝛿𝑚 = 0°

21% 40% 𝛿𝑚 = 2°

7% 70% 𝛿𝑚 = 3°

11% 34% 𝛿𝑚 = 5°

4% 39% 𝛿𝑚 = 10°

16% 70% 𝛿𝑚 = 15°

29% 127% 𝛿𝑚 = 20°

2% 295% 𝛿𝑚 = 25°

30% 290% 𝛿𝑚 = 30°

55% 700% 𝛿𝑚 = 35°

810% 𝛿𝑚 = 40°

83% The median similarity does not represent the similarity at each point of the analyses. As at some 𝛼 the similarities can be much higher or lower, take for example at 𝛿𝑚 = 3° the difference between XFLR5 and wind tunnel experiment was large, but the difference becomes smaller as 𝛼 increases. However, between 0° ≤ 𝛿𝑚 ≤ 15° XFLR5 can be used to approximate the performance of the morphing wing. The divergence of results that occur at 𝛿𝑚 = 10° and 𝛿𝑚 = 15° at 𝛼 = 4° and 𝛼 = 3, should be treated sceptically as 𝐶𝐿 values exceed 1.6.

The differences between the methods are depicted in the Appendix E, where at low 𝛼, XFLR5 results resemble the experimental results more closely than TORNADO.

It could be argued that TORNADO is suitable for the undeflected morphing wing (𝛿𝑚 = 0°). As 𝛿𝑚 increases, the accuracy for TORNADO diminishes, this is seen particularly at higher 𝛿𝑚. The similarity between XFLR5 and TORNADO also decreases as 𝛿𝑚 increases. Which is due TORNADO treating the wing as a thin lifting surface.

Hence XFLR5 could be used as an initial estimate for morphing wing performance but be aware of the overestimation of lift.

7.3.5 Summary of Comparison – Conventional T240 vs Morphing Wing This section will cover the direct comparison of aerodynamic performance between the morphing wing and the conventional T240. It will also detail whether or not the research questions have been addressed and in what manner.

From section 4 the research questions are as follows:

• How does theoretical aerodynamic analysis of morphing wings compare to wind tunnel tests? • How does wing morphing perform in terms of roll control, i.e. asymmetric morphing, and as a

high-lift device for low-speed performance?

• How does the aerodynamic performance of a morphing wing compare to its conventional

counterpart with the same geometry?

How does theoretical aerodynamic analysis of morphing wings compare to wind tunnel tests?

The theoretical aerodynamic analyses were conducted using XFLR5 and TORNADO. As discussed in section 5.2.1, 5.2.2 and 7.3.3, the theoretical results do compare well with the wind tunnel tests for low morphing deflections and low angles of attack. XFLR5 and TORNADO both use inviscid methods and are best suited for pre stall angles of attack, low morphing deflections hence the software is not well suited for highly cambered profiles.

From observing Figure 113 located in APPENDIX E, XFLR5 tracks well with the experimental results of the morphing wing for 𝛿𝑚 < 10°. It does however overpredict lift which is understandable, XFLR5 does tend to overpredict lift and underpredict drag. Although as morphing deflection increases the overprediction in lift decreases and results become very similar. When at 𝛿𝑚 = 10° from -5° ≤ 𝛼 ≤ 4°, XFLR5 and the wind tunnel results are almost identical, and diverges from 𝛼 ≥ 5° which is likely where separation occurs. Once 𝛿𝑚 ≥ 10°, XFLR5 tracks well particularly for low angle of attack until 𝛿𝑚 ≥ 35°, where XFLR5 underpredicts the performance of the morphing wing. From this XFLR5 theoretical results are accurate for pre-stall angle of attacks and can still predict the behaviour of highly and low cambered airfoils quite well. However predictions for highly cambered airfoils should verified since stall occurs much earlier for highly cambered airfoils. TORNADO does not perform as well as XFLR5, for 𝐶𝐿 vs 𝛼 likely due to assumption that airfoils are thin bodies and is unsuited for highly cambered airfoils. TORNADO however does accurately predict roll coefficient well for linear flow for lightly cambered airfoils as results for 𝛿𝑎 ≤ 10° and 𝛿𝑚 ≤ 10° were accurate.

Hence theoretical predictions of the performance of the morphing wing were quite accurate to the experimental results of the morphing wing for pre-stall angles of attack and for small deflections which coincides with the accuracy conditions of both XFLR5 and TORNADO. However to understand non- linear behaviour of the morphing wing and to confirm the theoretical results a wind tunnel test was necessary.

How does wing morphing perform in terms of roll control, i.e. asymmetric morphing, and as a high- lift device for low-speed performance?

Theoretical and static analyses were conducted to predict the performance of the morphing wing. The performance of the morphing wing was compared to the performance of the flaps and ailerons of the conventional T240 wing. The comparisons are conducted with take-off and landing phase in mind for high-lift generation and during roll manoeuvres for roll control.

The performance of the morphing was analysed as a high-lift device for low-speed performance, hence the performance of the morphing wing in the setting of take-off and landing where low speed and high-lift was required. From Figure 2 the conventional T240 flaps uses 36% of the wingspan and approximately 23% of the chord of the wing. While from Figure 3 the morphing wing as a high-lift device uses 70% of the chord and 85% of the wingspan (the wingtip and the fuselage wingbox are rigid). Hence the morphing wing as a high-lift device has a much larger surface area than the conventional T240 wing’s flaps. In addition, the morphing wing profile changes from deflections are continuous and smooth while the wing profile changes due to flaps are discontinuous and sharp.

In Table 5 the low-speed performance of the conventional T240 and the morphing wing are summarized which was taken from section 7.3. From Table 5, the deflections for the conventional T240 and the morphing indicate the deflection angle for the flaps and the morphing wing, respectively. 𝐶𝐿 𝑚𝑎𝑥 indicates the highest value of the coefficient of lift of the lifting surface while still in the linear region of performance hence coefficients of lift past stall behaviour are excluded. Hence from Table 5 the 𝐶𝐿 𝑚𝑎𝑥 occurs at 𝛿𝑓 = 28° and 𝛿𝑚 = 5° for the conventional T240 and the morphing wing, respectively. In landing and take-off configuration, 𝐿 = 𝑊 by rearranging the Lift equation (Equation 4) and solving for 𝑉, which is 𝑉𝑠𝑡𝑎𝑙𝑙 in take-off and landing. 𝑉𝑠𝑡𝑎𝑙𝑙 is also shown in Table 5, where the morphing wing has a larger 𝑉𝑠𝑡𝑎𝑙𝑙 than the conventional T240, even with the increased 𝐶𝐿 𝑚𝑎𝑥. The increase in the 𝑉𝑠𝑡𝑎𝑙𝑙 is attributed to the increase in the morphing wing weight thereby increasing the total weight of the system.

Table 5 High-lift device comparison of the conventional T240 and the morphing wing at Re 168000.

However, considering that the take-off and landing phase of the aircraft mission would be considerably less than that of the cruise phase. The increase in stall speed of 2 m/s is not significant given that the aircraft can take-off/land in the prospective runway. It should also be considered that this difference in stall speed would only decrease since the current morphing wing prototype has not been optimised for weight.

Regarding the differences in roll between the two configurations, the morphing wing rolls through asymmetric morphing whilst the conventional wing rolls through symmetric deflection. Another difference is in the geometry of the roll moment inducing element, the morphing wing deflects 70% of the chord and the entire span of one wing to conduct a roll motion. While the conventional wing’s ailerons use 30% chord of both wings and half of the span of both wings to conduct a roll motion.

Table 6 Comparison of the roll performance between the conventional T240 wing and the morphing wing at Re 337000.

Table 6 compares the roll performance of both configurations, from the table we can see that for an equivalent rolling moment coefficient the morphing wing will achieve it at lower deflection. This also extends to roll rate but not roll acceleration. In other words for an equivalent deflection the morphing wing will have a larger rolling moment coefficient and roll rate but lower roll acceleration than the conventional T240 which can be observed in Table 6 at 𝛿𝑎 = 3° and 𝛿𝑚 = 3°. The effectiveness or the efficiency of morphing wing is larger than that of the conventional T240 also seen in Table 6, where in linear flow 𝐶𝑙𝛿, for the morphing wing 𝐶𝑙𝛿 = 0.0098 while for the conventional T240 𝐶𝑙𝛿 = 0.005.

In short, the performance of the morphing wing compared to the conventional wing for roll control can be summarised:

• The morphing wing achieves a required rolling moment coefficient at a lower deflection angle

than the conventional wing.

• The morphing wing rolls faster than the conventional T240 given no further roll acceleration. • Due to increase in weight, the morphing wing has a slower roll acceleration than the

conventional T240 wing.

Given the current morphing wing prototype has not been optimised for weight, the increased weight has resulted in the morphing wing having slightly lower roll acceleration to the conventional wing.

However, as a high-lift device for low speed the morphing wing does generate more lift than the conventional counterpart, but it does not perform as well as the conventional wing due to the increased weight of 2.63 kg. The increased weight has also resulted in higher stall speed.

In summation the morphing wing, has overall greater roll performance than the conventional counterpart but with a similar roll acceleration. The stall speed of the morphing wing is higher than that of the conventional wing due to the increased system weight, which is unavoidable however the increase can be mitigated with weight reductions in the design of the morphing wing.

How does the aerodynamic performance of a morphing wing compare to its conventional counterpart with the same geometry?

The aerodynamic performance of both configurations was examined by theoretical and experimental methods. Both theoretical (XFLR5 and TORNADO) and experimental (Wind tunnel testing) showed that the FishBAC morphing wing was superior to the conventional T240 wing for almost all parameters. The two wings were compared in cruise scenario, i.e. where maximum lift and minimal drag were required, therefore the key parameters observed were 𝐶𝐿, 𝐶𝐷 and 𝐿/𝐷.

Table 7 Comparison of conventional T240 and morphing wing in cruise condition at Re 337000

Table 7 illustrates this with the experimental results compiled from section 7.3 at the maximum Reynolds number observed in the study. Observing Table 7, the morphing wing consistently generates a larger lift coefficient than the conventional T240 wing for 𝛿𝑚 > 0° with the exception at 𝛿𝑚 = 40° at high angles of attack. The morphing wing can achieve a much larger maximum lift-drag ratio than the conventional T240 wing, where for the morphing wing (𝐿/𝐷)𝑚𝑎𝑥 = 20.4 while for the conventional wing (𝐿/𝐷)𝑚𝑎𝑥 = 10.3. However, the base morphing wing i.e. 𝛿𝑚 = 0° was 𝐿/𝐷 = 13.4 therefore the increase maximum increase in lift-drag ratio due to the morphing configuration was 52% while compared to the conventional T240 the maximum increase was 98%. The morphing wing can consistently maintain a large lift-drag ratio given that the morphing deflection is not fixed, this can be seen in Table 7 where the morphing wing can maintain a 𝐿/𝐷 > 10.3. The morphing wing can achieve a 𝐿/𝐷 > 10.3 from a range of -5° ≤ 𝛼 ≤ 9° while the conventional wing can only achieve a 𝐿/𝐷 = 10.3° at 𝛼 = 3°. If 90% of the performance of the maximum lift-drag ratio of the conventional wing is desired, then the effective range of angles of attack for the morphing wing which achieves desired lift-drag ratio then becomes -5° ≤ 𝛼 ≤ 11°. If an increase of 25% of the (𝐿/𝐷)𝑚𝑎𝑥 of the conventional wing was required, the applicable range of angles of attack for the morphing would be from -5° ≤ 𝛼 ≤ 5°.

The drag encountered by the morphing wing can also be lower than that of the conventional wing which could likely be due to the lack of discontinuities in the surface of the wing since there are no flaps or ailerons present in the morphing wing.

Hence the aerodynamic performance of a morphing wing, with the same geometry as a conventional wing is superior to that of the conventional wing. This is due to the morphing wing being able to consistently generate larger lift coefficients than the conventional counterpart, maintain a large lift- drag ratio over a wider range of angles of attack, generate larger lift-drag ratios than the conventional wing and generate larger lift-drag ratios for a given coefficient of lift.

The comparison between the morphing wing and the conventional T240 wing concludes that the morphing wing is aerodynamically superior to the conventional wing for most conditions. The morphing wing must be cross-examined against similar morphing wings found in literature to observe whether or not the behaviour morphing wing follows the behaviour of others.

Table 8 Experimental results of similar morphing concepts in literature [34, 49, 51, 76, 86].

Only a slight comparison can be made to other morphing concepts seen in literature review due to having multiple variables in wing properties such as wingspan, chord length, camber, airfoil, morphing concept, degree of morphing conducted by the wing and so on. Behaviour and performance trends of the morphing concepts will be compared as opposed to determining which morphing concept is superior to the others.

The studies used to compare were selected based on a similar morphing concept i.e. camber based and if aerodynamic performance was examined. From literature compiled in Table 8 the preferred 𝛼 range of morphing wings are 𝛼 < 10° at these angles’ lift-drag ratio is increased when being compared to a conventional wing of the same geometry and characteristics. We can also see that as morphing increases the lift curve slope and the lift-drag ratio also increases. From the same figures, lift-drag ratio for morphing wings performs best at lower angle of attack from 0° ≤ 𝛼 ≤ 4°.

The penalty in stall speed, 𝑉𝑠𝑡𝑎𝑙𝑙 due to increase in mass was also seen by Molinari, who saw an increase in stall speed by ~15% or 1.8 m/s [38]. This figure resembling the one seen in this study where stall speed increased by 2m/s or 18%. Regarding other aerodynamic parameters such as lift-drag ratio this study could be loosely compared to Woods 2015 [88] FishBAC work due to the differences in airspeed and geometrical differences in the wing and airfoil. Similar behaviour occurs particularly where, as 𝐶𝐿 increases the lift-drag ratio also increases but begins to decrease as 𝐶𝐿 increases further. Woods saw an increase in lift-drag ratio until 𝐶𝐿 ≈ 1 and from 𝐶𝐿 > 1, lift-drag ratio decreases [88]. In this study the same behaviour was observed but at different 𝐶𝐿, i.e. lift-drag ratio saw an increase due to morphing until 𝐶𝐿 ≈ 0.7 from where lift-drag ratio begins to decrease as 𝐶𝐿 increases further. Woods did not reach the “tipping point” of morphing, i.e. where further morphing is detrimental to aerodynamic performance.

In Woods’ experiment the FishBAC developed similar lift behaviour to a flapped airfoil i.e. lift polars move upward and toward the left [11, 49]. Woods’ FishBAC reached almost identical lift coefficients but achieves it at a lower angle of attack [11, 49]. From morphing, Woods’ FishBAC saw an increase in lift with a small drag penalty, hence the FishBAC had a smaller increase in drag than the conventional flap [11, 49]. Woods’ FishBAC achieved a 95% of its maximum lift-drag ratio from -1.75° ≤ 𝛼 ≤ 7.3° i.e. a range of 9.05° [11].

Yokozeki’s experiment their morphing wing had similar lift properties to their flapped wing reference wing [51]. Yokozeki observed that the drag penalty from morphing is smaller than the drag penalty occurred from flapped airfoils [51].

Communier found that ailerons and the morphing trailing edge had similar lift behaviour and found that a morphing trailing edge can replace ailerons which goes in line with this study [76]. Communier’s morphing trailing edge generated less lift and drag than the conventional aileron but resulted in a larger lift-drag ratio [76].

The overall behaviour of the morphing wing seen in this study shows similar behaviour to other morphing wing studies seen in literature. The similarities in behaviour which include:

• A larger if not almost identical maximum lift coefficient was achieved due to the morphing

configuration.

• Similar if not larger lift-drag ratio than the conventional counterpart. • Small penalty in drag due to morphing than a flapped wing.

• A high lift-drag ratio can be maintained over a larger range of lift coefficient or angle of attack

than a flapped wing.

• A penalty in stall speed is encountered due to increase weight of the system.

8 Conclusions In this study a morphing wing was designed and manufactured for the aerodynamic comparison for the RC aircraft Precedent T240. The morphing wing was designed to have the same geometry as the conventional counterpart for clear comparisons. The morphing wing was designed using computer aided design (CAD). The morphing aspect of the wing was achieved by internal mechanisms as a means of actuation. Manufacturing methods of components varied, some were available off the self, 3D printing and computer numerical control (CNC) methods. The conventional T240 wing and morphing wing were examined theoretically and experimentally.

The similarity in behaviour provides confidence in the methods used to design, manufacture and testing of the morphing wing.

A compliant morphing skin using the FMC concept with silicone and carbon fibre was designed, manufactured, and tested. The compliant morphing skin was laid-up and vacuum bagged before being bonded to the wing. The FMC skin was able to expand and contract without any damage to the skin during morphing process. The bond between the silicone and the carbon fibre laminates are not particularly as strong as they can be peeled apart and the skin is susceptible to shear. The skin however can be repaired by applying more silicone to any existing tears and/or holes.

The aerodynamic behaviour of the morphing wing was compared to that of the T240 and compared with similar camber morphing wings presented in the literature. As expected, given the same lift coefficient, the morphing wing has a higher lift-drag ratio than the conventional T240 wing. The morphing wing also has a larger 𝐶𝐿𝑚𝑎𝑥 than the conventional T240 wing. All of which occurred at a lower 𝛼 than the conventional T240 wing similar to the behaviour seen in other camber type morphing wings in literature. The 𝐶𝐿 𝑚𝑎𝑥 of the conventional T240 and the morphing wing were approximately 1.2 and 1.45 respectively an increase of 20%. The conventional T240 had a maximum lift-drag ratio of 𝐿/𝐷 = 10.3 which was achieved at 𝛼 = 3° while the morphing wing’s maximum lift to drag ratio was 𝐿/𝐷 = 20.4 at 𝛼 = -5° and 𝛿𝑚 = 10°. The lift-drag ratio of the base morphing wing (𝛿𝑚 = 0°) and the conventional wing was not identical, where at 𝛿𝑚 = 0° the morphing wing had 𝐿/𝐷 = 13.4 (𝛼 = 5°) and the conventional wing had 𝐿/𝐷 = 10.3 (at 𝛼 = 3°). Ignoring the lift-drag ratio difference between the base morphing wing (𝛿𝑚 = 0°) and the conventional wing, then the increase in maximum 𝐿/𝐷 seen was 98% (given 𝛼 is not fixed). However if compared to the base morphing wing (𝐿/𝐷 = 13.4 at 𝛼 = 5°, 𝛿𝑚 = 0°) then the maximum increase of lift-drag ratio was 52%(𝐿/𝐷 = 20.4 at 𝛼 = -5°, 𝛿𝑚 = 10°). The additional weight (of 2.63 kg) due to the more complex system in comparison to the conventional wing and the heavier but required compliant morphing skin was foreseen. However, the increased weight of the wing was not a significant factor in this study and will be looked at in future work. The increased weight of the morphing wing system did in fact result in a larger 𝑉𝑠𝑡𝑎𝑙𝑙, however it is only a 2m/s difference i.e. an increase of 18%. If the weight of the morphing wing is reduced by 49% i.e. 75% heavier than the conventional wing, the 𝑉𝑠𝑡𝑎𝑙𝑙 would be matching. It must be considered that the duration of take-off and landing phases of the flight of an aircraft are significantly smaller than the

cruise for a long duration mission. Therefore, given that the permissible take-off and landing distances are not exceeded the 𝑉𝑠𝑡𝑎𝑙𝑙 is a somewhat flexible parameter.

The asymmetric morphing of the morphing wing does incur a larger rolling moment compared to the conventional counterpart. However due to the weight penalty of the morphing system the resulting 𝑝̇ is slightly lower than the conventional counterpart. As discussed in section 7.3.3 if the same design is kept but the weight of the wing is reduced then the morphing wing will have a larger roll rate, 𝑝̇ than the conventional configuration.

The accuracy of the theoretical aerodynamic analysis of the morphing wing compared to experimental wind tunnel test is accurate for low 𝛿𝑚 and low 𝛼. Since XFLR5 and TORNADO use inviscid methods, flow separation was not considered in the analysis. Hence XFLR5 and TORNADO are best suited for low 𝛼 and 𝛿 and inaccurate for high 𝛿𝑚 and should be avoided. However, it can be used as an initial optimistic approximation. It should also be considered that benefits of morphing have diminishing returns for 𝛿𝑚> 15°.

8.1 Recommendations/Further research

This study has found that the aerodynamic performance of a morphing wing is overall superior to that of its conventional counterpart with the same geometry. The morphing wing consistently generated larger lift coefficients without too much of a drag penalty (for small morphing deflections) resulting in higher lift-drag ratios and being able to maintain it over a larger range of angles of attack. While the conventional wing was limited to smaller range of angles of attack. The morphing wing achieved a higher 𝐶𝐿𝑚𝑎𝑥 compared to its conventional counterpart, showing that the morphing wing performs better as a high-lift device for low speed. However, the increase in weight of 2.63 kg (total morphing wing weight being 3.73kg) does increase the stall speed of aircraft. Therefore, the morphing configuration would require a longer take-off/landing distance. The stall speed can be reduced by reducing the weight of the morphing wing as the current morphing wing prototype has not been optimised for weight. The roll performance comparison of the two configurations, showed morphing wing is more efficient in generating rolling moments as well as allows for a higher roll rate compared to the conventional counterpart. However, in the current state of the morphing wing, it has a slightly lower roll acceleration to the conventional wing. Therefore, the aerodynamic performance of the morphing wing is superior to the conventional counterpart with the exception of stall speed.

• Improving the build quality of the skin.

o Needs a rig to secure in strips of carbon fibre laminate. o Find a better way to bond silicone and carbon fibre. Or is it just a limitation that needs

to be acknowledged.

• Find a way to attach skin directly to the L shape carbon fibre.

o Swap flat laminate for the L-shape angles.

•

Improve the weight of the wing by utilizing light weight material whilst also retaining strength and flexibility.

o Look into corrugated structures for internal mechanisms. o Change the spar material into lightweight material such as carbon fibre spar. o Hollow out the leading edge.

▪ Use standard build structures; more ribs (even if it is only for the LE side). ▪ This would also allow for larger servos to be placed.

• The wingtip morphing could be worth exploring.

o The standard version does generate vortices.

References

Further work should focus on reducing the weight of the wing whilst retaining the flexible properties to reach a flight ready stage. The weight of the wing could be reduced by altering the design of the wing such as: exploring corrugated structures for the use of the morphing mechanism and improve the design of the leading edge. The leading edge could be hollowed out and use typical building techniques to increase empty space within the wing. Further work could also explore a morphing wingtip that would follow the morphing of the wing. The weakness of the morphing skin where silicone has difficulty being bonded to the carbon fibre laminates.

[1]

A. M. R. McGowan, A. E. Washburn, L. G. Horta, R. G. Bryant, D. E. Cox, E. J. Siochi, S. L. Padula and N. M. Holloway, “Recent results from NASA's morphing project,” in SPIE's 9th Annual International Symposium on Smart Structures and Materials, San Diego, 2002.

[2]

A. Y. N. Sofla, S. A. Meguid, K. T. Tan and W. K. Yeo, “Shape Morphing of Aircraft Wing: Status and Challenges,” Materials & Design, vol. 31, no. 3, pp. 1284-1292, 2010.

[3]

S. Siouris and N. Qin, “Study of the effects of wing sweep on the aerodynamic performance of a blended wing body aircraft,” Journal of Aerospace Engineering, vol. 221, no. 1, pp. 47-55, 2007.

[4] M. Sinapius, H. P. Monner, M. Kintscher and J. Riemenschneider, “Network, DLR's Morphing Wing Activities within the European,” Procedia IUTAM, vol. 10, pp. 416-426, 2014.

[5]

S. Vasista, L. Tong and K. C. Wong, “Realization of Morphing Wings: A Multidisciplinary Challenge,” Journal of Aircraft, vol. 49, no. 1, 2012.

[6]

R. M. Ajaj, M. I. Friswell, M. Bourchak and W. Harasani, “Span morphing using the GNATSpar wing,” Aerospace Science and Technology, vol. 53, pp. 38-46, 2016.

[7]

S. Barbarino, O. Bilgen, R. M. Ajaj, M. I. Friswell and D. J. Inman, “A Review of Morphing Aircraft,” Journal of Intelligent Material Systems and Structures, vol. 22, no. 9, pp. 823-877, 2011.

[8]

T. A. Weisshaar, “Morphing Aircraft Systems: Historical Perspectives and Future Challenges,” Journal of Aircraft, vol. 50, no. 2, pp. 337-353, 2013.

[9]

C. Bil, K. Massey and E. J. Abdullah, “Wing morphing control with shape memory alloy actuators,” Intelligent Material Systems and Structures, vol. 24, no. 7, pp. 879-898, 2013.

[10]

E. J. Abdullah, C. Bil and S. Watkins, “Application of Smart Materials for Adaptive Airfoil Control,” in 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando, 2009.

[11] B. K. S. Woods, O. Bilgen and M. Friswell, “Wind tunnel testing of the fish bone active camber morphing concept,” Journal of Intelligent Material Systems and Structures, vol. 52, no. 7, pp. 772-785, 2014.

[12]

L. D. Wiggins, M. D. Stubbs, C. O. Johnston, H. H. Robertshaw, C. F. Reinhotlz and D. J. Inman, “A Design and Analysis of a Morphing Hyper-Elliptic Cambered Span (HECS) Wing,” in 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, 2004.

[13]

T. M. Seigler, Dynamics and Control of Morphing Aircraft, Virginia Polytechnic Institute and State University, 2005.

[14] R. M. Ajaj, C. S. Beaverstock and M. I. Friswell, “Morphing aircraft: The need for a new design

philosophy,” Aerospace Science and Technology, vol. 49, pp. 154-166, 2016.

[15]

C. GIBBS-SMITH, AVIATION:AN HISTORICAL SURVERY FROM ITS ORIGINS TO THE END OF WORLD WAR II 2ND ED, 1985.

[16] J. Valasek, Morphing Aerospace Vehicles and Structures (Vol. 57), John Wiley & Sons, 2012.

[17]

J. Bowman, B. Sanders and T. Weisshaar, “Evaluating the Impact of Morphing Technologies on Aircraft Performance,” in 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, 2002.

[18] D. Scopelliti, Design, Manufacturing and Experimentation of a Morphing Wing, Polytechnic

University of Madrid & RMIT University, 2016.

[19]

J. M. M. Gou, Design, Numerical Analysis and Manufacturing of a Morphing Wing, Technical University of Madrid & RMIT University, 2016.

[20]

T. A. Weisshaar, “Morphing Aircraft Technology – New Shapes for Aircraft Design,” Aeronautics and Astronautics Department Purdue University WestLafayette,, Indiana, 2006.

[21]

C. Bereiter, “Innovation in the Absence of Principled Knowledge: The Case of the Wright Brothers,” CREATIVITY AND INNOVATION MANAGEMENT, vol. 18, no. 3, 2009.

[22] D. M. Elzey, A. Y. N. Sofla and H. N. G. Wadley, “A bio-inspired high-authority actuator for shape morphing structures,” in Proceedings Volume 5053, Smart Structures and Materials 2003: Active Materials: Behavior and Mechanics, San Diego, 2003.

[23] B. K. S. Woods, J. H. S. Fincham and M. I. Friswell, “Aerodynamic Modelling of the Fish Bone Active Camber Morphing Concept,” in RAeS Applied Aerodynamics Conference, Bristol, 2014.

[24] R. M. Ajaj, E. I. Saavedra Flores and M. I. Friswell, “Span Morphing Using the Compliant Spar,”

Journal of Aerospace Engineering, vol. 28, no. 4, 2015.

[25] R. M. Ajaj, E. I. Saavedra Flores, M. I. Friswell, G. Allegri, B. K. S. Woods and A. T. Isikveren, “The Zigzag wingbox for a span morphing wing,” Aerospace Science and Technology , vol. 28, no. 1, pp. 364-375, 2013.

[26]

J. J. Joo, S. Brian, T. Johnson and M. I. Frecker, “Optimal actuator location within a morphing wing scissor mechanism configuration,” in SPIE SMART STRUCTURES AND MATERIALS + NONDESTRUCTIVE EVALUATION AND HEALTH MONITORING, San Diego, 2006.

[27]

P. M. M. da Costa Alexio, Morphing aircraft structures design and testing an experimental UAV, Lisbon: Instituto Superior Tecnico, Universidade Tecnica de Lisboa, 2007.

[28]

J. Blondeau, J. Richeson and D. Pines, “Design of a Morphing Aspect Ratio Wing Using an Inflatable Telescoping Spar,” in 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Norfolk, 2003.

Configuration,” Adaptive Analysis Aircraft Fully of in a

[29] D. Neal, M. Good, C. Johnton, H. Robertshaw, W. Mason and D. Inman, “Design and Wind- Tunnel 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs , 2004.

[30]

J.-S. Bae, T. M. Seigler and D. J. Inman, “Aerodynamic and Static Aeroelastic Characteristics of a Variable-Span Morphing Wing,” Journal of Aircraft, vol. 42, no. 2, 2005.

[31]

I. K. Kuder, A. F. Arrieta, W. E. Raither and P. Ermanni, “Variable stiffness material and structural concepts for morphing applications,” Progress in Aerospace Sciences, vol. 63, pp. 33-55, 2013.

[32] D. A. Perkins, J. L. Reed and E. J. Havens, “Morphing Wing Structures for Loitering Air Vehicles,” in 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, 2004.

[33]

J. D. Anderson Jr, Fundamentals of Aerodynamics [In SI Units], Tata McGraw-Hill Education, 2010.

[34]

P. Poonsong, Design and Analysis of a Multi-Section Variable Camber Wing, UNIVERSITY OF MARYLAND, 2004.

[35] H. Rodrigue, S. Cho, M. W. Han, B. Bhandari, J. E. Shim and S. H. Ahn, “Effect of twist morphing wing segment on aerodynamic performance of UAV,” Journal of Mechanical Science and Technology, vol. 30, no. 1, pp. 229-236, 2016.

[36]

Smithsonian, Institution, “Wing-Warping,” Smithsonian Institution, [Online]. Available: https://airandspace.si.edu/multimedia-gallery/5791hjpg?id=5791. [Accessed 10 10 2020].

[37]

F. Austin, M. J. Rossi, W. Van Nostrand, G. Knowles and A. Jameson, “Static shape control for adaptive wings,” AIAA Journal, vol. 32, no. 9, 1994.

[38] G. Molinari, A. F. Arrieta, M. Guillaume and P. Ermanni, “Aerostructural Performance of Distributed Compliance Morphing Wings: Wind Tunnel and Flight Testing,” AIAA Journal, vol. 54, no. 12, 2016.

[39]

C. Thill, J. A. Etches, I. P. Bond, K. D. Potter and P. M. Weaver, “Corrugated composites structures for aircraft morphing skin applications,” in 18th international conference of adaptive structures and techonologies, Ottawa, 2007.

[40] A. Moosavian, F. Xi and S. M. Hashemi, “Design and Motion Control of Fully Variable

Morphing Wings,” Journal of Aircraft, vol. 50, no. 4, 2013.

[41]

S. Vasista, J. Riemenschneider and H. P. Monner, “Design and Testing of a Compliant Mechanism-Based Demonstrator for a Droop-Nose Morphing Device,” in 23rd AIAA/AHS Adaptive Structures Conference, Kissimmee, 2015.

[42]

P. Gamboa, P. Alexio, F. Lau and A. Suleman, “Design and Testing of a Morphing Wing for an Experimental UAV,” Universidade da Beira Interior, Covilha, 2007.

[43] H. P. Monner, H. Hanselka and E. J. Breitbach, “Development and design of flexible Fowler flaps for an adaptive wing,” in 5th Annual International Symposium on Smart Structures and Materials, San Diego, 1998.

[44]

J. Flanagan, R. Strutzenberg, R. Myers and J. Rodrian, “Development and Flight Testing of a Morphing Aircraft, the NextGen MFX-1,” in Session: ASC-2: Aeroelasticity and Flight Dynamics of Adaptive Systems, Honolulu, 2007.

[45]

Y. Yang, Z. Wang, B. Wang and S. Lyu, “Optimization, Design, and Testing for Morphing Leading Edge,” Journal of Mechanical Engineering Science, 2020.

[46]

S. M. Yang, J.-H. Han and I. Lee, “Characteristics of smart composite wing with SMA actuators and optical fiber sensors,” International Journal of Applied Electromagnetics and Mechanics, vol. 23, no. 3, pp. 177-186, 2006.

[47]

S.-H. Ko, J.-S. Bae and J.-H. Rho, “Development of a morphing flap using shape memory actuators: the aerodynamic characteristics of a morphing flap,” Smart Materials and Structures, vol. 23, no. 7, 2014.

[48]

J.-R. Poulin, P. Terriault, M. Dube and P.-L. Vachon, “Development of a morphing wing extrados made of composite materials and actuated by shape memory alloys,” Journal of Intelligent Material Systems and Structures, vol. 28, no. 11, pp. 1437-1453, 2016.

[49] B. K. Woods, A. E. Rivero, S. Fournier, M. Manolesos and J. E. Cooper, “Experimental Aerodynamic Comparison of Active Camber Morphing and Trailing-Edge Flaps,” AIAA Journal , vol. 59, no. 7, 2021.

[50] D. Kumar, S. F. Ali and A. Arockiarajan, “Structural and Aerodynamics Studies on Various Wing

Configurations for Morphing,” IFAC-PapersOnLine, 2018.

[51]

T. Yokozeki, A. Sugiura and Y. Hirano, “Development of Variable Camber Morphing Airfoil Using Corrugated Structure,” Journal of Aircraft, vol. 51, no. 3, 2014.

[52] G. Murray, F. Gandi and C. Bakis, “Flexible Matrix Composite Skins for One-dimensional Wing Morphing,” Journal of Intelligent Materials Systems and Structures, vol. 21, no. 17, pp. 1771- 1781, 2010.

[53] Flexsys, “flexfoil-A Potential Game Changer,” [Online]. [Accessed 19 April 2017].

[54] “flexfoil-uncompromising Flexibility,”

Flexsys, [Online]. Available: Strength and https://static1.squarespace.com/static/54946b7fe4b04a99c2e3353a/t/5498626de4b08142 c228d105/1419272813797/FACT+SHEET-Flight+Testing-141120.pdf. [Accessed 19 April 2017].

[55]

E. J. Miller, W. A. Lokos, J. Cruz, G. Crampton, C. A. Stephens, S. Kota, G. Ervin and P. Flick, “APPROACH FOR STRUCTURALLY CLEARING AN ADAPTIVE COMPLIANT TRAILING EDGE FLAP FOR FLIGHT,” 2015.

[56] NASA, “Go,Go, Green Wing! Mighty Morphing Materials in Aircraft Design,” [Online]. https://www.nasa.gov/ames/feature/go-go-green-wing-mighty-morphing-

Available: materials-in-aircraft-design. [Accessed 19 April 2017].

[57]

P. Zhang, L. Zhou, W. Cheng and T. Qiu, “Conceptual Design and Experimental Demonstration of a Distributedly Actuated Morphing Wing,” Journal of Aircraft, vol. 52, no. 2, pp. 452-461, 2015.

[58]

K. R. Olympio and F. Gandhi, “Zero Poisson’s Ratio Cellular Honeycombs for Flex Skins Undergoing One-Dimensional Morphing,” Journal of Intelligent Material Systems and Structures, vol. 21, no. 17, pp. 1737-1753, 2009.

[59] W. Liu, H. Zhu, S. Zhou, Y. Bai, Y. Wang and C. Zhao, “In-plane corrugated cosine honeycomb for 1D morphing skin and its application on variable camber wing,” Chinese Journal of Aeronautics, vol. 26, no. 4, pp. 935-942, 2013.

[60]

I. Dayyani, S. Ziaei-Rad and M. I. Friswell, “The mechanical behavior of composite corrugated core coated with elastomer for morphing skins,” Journal of Composite Materials, vol. 48, no. 13, pp. 1623-1636, 2013.

[61]

F. M. H. Aliabadi, S. Ricci, F. Semperlotti and R. Botez, Morphing Wing Technologies: Large Commercial Aircraft and Civil Helicopters, Oxford: Elsevier Science & Technology , 2017.

[62] R. Navarante, I. Dayyani, B. Woods and M. I. Friswell, “Development and Testing of a Corrugated Skin for a Camber Morphing Aerofoil,” in 23rd AIAA/AHS Adaptive Structures Conference, Kissimmee, 2015.

[63]

P. B. Leal, H. Stroud, E. Sheahan, M. Cabral and D. J. Hartl, “Skin-based camber morphing utilizing shape memory alloy composite actuators in a wind tunnel environment,” in 2018 AIAA/AHS Adaptive Structures Conference, Kissimmee, 2018.

[64]

I. Dayyani, A. D. Shaw, E. I. S. Flores and M. I. Friswell, “The mechanics of composite corrugated structures: A review with applications in morphing aircraft,” Composite Structures, vol. 133, pp. 358-380, 2015.

[65]

Y. Chen, W. Yin, Y. Liu and J. Leng, “Structural design and analysis of morphing skin embedded with pneumatic muscle fibers,” Smart Materials and Structures, vol. 20, no. 8, 2011.

[66]

J. Kirn, T. Lorkowski and H. Baier, “Development of flexible matrix composites (FMC) for fluidic actuators in morphing systems,” International Journal of Structural Integrity, vol. 2, no. 4, pp. 458-473, 2011.

[67]

I. Dayyani, H. H. Khodaparast, B. K. Woods and M. I. Friswell, “The design of a coated composite corrugated skin for the camber morphing airfoil,” Journal of Intelligent Material Systems and Structures, vol. 26, no. 13, pp. 1592-1608, 2015.

[68]

Y. Xia, O. Bilgen and M. I. Friswell, “The effect of corrugated skins on aerodynamic performance,” Journal of Intelligent Material Systems and Structures, vol. 25, no. 7, pp. 786- 794, 2014.

[69]

J. Vivian, T. C. Johnson, J. Z. J. Hng and U. Chandrasekera, “Precedent T-240 Morphing Wing Design,” RMIT University, Melbourne, 2015.

[70]

T. Booji, “DESIGN AND ANALYSIS OF A MORPHING WING,” University of TWENTE & RMIT University, 2017.

[71] N. K. Hieu and H. T. Loc, “Airfoil Selection for Fixed Wing of Small Unmanned Aerial Vehicles,” in AETA 2015: Recent Advances in Electrical Engineering and Related Sciences, 2016.

[72]

J. N. Counsil and K. G. Boulama, “Low-Reynolds-Number Aerodynamic Performances of the NACA 0012 and Selig-Donovan 7003 Airfoils,” Journal of Aircraft, vol. 50, no. 1, pp. 204-216, 2013.

[73] A. Koreanschi, O. Sugar-Gabor and R. M. Botez, “Drag Optimization of a Wing Equipped with a Morphing Upper Surface,” The Aeronautical Journal, vol. 120, no. 1225, pp. 473-493, 2016.

[74]

K. Gryte, R. Hann, M. Alam, J. Rohac, T. A. Johansen and T. I. Fossen, “Aerodynamic modeling of the Skywalker X8 Fixed-Wing Unmanned Aerial Vehicle,” in 2018 International Conference on Unmanned Aircraft Systems (ICUAS), Dallas, 2018.

[75]

C. Prameswari, Simulation Model Development of a Subscale Fighter Demonstrator: Aerodynamic Database Generation and Propulsion Modeling, Linkoping: Linkoping University, 2017.

[76] D. Communier, R. M. Botez and T. Wong, “Experimental validation of a new morphing trailing edge system using Price – Païdoussis wind tunnel tests,” Chinese Journal of Aeronautics, vol. 32, no. 6, pp. 1353-1366, 2019.

[77]

F. Kody and G. Bramesfeld, “Small UAV Design Using an Integrated Design Tool,” International Journal of Micro Air Vehicles, vol. 4, no. 2, pp. 151-163, 2012.

[78] A. Deperrois, About XFLR5 calculations and experimental measurements, XFLR5

documentation, 2009.

[79] A. Deperrois, Analysis of foils and wings operating at low Reynolds numbers. XFLR5 v6.02,

2013.

[80] D. Communier, M. F. Salinas, C. Moyao, Oscar and R. M. Botez, “Aero structural modeling of a wing using CATIA V5 and XFLR5 software and experimental validation using the Price- Païdoussis wing tunnel,” in AIAA Atmospheric Flight Mechanics Conference, Dallas, 2015.

[81] A. Deperrois, F.A.Q:Why do I get the message "Point is out of the flight envelope?", 2010.

[82]

T. Melin, A Vortex Lattice MATLAB Implementation for Linear Aerodynamic Wing Applications, Sweden: Royal Institute of Technology , 2000.

[83]

L. R. Pereira, Validation of software for the calculation of aerodynamic coefficients: with a focus on the software package Tornado, Linkoping: Linkoping University, 2010.

[84]

T. Melin, User's guide and reference manual for Tornado, Stockholm: Royal Institute of Technology, 2000.

[85]

S. F. Hoerner and H. V. Borst, FLUID-DYNAMIC LIFT, Practical Information on AERODYNAMIC and HYDRODYNAMIC LIFT, Liselotte A. Hoerner, 1985.

[86] O. S. Gabor, A. Koreanschi, R. M. Botez, M. Mamou and Y. Mebarki, “Numerical simulation and wind tunnel tests investigation and validation of a morphing wing-tip demonstrator aerodynamic performance,” Aerospace Science and Technology, vol. 53, pp. 136-153, 2016.

[87]

I. Abel, “EVALUATION OF A TECHNIQUE FOR DETERMINING AIRPLANE AILERON EFFECTIVENESS AND ROLL RATE BY USING AN AEROELASTICALLY SCALED MODEL,” NASA Langley Research Center, Hampton, 1969.

[88] B. K. S. Woods, I. Dayyani and M. I. Friswell, “Fluid/Structure-Interaction Analysis of the Fish-

Bone-Active-Camber Morphing Concept,” Journal of Aircraft, vol. 52, no. 1, 2015.

[89]

J. J. Bertin and R. M. Cummings, AERODYNAMICS FOR ENGINEERS Fifth Edition, Pearson Education International, 2009.

[90]

F. Mattioni, P. M. Weaver, K. D. Potter and M. I. Friswell, “The application of thermally induced multistable composites to morphing aircraft structures,” in SPIE SMART STRUCTURES AND MATERIALS + NONDESTRUCTIVE EVALUATION AND HEALTH MONITORING, San Diego, 2008.

[91] B. K. S. Woods and M. I. Friswell, “Preliminary Investigation of a Fishbone Active Camber Concept,” in ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems , Stone Mountain, 2012.

[92]

Flexsys, “flexfoil-Variable Geometry Control Surfaces,” Flexsys, [Online]. Available: https://static1.squarespace.com/static/54946b7fe4b04a99c2e3353a/t/549861e4e4b0148a 61444c64/1419272676679/FACT+SHEET-Retrofit-141211.pdf. [Accessed 19 April 2017].

[93]

J. D. Harrington and L. Williams, “NASA Successfully Tests Shape-Changing Wing for Next Generation Aviation,” NASA, [Online]. Available: https://www.nasa.gov/press-release/nasa- successfully-tests-shape-changing-wing-for-next-generation-aviation. [Accessed 19 April 2017].

[94]

E. B. Doepke, “DESIGN AND FLIGHT TESTING OF A WARPING WING FOR AUTONOMOUS FLIGHT CONTROL,” University of Kentucky, 2012.

[95] (goe365-il),” [Online]. AIRFOIL 365 Available:

“GOE http://airfoiltools.com/airfoil/details?airfoil=goe365-il. [Accessed 1 June 2018].

[96]

E. A. Bubert, HIGHLY EXTENSIBLE SKIN FOR A VARIABLE WING-SPAN MORPHING AIRCRAFT UTILIZING PNEUMATIC ARTIFICIAL MUSCLE ACTUATION, UNIVERSITY OF MARYLAND, 2009.

[97]

S. Heinze and M. Karpel, “Analysis and Wind Tunnel Testing of a Piezoelectric Tab for Aeroelastic Control Applications,” Journal of Aircraft, vol. 43, no. 6, 2006.

[98] O. Bilgen, E. I. Saavedra Flores and M. I. Friswell, “Optimization of Surface-Actuated Piezocomposite Variable-Camber Morphing Wings,” in ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems , Scottsdale, 2011.

[99] R. Vos, R. Barrett, R. de Breuker and P. Tiso, “Post-buckled precompressed elements: a new class of control actuators for morphing wing UAVs,” Smart Materials and Structures, vol. 16, no. 3, 2007.

APPENDIX A – Wind tunnel Calibration

This section details the calibration method for the wind tunnel experiment.

Before the wind tunnel tests were conducted the calibration for both the load cell and the wind tunnel pressure was necessary to determine difference between inputs and outputs for the load cell and the difference in dynamic pressure at the roof of the wind tunnel and the dynamic pressure at the wing. The positive and negative orientation of the forces for the load cell was determined.

It was discovered that the dynamic pressure at the roof was larger than the dynamic pressure recorded on the wing, to compensate for this the dynamic pressure is adjusted using equation 11.

𝑞𝑎𝑐𝑡𝑢𝑎𝑙 = 0.967 ∗ 𝑞𝑤𝑖𝑛𝑑 𝑡𝑢𝑛𝑛𝑒𝑙 𝑟𝑒𝑐𝑜𝑟𝑑𝑖𝑛𝑔

(11)

Figure 64 Calibration setup in the y-axis (drag axis) of the JR3 Load cell, measured at z= 1 m above the load cell.

100

To determine if the load cell was giving accurate results, the load cell must be calibrated. The load cell was calibrated using known loads in the form of weights, after each weight was added or removed the outputs were recorded shown in Figure 64. Using the outputs calibration curves were generated for 𝐷 and 𝐿. This was done by using pulley and rope system to apply the loads. The calibration was conducted at 𝑧 = 1 m above the centre of the load cell in both 𝑥 and 𝑦 axes of the load cell.

The wing was not used for the calibration of the force balance instead a beam was used with the same cross-sectional geometry as the spar of the wing. The turntable was set to 𝛼 = 0°, and known weights were loaded at 𝑥 and 𝑦 axes i.e. 𝛼 = 0° and 𝛼 = 90° which correspond to 𝐷 and 𝐿 respectively. Loads were applied in the positive direction of the axis i.e. in the direction of the positive force. Note that the outputs for both 𝐹𝑥 and 𝐹𝑦 were inverse since the inputs were in the positive direction of the 𝐿 and 𝐷, which was accounted for during the post processing of the wind tunnel results.

Table 9 Load results for the calibration of the JR3 load cell in the x-axis (Lift axis).

Input Input Output Output Output Output

Fx (kg) Fx (N) Fy (N)

0 0.455

0.455 0

put on put on remove remove put on put on remove remove put on put on remove remove 0 4.46355 0.91026 8.929651 4.46355 0 1.0005 9.814905 1.5009 14.72383 1.0005 9.814905 0 1.0006 9.815886 2.0011 19.63079 1.0006 9.815886 0 0 Fx (N) -0.0222 -4.01 -8.06 -4.36 -0.421 -8.91 -14.1 -9.82 -0.0997 -9.11 -18.2 -10.5 -1.31 -0.0225 -0.0898 -0.157 -0.0898 0 -0.157 -0.292 -0.202 -0.0449 -0.18 -0.359 -0.247 -0.0449 Fz (N) Mx (Nm) 0.0505 -1.16 -1.42 -1.21 0.101 -1.42 -1.82 -1.57 0 -1.47 -2.22 -1.67 0 -0.102 -0.211 -0.105 0 -0.229 -0.363 -0.247 -0.00726 -0.225 -0.461 -0.254 -0.00726 0.00363 0.0037 4.11 8.27 4.3 0.27 9.07 14.3 9.72 0.585 9.01 18.2 10.3 0.6 Output Output My (Nm) Mz (Nm) 0 0 0 0 0 0.00381 0 0.00381 -0.00381 0.00381 0.00381 0.00381 -0.00381

From Figure 65 there is a strong relationship between the 𝐹𝑥_𝑖𝑛𝑝𝑢𝑡 and 𝐹𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 where 𝐹𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 is roughly 95% of 𝐹𝑥_𝑖𝑛𝑝𝑢𝑡.

(12) 𝐹𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 = 0.95 ∗ 𝐹𝑥_𝑖𝑛𝑝𝑢𝑡

(13) 𝐹𝑦_𝑝ℎ𝑎𝑛𝑡𝑜𝑚 𝑜𝑢𝑡𝑝𝑢𝑡 = 0.02 ∗ 𝑀𝑦_𝑜𝑢𝑡𝑝𝑢𝑡

From Table 9 for a force input aligned with the x-axis there is additional force being output in the y- axis. The y-axis output, 𝐹𝑦 was correlated to the roll moment output, 𝑀𝑦 to determine the relationship between the rolling moment generated and the phantom 𝐹𝑦 force. From Figure 66 there is a linear relationship between 𝑀𝑦 and 𝐹𝑦, where phantom 𝐹𝑦 force is roughly 2% of the rolling moment, 𝑀𝑦.

101

Fx input vs Fx output - (Lift) taken at z=1m

-2

-4

)

Data points

-6

N

Linear (Data points)

-8

-10

-12

-14

( t u p t u o x F

y = -0.9489x R² = 0.9958

-16

-18

-20

Fx input (N)

Figure 65 Calibration curve for the Lift axis of the JR3 load cell – “Lift” Force output vs “Lift” Force input.

My output vs Fy output - (Rolling moment vs Drag) taken at z=1m 15

-0.05

-0.1

)

N

-0.15

-0.2

Data points

Linear (Data points)

-0.25

( t u p t u o y F

-0.3

y = -0.0203x R² = 0.9876

-0.35

-0.4

My output (Nm)

Figure 66 Calibration curve for the phantom outputs of the JR3 load cell – “Drag” Force output vs “Rolling” Moment output.

102

Table 10 Load results for the calibration of the JR3 load cell in the y-axis (Drag axis).

Input Input Output Output Output Output Output Output

Fz (N) Mx (Nm) My (Nm) Mz (Nm) Fy (N)

Fy (kg) 0 0.455

-0.105 -4.05 -8.24 -4.66

0.455 0

-9.13 -13.7 -10.1 -0.378 -9.04 -18.4 -10.4

add add remove remove add add remove remove add add remove remove 0 4.46355 0.91026 8.929651 4.46355 0 1.0005 9.814905 1.5009 14.72383 1.0005 9.814905 0 1.0006 9.815886 2.0011 19.63079 1.0006 9.815886 0 0 Fx (N) -0.0443 0.377 0.687 0.399 -0.0443 0.687 1.06 0.665 -0.199 0.554 1.4 0.62 -0.0332 Fy (N) -0.0898 -2.83 -5.84 -3.35 -0.18 -6.31 -9.79 -7.25 -0.404 -6.49 -13.4 -7.97 -0.764 0 -0.152 -0.303 -0.152 0 -0.354 -0.556 -0.404 -0.0505 -0.354 -0.809 -0.455 -0.0505 0 0 0.104 -0.0191 0.211 0.0343 0.0191 0.115 -0.367 0.00741 0.00381 0.042 0.233 0.061 0.352 0.256 0.0458 0.0037 0.00381 0.042 0.23 0.0839 0.478 0.0534 0.263 -0.364 0.00741 0.00381

(14) 𝐹𝑦_𝑜𝑢𝑡𝑝𝑢𝑡 = 0.69 ∗ 𝐹𝑦_𝑖𝑛𝑝𝑢𝑡

(15) 𝐹𝑥−𝑝ℎ𝑎𝑛𝑡𝑜𝑚 𝑜𝑢𝑡𝑝𝑢𝑡 = 0.073 ∗ 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡

From Figure 67 there is a relationship between the 𝐹𝑦_𝑖𝑛𝑝𝑢𝑡 and 𝐹𝑦_𝑜𝑢𝑡𝑝𝑢𝑡 where 𝐹𝑦_𝑜𝑢𝑡𝑝𝑢𝑡 is roughly 69% of 𝐹𝑦_𝑖𝑛𝑝𝑢𝑡. Due to this large discrepancy in the 𝐹𝑦_𝑜𝑢𝑡𝑝𝑢𝑡, pure moment inputs were examined. From Figure 68 it is apparent that there is a relationship between 𝐹𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 and 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 where 𝐹𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 is roughly 7.3% of 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡.

Fy output vs Fy input - (Drag) taken at z=1m

-2

-4

)

N

-6

-8

Data points

Linear (Data points)

-10

( t u p t u O y F

-12

-14

y = -0.6882x R² = 0.9941

-16

Fy input (N)

Figure 67 Calibration curve for the Drag axis of the JR3 load cell – “Drag” Force output vs “Drag” Force input.

103

Yawing moment vs Lift taken at z=1m

1.6

1.4

Data points

1.2

)

N

0.8

0.6

0.4

y = -0.0731x R² = 0.9776

( t u p t u o x F

0.2

-20

-15

-10

-5

-0.2

-0.4

Mx output (Nm)

Figure 68 Calibration curve for the Drag axis of the JR3 load cell – “Drag” Force output vs “Yawing” Moment input.

Pure moments were also applied this was done by modifying the beam into a T-beam and by hanging weights off the T sections. This was done in line with the at 𝑥 and 𝑦 axes i.e. 𝛼 = 0° and 𝛼 = 90° which correspond to yawing moment and rolling moment respectively. The same process as the force loading was used, however the moment loading was also done on the opposite end i.e. initial loading at 𝑥 = 0.3 m and 𝑥 = -0.3 m, seen in Figure 69 and Figure 70 and at 𝑦 = 0.3 m and 𝑦 = -0.3 m, seen in Figure 75.

Figure 69 Calibration of the JR3 load cell by applying pure moments in the Yaw axis, at x= -0.3m via T-beam.

Table 11 Pure moment Yaw results for the calibration of the JR3 load cell in the y-axis (Drag axis).

104

Figure 70 Calibration of the JR3 load cell by applying pure moments in the Yaw axis, at x= 0.3m via T-beam.

In Figure 71 there is a relationship between lift and applied yawing moment of around 8.4%. By conducting the pure moment calibration for the JR3 load cell we can see that in Figure 72 there is a strong relationship between and applied yawing moment and drag of up to 30%.

(16) (17) 𝐹𝑥_𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 = 0.084 ∗ 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 𝐹𝑦_𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 = 0.30 ∗ 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡

105

Drag output vs Yawing moment

0.8

0.6

)

N

0.4

y = -0.0836x R² = 0.9739

0.2

Data points

-8

-6

-4

-2

-0.2

Linear (Data points)

( t u p t u o x F

-0.4

-0.6

Mx output (Nm)

Figure 71 Pure Yaw moment configuration calibration in the Drag axis of the JR3 load cell.

Lift output vs Yawing moment

2.5

1.5

)

N

0.5

Data points

-8

-6

-4

-2

-0.5

Linear (Data points)

-1

( t u p t u o y F

-1.5

y = -0.3045x R² = 0.997

-2

-2.5

Mx output (Nm)

Figure 72 Pure Yaw moment configuration calibration in the Drag axis of the JR3 load cell.

By knowing that the 𝐹𝑦 is coupled with 𝑀𝑥, and by knowing the coupling factor is approximately 30% it can be used to decouple the 𝐹𝑦 from the 𝑀𝑥. When this is applied to the drag calibration earlier seen in Table 11, it results in Figure 73 which shows that the accuracy between the input drag, 𝐹𝑦_𝑖𝑛𝑝𝑢𝑡 and the output drag, 𝐹𝑦_𝑜𝑢𝑡𝑝𝑢𝑡 is 97%.

106

Fy decoupled output vs Fy input - (Drag) taken at z=1m

)

N

-5

-10

Data points

l

-15

Linear (Data points)

-20

( t u p t u O d e p u o c e D y F

y = -0.9729x R² = 0.9952

-25

Fy input (N)

Figure 73 Using calibration data from Yaw moment calibration, calibration curve for the Drag axis of the JR3 load cell.

𝐹𝑦𝑑𝑒𝑐𝑜𝑢𝑝𝑙𝑒𝑑 𝐹𝑦_𝑖𝑛𝑝𝑢𝑡

= 0.97 (18)

Table 12 Pure moment Roll results for the calibration of the JR3 load cell in the x-axis (Lift axis).

107

Figure 74 Calibration of the JR3 load cell by applying pure moments in the Roll axis, at y= -0.3m via T-beam.

Drag output vs Rolling moment output

0.5

0.4

0.3

)

0.2

m N

y = 0.0469x R² = 0.8905

0.1

Data points

Linear (Data points)

-8

-6

-4

-2

-0.1

( t u p t u o x F

-0.2

-0.3

-0.4 My output (Nm)

Figure 75 Using calibration data from Rolling moment calibration, calibration curve for the Lift axis of the JR3 load cell.

108

Lift output vs Rolling moment output

0.3

0.25

0.2

)

0.15

m N

0.1

Data points

0.05

Linear (Data points)

-8

-6

-4

-2

-0.05

-0.1

( t u p t u o y F

-0.15

-0.2

y = -0.024x R² = 0.5202

-0.25 My output (Nm)

Figure 76 Using calibration data from Rolling moment calibration, calibration curve for the Lift axis of the JR3 load cell.

Table 11 & Table 12 shows the results of when only a pure rolling moment was loaded on the setup. Figure 68 shows that there is a linear relationship between rolling moment, 𝑀𝑦 and a phantom drag, 𝐹𝑥, Where the phantom lift, 𝐹𝑥 is 4.7% of 𝑀𝑦.

From Table 11 & Table 12 the data shows that after the forces and moments were removed, they still had lingering effects on the load cell. This means that hysteresis was likely to have been affecting the load cell, which was treated as an undeterminable source of error.

From Figure 76 during the pure moment load there is no relation between loaded 𝑀𝑦 and the resultant phantom lift, 𝐹𝑦. Nevertheless, this was treated as another source of error.

(19) 𝐹𝑥_𝑝ℎ𝑎𝑛𝑡𝑜𝑚 𝑜𝑢𝑡𝑝𝑢𝑡 = 0.0469 ∗ 𝑀𝑦_𝑖𝑛𝑝𝑢𝑡

From both Table 11 & Table 12 the inputs for both yaw and rolling moment are near identical to their outputs.

(20) (21) 𝑀𝑥_𝑖𝑛𝑝𝑢𝑡 ≈ 𝑀𝑥_𝑜𝑢𝑡𝑝𝑢𝑡 𝑀𝑦_𝑖𝑛𝑝𝑢𝑡 ≈ 𝑀𝑦_𝑜𝑢𝑡𝑝𝑢𝑡

APPENDIX B – Assembly of the Wing and Preparation of the Wing

These relations must be applied to the results of the wind tunnel experiments during the data processing stage to determine approximate true values of the respective aerodynamic coefficients and performance.

109

Wing Assembly

Bonding agents: ARALDITE 420, Sil-poxy (used exclusively for silicone components)

Miscellaneous: bolts, nuts, screws, nails, washers, hose clamp

General notes:

Before bonding of any component, each of the bonding components (if necessary) were lightly abraded at the point of contact for the bond and cleaned to facilitate a better bonding surface.

Leading edge and Spar:

Initially the leading edge was abraded to remove the protruding feature left by the cutter on the router. The spar was abraded for each surface in contact with the leading edge and cleaned before adhesive was applied. Both components can be seen in Figure 77.

Figure 77 Layout of Leading edge and Spar to be bonded.

Fishbone ribs:

The bracket, fishbone rib and the rib ends were bonded together using ARALDITE 420 which was applied at the slots and the tabs. The excess adhesive was wiped away and components were allowed to cure.

Post cure, the rib end hole for the trailing edge was drilled to allow the bolt to easily slip through. Each of the ribs was at the desired span apart corresponding to the leading-edge locations of the ribs.

Torsion rod:

Holes are drilled into the rod at the each of the corresponding control arm location to lock in place the control arms.

Threaded rod:

Rods available were only 1m in length, one of the rods were cut and a coupler was used to join the two threaded rods.

110

Next all the components listed so far were combined, Fishbone and control arms are in pairs inserted to the torsion rod. Control arms are locked in the place using nuts and bolts. Threaded rod is then threaded through each of the rib and control arm pairs. Adhesive was then applied onto the corresponding trailing edge and leading-edge slots. The current assembly was then inserted into the corresponding slots in the leading edge and the trailing edge, excess adhesive was removed then the adhesive was then left to cure which depicted in Figure 78 and Figure 79. Additional force was needed to allow for sufficient bonding at the wing-root rib, seen in Figure 78 where the rib is sandwiched between the Leading edge and a plate.

Figure 78 Bonding Ribs to the Leading edge.

Figure 79 Bonding Ribs to the Trailing edge.

The thin aluminium sheet was bonded to the bottom of the leading edge at the marked indentation located on the underside of the leading edge. Weights were placed onto the assembly during the curing process to ensure a tighter bond between the aluminium sheet and the leading edge. The same process is applied to the trailing edge sleeve, both can be seen in Figure 80 and Figure 81.

111

Figure 80 Bonding the thin Al sheet to the Wing.

One ply carbon fibre plain weave strips were placed and hardened on the indentation locations for the skin to ensure a level surface once then skin was bonded to the wing, shown in Figure 81 and Figure 82.

Figure 81 Bonding the thin Al sleeve to the Trailing edge.

The carbon fibre support angles placed and bonded at one spine intervals on the fishbone ribs for each rib at the desired fish spine number, this process was done in pairs since the number of weights was limited seen inFigure 82. Following the aluminium sheet weights were placed to facilitate a stronger bond. This process was done in pairs since the number of weights was limited.

Figure 82 Bonding reinforcing L shape carbon fibre angles to the ribs.

A pretension was utilized for the morphing skin by applying adhesive to one end of the skin at a time. The trailing edge end of the morphing skin was bonded first with pressure once again being applied for the cure process. Afterwards the skin needed to be slightly stretched to reach the leading-edge side of the wing. The bonded skin can be seen in Figure 83.

112

Figure 83 Assembled morphing wing minus the wingtip.

In order to lock the desired morphing deflection with the templates, dowels were used. Dowels were bonded to wing by drilling a hole on both ends of the wing tip and wing root rib ends and inserting adhesive and the dowel.

Preparation for Wind Tunnel Testing

As the focus of this study is the aerodynamic performance of the morphing wing it was deemed not necessary to have the wing be actuated using servos, to remedy that template of the morphed deflections were used instead. The templates were manufactured in pairs to be placed at the wing root and the wingtip of the wing each template is manufactured from 12mm MDF. Each of the templates locks the wing in place at the desired morphing deflection; the templates were secured using hose clamps via the spar and dowels located in the rib ends of the wing. The spar box located in the wingtip base was removed to accommodate the hose clamp and sanded down to allow for the change seen in Figure 84. The wing was kept in desired deflection by dowels connecting the wing to the templates; each dowel was inserted and bonded to the wing at the rib end. Four small aluminium strips were manufactured to secure the wingtip to the templates, two of the strips were nailed and bonded to the top surface of the leading edge whilst the other two was nailed and bonded to the bottom surface of the leading edge each being spaced apart by ~30mm, seen in Figure 84 and Figure 85. The bottom strips were bent to match the angle of the wingtip base. The aluminium strips each had two holes, one would be used to fasten the templates and the other was nailed and bonded to the wingtip base.

Figure 84 Isometric view of Wing tip post modifications; removal of spar box and addition of thin Al strips.

113

Figure 85 Bottom view of Wing tip post modifications; removal of spar box and addition of thin Al strips.

Due to this alteration the wingtip cover was bonded to the wingtip base since it is no longer necessary to readily remove the wingtip cover from the wingtip base. The wingtip cover hole was sealed using the ARALDITE 420 structural adhesive and masking tape which was removed once the ARALDITE 420 adhesive in the hole was cured, seen in Figure 86 and Figure 87. The wingtip cover was bonded to the wingtip base by applying the adhesive to both sides and clamping the two parts together during the curing process. The wingtip cover was kept in place by the taping a support to the wingtip base to keep the wingtip cover level with the wingtip base, seen in Figure 86 and Figure 87.

Figure 86 Isometric view of the Bonding of the wingtip cover to the wingtip.

114

Figure 87 Top view of the Bonding of the wingtip cover to the wingtip.

To prepare for wind tunnel testing the foam components of the wing: wingtip, leading edge and trailing edge needed to be sealed. The parts were sealed with epoxy resin seen in Figure 88, the process involved applying an initial thin layer of resin, allowing it to cure then sanding for smoothness before sealing it with another thin layer of resin to close the remaining gaps before sanding once more for smoothness. Foam components of the wing were then painted using an acrylic based paint after covering other parts of the wing with masking tape or in plastic which can be seen in Figure 89 to Figure 91.

Figure 88 Curing of the Epoxy resin applied to the foam components of the Morphing wing and wingtip.

115

Figure 89 Morphing wing spray painted.

Figure 90 Wingtip spray painted.

Figure 91 Morphing wing - post cure of the spray paint.

The forward strut location was then marked and the strut was attached using two self-tapping screws. A flat sting board was manufactured with having the forward strut in mind, the sting board required additional holes for each of the morphing deflections.

116

APPENDIX C – Flow Visualization for Various Morphing Deflections

𝛿𝑚 = 0° 𝛼 = 10°

𝛿𝑚 = 0° 𝛼 = 0°

𝛿𝑚 = 0° 𝛼 = −5°

𝛿𝑚 = 0° 𝛼 = 5°

𝛿𝑚 = 0° 𝛼 = 15°

Top surface Re 168000

𝛿𝑚 = 0° 𝛼 = −5°

𝛿𝑚 = 0° 𝛼 = 0°

𝛿𝑚 = 0° 𝛼 = 15°

𝛿𝑚 = 0° 𝛼 = 5°

𝛿𝑚 = 0° 𝛼 = 10°

Re 269000 Top surface

𝛿𝑚 = 0° 𝛼 = −5°

𝛿𝑚 = 0° 𝛼 = 0°

𝛿𝑚 = 0° 𝛼 = 5°

𝛿𝑚 = 0° 𝛼 = 10°

𝛿𝑚 = 0° 𝛼 = 15°

Re 269000 Bottom surface

117

Observations 𝜶

Completely attached with no disturbance to the tufts -5

Completely attached with no disturbance to the tufts 0

Completely attached with no disturbance to the tufts 5

15 Tufts experience some disturbance at rib end but still attached for the top surface. Disturbance in the tufts is starting to occur at the carbon fibre crest location in the chordwise direction of the wing. Aft of the crest separation can be seen to the trailing edge.

Figure 92 Flow visualization for 𝜹𝒎 = 0°.

Re 168000

𝛿𝑚 = 2° 𝛼 = −5°

𝛿𝑚 = 2° 𝛼 = 0°

𝛿𝑚 = 2° 𝛼 = 5°

𝛿𝑚 = 2° 𝛼 = 15°

𝛿𝑚 = 2° 𝛼 = 10°

Re 269000

Top surface

118

𝛿𝑚 = 2° 𝛼 = −5°

𝛿𝑚 = 2° 𝛼 = 0°

𝛿𝑚 = 2° 𝛼 = 5°

𝛿𝑚 = 2° 𝛼 = 10°

𝛿𝑚 = 2° 𝛼 = 15°

𝛿𝑚 = 2° 𝛼 = 10°

𝛿𝑚 = 2° 𝛼 = 15°

𝛿𝑚 = 2° 𝛼 = −5° 𝛿𝑚 = 2° 𝛼 = 0°

𝛿𝑚 = 2° 𝛼 = 5°

Re 269000 Bottom surface

Observations 𝜶

Re 168000, Re 202000 - Displays slight disturbance at the rib end to the trailing edge.

-5 Re 236000, Re 269000, Re 337000- Tufts experience more disturbance than at Re 168000 and Re 202000

Re 168000 – Slight disturbance of the tufts seen at rib end to trailing edge.

Re 202000, Re 236000, Re 269000, Re 337000 - flow seems to begin to reattach as tufts at rib end and trailing edge begin to realign with the airflow, as speed increases the realignment with the airflow increases. Re 168000, Re 202000 - Disturbance of tufts seen at rib end to trailing edge.

5 Re 236000, Re 269000, Re 337000 - Increased frequency of the disturbances of the tufts but it also begins to realign with the airflow.

119

Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Disturbance of tufts occurs at silicone to rib end, trailing edge has mostly separation it does experience some disturbance as the speed increases. Re 168000, Re 202000 - Disturbance and separation of the tufts throughout the wing was not as pronounced at leading edge, but fully separated at the trailing edge. 15

Re 236000, Re 269000, Re 337000 – Sees some realignment of the tufts at the leading edge and very little at the crest, disturbance frequency increased with the speed.

Figure 93 Flow visualization for 𝜹𝒎 = 2°.

𝛿𝑚 = 3° 𝛼 = −5°

𝛿𝑚 = 3° 𝛼 = 0°

𝛿𝑚 = 3° 𝛼 = 5°

𝛿𝑚 = 3° 𝛼 = 10° 𝛿𝑚 = 3° 𝛼 = 15°

Re 168000 Top surface

𝛿𝑚 = 3° 𝛼 = 0°

𝛿𝑚 = 3° 𝛼 = 5°

𝛿𝑚 = 3° 𝛼 = 10° 𝛿𝑚 = 3° 𝛼 = 15°

𝛿𝑚 = 3° 𝛼 = −5°

Re 269000 Top surface

120

𝛿𝑚 = 3° 𝛼 = 5°

𝛿𝑚 = 3° 𝛼 = 10°

𝛿𝑚 = 3° 𝛼 = 15°

𝛿𝑚 = 3° 𝛼 = −5° 𝛿𝑚 = 3° 𝛼 = 0°

Re 269000 Bottom surface

𝜶 Observations Re 168000 – Separation seen at specific tufts across the wing otherwise all flow is attached.

-5

Re 202000, Re 236000, Re 269000, Re 337000 – The separation of the specific tufts seen at Re 168000 has reattached. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Separation can be seen at from the rib end to the trailing edge although it is not through the complete span of the wing. Unlike at 𝛿𝑚 = 2° the only a few of the tufts do not reattach when speed is increased. Small disturbances are seen in the rib end to the trailing edge. Re 168000, Re 202000, Re 236000 – Disturbances are seen in the silicone which then progressively increases towards the trailing edge, some separation can be seen at the rib end with more at the trailing edge. Disturbance frequency increases as airspeed increases. 5

Re 269000, Re 337000 – The same as the lower speeds except that the tufts are showing signs of realignment i.e. flow is starting to reattach. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Disturbance of the tufts and some realignment occurring at the silicone. However, rib end and trailing edge are separated but it did reattach slightly, disturbances in the tufts occurs as speed increases. Rough realignment for the silicone tufts is achieved at roughly Re 269000 but there is still disturbances at that chordwise location. Re 168000 – Disturbances effects specific tufts at the leading edge and tufts aft of that experience separation. Disturbances seen in the tufts from silicone section and separation seen from rib end onward. 15

Re 202000, Re 236000, Re 269000, Re 337000 – The separation behaviour seen at the crest has disappeared, likely that the tufts have reattached with the increase in airspeed, all else behaviour is similar to Re 168000.

Figure 94 Flow visualization for 𝜹𝒎 = 3°.

Re 168000 Top surface

121

𝛿𝑚 = 5° 𝛼 = 10°

𝛿𝑚 = 5° 𝛼 = 5°

𝛿𝑚 = 5° 𝛼 = 15°

𝛿𝑚 = 5° 𝛼 = −5° 𝛿𝑚 = 5° 𝛼 = 0°

𝛿𝑚 = 5° 𝛼 = 5°

𝛿𝑚 = 5° 𝛼 = 10° 𝛿𝑚 = 5° 𝛼 = 15°

Re 269000 Top surface

𝛿𝑚 = 5° 𝛼 = −5°

𝛿𝑚 = 5° 𝛼 = 0°

𝛿𝑚 = 5° 𝛼 = 5°

𝛿𝑚 = 5° 𝛼 = 10° 𝛿𝑚 = 5° 𝛼 = 15°

Re 269000 Bottom surface

122

𝜶

-5

Observations Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Disturbances can be seen in the rib end, frequency of disturbances increases with increasing airspeed similar to that of 𝛿𝑚 = 2°, 𝛼 = -5°. Re 168000, Re 202000, Re 236000 – Disturbances of the tufts seen at rib end and trailing edge location across the span of the wing, Specific tufts at the rib end and the trailing edge are separated. 0

15 Re 269000, Re 337000 - The separation at the rib end location was reattached with the increase in airspeed, however the separation at the trailing edge remains. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 - Disturbances of the tufts seen in the silicone section. Separation and disturbance seen at the rib end, while mostly separation with small disturbances seen at the trailing edge. Frequency of the disturbances increases with airspeed, no realignment occurs. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 - Disturbances of the tufts at the crest which progresses aft wards and increases in magnitude. Some separation is seen in the silicone, much of the separation occurs at the rib end and the trailing edge. Increasing airspeed does not result in realignment/reattachment of the flow but it does increase the frequency of the disturbances of the tufts. Re 168000 - Disturbances and separation can now be seen at the leading edge particularly at the centre of the wing, immediately behind it there is separation at the crest for the same spanwise location. There seems to be a splitting effect where the tufts go upwards in the towards the roof of the tunnel instead of drooping to the floor when experiencing separation although this effect is limited to the centre of the wing and disappears at the trailing edge. Disturbances still occurs throughout the wing.

Re 202000, Re 236000, Re 269000, Re 337000 – At the leading edge, disturbances and separation has been resolved, splitting effect is not limited to the silicone section, disturbances of the tufts still occur at all other regions.

Figure 95 Flow visualization for 𝜹𝒎 = 5°.

Re 168000 Top surface

123

𝛿𝑚 = 10° 𝛼 = 15°

𝛿𝑚 = 10° 𝛼 = −5° 𝛿𝑚 = 10° 𝛼 = 0°

𝛿𝑚 = 10° 𝛼 = 5°

𝛿𝑚 = 10° 𝛼 = 10°

𝛿𝑚 = 10° 𝛼 = −5° 𝛿𝑚 = 10° 𝛼 = 0°

𝛿𝑚 = 10° 𝛼 = 5°

𝛿𝑚 = 10° 𝛼 = 10° 𝛿𝑚 = 10° 𝛼 = 15°

Re 269000 Top surface

𝛿𝑚 = 10° 𝛼 = 5° 𝛿𝑚 = 10° 𝛼 = 15°

𝛿𝑚 = 10° 𝛼 = −5° 𝛿𝑚 = 10° 𝛼 = 0° 𝛿𝑚 = 10° 𝛼 = 5°

Re 269000 Bottom surface

Observations 𝜶

124

-5

Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 - Disturbance of the tufts from the rib end aft-wards, some separation noticed at specific tufts at rib end otherwise complete separation at the trailing edge across the wing. Disturbance frequency increases as airspeed increases. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 - Separation occurs across span of rib end and trailing edge, slight disturbance of the tufts is apparent in the silicone. Disturbance frequency increases with airspeed. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar behaviour to 𝛿𝑚 = 5°,𝛼 = 5°. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar behaviour to 𝛿𝑚 = 5°, 𝛼 = 10°, silicone section has a bit more separation as tufts are not in contact with the skin and there is a slight splitting behaviour, which is more noticeable as speed increases. Re 168000 – Disturbances/separation seen from the wing root to the centre span of the leading edge with separation behind it at the crest. The splitting effect is present at the centre of the wing at the silicone and the rib end locations. The rib end and trailing edge are clearly separated but disturbances still occur because of the flow whilst the silicone region is similar but not to the degree seen at the rib end and trailing edge.

Re 202000, Re 236000, Re 269000, Re 337000 – Disturbances/separation seen at the leading edge, has been resolved as the flow has been reattached at the leading edge. Which has also reduced the disturbances seen at the crest however one tuft remains separated (which changes to disturbance of the tufts once airspeed is reaches Re 236000 and above). The splitting effect is still present and covers the majority of the rib end and silicone sections. Disturbances occur periodically at the leading edge.

Figure 96 Flow visualization for 𝜹𝒎 = 10°.

𝛿𝑚 = 15° 𝛼 = −5° 𝛿𝑚 = 15° 𝛼 = 0°

𝛿𝑚 = 15° 𝛼 = 5° 𝛿𝑚 = 15° 𝛼 = 10° 𝛿𝑚 = 15° 𝛼 = 15°

Re 168000 Top surface

Re 269000 Top surface

125

𝛿𝑚 = 15° 𝛼 = −5° 𝛿𝑚 = 15° 𝛼 = 0°

𝛿𝑚 = 15° 𝛼 = 5° 𝛿𝑚 = 15° 𝛼 = 10°

𝛿𝑚 = 15° 𝛼 = 15°

𝛿𝑚 = 15° 𝛼 = 5°

𝛿𝑚 = 15° 𝛼 = −5° 𝛿𝑚 = 15° 𝛼 = 0°

𝛿𝑚 = 15° 𝛼 = 10° 𝛿𝑚 = 15° 𝛼 = 15°

Re 269000 Bottom surface

𝜶

-5

Observations Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Separation seen along the span for both the rib end and trailing edge sections. Silicone section experiences disturbances. The wing tip side of the rib end and trailing edge sees the splitting phenomenon as the tuft is pointed toward the roof of the tunnel. Disturbance frequency increases with airspeed.

0 Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Very similar to 𝛿𝑚 = 10°, 𝛼 = 0°. Disturbance frequency increases with airspeed.

Re 168000 – Splitting phenomenon only seen at the rib end and trailing edge at the wing tip. Separation occurs but disturbances seems to be the major behaviour seen at the silicone section. Rib end and trailing edge sees a majority of separation along the span of the wing.

126

10 Re 202000, Re 236000, Re 269000, Re 337000 – Splitting phenomenon is now seen at the centre of the wing at silicone region and tufts closer to the wingtip. Disturbance frequency increases with airspeed. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 10°, 𝛼 = 10°. Splitting phenomenon noticed as speed increases, and Disturbance frequency increases with airspeed.

Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Disturbances are seen at the centre of the wing along the leading edge and aftwards has separation with some disturbances occurring. Silicone section experiences disturbances with some separation whilst for the rib end and trailing edge it is mostly separated. Splitting phenomenon is present from silicone region and progressively moving towards the wingtip as it travels from the silicone region towards the trailing edge. Disturbance frequency increases with airspeed.

Figure 97 Flow visualization for 𝜹𝒎 = 15°.

𝛿𝑚 = 20° 𝛼 = −5°

𝛿𝑚 = 20° 𝛼 = 0°

𝛿𝑚 = 20° 𝛼 = 5°

𝛿𝑚 = 20° 𝛼 = 10°

𝛿𝑚 = 20° 𝛼 = 15°

Re 168000 Top surface

𝛿𝑚 = 20° 𝛼 = −5° 𝛿𝑚 = 20° 𝛼 = 0°

𝛿𝑚 = 20° 𝛼 = 15°

𝛿𝑚 = 20° 𝛼 = 5° 𝛿𝑚 = 20° 𝛼 = 10°

Re 269000 Top surface

127

𝛿𝑚 = 20° 𝛼 = 5°

𝛿𝑚 = 20° 𝛼 = −5° 𝛿𝑚 = 20° 𝛼 = 0°

𝛿𝑚 = 20° 𝛼 = 10° 𝛿𝑚 = 20° 𝛼 = 15°

Re 269000 Bottom surface

𝜶

-5

Observations Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – From the silicone region and aftwards there is separation. Disturbances of the tufts occur in the silicone region. Splitting phenomenon seen at the wingtip side. Disturbance frequency increases with airspeed. Progressive increase in splitting phenomenon increases as airspeed increases.

Re 168000 – A specific tuft at the crest (around the wing root) sees separation, some tufts in the silicone region sees separation but still experiences disturbances. Progressive splitting phenomenon seen but it is very weak likely due to the low airspeed.

Re 202000, Re 236000, Re 269000, Re 337000 – The specific tuft that was separated has reattached/realigned at airspeeds greater than Re 168000. Disturbance frequency increases with airspeed. Progressive splitting phenomenon originating at the centre span becomes more obvious at higher airspeeds. 5 Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 15° 𝛼 = 5°.

Re 168000 – Tufts at the Leading edge experiences disturbances, the tufts behind the leading edge at the crest experiences separation. Progressive splitting phenomenon from the crest however this ends around the rib end. 10

Re 202000, Re 236000, Re 269000, Re 337000 – Disturbances at the leading edge stops and crest realigns/reattaches, some of the splitting phenomenon occurs at the trailing edge.

Re 168000 – Leading edge experiences more disturbances than at 𝛼 = 10°, the splitting phenomenon is present from the centre span of the crest advancing to the wing tip. The separation can be seen from the crest towards the trailing edge. 15

Re 202000, Re 236000, Re 269000, Re 337000 – Leading edge sees more stability at the higher airspeeds, the rest of the wing experiences more frequent disturbances due to the increased airspeed and the rest of the behaviour is similar to that of the lower speeds.

Figure 98 Flow visualization for 𝜹𝒎 = 20°.

128

𝛿𝑚 = 25° 𝛼 = −5°

𝛿𝑚 = 25° 𝛼 = 0°

𝛿𝑚 = 25° 𝛼 = 5°

𝛿𝑚 = 25° 𝛼 = 10°

𝛿𝑚 = 25° 𝛼 = 15°

Re 168000 Top surface

𝛿𝑚 = 25° 𝛼 = −5°

𝛿𝑚 = 25° 𝛼 = 0°

𝛿𝑚 = 25° 𝛼 = 5°

𝛿𝑚 = 25° 𝛼 = 10°

𝛿𝑚 = 25° 𝛼 = 15°

Re 269000 Top surface

𝛿𝑚 = 25° 𝛼 = 10° 𝛿𝑚 = 25° 𝛼 = 15°

𝛿𝑚 = 25° 𝛼 = 5°

𝛿𝑚 = 25° 𝛼 = −5° 𝛿𝑚 = 25° 𝛼 = 0°

Re 269000 Bottom surface

129

𝜶

Observations Re 168000 – From the silicone region to the trailing edge separation is apparent. The silicone region does not see as much separation than the rib end and trailing edge. Splitting phenomenon is not as apparent. Frequency of the disturbances around the wingtip and trailing edge are more frequent and larger in magnitude than disturbances towards the centre of the wing. -5

Re 202000, Re 236000, Re 269000, Re 337000 – As the speed increases the progressive splitting phenomenon becomes more noticeable as more tufts begin to split. The frequency of the disturbances of the trailing edge around the wingtip are greater than the disturbances of the tufts at the centre of the wing.

Re 168000, Re 202000 – Separation seen from silicone region towards trailing edge. Progressive splitting phenomenon is not present. Disturbances around the wingtip trailing edge region are more frequent than the disturbances seen at the centre of the wing. 0

Re 236000, Re 269000, Re 337000 – Splitting phenomenon is present and based around the wingtip. Disturbance frequency increases with airspeed, all else behaviour is similar to that at lower speeds.

5 Re 168000, Re 202000 – Disturbances can be seen in the crest. Silicone section sees both disturbances and separation although at this stage it is mostly separation. The trailing edge and rib end sections see separation and disturbances (which is larger than the silicone section this could be due the flow from the bottom surface). Disturbance frequency increases with airspeed.

Re 236000, Re 269000, Re 337000 – Splitting phenomenon is present, located around the trailing edge around the wingtip, all else behaviour is similar to the lower speeds.

Re 168000 – Disturbances of the tufts is present from the leading edge to the crest, disturbances appear to be periodic for these regions. Splitting phenomenon are visible from the silicone to the trailing edge. Disturbances are also seen at the trailing edge and the rib end than the silicone region. 10

Re 202000, Re 236000, Re 269000, Re 337000 – Splitting phenomenon is more pronounced. Disturbances from the leading edge is more settled, crest still sees a disturbance. Disturbance frequency increases with airspeed.

Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Leading edge sees separation, disturbances are seen at the leading edge and progresses through the wing to the trailing edge. Splitting phenomenon can be seen from the centre span to the wing tip in the silicone region to trailing edge. Disturbance frequency increases with airspeed. However, it reattaches as higher speeds (Re> 202000).

Figure 99 Flow visualization for 𝜹𝒎 = 25°.

130

𝛿𝑚 = 30° 𝛼 = −5° 𝛿𝑚 = 30° 𝛼 = 0°

𝛿𝑚 = 30° 𝛼 = 5°

𝛿𝑚 = 30° 𝛼 = 10° 𝛿𝑚 = 30° 𝛼 = 15°

Re 168000 Top surface

𝛿𝑚 = 30° 𝛼 = 15°

𝛿𝑚 = 30° 𝛼 = 5°

𝛿𝑚 = 30° 𝛼 = −5° 𝛿𝑚 = 30° 𝛼 = 0°

𝛿𝑚 = 30° 𝛼 = 10°

Re 269000 Top surface

𝛿𝑚 = 30° 𝛼 = 5°

𝛿𝑚 = 30° 𝛼 = −5° 𝛿𝑚 = 30° 𝛼 = 0°

𝛿𝑚 = 30° 𝛼 = 10° 𝛿𝑚 = 30° 𝛼 = 15°

Re 269000 Bottom surface

131

𝜶

Observations Re 168000 – Frequency of the disturbances at the trailing edge from the wingtip end is larger than that seen at the centre of the wing. Behaviour is similar to that of 𝛿𝑚 = 25°, 𝛼 = -5°. -5

Re 202000, Re 236000, Re 269000, Re 337000 - Progressive splitting phenomenon occurs from airspeeds of 30km/h and higher. All else behaviour looks similar to that of 𝛿𝑚 = 25°, 𝛼 = -5°.

0 Re 168000, Re 202000 – Splitting phenomenon not seen at these airspeeds. Silicone region to the trailing edge sees separation, the frequency of the disturbances seen at the trailing edge side closer to the wing tip is larger than that of the silicone region. This behaviour is very similar to the behaviour seen in 𝛿𝑚 = 25°, 𝛼 = 0°.

Re 236000, Re 269000, Re 337000 – Splitting phenomenon seen, behaviour is similar to 𝛿𝑚 = 25°,𝛼 = 0° at these speeds.

Re 168000, Re 202000 – Similar to 𝛿𝑚 = 25°, 𝛼 = 5° 5 Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 25°,𝛼 = 5°

Re 168000 - Disturbances are seen from the leading edge and the crest, disturbances of the tufts seems to be erratic and periodic for these regions. Splitting phenomenon is present from the silicone to the trailing edge. Higher frequency of disturbances were noticed at the trailing edge and the rib end than the silicone region. This behaviour is similar to 𝛿𝑚 = 25°, 𝛼 = 10°. 10

15 Re 202000, Re 236000, Re 269000, Re 337000 - Splitting phenomenon is more pronounced. Disturbances from the leading edge is more consistent but is still periodically erratic just less frequent. Crest still sees a lot of erratic disturbances. Disturbance frequency increases with airspeed. Appears to be hints of turbulent flow. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Behaviour similar to 𝛿𝑚 = 25°,𝛼 = 15°.

Figure 100 Flow visualization for 𝜹𝒎 = 30°.

𝛿𝑚 = 35° 𝛼 = −5° 𝛿𝑚 = 35° 𝛼 = 0°

𝛿𝑚 = 35° 𝛼 = 5°

𝛿𝑚 = 35° 𝛼 = 10° 𝛿𝑚 = 35° 𝛼 = 15°

Re 168000 Top surface

132

𝛿𝑚 = 35° 𝛼 = −5° 𝛿𝑚 = 35° 𝛼 = 0°

𝛿𝑚 = 35° 𝛼 = 5°

𝛿𝑚 = 35° 𝛼 = 10° 𝛿𝑚 = 35° 𝛼 = 15°

Re 269000 Top surface

𝛿𝑚 = 35° 𝛼 = −5°

𝛿𝑚 = 35° 𝛼 = 0°

𝛿𝑚 = 35° 𝛼 = 5° 𝛿𝑚 = 35° 𝛼 = 10° 𝛿𝑚 = 35° 𝛼 = 15°

Re 269000 Bottom surface

𝜶

Observations Re 168000, Re 202000 – From the silicone region to the trailing edge there is separation, some tufts still flow in the silicone region. The trailing edge and the rib end experience disturbances whilst the silicone region does not. Splitting phenomenon is seen at the wingtip end for the rib end and the trailing edge.

-5

Re 236000, Re 269000, Re 337000 – Progressive splitting phenomenon occurs however it does not occur from the centre span but from roughly 1/3rd of the span from the wing tip. Disturbances of the tufts at the trailing edge around the wingtip is more frequent than that of the tufts at the centre of the wing.

0 Re 168000 – Two strands are separated at the crest, the tufts at the crest experience minor disturbance. Separation seen from silicone region towards trailing edge. Progressive splitting

133

phenomenon is not present. Disturbances around the wingtip trailing edge region is more frequent than the disturbances seen at the centre of the wing. This behaviour is very similar to 𝛿𝑚 = 25° and 𝛿𝑚 = 30° at this condition, except for the two strands at the crest. Disturbance frequency increases with airspeed.

Re 202000, Re 236000, Re 269000, Re 337000 – The abnormality at the crest has disappeared as tufts are now reattached/realigned with the flow. Splitting phenomenon is now periodic along with the disturbance of the tufts, which effects about ½ span from wingtip to roughly centre span. Disturbance frequency increases with airspeed.

Re 168000, Re 202000 – Disturbances are visible in the crest. Silicone section undergoes both disturbances and separation although at this stage it is mostly separation. The trailing edge and rib end sections see separation and disturbances (which is larger than the silicone section this could be due the flow from the bottom surface). Splitting phenomenon occurs when tufts experience disturbance, it occurs from the wing tip to roughly 1/3 wingspan and effects trailing edge and rib end with only minor effects in the silicone region. Disturbance frequency increases with airspeed.

10 Re 236000, Re 269000, Re 337000 – Splitting phenomenon is constant. The crest experiences disturbances, likely due to the increase in airspeed. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Behaviour is similar to the behaviour seen at 𝛿𝑚 = 25°, 𝛼 = 10° at the same airspeed.

15 Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 25° and 𝛿𝑚 = 30° at the same angle of attack the crest also sees the splitting phenomenon for about 1/3 of the wingspan form the wing tip.

Figure 101 Flow visualization for 𝜹𝒎 = 35°.

𝛿𝑚 = 40° 𝛼 = −5° 𝛿𝑚 = 40° 𝛼 = 0°

𝛿𝑚 = 40° 𝛼 = 5°

𝛿𝑚 = 40° 𝛼 = 10° 𝛿𝑚 = 40° 𝛼 = 15°

Re 168000 Top surface

134

𝛿𝑚 = 40° 𝛼 = 0°

𝛿𝑚 = 40° 𝛼 = −5°

𝛿𝑚 = 40° 𝛼 = 10°

𝛿𝑚 = 40° 𝛼 = 5°

𝛿𝑚 = 40° 𝛼 = 15°

Re 269000 Top surface

𝛿𝑚 = 40° 𝛼 = 5°

𝛿𝑚 = 40° 𝛼 = −5° 𝛿𝑚 = 40° 𝛼 = 0°

𝛿𝑚 = 40° 𝛼 = 10°

𝛿𝑚 = 40° 𝛼 = 15°

Re 269000 Bottom surface

Observations 𝜶

-5 Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 35° Progressive splitting phenomenon seen in the silicone to trailing edge regions.

Re 168000 - Splitting phenomenon not seen at these airspeeds. Silicone region to the trailing edge sees separation, the disturbances at the trailing edge side closer to the wing tip is larger than that seen at the silicone region. This behaviour is very similar to the behaviour seen in 𝛿𝑚 = 25°, 𝛿𝑚 = 30° and 𝛿𝑚 = 35° at 𝛼 = 0°. 0

5 Re 202000, Re 236000, Re 269000, Re 337000 - Splitting phenomenon seen, behaviour is similar to 𝛿𝑚 = 25°, 𝛿𝑚 = 30° and 𝛿𝑚 = 35° at 𝛼 = 0° at these speeds. Crest sees separation for specific tufts but becomes realigned/reattached at Re 269000. Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 - Disturbances of the tufts are present in the crest. Silicone section experiences both disturbances and separation although at this stage it is mostly separation. The trailing edge and rib end sections see separation and

135

disturbances (which is larger than the silicone section this could be due the flow from the bottom surface). Disturbance frequency increases with airspeed. Splitting phenomenon can be seen around the silicone region to the trailing edge for about ½ the wingspan. Re 168000 – Similar behaviour to 𝛿𝑚 = 25°, 𝛿𝑚 = 30° and 𝛿𝑚 = 35°.

Re 202000, Re 236000, Re 269000, Re 337000 – Similar behaviour to 𝛿𝑚 = 25°, 𝛿𝑚 = 30° and 𝛿𝑚 = 35°. Splitting phenomenon affects roughly ½ the wingspan from the wing tip.

15 Re 168000, Re 202000, Re 236000, Re 269000, Re 337000 – Similar to 𝛿𝑚 = 25°, 𝛿𝑚 = 30° and 𝛿𝑚 = 35° at this condition.

Figure 102 Flow visualization for 𝜹𝒎 = 40°.

136

APPENDIX D – Experimental Results

1.6

1.4

1.2

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 28degrees T240 flap 28degrees

0.8

0.6

Re 202000

t f i L f o t n e i c i f f e o C

0.4

, 𝐿 𝐶

0.2

-10

-5

-0.2

This section contains the remaining experimental results of both the conventional and morphing wing that are not shown in the main text.

1.6

1.4

1.2

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.8

0.6

Re 269000

0.4

0.2

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

-10

-5

-0.2

-0.4

𝛼, Angle of Attack, in 𝑑𝑒𝑔

137

0.35

0.3

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.25

0.2

g a r D

0.15

f o t n e i c i f f e o C

0.1

Re 202000

𝐷 𝐶

0.05

-10

-5

5 𝛼, Angle of Attack, in 𝑑𝑒𝑔

0.35

0.3

T240 flap 0degrees T240 flap 07degrees T240 flap 14degrees T240 flap 21degrees T240 flap 28degrees

0.25

g a r D

0.2

0.15

f o t n e i c i f f e o C

𝐷 𝐶

0.1

Re 269000

0.05

-10

-5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 103 Conventional T240 Wing Experimental results for 𝑪𝑳 vs 𝜶 and 𝑪𝑫 vs 𝜶 at Re 202000 and Re 269000.

138

delta_m = 2 degrees delta_m = 5 degrees delta_m = 15 degrees delta_m = 25 degrees delta_m = 35 degrees

delta_m = 0 degrees delta_m = 3 degrees delta_m = 10 degrees delta_m = 20 degrees delta_m = 30 degrees delta_m = 40 degrees

Re 202000

1.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

0.5

-10

-5

-0.5

delta_m = 2 degrees delta_m = 5 degrees delta_m = 15 degrees delta_m = 25 degrees delta_m = 35 degrees

delta_m = 0 degrees delta_m = 3 degrees delta_m = 10 degrees delta_m = 20 degrees delta_m = 30 degrees delta_m = 40 degrees

1.5

t f i L f o t n e i c i f f e o C

, 𝐿 𝐶

0.5

Re 269000

-10

-5

-0.5

𝛼, Angle of Attack, in 𝑑𝑒𝑔

139

0.8

Re 202000

0.6

g a r D

0.4

f o t n e i c i f f e o C

𝐷 𝐶

0.2

-10

-5

0 𝛼, Angle of Attack, in 𝑑𝑒𝑔

0.8

Re 269000

0.7

0.6

0.5

0.4

g a r D

0.3

0.2

f o t n e i c i f f e o C

𝐷 𝐶

0.1

-10

-5

5 𝛼, Angle of Attack, in 𝑑𝑒𝑔

Figure 104 Morphing Wing Experimental results for 𝑪𝑳 vs 𝜶 and 𝑪𝑫 vs 𝜶 at Re 202000 and Re 269000.

140

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 168000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.5

0.5

1.5

-5

-10

T240

delta_m = 0 degrees

delta_m = 2 degrees

delta_m = 3 degrees

delta_m = 5 degrees

delta_m = 10 degrees

delta_m = 15 degrees

delta_m = 20 degrees

delta_m = 25 degrees

delta_m = 30 degrees

delta_m = 35 degrees

delta_m = 40 degrees

Ideal

Re 202000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.5

0.5

1.5

-5

-10

𝐶𝐿, Coefficient of Lift

141

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 236000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.5

0.5

1.5

-5

-10

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 269000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.5

0.5

1.5

-5

-10

𝐶𝐿, Coefficient of Lift

142

delta_m = 0 degrees delta_m = 5 degrees delta_m = 20 degrees delta_m = 35 degrees

delta_m = 2 degrees delta_m = 10 degrees delta_m = 25 degrees delta_m = 40 degrees

T240 delta_m = 3 degrees delta_m = 15 degrees delta_m = 30 degrees Ideal

Re 337000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.5

0.5

1.5

-5

-10

𝐶𝐿, Coefficient of Lift

Figure 105 Experimental results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers with error bars.

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

T240 flap 0 degrees T240 flap 21 degrees 25

Re 168000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

𝐶𝐿, Coefficient of Lift

143

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

T240 flap 0 degrees T240 flap 21 degrees 25

Re 202000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

T240 flap 0 degrees T240 flap 21 degrees

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

𝐶𝐿, Coefficient of Lift

Re 236000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

𝐶𝐿, Coefficient of Lift

144

T240 flap 0 degrees T240 flap 21 degrees

T240 flap 07 degrees T240 flap 28 degrees

T240 flap 14 degrees Ideal

Re 269000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-5

T240 flap 0 degrees T240 flap 14 degrees T240 flap 28 degrees

T240 flap 07 degrees T240 flap 21 degrees Ideal

𝐶𝐿, Coefficient of Lift

Re 337000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.4

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

-2

-4

-6

𝐶𝐿, Coefficient of Lift

Figure 106 Wind tunnel results of 𝑳/𝑫 vs 𝑪𝑳 at various Reynolds numbers for Morphing Wing and Conventional Wing with flaps and error bars.

145

T240 flap 0 degrees T240 flap 14 degrees T240 flap 28 degrees

T240 flap 07 degrees T240 flap 21 degrees Ideal

Re 337000

o i t a R g a r D o t t f i L ,

𝐷 / 𝐿

-0.2

0.2

0.4

0.6

0.8

1.2

1.4

1.6

-2

-4

𝐶𝐿, Coefficient of Lift

Figure 107 𝑳/𝑫 vs 𝑪𝑳 comparison of the ideal morphing deflection and conventional wing with flaps and error bars (using the agreeable data).

Note: In regard to error bars throughout the paper and specifically Figure 106 and Figure 107, as mentioned in section 7.3 the error bars were constructed from six runs of 𝛿𝑚 = 3°, 𝛼 = 0°. Out of the six runs, five were in agreement with each other, and the sixth run had abnormal results affecting the standard deviation largely. Using the six runs, the most affected standard deviation was in the 𝐿/𝐷 where the standard deviation ranged from 1.6 to 1.9, depending on Reynolds number. If the sixth run is treated as an outlier, then the standard deviation for 𝐿/𝐷 ranges from 1 to 1.3. This difference is illustrated in Figure 106 and Figure 107. It should be noted that the testing method for the six runs were consistent and that they were conducted at different times of the day and over multiple days.

146

Figure 108 TORNADO and wind tunnel testing results for𝑪𝒍 vs 𝜹 and 𝒑̇ vs 𝜹 at Re 202000 and Re 269000.

147

Figure 109 XFLR5 Analysis for 𝑪𝑳 vs 𝜶 at Re 202000 and Re 269000.

Figure 110 TORNADO Analysis for 𝑪𝑳 vs 𝜶 at Re 202000 and Re 269000.

148

Figure 111 𝑪𝑳 and 𝒑̇ comparison between Conventional T240 and Morphing Wing at Re 202000 and Re 269000.

149

150

Figure 112 𝒑 comparison between Conventional T240 and Morphing Wing at various Reynolds Numbers.

APPENDIX E – Comparison between Wind Tunnel Test and Simulation

This section contains the direct comparisons between the experimental and XFLR5 and TORNADO results for each wing configuration and flight condition.

Direct comparisons between theoretical and experimental

For direct comparison between XFLR5, TORNADO and wind tunnel data has been corrected for the offset; the offset is now -0.3°. So true 𝛼 = 0° now occurs at 𝛼 = 0.3°.

151

152

153

154

155

156

157

158

Figure 113 Morphing Wing performance comparisons at 𝜹𝒎 = 0° to 𝜹𝒎 = 40° at various Reynolds numbers

APPENDIX F – XFLR5 Convergence When the solution does not converge there is no predicted answer

Table 13 List of non-converged conditions in XFLR5

Conditions that didn’t converge in 2D XFLR5

Re 𝛼 𝛿𝑚

20 168000 0

-1 to 8.5 168000 20

-5 to 20 168000 25

-2.5 to 1 168000 30

7.5 to 20 168000 30

-5 to 7 168000 35

16.5 to 20 168000 35

4 to 7.5 168000 40

12.5 to 14 168000 40

159

Conditions that didn’t converge in 2D XFLR5

Re 𝛼 𝛿𝑚

202000 5 19

202000 5 19.5

202000 5 20

202000 10 15 to 20

202000 15 4.5 to 8

202000 20 -0.5 to 7

202000 20 12 to 20

202000 25 -5 to 20

202000 30 -1.5 to 3.5

202000 30 8 to 20

202000 35 -5 to -1

202000 35 4.5 to 18

202000 40 -3.5

202000 40 0 to 2

202000 40 4

202000 40 10.5 to 11.5

202000 40 14.5 to 20

Conditions that didn’t converge in 2D XFLR5

Re 𝛼 𝛿𝑚

236000 2 11

236000 3 10

160

10 236000 10 to 20

15 236000 4.5 to 5.5

20 236000 -0.5 to 2

20 236000 16.5 to 20

25 236000 -5 to 3

25 236000 7.5 to 20

30 236000 -5 to -4.5

30 236000 -1.5 to 4

30 236000 8 to 20

35 236000 -3.5 to 19.5

40 236000 -4

40 236000 4 to 5

40 236000 14 to 15

40 236000 16 to 16.5

40 236000 18.5

Conditions that didn’t converge in 2D XFLR5

Re 𝛼 𝛿𝑚

15 269000 5 to 10.5

20 269000 -0.5 to 2

20 269000 11.5 to 20

25 269000 -5 to 20

30 269000 0

30 269000 16.5 to 20

35 269000 -3.5 to 0

35 269000 11.5 to 20

161

40 -0.5 to 3 269000

40 14 to 15.5 269000

Conditions that didn’t converge in 2D XFLR5

Re 𝛼 𝛿𝑚

2 10 337000

10 6 337000

10 17 to 20 337000

15 -3 337000

20 -0.5 to 20 337000

25 -5 to 4 337000

25 8 to 20 337000

30 0 to 1 337000

30 8.5 to 20 337000

35 -5 to 0 337000

35 6 to 7.5 337000

35 17 to 20 337000

40 -4.5 337000

40 -2.5 to 0.5 337000

40 11 to 14.5 337000

162

APPENDIX G – Further Information on the Vortex Lattice Method

Vortex lattice method is a simpler approach to the lifting surface method. Hence the lifting surface method will be explored briefly in this section. Prandtl’s classic lifting line theory yields reasonable results for straight wings with moderate to high aspect ratios. Lifting line theory is not suitable for wings with low aspect ratio (straight wings), swept wings and delta wings [33]. Lifting surface method covers for this weakness of lifting line theory. Imagine several horseshoe vortices superimposed along a lifting line, now impose a series of further lifting lines at different chordwise positions (parallel to the 𝑦-axis), this is illustrated in Figure 114.

Figure 114 Lifting lines in both spanwise and chordwise directions superimposed onto a wing [33, 89]

A vortex sheet is formed where the vortex lines are parallel to the 𝑦 axis [33]. The strength of the vortex sheet is 𝛾 (per unit length in x direction), where 𝛾 varies in 𝑦 direction. Like a single lifting line, Γ varies along the vortex sheet.

Remember that each lifting line will generally have different strength, so 𝛾 varies also varies with 𝑥. Therefore 𝛾 is dependent on both 𝑥 and 𝑦 i.e. 𝛾 = 𝛾(𝑥, 𝑦). Also remember that each lifting line has a

163

system of trailing vortices, therefore the lifting lines are crossed by superimposed trailing vortices parallel to the 𝑥-axis [33]. The trailing vortices form another vortex sheet of strength 𝛿 (per unit length in the 𝑦 direction). From the leading edge to the trailing edge, additional superimposed trailing vortices are picked up each time a lifting line is crossed (since lifting lines run parallel to the 𝑥 axis and trailing vortices in 𝑦 axis).

Trailing vortices are part of horseshoe vortex systems, where the leading edges/bound vortices make up various lifting lines [33]. Since circulation about each lifting line varies in the 𝑦 direction, so does the strength of trailing vortices, therefore 𝛿 = 𝛿(𝑥, 𝑦), which is seen in Figure 114. There are now two vortex sheets, one running parallel in the 𝑥 axis and the other parallel in the 𝑦 axis. Where the one running parallel to 𝑦 is 𝛾 (per unit length in 𝑥 direction) and the one running parallel to 𝑥 is 𝛿 (per unit length in 𝑦 direction). Which results in a lifting surface distributed over the entire wing seen in Figure 114. At any point of the lifting surface, the strength of the lifting surface is determined by both 𝛾 and 𝛿, where both are functions of 𝑥 and 𝑦 [33]. 𝛾 = 𝛾(𝑥, 𝑦) is the spanwise vortex distribution and 𝛿 = 𝛿(𝑥, 𝑦) is the chordwise vortex strength distribution. Downstream of the trailing edge there are no spanwise vortex distribution hence only chordwise vortices are present in the wake. The strength of the wake vortex sheet is 𝛿𝑤 (per unit length in the 𝑦 direction). Remembering that no vortex lines are present in the wake, the strength of the trailing vortex is constant with 𝑥. Hence 𝛿𝑤 is solely a function of 𝑦 i.e. 𝛿𝑤(𝑦) is equal to its value at the trailing edge.

At point P (refer to Figure 114), both the lifting surface and wake vortex sheet induce a normal component of velocity, the normal velocity is 𝑤(𝑥, 𝑦). Because the wing planform needs to be a stream surface of flow, the sum of the induced 𝑤(𝑥, 𝑦) and normal component of the freestream velocity must be zero at all points on the wing (including point P), this is called the flow-tangency condition on the wing surface [33]. Hence the main point of the lifting-surface theory is to find 𝛾 = 𝛾(𝑥, 𝑦) and 𝛿 = 𝛿(𝑥, 𝑦), so that flow-tangency condition is satisfied on all points of the wing.

Figure 115 Velocity (the direction is coming out of the paper) induced at point P by the infinitesimal segment of the lifting surface[33].

An expression for induced normal velocity can be derived from Figure 115, considering point with coordinates (𝜉, 𝜂). The spanwise vortex strength is 𝛾(𝜉, 𝜂). Imagine a thin segment of the spanwise vortex sheet of incremental length 𝑑𝜉 in the 𝑥 direction, the strength of the segment is 𝛾 𝑑𝜉 and the

164

filament stretches in the 𝑦 (𝜂 direction in this case). Consider point P at (𝑥, 𝑦), which is at a distance of 𝑟 from point (𝜉, 𝜂). From Biot-Savart law, the incremental velocity induced at 𝑃 by a segment 𝑑𝜂 of this vortex filament of strength 𝛾 𝑑𝜉

Γ 4𝜋

𝑑𝑙∗𝑥 |𝑟|3 | =

𝛾𝑑𝜉 4𝜋

(𝑑𝜂)𝑟 sin θ 𝑟3

|𝑑𝑉| = | (23)

In Figure 115, following right-hand rule for strength 𝛾, note that |𝑑𝑉| is induced downward into the plane of the wing (in the negative z direction). Following usual sign convention that 𝑤 is positive in the upward direction (positive 𝑧 direction). Induced velocity 𝑤 can be defined as (𝑑𝑤)γ = −|𝑑𝑉| and sin 𝜃 = (𝑥 − 𝜉)/𝑟 now |𝑑𝑉| equation can be written as:

𝛾 4𝜋

(𝑥−𝜉)𝑑𝜉𝑑𝜂 𝑟3

(24) (𝑑𝑤)γ = −

Considering contribution of elemental chordwise vortex of strength 𝛿 𝑑𝜂 to induced velocity at point P then

𝛿 4𝜋

(𝑥−𝜂)𝑑𝜉𝑑𝜂 𝑟3

(25) (𝑑𝑤)δ = −

Note that 𝑟 = √(𝑥 − 𝜉)2 + (𝑦 − 𝜂)2

(𝑥−𝜉)𝛾(𝜉,𝜂)+(𝑦−𝜂)𝛿(𝜉,𝜂)

(𝑦−𝜂)𝛿𝑤(𝜉,𝜂)

Both equations must be integrated over the wing planform (designated point S) to obtain the velocity induced at point P by the entire lifting surface. Note that velocity at point P by the complete wake is given by equation (24) but with 𝛿𝑤 instead of 𝛿 and integrated over the wake, region W in Figure 115. Note that normal velocity induced at point P by both lifting surface and wake is:

1 4𝜋

[(𝑥−𝜉)2+(𝑦−𝜂)2]3/2 𝑑𝜉𝑑𝜂

1 4𝜋

[(𝑥−𝜉)2+(𝑦−𝜂)2]3/2 𝑑𝜉𝑑𝜂

𝑤(𝑥, 𝑦) = − − (26) ∬ 𝑠 ∬ 𝑤

The problem of lifting-surface theory is to solve equation 26 for both 𝛾(𝜉, 𝜂) and 𝛿(𝜉, 𝜂) such that the sum of 𝑤(𝑥, 𝑦) and the normal component of the freestream is zero. So that the flow is tangent to planform surface S.

Now for the vortex lattice method, the wing is represented by a surface with many horseshoe vortices superimposed onto it, where the horseshoe vortices have different strengths. The velocities induced by all the horseshoe vortices at control point is calculated by the Biot-Savart law [33, 89].

Performing a summation for all the control points on the wing leads to a set of linear algebraic equations for the horseshoe vortices strengths that satisfy the no flow boundary condition of the wing [89]. The strength of the horseshoe vortices is related to the wing circulation and pressure differential between the upper and lower surfaces of the wing [33]. Integrating the pressure differentials yield the total forces and moments on the wing[33].

165

Figure 116 Single horseshoe to a system of horseshoe vortices (Vortex lattice) on a finite wing [33].

In the theoretical analysis, the vortex lattice panels are located on the mean camber surface of the wing and trailing vortices follow a curved path once they leave the wing. In general, using linear straight-line trailing vortices extending downstream to infinity yields acceptable accuracy. For a linear approach, trailing vortices are either aligned parallel to the free stream or parallel to the vehicle axis, both orientations provide similar accuracy within assumptions of linearized theory.

In general, the trailing vortices are aligned to be parallel to the vehicle axis, because the orientation’s influence coefficients of other vortices are simpler to solve. It should be noted that geometric coefficients do not change as angle of attack is changed.

Examining Figure 116, where the panel of size 𝑙 (in the length of the flow direction), note that the panels in this method are trapezoidal. A horseshoe vortex (𝑎𝑏𝑐𝑑) of strength Γ𝑛 is placed so that the leading edge or the bound vortex of the horseshoe (𝑏𝑐) is 𝑙/4 from the front of the panel (25% from

3 4

the front of the panel) [33, 89]. A control point is placed at 𝑙 from the front of the panel (75% from

the front of the panel) and on the centerline, the derivation of this location is shown in “aerodynamics for engineers” work [89].

Velocity induced by general horseshoe vortex

There are now many horseshoe vortices covering the entire wing such as 𝑎𝑏𝑐𝑑, 𝑎𝑒𝑓𝑑, 𝑎𝑔ℎ𝑑, 𝑎𝑖𝑗𝑑 and etc. Remember each horseshoe vortex has it’s a different strength of Γ𝑛, hence why a summation of all the horseshoe vortices must be conducted.

The induced velocity by a vortex filament of strength Γ𝑛 and length of 𝑑𝑙 is given by the Biot-Savart law [89]:

Γ𝑛(𝑑𝑙⃗⃗⃗⃗ X 𝑟 ) 4𝜋𝑟3

𝑑𝑉⃗⃗⃗⃗⃗ = (27)

From Figure 117, the magnitude of the induced velocity is:

Γ𝑛 sin 𝜃𝑑𝑙 4𝜋𝑟2

𝑑𝑉⃗⃗⃗⃗⃗ = (28)

166

Figure 117 Nomenclature for calculating induced velocity by a finite length vortex segment [89].

The flow field induced by the horseshoe vortex of three straight segments, using equation 27 to calculate the effect of each segment. Where 𝐴𝐵 (Figure 117) be the segment where the vorticity vector is directed from point A to point B. And point C be where the normal distance from the line 𝐴𝐵 is 𝑟𝑝. Integrating between point A and point B, calculates the magnitude of the induced velocity:

𝜃2 ∫ sin 𝜃 𝑑𝜃 𝜃1

Γ𝑛 4𝜋𝑟𝑝

𝑉 = = (29) (cos 𝜃1 − cos 𝜃2)

Considering that the vortex filament extends to infinity in both directions then 𝜃1 = 0 and 𝜃2 = 𝜋

Γ𝑛 4𝜋𝑟𝑝

𝑉 = (30)

(Remember, this is for infinite span airfoils). For ease of reading let 𝑟0⃗⃗⃗ , 𝑟1⃗⃗⃗ , 𝑟2⃗⃗⃗ designate the vectors 𝐴𝐵⃗⃗⃗⃗⃗ , 𝐴𝐶⃗⃗⃗⃗⃗ , 𝐵𝐶⃗⃗⃗⃗⃗ , respectively this is illustrated in Figure 117, hence

𝑟𝑝 = cos 𝜃1 = cos 𝜃2 = |𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ | 𝑟0 𝑟0⃗⃗⃗ ∙ 𝑟1⃗⃗⃗ 𝑟0𝑟1 𝑟0⃗⃗⃗ ∙ 𝑟2⃗⃗⃗ 𝑟0𝑟2

Note: 𝑟0⃗⃗⃗ is vector, 𝑟0 is the magnitude of vector 𝑟0⃗⃗⃗ , |𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ | is the magnitude of the vector cross product. The direction of induced velocity is given by unit vector

𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ |𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ |

Results in

Γ𝑛 4𝜋

𝑟1⃗⃗⃗⃗ x 𝑟2⃗⃗⃗⃗ |𝑟1⃗⃗⃗⃗ x 𝑟2⃗⃗⃗⃗ |2 [𝑟0⃗⃗⃗ ∙ (

𝑟1⃗⃗⃗⃗ 𝑟1

𝑟2⃗⃗⃗⃗ 𝑟2

𝑉⃗ = − )] (31)

167

This equation is for the calculation of the induced velocity by the horseshoe vortices in VLM [89]. This equation can be used for either vortex orientations. Using equation 31 to calculate the velocity that is induced at a general location (𝑥, 𝑦, 𝑧) by the horseshoe vortex, illustrated in Figure 118.

Figure 118 A typical horseshoe vortex [89].

Segment 𝐴𝐵 represents the bound vortex portion of the horseshoe system and is located on the ¼ chord line of the panel. The trailing vortices are parallel to the 𝑥-axis. The resultant induced velocity vector is calculated by considering the influence of each of the elements.

For the bound vortex, segment 𝐴𝐵⃗⃗⃗⃗⃗

(32) 𝑟0⃗⃗⃗ = 𝐴𝐵⃗⃗⃗⃗⃗ = (𝑥2𝑛 − 𝑥1𝑛)𝑖̂ + (𝑦2𝑛 − 𝑦1𝑛)𝑗̂ + (𝑧2𝑛 − 𝑧1𝑛)𝑘̂

(33) 𝑟1⃗⃗⃗ = (𝑥 − 𝑥1𝑛)𝑖̂ + (𝑦 − 𝑦1𝑛)𝑗̂ + (𝑧 − 𝑧1𝑛)𝑘̂

(34) 𝑟2⃗⃗⃗ = (𝑥 − 𝑥2𝑛)𝑖̂ + (𝑦 − 𝑦2𝑛)𝑗̂ + (𝑧 − 𝑧2𝑛)𝑘̂

168

Figure 119 Vector elements for the calculation of induced velocities [89].

Using equation 31 to calculate the velocity induced at some point 𝐶 (x, y, z) by the vortex filament 𝐴𝐵 (shown in Figure 118 and Figure 119) then,

Γ𝑛 4𝜋

(35) 𝑉𝐴𝐵⃗⃗⃗⃗⃗⃗ = {F𝑎𝑐1𝐴𝐵}{F𝑎𝑐2𝐴𝐵}

Where,

{F𝑎𝑐1𝐴𝐵} = 𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ |𝑟1⃗⃗⃗ x 𝑟2⃗⃗⃗ |2

{F𝑎𝑐1𝐴𝐵} = {[(𝑦 − 𝑦1𝑛)(𝑧 − 𝑧2𝑛) − (𝑦 − 𝑦2𝑛)(𝑧 − 𝑧1𝑛)]𝑖̂

− [(𝑥 − 𝑥1𝑛)(𝑧 − 𝑧2𝑛) − (𝑥 − 𝑥2𝑛)(𝑧 − 𝑧1𝑛)]𝑗̂ + [(𝑥 − 𝑥1𝑛)(𝑦 − 𝑦2𝑛) − (𝑥 − 𝑥2𝑛)(𝑦 − 𝑦1𝑛)]𝑘̂} / {[(𝑦 − 𝑦1𝑛)(𝑧 − 𝑧2𝑛) − (𝑦 − 𝑦2𝑛)(𝑧 − 𝑧1𝑛)]2 + [(𝑥 − 𝑥1𝑛)(𝑧 − 𝑧2𝑛) − (𝑥 − 𝑥2𝑛)(𝑧 − 𝑧1𝑛)]2 + [(𝑥 − 𝑥1𝑛)(𝑦 − 𝑦2𝑛) − (𝑥 − 𝑥2𝑛)(𝑦 − 𝑦1𝑛)]2}

And

) {F𝑎𝑐2𝐴𝐵} = (𝑟0⃗⃗⃗ ∙ − 𝑟0⃗⃗⃗ ∙ 𝑟1⃗⃗⃗ 𝑟1 𝑟2⃗⃗⃗ 𝑟2

{F𝑎𝑐2𝐴𝐵} = { [(𝑥2𝑛 − 𝑥1𝑛)(𝑥 − 𝑥1𝑛) + (𝑦2𝑛 − 𝑦1𝑛)(𝑦 − 𝑦1𝑛) + (𝑧2𝑛 − 𝑧1𝑛)(𝑧 − 𝑧1𝑛)] √(𝑥 − 𝑥1𝑛)2 + (𝑦 − 𝑦1𝑛)2 + (𝑧 − 𝑧1𝑛)2

− } [(𝑥2𝑛 − 𝑥1𝑛)(𝑥 − 𝑥2𝑛) + (𝑦2𝑛 − 𝑦1𝑛)(𝑦 − 𝑦2𝑛) + (𝑧2𝑛 − 𝑧1𝑛)(𝑧 − 𝑧2𝑛)] √(𝑥 − 𝑥2𝑛)2 + (𝑦 − 𝑦2𝑛)2 + (𝑧 − 𝑧2𝑛)2

To calculate the velocity induced by the filament that extends from point 𝐴 to infinity, first the velocity induced by the collinear, finite-length filament that extends from point 𝐴 to point 𝐷 (seen in Figure 119) needs to be determined. Since 𝑟0⃗⃗⃗ is in the direction of the vorticity vector,

(36) 𝑟0⃗⃗⃗ = 𝐷𝐴⃗⃗⃗⃗⃗ = (𝑥1𝑛 − 𝑥3𝑛)𝑖̂

169

(37) 𝑟1⃗⃗⃗ = (𝑥 − 𝑥3𝑛)𝑖̂ + (𝑦 − 𝑦1𝑛)𝑗̂ + (𝑧 − 𝑧1𝑛)𝑘̂

(38) 𝑟2⃗⃗⃗ = (𝑥 − 𝑥1𝑛)𝑖̂ + (𝑦 − 𝑦1𝑛)𝑗̂ + (𝑧 − 𝑧1𝑛)𝑘̂

From Figure 119, the induced velocity is

Γ𝑛 4𝜋

(39) 𝑉𝐴𝐷⃗⃗⃗⃗⃗⃗ = {F𝑎𝑐1𝐴𝐷}{F𝑎𝑐2𝐴𝐷}

Where,

{F𝑎𝑐1𝐴𝐷} = (𝑧 − 𝑧1𝑛)𝑗̂ + (𝑦1𝑛 − 𝑦)𝑘̂ [(𝑧 − 𝑧1𝑛)2 + (𝑦 − 𝑦1𝑛)2](𝑥3𝑛 − 𝑥1𝑛)

And

{F𝑎𝑐2𝐴𝐷} = (𝑥3𝑛

− 𝑥1𝑛) { 𝑥3𝑛 − 𝑥 √(𝑥 − 𝑥3𝑛)2 + (𝑦 − 𝑦1𝑛)2 + (𝑧 − 𝑧1𝑛)2

+ } 𝑥 − 𝑥1𝑛 √(𝑥 − 𝑥1𝑛)2 + (𝑦 − 𝑦1𝑛)2 + (𝑧 − 𝑧1𝑛)2

Setting 𝑥3 go to infinity, the first term of {F𝑎𝑐2𝐴𝐷} goes to 1.0. Therefore, velocity induced by the vortex filament which extends from point 𝐴 to inifinity in the positive direction that is parallel to the 𝑥-axis is given by:

Γ𝑛 4𝜋

(𝑧−𝑧1𝑛)𝑗̂+(𝑦1𝑛−𝑦)𝑘̂ { [(𝑧−𝑧1𝑛)2+(𝑦1𝑛−𝑦)2]

𝑥−𝑥1𝑛 √(𝑥−𝑥1𝑛)2+(𝑦−𝑦1𝑛)2+(𝑧−𝑧1𝑛)2]

} [1.0 + (40) 𝑉𝐴∞⃗⃗⃗⃗⃗⃗⃗ =

Velocity induced by vortex filament that extends from point 𝐵 to infinity in positive direction that is parallel to the 𝑥 axis given by:

Γ𝑛 4𝜋

(𝑧−𝑧2𝑛)𝑗̂+(𝑦2𝑛−𝑦)𝑘̂ { [(𝑧−𝑧2𝑛)2+(𝑦2𝑛−𝑦)2]

𝑥−𝑥2𝑛 √(𝑥−𝑥2𝑛)2+(𝑦−𝑦2𝑛)2+(𝑧−𝑧2𝑛)2]

} [1.0 + (41) 𝑉𝐵∞⃗⃗⃗⃗⃗⃗⃗⃗ = −

Total velocity induced at some point (𝑥, 𝑦, 𝑧) by horseshoe vortex representing one of the surface elements is the sum of components in equation 39,40,41. Let point (𝑥,𝑦,𝑧) be the control point of the 𝑚th panel, which is designated by coordinates (𝑥𝑚, 𝑦𝑚, 𝑧𝑚). The velocity induced at the 𝑚th control point by the vortex representing the 𝑛th panel is designated by 𝑉𝑚,𝑛⃗⃗⃗⃗⃗⃗⃗⃗ . Implementing this into 39,40,41.

(42) 𝑉𝑚,𝑛⃗⃗⃗⃗⃗⃗⃗⃗ = 𝐶𝑚,𝑛 ⃗⃗⃗⃗⃗⃗⃗⃗ Γ𝑛

⃗⃗⃗⃗⃗⃗⃗⃗ is dependent on the geometry of the 𝑛th horseshoe vortex and Where the influence coefficient 𝐶𝑚,𝑛 the distance from the control point of 𝑚th panel. Because the governing equation is linear, velocities induced by 2𝑁 vortices are added together for the total induced velocity at 𝑚rh control points:

2𝑁 𝑛=1

(43) 𝑉𝑚,𝑛⃗⃗⃗⃗⃗⃗⃗⃗ = ∑ ⃗⃗⃗⃗⃗⃗⃗⃗ Γ𝑛 𝐶𝑚,𝑛

Application of boundary conditions

We Have 2𝑁 of these equations, one for each of the control points.

170

It is possible to determine the resultant induced velocity at any point in space if the strengths of the 2𝑁 horseshoe vortices are known. Using The boundary condition of a streamline surface, the strength of the vortices Γ𝑛 can be determined, where Γ𝑛 represents the lifting flow field of the wing. The boundary condition of a streamline surface, where resultant flow is tangent to the wing for each control point, where the control point lies ¾ chord and on the centerline of each panel. If the trailing vortices are parallel to the vehicle axis [i.e., the x axis for equation 39,40,41 is the vehicle axis] then the induced velocity components can be evaluated.

Figure 120 Nomenclature for tangency condition: (a) normal to element of mean camber surface, (b) section AA, (c) section BB [89]

From Figure 120 the tangency requirement yields the relation,

(44) −𝑢𝑚 sin 𝛿 cos 𝜙 − 𝜐𝑚 cos 𝛿 sin 𝜙 + 𝑤𝑚 cos 𝜙 cos δ + 𝑈∞ sin(𝛼 − 𝛿) cos 𝜙 = 0

Figure 121 Dihedral angle [89].

Where 𝜙 is the dihedral angle (shown in Figure 121) and 𝛿 is slope of mean camber line at the control point hence,

𝑑𝑧 𝑑𝑥

𝛿 = tan−1 ( (45) ) 𝑚

171

For wings where the slope of the mean camber line is small and at small angles of attack equation 44 can be simplified to,

𝑑𝑧 𝑑𝑥

(46) ] = 0 𝑤𝑚 − 𝜐𝑚 tan 𝜙 + 𝑈∞ [𝛼 − ( ) 𝑚

Noting that the approximation is consistent with the assumptions of linearized theory. The circulation strengths Γ𝑛 are required to satisfy the tangent flow boundary conditions, by solving the simultaneous equations represented by equation 43.

Relations for a planar wing

For a planar wing, 𝑧1𝑛 = 𝑧2𝑛 = 0 for all bound vortices and 𝑧𝑚 = 0 for all control points hence

Γ𝑛 4𝜋

𝑘̂ (𝑥𝑚−𝑥1𝑛)(𝑦𝑚−𝑦2𝑛)+(𝑥𝑚−𝑥2𝑛)(𝑦𝑚−𝑦1𝑛)

(𝑥2𝑛−𝑥1𝑛)(𝑥𝑚−𝑥2𝑛)+(𝑦2𝑛−𝑦1𝑛)(𝑦𝑚−𝑦1𝑛) √(𝑥𝑚−𝑥1𝑛)2+(𝑦𝑚−𝑦1𝑛)2

− [ 𝑉𝐴𝐵⃗⃗⃗⃗⃗⃗ =

(𝑥2𝑛−𝑥1𝑛)(𝑥𝑚−𝑥2𝑛)+(𝑦2𝑛−𝑦1𝑛)(𝑦𝑚−𝑦2𝑛) √(𝑥𝑚−𝑥2𝑛)2+(𝑦𝑚−𝑦2𝑛)2

] (47)

Γ𝑛 4𝜋

𝑘̂ 𝑦1𝑛−𝑦𝑚

𝑥𝑚−𝑥1𝑛 √(𝑥𝑚−𝑥1𝑛)2+(𝑦𝑚−𝑦1𝑛)2]

[1 + (48) 𝑉𝐴∞⃗⃗⃗⃗⃗⃗⃗ =

Γ𝑛 4𝜋

𝑘̂ 𝑦2𝑛−𝑦𝑚

𝑥𝑚−𝑥2𝑛 √(𝑥𝑚−𝑥2𝑛)2+(𝑦𝑚−𝑦2𝑛)2]

[1 + (49) 𝑉𝐵∞⃗⃗⃗⃗⃗⃗⃗⃗ = −

For planar wings, the three components of the vortex representing 𝑛th panel induce a velocity at the control point of the 𝑚th panel in the 𝑧 direction, i.e. downwash. Combining the three components,

Γ𝑛 4𝜋

1 (𝑥𝑚−𝑥1𝑛)(𝑦𝑚−𝑦2𝑛)−(𝑥𝑚−𝑥2𝑛)(𝑦𝑚−𝑦1𝑛)

(𝑥2𝑛−𝑥1𝑛)(𝑥𝑚−𝑥1𝑛)+(𝑦2𝑛−𝑦1𝑛)(𝑦𝑚−𝑦1𝑛) √(𝑥𝑚−𝑥1𝑛)2+(𝑦𝑚−𝑦1𝑛)2

[ − { 𝑤𝑚,𝑛 =

1 𝑦1𝑛−𝑦𝑚

1 𝑦2𝑛−𝑦𝑚

(𝑥2𝑛−𝑥1𝑛)(𝑥𝑚−𝑥2𝑛)+(𝑦2𝑛−𝑦1𝑛)(𝑦𝑚−𝑦2𝑛) √(𝑥𝑚−𝑥2𝑛)2+(𝑦𝑚−𝑦2𝑛)2

(𝑥𝑚−𝑥1𝑛) √(𝑥𝑚−𝑥1𝑛)2+(𝑦𝑚−𝑦1𝑛)2] −

(𝑥𝑚−𝑥2𝑛)

+ [1 + [1 +

√(𝑥𝑚−𝑥2𝑛)2+(𝑦𝑚−𝑦2𝑛)2]]}

(50)

Summing the contributions of all the vortices to the downwash at the control point of the 𝑚th panel,

2𝑁 𝑛=1

(51) 𝑤𝑚 = ∑ 𝑤𝑚,𝑛

Applying the tangency condition defined by equations 44 and 46, because a planar wing is used then (𝑑𝑧 𝑑𝑥⁄ )𝑚 = 0 at all locations and 𝜙 = 0. Since the 𝑈∞ sin 𝛼 is the component of the freestream velocity that is perpendicular to the wing at any point on the wing. Hence resultant flow is tangent to the wing if the total vortex-induced downwash at the control point of 𝑚th panel, which is determined using equation 51, balances the normal component of the freestream velocity

(52) 𝑤𝑚 + 𝑈∞ sin 𝛼 = 0

For small angles of attack,

𝑤𝑚 = −𝑈∞

172

Once the strength of the horseshoe vortices is determined by fulfilling the boundary condition that flow is tangent to the surface at each of the control points, the lift of the wing can be determined [89]. For wings with no dihedral, lift is generated by the freestream velocity crossing the spanwise vortex filaments, since there are no sidewash or backwash velocities. Since panels extend from the leading edge to the trailing edge then the lift (per unit span) acting on the 𝑛th panel is,

(53) 𝑙𝑛 = 𝜌∞𝑈∞Γ𝑛

Since flow is symmetric then total lift of the wing is,

0.5𝑏 𝐿 = 2 ∫ 0

(54) 𝜌∞𝑈∞Γ(𝑦) 𝑑𝑦

(in terms of finite element panels)

4 𝐿 = 2𝜌∞𝑈∞ ∑ 𝑛=1

(55) Γ𝑛Δ𝑦𝑛

The section lift coefficient for the 𝑛th panel is

2Γ 𝑈∞𝑐𝑎𝑣

𝑙𝑛 𝜌∞𝑈∞

2𝑐𝑎𝑣

1 2

= (56) 𝐶𝑙(𝑛𝑡ℎ) =

The values of Γ for those bound vortex filaments at the spanwise location (chordwise strip) of interest, for a chordwise row,

𝐽𝑚𝑎𝑥 𝑗=1

𝐶𝑙𝑐 𝑐𝑎𝑣

𝑙 ( 𝑞∞𝑐𝑎𝑣

= ∑ (57) ) 𝑗

Where 𝑐𝑎𝑣 is average chord and is equal to 𝑆/𝑏, 𝑐 is local chord, and 𝑗 is the index for an elemental panel in the chordwise row. By integrating the lift over the span, the total lift coefficient is determined.

1 𝐶𝐿 = ∫ 0

2𝑦 𝑏

𝐶𝑙𝑐 𝑐𝑎𝑣

𝑑 ( ) (58)

Once section lift coefficient for the chordwise strip of the wing, the induced drag coefficient may be calculated with,

+0.5𝑏 ∫ −0.5𝑏

1 𝑆

(59) 𝐶𝐷𝑣 = 𝐶𝑙𝑐𝛼𝑖𝑑𝑦

Where 𝛼𝑖, which induced incidence,

+0.5𝑏 ∫ −0.5𝑏

1 8𝜋

𝐶𝑙𝑐 (𝑦−𝜂)2

𝑑 (60) 𝛼𝑖 = −

For symmetrical loading then 𝛼𝑖 becomes,

0.5𝑏 ∫ 0.5𝑏

1 8𝜋

𝐶𝑙𝑐 (𝑦−𝜂)2 +

𝐶𝑙𝑐 (𝑦+𝜂)2]

[ (61) 𝑑 𝛼𝑖 = −

Approximating the spanwise lift distribution across the strip by a parabolic function, at the 𝑚th chordwise strip with semi-width 𝑒𝑚 and centerline at 𝜂 = 𝑦𝑚,

𝐶𝑙𝑐 ) ( 𝐶𝐿𝑐̅ 𝑚

= 𝑎𝑚𝜂2 + 𝑏𝑚𝜂 + 𝑐𝑚

173

Solving for 𝑎𝑚, 𝑏𝑚 and 𝑐𝑚,

𝑦𝑚+1 = 𝑦𝑚 + (𝑒𝑚 + 𝑒𝑚+1)

𝑦𝑚−1 = 𝑦𝑚 − (𝑒𝑚 + 𝑒𝑚−1)

Hence

𝐶𝑙𝑐 ) 𝐶𝐿𝑐̅ 𝑚

(62) 𝑐𝑚 = ( − 𝑎𝑚𝜂2 − 𝑏𝑚𝜂

𝑚

) } 𝑎𝑚 = {𝑑𝑚𝑖 ( − (𝑑𝑚𝑖 + 𝑑𝑚𝑜) ( + 𝑑𝑚𝑜 ( 1 𝑑𝑚𝑖𝑑𝑚𝑜(𝑑𝑚𝑖 + 𝑑𝑚𝑜) 𝐶𝑙𝑐 𝐶𝐿𝑐̅ 𝐶𝑙𝑐 𝐶𝐿𝑐̅ 𝐶𝑙𝑐 𝐶𝐿𝑐̅ ) 𝑚+1 ) 𝑚−1

− ( ] 𝑏𝑚 = {𝑑𝑚0(2𝜂𝑚 − 𝑑𝑚𝑜) [( 1 𝑑𝑚𝑖𝑑𝑚𝑜(𝑑𝑚𝑖 + 𝑑𝑚𝑜) 𝐶𝑙𝑐 𝐶𝐿𝑐̅ 𝐶𝑙𝑐 𝐶𝐿𝑐̅ ) 𝑚 ) 𝑚−1

− ( ]} − 𝑑𝑚𝑖(2𝜂𝑚 − 𝑑𝑚𝑖) [( 𝐶𝑙𝑐 𝐶𝐿𝑐̅ 𝐶𝑙𝑐 𝐶𝐿𝑐̅ ) 𝑚+1 ) 𝑚

Where

𝑑𝑚𝑖 = 𝑒𝑚 + 𝑒𝑚−1

𝑑𝑚𝑜 = 𝑒𝑚 + 𝑒𝑚+1

For symmetrical load distribution

𝑚

( = ( ) 𝐶𝑙𝑐 𝐶𝐿𝑐̅ 𝐶𝑙𝑐 𝐶𝐿𝑐̅ ) 𝑚−1

𝑒𝑚−1 = 𝑒𝑚

At the root,

𝑚+1

( ) = 0 𝐶𝑙𝑐 𝐶𝐿𝑐̅

𝑒𝑚+1 = 0

At the tip, the numerical form for the induced incidence

𝑁 𝑚=1

1 4𝜋

𝛼𝑖(𝑦) 𝐶𝐿𝑐

𝑦2(𝑦𝑚−𝑒𝑚)𝑎𝑚+𝑦2𝑏𝑚+(𝑦𝑚−𝑒𝑚)𝑐𝑚 𝑦2−(𝑦𝑚−𝑒𝑚)2

𝑦2(𝑦𝑚+𝑒𝑚)𝑎𝑚+𝑦2𝑏𝑚+(𝑦𝑚+𝑒𝑚)𝑐𝑚 𝑦2−(𝑦𝑚+𝑒𝑚)2 2

∑ = − − + {

1 2

1 4

(𝑦−𝑒𝑚)2−𝑦𝑚 (𝑦+𝑒𝑚)2−𝑦𝑚

𝑦2−(𝑦𝑚+𝑒𝑚)2 𝑦2−(𝑦𝑚−𝑒𝑚)2]

+ 63) 𝑦𝑎𝑚 log [ 𝑏𝑚 log [ + 2𝑒𝑚𝑎𝑚} (

Assuming that the product 𝐶𝑙𝑐𝛼𝑖 has a parabolic variation across the strip,

𝐶𝑙𝑐 𝐶𝐿𝑐̅

𝛼𝑖 𝐶𝐿𝑐̅

𝑛

) ( [( )] (64) = 𝑎𝑛𝑦2 + 𝑏𝑛𝑦 + 𝑐𝑛

Coefficients of 𝑎𝑛, 𝑏𝑛 and 𝑐𝑛 are determined using the same approach as determining 𝑎𝑚, 𝑏𝑚 and 𝑐𝑚. The numerical form of the induced drag coefficient, is then a generalization of Simpson’s rule:

174

2 =

2] 𝑎𝑛 + 𝑦𝑛𝑏𝑛 + 𝑐𝑛}

𝑁 𝑛=1

4 𝐴𝑅

1 2 + ( 3

𝐶𝐷𝑣 𝐶𝐿

∑ (65) 𝑒𝑛 {[𝑦𝑛 ) 𝑒𝑛

175