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Gull wing morphing allows active control of trade-offs in efficiency, maneuverability and stability Harvey, Christina 2018

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Gull wing morphing allows active control oftrade-offs in efficiency, maneuverability and stabilitybyChristina HarveyB.Eng., McGill University, May 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Zoology)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2018c© Christina Harvey, 2018ABSTRACTBirds flying in turbulent conditions demonstrate impressive flight stability and control. Thisversatility is hypothesized to derive from dynamic wing shape changes, an ability termed wingmorphing. Bird wings can morph passively through inertial or aerodynamic loading of flexiblecomponents or actively when birds stimulate their network of intrinsic wing muscles. Themajority of active wing morphing is actuated through the wrist or elbow joints. Wrist flexionimproves high-speed and turning performance, but little is known about the morphology oraerodynamic consequences of morphing the elbow joint. Here we show that gulls gliding inunsteady environments reduce their passive stability by actively reducing their elbow angle.We first photographed gulls in gliding flight to quantify their wing shapes. We next usedcadavers to determine the viable range of elbow angles and isolate the subset that was usedby gliding gulls. The behavioral observations and cadaver manipulations revealed an in vivogliding elbow angle range of 90◦-154◦ and that there is a significant reduction of the elbowangle used by gulls as local wind speeds and gusts increase. Next, wings were prepared anddried across the full range of elbow angles and tested in a wind tunnel at varied turbulenceintensities. These force measurements revealed that the lower elbow angles used by glidinggulls had improved aerodynamic efficiency but reduced passive pitch stability. Moreover, wefound that the in vivo elbow range captures the majority of the available aerodynamic variation.Collectively, our results indicate a coupling in efficiency and stability in avian gliding and thatwing morphing allows gulls to modulate aerodynamic trade-offs which may allow for a steadierflight path in an unsteady environment.iiLAY SUMMARYBirds flying in turbulent conditions demonstrate impressive versatility, hypothesized to de-rive from active wing shape changes. Photographs of gliding gulls demonstrated a range ofwing shapes and additional measurements with gull cadavers revealed that gulls use lower el-bow angles as wind speed and gust increase. To determine the functional consequences ofthis behavior, we prepared and tested gull wings in a variable-turbulence wind tunnel. Overthe observed range of wing shapes, elbow extension reduced aerodynamic efficiency but im-proved passive pitch stability. Moreover, the in vivo range captures the majority of the availableaerodynamic variation. Our results indicate a coupling of efficiency and stability in avian glid-ing, and that wing morphing allows active control of aerodynamic trade-offs in response to anunsteady environment.iiiPREFACEAll of the preliminary and functional anatomy work presented was conducted in the Alt-shuler laboratory in the Department of Zoology at the University of British Columbia, Vancou-ver campus. All wind tunnel experiments were conducted at the University of Toronto Institutefor Aerospace Studies. The observational experiments were conducted at various locations onthe Pacific coast.The research chapter (Chapter 2) is original and unpublished. A version of the chapter hasbeen prepared for submission as a joint manuscript between V.B. Baliga, P. Lavoie, D.L. Alt-shuler and myself. I was the lead investigator, responsible for concept formation, experimentaldesign, data collection and analysis, and manuscript composition. V.B. Baliga was involved inthe observational/functional anatomy concept formation, data collection and analysis portionof the work as well as manuscript composition. P. Lavoie was involved with wind tunnel ex-perimental set up, analysis and manuscript composition. D.L. Altshuler was the supervisoryauthor and was involved throughout all phases of the project including experiments, analysisand writing.This research was funded by the US Air Force Office of Scientific Research (under grantnumber FA9550-16-1-0182, titled Avian-Inspired Multifunctional Morphing Vehicles moni-tored by Dr. B.L. Lee), the Werner and Hildegard Hesse Research Award in Ornithology andNSERC (CGS-M).ivTABLE OF CONTENTSAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The bio-inspired origins of human flight . . . . . . . . . . . . . . . . . . . . . 11.2 Birds still do some things better . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Wing morphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Gliding aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.1 Aerodynamic performance . . . . . . . . . . . . . . . . . . . . . . . . 71.4.2 Aerodynamic stability . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Aerodynamic consequences of wing morphing . . . . . . . . . . . . . . . . . . 13v2 Gull Wing Morphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Determining the in vivo wing morphology . . . . . . . . . . . . . . . . . . . . 162.3.1 Observational study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.2 Cadaver wing morphology study . . . . . . . . . . . . . . . . . . . . . 172.3.3 Prediction of the in vivo wing morphology . . . . . . . . . . . . . . . . 182.3.4 Sensitivity and prediction error analysis . . . . . . . . . . . . . . . . . 202.4 Aerodynamic Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.1 Wind tunnel specimen preparation . . . . . . . . . . . . . . . . . . . . 252.4.2 Wind tunnel experimental set up . . . . . . . . . . . . . . . . . . . . . 272.4.3 Aerodynamic efficiency results . . . . . . . . . . . . . . . . . . . . . . 312.4.4 Longitudinal static stability results . . . . . . . . . . . . . . . . . . . . 332.4.5 Uncertainty, error and statistical analysis . . . . . . . . . . . . . . . . . 342.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1 Pure science to applied science and back again . . . . . . . . . . . . . . . . . . 463.1.1 Multi-functional materials and structural design . . . . . . . . . . . . . 463.1.2 Integrated system design, actuation and control . . . . . . . . . . . . . 473.1.3 Accurate implementation of fundamental knowledge . . . . . . . . . . 483.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50viLIST OF TABLES2.1 Model selection and sensitivity results . . . . . . . . . . . . . . . . . . . . . . 232.2 AIC Model selection for aerodynamic parameters . . . . . . . . . . . . . . . . 372.3 ANOVA analysis of full vs reduced model . . . . . . . . . . . . . . . . . . . . 38viiLIST OF FIGURES1.1 Birds morph their wing configuration in flight . . . . . . . . . . . . . . . . . . 41.2 Free body diagram of a gliding bird . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Free body diagram of an equilibrium glide . . . . . . . . . . . . . . . . . . . . 81.4 The effects of induced drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Longitudinal static stability condition . . . . . . . . . . . . . . . . . . . . . . . 112.1 Freely gliding gull with five peripheral tracked points . . . . . . . . . . . . . . 162.2 Cadaver wing ventral view through flexion and extension . . . . . . . . . . . . 182.3 Prediction of in vivo joint angles from cadaver morphospace . . . . . . . . . . 192.4 Elbow angle relationship with wind speed and gust . . . . . . . . . . . . . . . 202.5 Sensitivity analysis of predictor model . . . . . . . . . . . . . . . . . . . . . . 222.6 Prediction error and sensitivity analysis of photographs . . . . . . . . . . . . . 242.7 Spanwise camber as a function of elbow angle . . . . . . . . . . . . . . . . . . 252.8 Morphometric parameters of wind tunnel wings . . . . . . . . . . . . . . . . . 272.9 Prepared wing specimen mounted in the wind tunnel . . . . . . . . . . . . . . 282.10 Power spectral density analysis of the turbulence intensity . . . . . . . . . . . . 302.11 Lift-drag polar for all tested wings across varied turbulence intensities . . . . . 322.12 Aerodynamic performance metrics . . . . . . . . . . . . . . . . . . . . . . . . 322.13 Relationship between pitching moment and lift . . . . . . . . . . . . . . . . . 342.14 Aerodynamic longitudinal static stability metrics . . . . . . . . . . . . . . . . 342.15 Investigation of induced drag over the wing root . . . . . . . . . . . . . . . . . 362.16 Summary of morphometrics, performance, stability, and behaviour . . . . . . . 402.17 Aerodynamic efficiency by aspect ratio of varied flyers . . . . . . . . . . . . . 42viiiLIST OF SYMBOLSSymbol Definition Unitsa Speed of sound m/sb Wing span (wing tip to wing tip) mc Chord (characteristic length) me Span efficiency factorAR Aspect ratioCM Pitch coefficientCD Drag coefficientCL Lift coefficientD Drag NGuu One-sided power spectral density m2 · s−1L Lift NRe Reynolds numberS Wing area m2U∞ Freestream velocity m · s−1W Weight Nα Angle of attack ◦θ Glide angle ◦µ Dynamic viscosity kg ·m−1 · s−1ρ Fluid density kg ·m−3ω Frequency s−1ixGLOSSARYAerodynamic efficiency Maximum ratio of lift to dragInduced drag Drag due to finite nature of the wingsLateral mode Concerning the coupled roll and yaw axesLongitudinal mode Concering the pitch axisMach Number Non-dimensional measure of velocity (U∞a)Morphing Gradual transformation from one shape to anotherPitch stability derivative The change of pitching moment with a change in liftPlanform 2D surface of the wing when viewed from aboveReynolds Number Non-dimensional measure of inertial to viscous forces(ρ · U∞ · c · µ−1)Spanwise camber Curvature along the span of the wingStability - dynamic The time dependant characteristic of a body to damp os-cillations and return to its equilibrium after an initial dis-turbanceStability - static The time invariant development of forces and momentsthat tend to restore an objects’ equilibrium after an initialdisturbanceTrim point Position where all moments about the center of gravityare balancedTurbulence intensity Fluctuation of the freestream velocity about the mean ve-locity (%)Zero-lift pitching moment Pitching moment when no lift is producedAIC Akaike Information CriterionAR Aspect Ratio ( b2S)RMS Root Mean SquareUAV Umanned Aerial VehicleTI Turbulence IntensityxACKNOWLEDGEMENTSI must begin by thanking my advisor, Douglas Altshuler, for taking a chance on an engi-neer with a more-than-limited knowledge of biological systems. He was patient, supportiveand instilled a passion for a multi-disciplinary approach. I have also greatly benefited from thediverse knowledge of my colleagues who have continuously inspired me to explore new av-enues whenever confronted with a difficult problem. As a member of the Altshuler lab, I havelearned a powerful way to approach bio-inspired design that I plan to use from this point for-ward in my career. That is by understanding a behaviour (when, where, who, what) and thenby investigating the mechanism (how), a consequence (why) may be found that has muchbroader implications for both biologists and engineers than any one of these steps alone.Thank you to Phillipe Lavoie and the students at the University of Toronto Institute forAerospace Studies for lending their time, facilities and expertise during the wind tunnel testing.A big thank you also goes to Ildiko Szabo at the Beaty Biodiversity Museum who was anindispensable part of this project as she not only provided sources for specimens but also gaveher time to teach me about birds and specimen preparation and, was always available to answerany questions. Many thanks to my labmates, officemates and everyone whose path has crossedmine in the Zoology department. I cannot iterate enough how much I have gained from thediversity and knowledge that exists in the department. Also, we had beer, so that was great.Thank you to my mom, dad and grampa for the long phone calls, continual encouragementand for patiently listening to me re-read the same paragraph or re-do the same presentation overand over. Thanks to James and Sam for your (often) encouraging words and drinking fancydrinks whenever possible. Thank you to Mikel for being my partner and inspiration throughoutthis whole process. Finally, thank you to all of my friends and family for encouraging mealong the way. Prior to my Masters, pursuing bird flight felt like a crazy dream but, all of myexperiences have shaped this dream into a passion and I couldn’t be more thankful.xi1 INTRODUCTIONIf I had three minutes in which to solve a problem upon which my lifedepended, I would spend the first two in deciding upon a method of solution,before making a figure.– Professor Tillingbast, 18841.1 THE BIO-INSPIRED ORIGINS OF HUMAN FLIGHTThe earliest records of man’s attempts to fly are found within myths and legends throughoutdiverse cultures and geographic locations. From the cautionary tales of Icarus who flew tooclose to the sun to Kibaga the invisible flying warrior killed by an arrow, legends of flight canoften be interpreted as an attempt to caution humans from getting too close to the heavenlyrealms [1]. Despite these somber warnings many scientists, inventors and adventurers havestudied and attempted to mimic how birds fly. This includes those with (perhaps) misplacedenthusiasm who jumped out of towers with feathers on their arms as well as the more rigorousobservational vulture studies done by Louis Mouillard whom Wilbur Wright called “one of thegreatest missionaries of the flying cause” [2, 3]. In fact, Wilbur Wright himself credited thelateral stability of the successful 1903 Wright Flyer to observations of buzzards twisting theirwing tips in response to wind gusts [4].However, after the first powered aircraft flight was completed, designers began iteratingon known and tested man-made designs rather than focusing on drawing continued inspirationfrom birds. In fact, Orville Wright eventually proclaimed that he could not ”think of any partbird flight had in the development of human flight excepting as an inspiration” [4]. Withoutquestion, in the hands of human designers, aircraft have improved drastically since the days ofthe Wright Flyer. This is in part due to improvements in the strength-to-weight ratio of modern11. INTRODUCTIONmaterials, specific fuel consumption of engines and a better understanding of the underlyingfluid mechanics and dynamics that govern flight. We now have aircraft capable of in-flightstructural health monitoring [5], carrying hundreds of passengers across oceans, achievingspeeds in excess of Mach 6 [6] and those that can be remotely piloted from anywhere in theworld [7].1.2 BIRDS STILL DO SOME THINGS BETTERDespite these extraordinary advances in aerospace engineering there are still a few key as-pects of bird flight that elude aircraft designers. This includes self-organized flocking suchas the behaviour seen in starlings and pigeons. These flocks are capable of close formationflying and maneuvering that has inspired work in “swarm” technology [8, 9]. This challengingtask involves intricate control feedback loops that permit collision avoidance and that can copewith the unsteady fluid flows caused by flying close to another animal. Determining how ani-mals coordinate and navigate through these complex maneuvers requires an understanding oftheir complex somatosensory and visual guidance systems [10]. Some bio-inspired techniquesused to adjust to the unsteady flows in swarm flight may eventually allow UAVs to adjust forenvironmental disturbances.Flight in turbulent flow environments is another challenging task regularly accomplishedby birds. It is well known that atmospheric conditions in the troposphere play a significantrole in the lives of flying animals [11]. Thermal gradients and mechanical friction can produceturbulence, a complex air flow phenomena characterized by a chaotic assembly of vortices andeddies that spans across spatial and temporal scales [12, 13]. Flyers can experience turbulentflows as either steady or unsteady fluctuations in the flow dependent on the length scale of thevortices relative to the length scale of the flyer. Generally, if the vortices are larger than theflyer this will be felt by the flyer as an unsteady turbulent flow. Turbulence can be detrimentalto birds’ flight stability and performance, and requires birds to adjust their in-flight kinematicsto maintain a stable flight path [14–16]. This can complicate foraging, roosting, and display21. INTRODUCTIONbehaviours and may increase the energetic cost of flight [13, 17].Flying animals can adapt their flight dynamics or behaviour to account for atmosphericturbulence levels [16]. Orchard bees exhibit large roll oscillations in turbulent flow and laterallyextend their hind legs to increase their moment of inertia [18]. This in-flight adjustment permitsimproved flight stability in turbulent flow. Birds can adjust for these challenging environmentsby changing the shape of their wings while flying, an ability termed wing morphing. Forexample, steppe eagles tuck their wings below their bodies as a response to gusts and swiftsand pigeons decrease their wingspan as wind speeds increase [12, 19, 20].Similar to birds, unmanned aerial vehicles (UAVs) fly in the troposphere, but are oftendamaged or difficult to control in turbulent conditions [21–23]. As birds adjust their wingmorphology in response to environmental variations, exploring the consequences of varied birdwing shapes used when gliding in fluctuating conditions has been identified as a key designtarget to improve UAV adaptability [24].1.3 WING MORPHINGWing morphing allows birds to modulate their aerodynamic performance and it has beenhypothesized that morphing allows birds to adjust their stability characteristics [15, 25]. Thisversatile design has increased interest in bio-inspired flight because aircraft designers are cur-rently operating under heavy constraints during the design process. Aircraft must be designedto be safely within selected aerodynamic performance, stability and control parameters whichmay require the aircraft to perform sub-optimally across the operating range [26]. The task-oriented, fixed-wing design of aircraft is in contrast to the variable morphology of birds thatallows adaptive flight styles. This adaptability is apparent in the raven, a skilled glider ca-pable of sudden and impressive manuevers [27, 28], and the gull, a low-level glider that canquickly transition into a steep dive [29]. It is thought that birds’ ability to dynamically shiftbetween flight modes allows them to occupy a greater wing design morphospace than a fixedwing aircraft (Fig. 1.1, UAV figures adapted from [30, 31]).31. INTRODUCTIONFigure 1.1. Birds morph their wing configuration in flight. Aircraft are designedwith fixed wing shapes that satisfy pre-defined stability and performance requirements,thereby restricting their ability to adapt to changing environmental conditions. In con-trast, birds can vary their wing configuration during flight.Despite the large differences between birds and modern aircraft, wing morphing technolo-gies are far from new in the aerospace industry. A few large-scale morphing wing aircraft havebeen produced including the variable wing sweep in the Grumman F-14 Tomcat, variable spanbending in the supersonic North American XB-70 Valkyrie, and variable chordwise camber inNASA’s Adaptive Compliant Trailing Edge (ACTE) (installed on a Gulfstream III experimen-tal aircraft). In actuality, all modern aircraft are capable of varying their chordwise camberthrough activation of flaps and slats and could technically be considered morphing vehicles,if morphing is defined as the ability to change wing shape in flight. However, these controlsurfaces often have gaps that can substantially affect drag production. Therefore, developingan fully-integrated morphing mechanism could improve aerodynamic performance [26, 32].However, morphing wings are difficult to implement successfully in large-scale aircraft, es-pecially for extreme avian-like wing shape changes, due to cost, safety and scale-dependenteffectiveness.UAVs provide a novel test bed for exploring these avian-inspired morphing techniques be-41. INTRODUCTIONcause they fly in similar Mach and Reynolds numbers regimes [33]. The Mach number is a non-dimensional ratio of the flow velocity to the speed of sound in the fluid. The Reynolds numberis non-dimensionalized ratio of inertial forces to viscous forces in a flow. Low Reynolds num-ber flows (Re < 104) experienced by insects are characterized by largely viscous forces (andtherefore laminar flow regimes) whereas high Reynold’s numbers (Re > 106) experienced bylarge or high speed aircraft are dominated by the inertial forces in the flow [34]. Birds andUAVs fly in an intermediate Reynold’s number range (Re ≈ 104 − 105) where neither theeffects of viscosity nor inertial forces can be neglected. This makes numerical solutions us-ing computational fluid dynamics very taxing and complex. Since birds and UAVs have Machnumber and Reynolds number in common, the fluid properties between the two types of flyersare comparable and it becomes possible and perhaps advantageous to use bird wing morphingas an inspiration for UAV design.Bird wings can morph passively or actively [10]. Passive morphing is caused by inertial oraerodynamic loads acting on the wing’s flexible materials (such as the skin and feathers). Theshape changes caused by passive deformation are often assumed to be much more subtle thanthose caused by active morphing. Active wing morphing occurs when birds actuate their skele-tal joints through activation of their network of intrinsic wing muscles. Active wing morphingcan include motions such as pronation or supination of their wrist, and flexion or extension ofthe elbow, manus or digits. Bird wing morphing research in the past has focused on largely two-dimensional active shape changes such as those that affect the planform or the airfoil. However,recently it was shown that actuating the elbow and manus angles yield three-dimensional, out-of-plane, changes to the overall wing morphology [35]. Relatively little is known about thethree-dimensional shape of bird wings and the relevant aerodynamic consequences. Investigat-ing the non-planar characteristics of bird wings may advance UAV design as recent numericalstudies have suggested that non-planar designs may outperform an equivalent planar wing [36].51. INTRODUCTION1.4 GLIDING AERODYNAMICSBird flight can be compared most directly to UAVs during gliding (Fig. 1.1) because avianwing shape changes are not as substantial as those in flapping flight, and includes shapes sim-ilar to those currently used in UAVs [24]. Gliding capabilities are governed by the flyer’sperformance, stability and control which in turn are a result of the forces and moments that acton a bird (Fig. 1.2). The performance of an aircraft can be evaluated by determining how forceproduction relates to range, endurance and maximum speed among many other translationalattributes of flight. Aircraft stability and control focus on how the moments developed aroundthe center of gravity contribute to the rotational attributes of the flyer [37].xzLiftDrag Side ForceRoll YawPitch  WeightyAerodynamic CentreFigure 1.2. Free body diagram of a gliding bird. The main forces and momentsacting on a gull during steady, gliding flight are summarized as point loads acting on theaerodynamic center.61. INTRODUCTION1.4.1 AERODYNAMIC PERFORMANCEThe translational properties of a flyer are governed by its weight (W ) and the developedaerodynamic forces. In gliding flight the aerodynamic forces and moments are the result ofpressure and shear stress distributions along the surface of the flyer [37]. In an airflow therewill be a low pressure region on an airfoil’s upper surface and a high pressure region on thelower surface. The shear stress distribution arises due to the viscous properties of the fluidmoving along the surface of the wing. The vector summation of these distributed loads overthe surface area gives the resultant aerodynamic force on the wings that can be approximatedas a point load acting on the aerodynamic center of the wing (Fig. 1.2). We can deconstructthe resultant force into three components: lift (L), drag (D) and side force (Y ). Lift and dragare defined as the forces that act along the perpendicular and parallel vectors of the effectivefreestream velocity (U∞). Side force acts along the orthogonal direction to these two forces(Fig. 1.2). The magnitude of these forces are associated with the angle of attack of the wingwhich is the angle between the effective freestream velocity and the mean aerodynamic chord(the straight line between the leading edge and trailing edge at the aerodynamic center). Theaerodynamic center differs from the center of pressure because the pitching moment about theaerodynamic center remains constant despite changes to the angle of attack.Dimensionless forces are used to compare between dissimilar objects and testing condi-tions. These coefficients normalize wing area (S), air density (ρ) and effective freestreamvelocity (U∞) (Eq. 1.1 and 1.2). Wing aerodynamic performance can be evaluated based onthe maximum lift coefficient and minimum drag coefficient across a range of angles of attack.CL =L1/2 · ρ · U2∞ · S(1.1)CD =D1/2 · ρ · U2∞ · S(1.2)71. INTRODUCTIONAerodynamic efficiency is another useful metric to evaluate a wings’ aerodynamic perfor-mance. This is important for gliding because it is a measure of the maximum glide range.A glider (bird or plane) is considered to be in equilibrium when all the forces and momentsacting on the body are balanced. At equilibrium, if a glider can maximize the amount of lift todrag produced this will allow them to minimize their glide angle (θ) and therefore maximizetheir range or the horizontal distance covered for vertical distance lost (Fig. 1.3 and Eq. 1.5).This maximum ratio of lift to drag is the maximum aerodynamic efficiency of the flyer and willbe the main aerodynamic performance metric investigated in this thesis.LiftDragWeightHorizontal distanceFlight pathθVertical distanceθFigure 1.3. Free body diagram of an equilibrium glide. Maximum aerodynamicefficiency is defined as a flyers ability to maximize the ratio of lift produced to dragincurred at equilibrium, and thus to maximize glide range. A bird is at equilibrium if allforces and moments are balanced.D = W · sinθ (1.3)L = W · cosθ (1.4)CLCD=LD=W · cosθW · sinθ =1tanθ=HdistVdist(1.5)There are significant effects on aerodynamic force production caused by the finite length of thewings. At the wing tips there will be a pressure gradient that allows air to flow from the highpressure region on the lower surface into the low pressure region on the upper surface [38].This flow creates a wing tip vortex that directly affects the effective freestream velocity byinducing a downwash and increasing the angle of attack. As a result, the lift and drag vectorsare rotated such that a component of the lift is oriented posteriorly and is known as the lift-81. INTRODUCTIONinduced drag (Fig. 1.4). Induced drag reduces the aerodynamic efficiency of a wing. Theaspect ratio (AR), which is the measure of wing length (b) to wing area (S) (Eq. 1.6) playsa role in reducing the effects of induced drag and improving aerodynamic efficiency. This isbecause the effects of the wing tip vortex are reduced at positions further from the wing tip(Fig. 1.4). As a result, long narrow wings with a large aspect ratio will have less of their liftingsurface affected by the downwash. This effect can be determined analytically for a planar wing(Eq. 1.7) by incorporating a span efficiency factor (e) which is a measure of the lift distributionon a wing planform relative to an elliptical lift distribution (e = 1).AR =b2S(1.6)CDi =C2Lpi · AR · e (1.7)low pressurehigh pressureinduced velocitydownwashfreestream velocityinduced velocityfreestream velocityeffective velocitydownwashLiftDragLiftDragLift-induced dragInfinite wing:Finite wing:Figure 1.4. The effects of induced drag. Induced drag is a result of the wing tipinduced velocity that causes a component of the lift to contribute to drag production.91. INTRODUCTION1.4.2 AERODYNAMIC STABILITYAlthough aerodynamic performance may play a large role in a flyers’ flight characteristics,it is also necessary to maintain a stable and controlled flight path to successfully forage, hunt ornavigate [13]. Despite this critical function, flight stability is often overlooked when evaluatingbird flight and currently there is little experimental analysis of bird flight stability [15].Stability is evaluated based on the moments developed about the axes defined in Figure 1.2.We can separate stability analyses into pitch stability (longitudinal stability, about the y axis)or roll-yaw stability (lateral stability, about the x and z axis). In this study we focus on thelongitudinal stability as it is considered to be the most important stability characteristic and oursensors had the best resolution in this axis [37].In addition to the differentiation between longitudinal and lateral stability, there are alsotwo distinct types of stability analyses for each of these modes [37]. First, we can evaluatethe static stability which is the time-invariant, inherent tendency for the bird to return to anequilibrium state after an initial disturbance. Second, we can evaluate the dynamic stability,which is the time-dependent stability that measures the time and the path the bird takes to returnto the equilibrium state. Static stability is a necessary but insufficient condition for stabilityas it is possible to continually oscillate about an equilibrium point. To begin to develop abasic understanding of bird flight stability, in this thesis we investigate only the static stabilitycharacteristics.Both static and dynamic stability analyses can be forms of passive stability, that rely ona flyer’s initial morphology to develop the appropriate moments to return to the equilibriumafter a disturbance. However, both birds and aircraft can also use active control inputs toreturn their equilibrium position. It has long been assumed that birds rely solely on activecontrol of stability and a study investigating the evolution of stability appeared to confirm thishypothesis [39,40]. However, the findings suggest that gulls are highly unstable such that evena small change in the angle of attack on the wing would cause a pitching moment to develop thatrotates the bird away from its equilibrium position. This indicates that gulls must constantlyadjust their wing shape or tail to maintain a stable flight path even while foraging. Observations101. INTRODUCTIONof gulls in steady, gliding flight do not seem support this conclusion as they are often nearlymotionless. Instead, a second competing hypothesis proposes that birds use a combination ofpassive and active stability [15]. To investigate this possibility further, this thesis will focus onevaluating the passive longitudinal static stability in gliding bird flight.Similar to lift and drag, we can non-dimensionalize the pitching moment by including themean aerodynamic chord (c) (Eq. 1.8). For this study we use the root chord of the wing, as thelocation of the aerodynamic center is not precisely known.CM =L1/2 · ρ · U2∞ · S · c(1.8)Equilibrium UnstablexStableLift LiftC (α)C ML C (α)C ML C (α)C MLUnable to trim at useful liftNo tendency to return to equilibriumStatically stable Figure 1.5. Longitudinal static stability condition. Zero-lift pitching moment and thepitch stability derivative are, respectively the intercept and the slope of the relationshipbetween the pitching moment and lift.For a flyer to be considered statically stable in the longitudinal axis two conditions must besatisfied. First, the flyer must be able to trim (fly at a position where no unbalanced momentsact on the center of gravity) at an angle of attack that produces useful (positive) lift. This will111. INTRODUCTIONbe satisfied if the pitching moment when no lift is produced is positive. Second, a flyer musttend to return to its equilibrium after an initial disturbance. This will occur if the change ofpitching moment with a change in lift (the slope of the pitching moment with lift, known asthe pitch stability derivative) is negative. For example, if a flyer experiences a gust that in-creases the lift and its configuration develops a positive (nose up) pitching moment, this wouldbe considered an unstable configuration and vice versa (Fig. 1.5). Often, the pitch stabilityderivative is calculated relative to the change of angle of attack rather than lift. However, birdwings are flexible and it is difficult to define a consistent measure of angle of attack throughoutexperiments so instead we monitor changes relative to lift. These two ways of calculating thepitch stability derivative are related by a constant as long as the lift-slope remains linear priorto stall (Eq. 1.9) [41]. Importantly, all components of a flyer, including the wing, body and tailcontribute in an additive fashion to the overall static stability. For this study, we focus solelyon the contributions of the wings to the overall stability.dCMdα=dCMdCLdCLdα(1.9)Passive stability is not always a desirable trait. The main issue is that if a flyer is very stable,the large restorative forces can result in a sluggish response to a control input [15]. This isproblematic for two reasons. One reason is that stability necessitates a direct trade-off withmaneuverability because to perform a maneuver a flyer must intentionally and abruptly departfrom its equilibrium position. By lowering the restorative forces (or reducing static stability)a flyer can more easily perform a maneuver. Another issue is that sluggish control response ingusty or turbulent environments can result in erratic flight paths which are difficult to control.In these conditions it has been hypothesized that flyers can benefit from reducing their passivestatic stability and instead use more active stability control [15].121. INTRODUCTION1.5 AERODYNAMIC CONSEQUENCES OF WING MORPHINGThis thesis focuses on examining how wing morphing and environmental conditions in-fluence the gliding aerodynamic performance and static stability characteristics of bird wings.We studied Glaucous-winged (Larus glaucescens) x Western (Larus occidentalis) hybrid gullsgliding in local areas. We chose to work with gulls because of their adaptive flight capabil-ities and their intriguing three-dimensional wing morphology that exhibits a large degree ofcurvature along the wing span [29]. This shape has inspired many aircraft designs in the pastbut no direct investigation has been done on the gull wing itself. We first examined the wingshapes used by gliding gulls in varied environmental conditions. We next investigated the re-lationship between the skeletal joints and overall wing shape using gull wing cadavers. Thisallowed us to identify the range of wing shapes used while gliding in variable wind speeds andgusts. Finally, we tested prepared gull wings in a wind tunnel to explore how varying the wingshape and steady environmental turbulence affected aerodynamic performance and stability.This interdisciplinary study includes an investigation of gull gliding behaviour under variedenvironmental conditions, the development of a method to determine skeletal joint angles infreely gliding birds, and an experimental analysis of the aerodynamic consequences behindgull wing morphing.132 GULL WING MORPHINGOne meteorologist remarked that if the theory were correct, one flap of a seag-ull’s wings would be enough to alter the course of the weather forever. The con-troversy has not yet been settled, but the most recent evidence seems to favor theseagulls.– Edward Lorenz, 19632.1 SUMMARYBirds flying in turbulent conditions demonstrate impressive versatility and adaptability, hy-pothesized to derive from wing shape changes [42, 43]. Wings can morph passively due toinertial and aerodynamic loads or actively when birds stimulate their network of intrinsic wingmuscles [10, 44]. Observations have found that birds actively morph their wings in responseto changing environmental conditions such as the steppe eagle that tucks its wings underneathits body during gusts, or when swifts and pigeons decrease their wingspan as wind speed in-creases [12, 19, 20]. UAVs are similar to birds in terms of size, speed, and flight environmentbut lack the ability to morph their wings to adjust for variable conditions. In fact, as UAVsare often damaged or adversely affected when traversing turbulent flow environments, under-standing how specific wing shape changes allow birds to fly in unsteady conditions representsa key design target for improving UAV versatility [23,24,29]. Here we show that gulls glidingin unsteady environments reduce their passive stability by actively morphing their wings. Bydetermining the relationship between wing shape and skeletal joint angles in gull cadavers, weidentify the joint angles used by freely gliding gulls. This reveals that gulls use lower elbowangles as wind speeds and gusts increase. Wind tunnel testing over the identified in vivo elbow142. GULL WING MORPHINGangle range shows that lower elbow angles have increased aerodynamic efficiency but reducedpassive pitch stability. Our results suggest a coupling in efficiency, maneuverability and stabil-ity in avian gliding. Furthermore, we found that wing morphing allows birds to actively controlthese aerodynamic trade-offs in response to turbulent conditions.2.2 BACKGROUNDGliding dynamics are strongly influenced by a flyer’s efficiency, maneuverability and sta-bility. There is a fundamental trade-off between maneuverability and stability; a stable flyerwill experience restorative moments tending to return its equilibrium position following a dis-turbance, be it a gust or an intended maneuver. A stable configuration is favorable when per-turbations are small but this configuration could be detrimental in highly turbulent conditionsbecause the passive restorative moments can lead to an over-corrected, and thus erratic flightpath [15]. A maneuverable flyer, in contrast, has the ability to more easily depart from itsequilibrium and can actively respond to unsteady flows. In addition to this trade-off with ma-neuverability, stability can, in some conditions, be coupled to aerodynamic efficiency, definedas the ratio of lift produced to drag incurred (Fig. 1.3) [37]. Such coupling will occur ifthe developed aerodynamic forces cause the location of the aerodynamic center to shift (Fig.1.2) [45, 46].Wing morphing has been found to allow birds to alter aerodynamic efficiency,and is also hypothesized to allow birds to control the trade-off in maneuverability and stabil-ity [15, 25].The majority of variation in bird wing morphing is accomplished by flexing or extendingthe elbow and manus joints, which yields three-dimensional, non-planar wing morphologies[35]. Non-planar wings are of increasing interest to engineers as they offer a diverse rangeof benefits [45]. For example, wings with curvature along the span of the wing, known asspanwise camber, can be more aerodynamically efficient than their planar equivalent [36, 47].Direct actuation of a wing’s spanwise camber can provide both longitudinal and lateral controlbut was found to reduce the aerodynamic efficiency [48]. Gull wings are an iconic example152. GULL WING MORPHINGof spanwise camber found in natural flyers, and due to their varied flight styles have served asbiological inspiration for experimental morphing vehicles and wing designs [29, 36, 47, 48].2.3 DETERMINING THE in vivo WING MORPHOLOGY2.3.1 OBSERVATIONAL STUDYGulls regularly fly in urban and coastal areas which are characterized by highly turbulentflow. To examine the potential of using wing morphing for adaptive flight in variable windenvironments, we began by measuring the wing shapes used by local gulls during glides. Weperformed an observational study of Glaucous-winged (Larus glaucescens) x Western (Larusoccidentalis) gulls gliding on the northwest Pacific coast over 9 outings and 5 locations. Acamera (Sony α-350 equipped with 75-300 mm lens or 18-70 mm lens/iPhone 5S) was posi-tioned in areas where the gulls would glide directly above the camera lens. This allowed usto capture a ventral view of the wings during glides (Fig. 2.1). Five landmarks on the ventralwing perimeter (Fig. 2.1, blue dots) were later identified using Image J1 (version 1.51h) toprovide a measure of wing shape [49]. The wind speed and maximum wind gust speed werenoted from local weather stations. Prior to digitization and data analyses, photos were checkedby two independent investigators to ensure that the wing planform was approximately perpen-dicular to the camera lens. This verification was informed by an analysis of how sensitive thepredicted elbow angle is to the orientation of the wing relative to the camera lens (see Section2.2.4). In total we selected 182 photos from the observational study.Figure 2.1. Freely gliding gull with five peripheral tracked points. Blue pointsillustrate the: shoulder, P10, P7, S1 and where the secondary feathers rejoin the body.162. GULL WING MORPHING2.3.2 CADAVER WING MORPHOLOGY STUDYTo determine if joint angles can be predicted from the observed wing shape, it is necessaryto make both measurements on the same wings. Frozen cadavers of adult Glaucous-winged(Larus glaucescens) x Western (Larus occidentalis) gulls were acquired from local bird rescueassociations between Fall 2016 and Spring 2017. We selected wings for experimental use thatwere undamaged and not molting. Wings were defrosted and removed at the shoulder from gullcadavers (n=3). We took special care to ensure that the skin (including the propatagium) andfeathers remained intact. Wings were then mounted horizontally to a support frame close tothe head of the humerus, with the ventral side of the wing facing up. We manually manipulatedthe wings through the full range of extension and flexion of the elbow and manus joints whilethree cameras recorded the position of markers on the humerus head, elbow, manus and distalcarpometacarpus (Fig. 2.2, purple points). This 3D wing motion was captured at 50 frames/secat 640 x 480 pixel resolution using three Allied Vision Technologies Prosillica GE680 camerasequipped with 4-8 mm lenses. One camera was oriented to give a top-down view of the ventralsurface throughout the wing motion (this view is shown in Fig. 2.2). The other two cameraswere positioned such that all four markers could be visualized throughout the range-of-motionactuation. We digitized the videos to determine 3D positions of the four tracked points andthen used a custom code to calculate the elbow and manus angles of the wing for each cameraframe [50]. From the camera recording of the ventral surface of the wing, we also tracked thesame five points identified on the live gull: shoulder, tenth primary feather tip (P10), seventhprimary feather tip (P7), first secondary feather tip (S1) and the location where the feathersrejoined the body (Fig. 2.2, blue points) for geometric morphometric analysis. Prior to theanalysis, we removed frames from the cadaver data that had calculated manus angles under100◦ and elbow angles under 30◦. We did so because after this point the wing became so flexedthat the landmark on S1 is often obscured and no longer reliable. In addition, we subsampledthe cadaver data to ensure an even distribution of elbow and manus angles for each tested wingto avoid clustering of data points that could adversely affect subsequent analysis.172. GULL WING MORPHINGElbow angleManus angleFigure 2.2. Cadaver wing ventral view through flexion and extension. Blue pointsillustrate the five selected peripheral points: shoulder, P10, P7, S1 and where the sec-ondary feathers rejoin the body. Purple points illustrate the four markers on the humerus,elbow, manus and distal carpometacarpus.2.3.3 PREDICTION OF THE in vivo WING MORPHOLOGYWe used geometric morphometrics to determine the diversity of shapes associated with thefive 2D landmarks placed around the periphery of the wing from the cadaver videos, observa-tional photos and photos of the ventral surface of wings prepared for the wind tunnel (Fig. 2.1and Fig. 2.2, blue points). We used RStudio (version 1.0.153) running R (version 3.4.1- SingleCandle) and the package geomorph to perform a General Procrustes Analysis [51, 52]. Thisanalysis superimposes the subsampled landmark sets to remove effects of size variation, ori-entation and location. We then used the aligned and pooled landmarks from only the cadaversto perform a principal components analysis (Fig. 2.3D, gray circles). This analysis revealedthat the first and second principal components explained approximately 56% and 22% of thevariation in wing shape and scaled with manus and elbow angle, respectively (Fig. 2.3B and C,gray circles). Next, using the computed eigenvectors from the cadaver-defined morphospace,we projected the landmarks from in vivo and wind tunnel wings into the morphospace (Fig.2.3D, gray triangles and green squares respectively).We next combined the geometric morphometric analyses with machine learning techniquesto infer elbow and manus angles used by freely gliding gulls [53]. To select the predictionmodel we used the principal component scores from the cadaver manipulations as trainingdata, because each frame of the cadaver videos had both peripheral landmarks and knownelbow and manus angles. We then fit a variety of models using a varied number of principal182. GULL WING MORPHINGcomponents (from two to ten) as inputs to the model to determine the relationship betweenwing shape and elbow or manus angle (Table 2.1). During model training, we used a 10-foldcross-validation to inform the selection of parameters within a given model; parameters wereadjusted to minimize cross-validation error. We then used two test data sets: (I) the set of allwind tunnel wings, and (II) wind tunnel wings with intermediate/high (>80) elbow angles.We found that a random forests model using scores from the first four principal componentsperformed the best (model ID: t) (Fig. 2.5A). This model minimized the combined root meansquare (RMS) error of known elbow angles of the cadaver specimens (training data; RMS error:1.82), all wind tunnel wings (test set I; RMS error: 9.42) and of intermediate/high (elbow angle> 80) wind tunnel wings (test set II; RMS error: 11.65) (Fig. 2.5A).PC1 (55.9%)PC2 (21.9%)ACManus Angle (°)Elbow Angle (°)Dwind tunnel wingsin vivo gliding gulls100120140160180− 50 70 90 110 130 150 170 −0.3 −0.2 −0.1 0.0 0.1 0.2cadaver specimensBFigure 2.3. Prediction of in vivo joint angles from cadaver morphospace. (A) Therange of viable elbow and manus angles was determined for the cadaver wings. (B)A morphospace of cadaver wing shapes was generated, and the in vivo (gray triangles)and prepared wing shapes (green squares) were projected into the space. (C) The firstprincipal component scales with manus angle (D) and the second scales with elbowangle. The relationship between principal component data and the known joint anglesof cadavers allowed us to predict the elbow and manus angles used in flight (translucentgray triangles).192. GULL WING MORPHINGUsing this model we found that gliding gulls used elbow and manus angles that rangedfrom 90◦-154◦ and 110◦-173◦, respectively (Fig. 2.3A). Additionally, we analyzed how thejoint angles varied with the local environmental conditions. We observed gulls flying in windspeeds ranging from 2.2 to 16.9 m/s, and with maximum wind gusts ranging from 3.9 to 25.6m/s. This analysis revealed that as both wind speed and maximum gust increased, elbow angledecreased significantly (Fig. 2.4) (wind speed: -0.61◦/(m/s), t180 = -3.415, p = 0.000789; windgust: -0.40◦/(m/s), t180 = -3.253; p = 0.00136) .901101301502 6 10 14 18 2 6 10 14 18 22 26Wind speed (m/s) Maximum wind gust (m/s)Elbow Angle (°)Figure 2.4. Elbow angle relationship with wind speed and gust. The observed elbowangle used by gliding gulls significantly decreased as both wind speed and maximumwind gust increased. Colours represent elbow angle for consistency with upcomingfigures.2.3.4 SENSITIVITY AND PREDICTION ERROR ANALYSISWe performed a sensitivity analysis to evaluate if the selected model impacts the conclu-sions of the study. We investigated 23 models with a range of four to ten principal componentsas the predictor variables. We found that all models (except f and k, whose RMS error was veryhigh), predicted an elbow range that is relatively constant and contains both intermediate andhigh elbow angles (Fig. 2.5B). Therefore, our inference of elbow angle from wing shapes is202. GULL WING MORPHINGnot wholly dependent on model selection. We also investigated whether model selection wouldaffect the result that elbow angle reduced as wind speed and wind gust increases. We foundagain that all models except for f and k have overlapping 95% confidence intervals and predicta similar relationship between elbow angle and wind speed and gust (Fig. 2.5C).It was not feasible to mark individual birds during our observational study and it is pos-sible that individual observations are from the same bird. We also investigated the quantileregressions (10%, 50% and 90%) of elbow angle with wind speed and gust respectively for ourselected model (model ID: t). The 95% confidence intervals on the slopes overlapped such thatthey were not significantly different.We investigated the prediction error of our selected model by using prepared wings withknown elbow angle. We found the elbow angle prediction error to be below 23◦ (Fig. 2.6A).This error was determined three times per wing, each time changing the plane that was parallelto the camera lens. The three planes used were the a) full plane: the plane made by wingtip and root chord b) hand plane: the plane made of the wing tip and a chord approximatelythrough the hand wing and, c) interior plane: the plane made by the root chord and the elbowjoint. These orientations also tested the sensitivity of wing rotation relative to the camera andthe best orientation was the hand plane with a maximum error of 20◦.We then explored how sensitive the prediction error was to the rotation of the wing relativeto the camera again using prepared wings with known elbow angles (Fig. 2.6C, D, E and F).We rotated the wing towards or away from the camera (positive or negative on the body axis)through a range of approximately 100◦. We found that as the wing tip rotated about the bodyaxis towards the camera, the error increased significantly but as the wing tip rotated in theopposite direction, the error reduced. We would expect that this error would begin to increaseas wing is rotated away from the camera causing the ventral surface to be obscured from thecamera. The very large errors are associated with photos where the non-parallelism of thewings is obvious. The error was less sensitive to rotations about the spanwise axis but didincrease at higher rotations.212. GULL WING MORPHING0102030708090100110120130140150160170180f k n m p r u o q b i a l g e c h d j s tModel IdentifierClosest NeighborLinearLoessRandom ForestModel TypeCadaversAll wind tunnel wingsWind tunnel wings > 80°Prediction group Explanatory variableWind GustWind SpeedRMS error (°)Predicted Elbow Angle (°)Slope of Regression (°/m/s)ABC−1.5−1.0−0.50.0Figure 2.5. Sensitivity analysis of predictor model (A) RMS error of the elbow angleprediction was computed for the training data, test set I and test set II. We then used thecombined RMS of the three plotted errors to inform the ordering of the models fromworst to best. (B) Predictions of in vivo elbow angles from each model. The predictedrange for all models (except for f and k) spans our range of aerodynamic trade-offs andchoice of model does not affect our conclusions. (C) The predicted elbow angle found atrend with wind speed and wind gust despite the choice of model (except for f and k).222. GULL WING MORPHINGID Model equationRMS error (◦) Slope (◦/m/s)cadaver Test I Test II score Wind Gusta lm(elbow.angle∼PC1+PC2) 17.72 6.99 7.86 20.60 -0.46 -0.32b lm(elbow.angle∼PC1* PC2) 17.15 9.42 11.13 22.51 -0.72 -0.50c lm(elbow.angle∼PC1+PC2+PC3+PC4) 16.63 7.52 8.42 20.10 -0.39 -0.26d lm(elbow.angle∼PC1*PC2*PC3*PC4) 13.35 9.78 10.34 19.51 -0.80 -0.57e lm(elbow.angle∼PC1+PC2+PC3+PC4+PC5+PC6+PC7+PC8+PC9+PC10)16.45 8.28 8.26 20.18 -0.61 -0.42f lm(elbow.angle∼PC1*PC2*PC3*PC4*PC5*PC6*PC7*PC8*PC9*PC10)7.86 749.39 849.55 1132.86 -5964.79 -4047.11g loess(elbow.angle∼PC1+PC2) 14.82 9.35 10.70 20.53 -0.16 -0.11h loess(elbow.angle∼PC1+PC2+PC3+PC4) 10.75 11.12 12.18 19.69 -0.30 -0.19i lm(elbow.angle∼PC12+PC22) 16.31 10.53 7.40 20.78 -0.27 -0.18j lm(elbow.angle∼PC13+PC23) 15.73 7.28 7.53 18.90 -0.21 -0.14k lm(elbow.angle∼cos(PC1)+cos(PC2)) 33.88 33.85 31.65 57.41 0.13 0.09l lm(elbow.angle∼sin(PC1)+sin(PC2)) 17.71 6.99 7.87 20.60 -0.46 -0.32m Closest Neighbor - 2PCs 0.00 19.79 21.93 29.54 -0.70 -0.45n Closest Neighbor - 2PCs (Mean of 3) 16.22 16.78 18.90 30.03 -0.62 -0.42o Closest Neighbor - 6PCs 0.00 14.66 18.12 23.31 -1.00 -0.65p Closest Neighbor - 6PCs (Mean of 3) 3.34 15.29 18.61 24.32 -1.04 -0.68q Closest Neighbor - 10PCs 0.00 14.66 18.12 23.31 -1.00 -0.65r Closest Neighbor - 10PCs (Mean of 3) 3.34 15.29 18.61 24.32 -1.04 -0.68s rf(elbow.angle∼PC1+PC2) 1.61 10.75 13.55 17.38 -0.69 -0.47t rf(elbow.angle∼PC1+PC2+PC3+PC4) 1.82 9.42 11.65 15.09 -0.65 -0.42u rf(elbow.angle∼PC1+PC2+PC3+PC4+PC5+PC6+PC7+PC8+PC9+PC10)6.31 15.60 16.72 23.72 -0.61 -0.40Table 2.1. Model selection and sensitivity results. We tested 23 models and predictedelbow angles from fully characterized wings. We used the root-mean-square error fromthe prediction groups to define an overall score for each model. The four PC randomforest model (gray shading) best minimized the error between the three categories. Ad-ditionally, we computed the regression coefficient for how elbow angle changed withwind and gust speed and found minimal differences between models.232. GULL WING MORPHINGAbsolute prediction error (°)Absolute elbow predition error (°)Rotation about the body axis (°) Rotation about the span axis (°)Absolute manus prediction error (°)True elbow angle (°) True manus angle (°)A BC DE F010203030 50 70 90 110 130 150 170 120 130 140 150 160 1702040608001020−80 −60 −40 −20 0 20 −75 −50 −25 0 250Figure 2.6. Prediction error and sensitivity analysis of photographs. (A) Elbowangle prediction was found to have 23◦ maximum absolute error and 6.9◦ average error.(B) Manus angle prediction had 12◦ maximum absolute error and 3.8◦ average error.Sensitivity to the camera perpendicularity was investigated and (C) found elbow angleerror grew as the wing rotated about the body axis and was relatively constant as the wingrotated away from the camera about the same axis. (D), The model was less sensitiveto rotations about the span-axis. (E, F) Similar yet diminished trends were observed formanus angle predictions. The sensitivity analysis was completed with wings of knownelbow angles of 149◦ (black dots) and 108◦ (purple dots).242. GULL WING MORPHING2.4 AERODYNAMIC CONSEQUENCES2.4.1 WIND TUNNEL SPECIMEN PREPARATIONWe next explored how variation in wing morphing configurations affected aerodynamicperformance and stability. We focused further measurements on elbow angle because of itsrelationship to spanwise camber (Fig. 2.7). Wings (n=12) were hand positioned, pinned anddried at the desired elbow angles and the maximal manus angle for that position (Fig. 2.3A,green squares). Once dried, each wing had a 10-24 plated steel rod threaded and epoxied intothe humerus to permit mounting in the wind tunnel. We assigned wings to an elbow angle tak-ing into account the bird weight and ensuring that the weight variation was equally distributedacross the range.0510152030 50 70 90 110 130 150Elbow Angle (°)Maximum spanwise camber (% of span) Maximum heightSpanMaximum heightSpanFigure 2.7. Spanwise camber as a function of elbow angle. Gull wing spanwisecamber reduces across the in vivo elbow angle range. Maximum spanwise camber isdetermined as the ratio of maximum height of the leading edge to the wing span.We measured the final elbow and manus angles after the drying period using 3D pointimagery and found a final elbow angle range of 34◦-149◦ (Fig. 2.3A). To calculate the wingarea we determined the 3D position of 9 peripheral points and rotated the points, using rotationmatrices until the hand wing was flat and parallel with the horizontal. We then rotated the252. GULL WING MORPHINGpoints until the root chord was also parallel with the horizontal (Fig. 2.8B). From this positionwe used the 2D projection of these points and the bootlace method to calculate the planformarea. The root chord was determined as the straight distance between points placed on theshoulder and the final secondaries (Fig. 2.8A). Effective wing span was determined from the2D projection of points on the humerus and the first primary (P10) (Fig. 2.8C). Span-wisecamber was determined from 3D imaging of 7-8 points on the leading edge of the wing. Thesepoints were rotated using rotation matrices until the vector defining the hand wing was flat andparallel to the horizontal and until a point on the distal carpometacarpus was parallel with thehand wing (because we could not track the root chord for this set up). Results were comparedto the true wings to visually assess proper rotation results. Finally, to determine a comparablemetric for the spanwise camber of the wings the points were rotated to ensure that the humerusand the distal P10 point was aligned on the horizon (as seen in the wing leading edge outlinedisplayed in Fig. 2.7). From this orientation, the maximum spanwise camber was determinedto be the maximum height of the leading edge over the wing span (Fig. 2.7) [54].There are some key limitations to testing aerodynamic consequences on a prepared wingspecimen. Dried wings no longer have the same material qualities as a live bird and are onlyheld in position by the dried muscles, ligaments and skin. It is possible that the flexibility ofthe wings is different than a live bird. However, it is doubtful that the flexibility of the featherswould be drastically changed by drying, though their anchoring may have been affected. Wedecided to air dry our wings over other preparation methods because of the difficulties in posi-tioning a fresh wing and the adverse effects to material brittleness when freeze-drying [55]. Itis also likely that a live bird would provide some active muscular reinforcement to maintain aposture under aerodynamic loading and thus prepared specimens may actually flex more than alive bird would permit. Additionally, these wings were tested alone and do not account for anyinterference effects cause by the near proximity of the body to the root chord. Despite theselimitations, prepared specimens can provide an idea of the aerodynamic effects that varyingmorphology would have on a live animal.262. GULL WING MORPHINGACBD0. 60 90 120 150Elbow Angle (°)Root Chord (m)Effective Wing Span (m) 60 90 120 150Elbow Angle (°)Projected Area (m )Aspect Ratio2Figure 2.8. Morphometric parameters of wind tunnel wings. (A) Chord measuredat the root, (B) 2D projected area of the wings, (C) effective wing span, (D) aspect ratiobased on effective area and effective span.2.4.2 WIND TUNNEL EXPERIMENTAL SET UPWe tested the prepared wings at the University of Toronto variable-turbulence low speedwind tunnel (Fig. 2.9). The test section is 5 m long and has a cross-sectional area of 1.2 mx 0.8 m. Further information on the wind tunnel can be found in Hearst, 2016 [56]. Due tosize constraints, wings were individually mounted to the side wall approximately 1.73 m fromthe diffuser. Wings were mounted outside of the wall boundary layer, on a load cell and astepper motor (Velmax B4836TS, accuracy 100 arc-sec). This allowed us to vary the angle ofattack over a range of 80◦-100◦, starting at approximately 0◦ up to the maximum, down to theminimum and back up to 0◦. We measured the loads generated with a six-axis load cell (AMTI272. GULL WING MORPHINGFS6) sampling at 4000 Hz for 10 seconds, amplified (AMTI Gen5, force gain = 2000, momentgain = 500) to the data acquisition system (National Instruments NI 6529 PX). Readings weretaken 10 seconds after the angle of attack was adjusted to permit a steady state reading. Theload cell axes were independently calibrated using a series of 11 weights from 0 - 2.5kg andfitting a linear model to voltage output.Figure 2.9. Prepared wing specimen mounted in the wind tunnel.Wings were mounted such that the distal part of each wing (hand wing) was perpendicularto the flow. Wings were tested at a mean velocity of 10 m/s to simulate gliding conditions(Reynolds number: 92,000-179,000) [57]. Tare runs (runs of the mounting system only, with-out the wing installed) were completed so that effects of the support system could be removedfrom the final measurements. Results were also corrected for the rotation of the load cell withthe wing and the effect of mass. The pitching moment was defined to be about the humerushead of the wing approximated as the location of the joint between the steel rod and humerusbone. As wings were mounted at an offset from the load cell, we determined the equivalentsystem by measuring the horizontal and vertical offset for each individual run. These valuesand the lift and drag forces allowed to us compute the moment about the humerus head andallowed us to have a common comparable location for the moment between wings (Refer tocustom code rotatetoWTaxis.R for details: Asminimal hysteresis was present in the pre-stall readings, data from the up and down portions of282. GULL WING MORPHINGthe angle of attack tested were pooled [25].To examine effects of turbulence intensity on gull wings, we also tested each wing at var-ied turbulence intensities using turbulence generating grids. We had three conditions: a) lowturbulence, no grid b) low/medium turbulence, grid ID: Rd38 c) medium turbulence, grid ID:Sq39. Rd38 is a bi-planar round rod grid consisting of round aluminum rods with a 6.8 mmnominal diameter mounted in a machined frame with a mesh length of 32 mm. Sq39 is a squaremesh consisting of a single piece of 6.35 mm thick aluminum that was water cut with a meshlength of 100 mm. The two grids generate a uniform mean flow with homogeneous turbulenceas verified in previous studies [56].For each turbulence grid, we used a single hot-wire probe operated with a constant tem-perature anemometer built by the University of Newcastle to measure turbulence intensity atthe stream-wise plane approximately at the leading edge of the mounted wings [58]. The hot-wire was calibrated against 19 known velocities spanning 2 m/s and 20 m/s, to which King’sLaw was fitted. King’s Law defines the general form of the relationship between the heattransfer coefficient of a cylinder immersed in a flow to the fluid velocity. This allows us to cali-brate the flow velocity to the current needed to maintain a constant temperature in the hot-wireanemometer. The calibration points were sampled at 20kHz for 120 seconds.The turbulence intensity was calculated from the hot-wire time series data as the root meansquare of the velocity fluctuations (σu) over the average velocity (U ) (Eq. 2.1). The one-sidedpower spectral density (Guu) of the velocity time series was determined from the fast Fouriertransform of the signal. These results were normalized to streamwise velocity and the meanroot chord (c) of the models tested, which is approximately 0.21 m (Fig. 2.10A). The totalmean-square fluctuation of the time series is given by the integral of the spectral density overthe relevant frequency (ω) domain (Eq. 2.2 and Fig. 2.10A). The calculated values agreed withresults from previous studies [56]. We found that the energy peaks (Fig. 2.10B) were close tothe convective time scale of the wings. This indicates that the turbulence intensity in our studywould be a similar to a steady fluctuation. This value is well below the unsteady turbulenceintensity that gulls may encounter but does represent a large steady fluctuation for the wing.292. GULL WING MORPHINGTI =σuU(2.1)σ2u =∫ 3000Hz5HzGuudω (2.2)10-910-810-710-610-510-410-310-2Normalized power spectral density10-2 10-1 100 101 102 103Normalized frequency 0123456789 10-4Normalized turbulent kinetic energyABc(   )ωU(   )UcG uuUG uu2ω(    )Figure 2.10. Power spectral density analysis of the turbulence intensity.(A) Turbu-lence intensity was calculated from the power spectral density as the root-mean-squareof velocity by the mean streamwise velocity. Freestream turbulence intensity with nogrid (teal) was 0.04%, the medium grid (blue) had 1.42% turbulence intensity and thecoarse grid (dark purple) had 4.61% turbulence intensity. (B) The compensated semi-log plot is a visually proportional representation of the true distribution of the turbulentkinetic energy over the relevant time scales.302. GULL WING MORPHING2.4.3 AERODYNAMIC EFFICIENCY RESULTSAnalysis of aerodynamic loads revealed that the intermediate elbow angle was the bestperforming wing configuration. This can be seen in the performance envelopes, defined by thecurvature of the lift-drag polar [25]. Lift-drag polars demonstrate how the lift and drag varyas a wing is rotated through a range of angles of attack. These polars are visualized for eachindividual wing and are coloured based on their elbow angle (Fig. 2.11). The highest elbowangles (darker lines) had reduced envelopes across all turbulence intensities (TI) (Fig. 2.11).From these same polars we can next evaluate the maximum lift coefficient and the minimumdrag coefficient. We found that the maximum lift coefficient decreased as the elbow angleincreased (Fig. 2.12A), but that minimum drag was lowest at an intermediate elbow angle(Fig. 2.12B). Finally, we can determine the maximum aerodynamic efficiency (the maximumratio of lift to drag) which can be visualized as the steepest tangent line from the origin toeach wing’s polar. This revealed that intermediate elbow angles are the most aerodynamicallyefficient configuration, and that elbow extension across the in vivo range is accompanied by areduction in efficiency (Fig. 2.12C). This indicates that the most extended wings had the worstperformance in regards to all three performance metrics. Turbulence intensity had a modestbut significant positive effect on maximum lift and thus on aerodynamic efficiency, consistentwith experimental studies of rigid wing models [59]. It is also notable that the in vivo rangeof elbow angles (gray region) encompassed the full range of maximum aerodynamic efficiencyvalues (Fig. 2.12C).312. GULL WING MORPHINGDrag coefficientLift coefficientTI = 0.04% TI = 1.42% TI = 4.61%Drag coefficient Drag coefficient-0.50- 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.030507090110130150Elbow Angle (°)Figure 2.11. Lift-drag polar for all tested wings across varied turbulence intensities(TI). Wings with high elbow angles show a reduced aerodynamic performance envelope.Maximum liftAerodynamic efficiencyElbow Angle (°)Minimum dragElbow Angle (°) 50 70 90 110 130 150 30 50 70 90 110 130 1502345Turbulence intensity (%) in vivoelbow angles 0.041.424.61ABCFigure 2.12. Aerodynamic performance metrics. Elbow extension across the in vivorange (gray shading) significantly (A) decreases maximum lift coefficient, (B) increasesminimum drag coefficient and (C) decreases aerodynamic efficiency. Turbulence inten-sity increases aerodynamic efficiency and maximum lift but has no effect on minimumdrag. Error bars represent the uncertainty due to bias and precision errors.322. GULL WING MORPHING2.4.4 LONGITUDINAL STATIC STABILITY RESULTSAs our previous results support the hypothesis that wing morphing allows control of aero-dynamic efficiency, we next asked how the in vivo elbow angle variation affects the trade-off inmaneuverability and stability. The trade-off can be quantified through passive pitch stability,which requires two conditions to be satisfied. To evaluate these conditions we investigated therelationship between the pitching moment and the lift produced as we varied the angle of attackfor each wing where the lines represent individual wings, coloured based on their elbow angle(Fig. 2.13). First, the flyer must be able to trim, defined as producing useful lift at its equi-librium, which occurs if the zero-lift pitching moment is positive [37]. This can be evaluatedthrough the y-intercept of the relationship between pitching moment and lift (Fig. 2.13). Thewings contribution alone for the majority of tested wings did not meet this condition due to anegative zero-lift pitch moment (Fig. 2.14A). However, the most extended wings had positivezero-lift moments, which would make it easier for the bird to trim. It would be possible forbirds with more folded wings to trim using other body components (tail, body) but they couldnot trim with only the wing’s contribution. The second condition for pitch stability is thatits derivative (for non-stalled flight conditions) must be negative, evaluated through the slopeof the relationship between pitching moment and lift (Fig. 2.13). The pitch stability deriva-tive becomes increasingly negative as the elbow extends providing a larger restorative moment(Fig. 2.14B). Turbulence had a destabilizing effect on both stability parameters. It is notablethat the in vivo range of elbow angles (gray region in Fig. 2.14) allows gulls to shift the trimpoint. Moreover, the in vivo range also encompassed most, but not all, of the full range of pitchstability derivative values.332. GULL WING MORPHINGLift coefficientPitch moment coefficientLift coefficient Lift coefficient-0.6-0.4-0.20.0-0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25TI = 0.04% TI = 1.42% TI = 4.61%30507090110130150Elbow Angle (°)Figure 2.13. Relationship between pitching moment and lift. Passive pitch stabil-ity increases as the elbow extends as is evaluated from the slope and intercept of thisrelationship.Zero-lift pitchPitch stability derivativeElbow Angle (°)Elbow Angle (°)−0.0670.02730 50 70 90 110 130 150 30 50 70 90 110 130 150−0.8−0.6−0.4−0.20.0Turbulence intensity (%) in vivoelbow angles 0.041.424.61ABFigure 2.14. Aerodynamic longitudinal static stability metrics. Passive pitch stabilityincreases as the elbow extends across the in vivo range (gray shading) evidenced by (A)the increasing zero lift pitching moment and (B) the decreasing pitch stability derivative.Turbulence intensity had a destabilizing effect on both parameters. Error bars on (A)represent the uncertainty due to bias and precision errors. The horizontal dashed line in(A) represents zero. Error bars on (B) represent 95% confidence intervals of the linearmodel slope prediction.2.4.5 UNCERTAINTY, ERROR AND STATISTICAL ANALYSISWe calculated the uncertainty of the time series readings of the pressure, force and momentdata using the integrated autocorrelation time calculated by the R package dirmcmc [60]. Thisresult was propagated through all calculations. Additionally, this propagation included error ofwing area (4%), root chord (3%) and bias errors from machinery. Error from measurements andequipment was also included within the uncertainty propagation as applicable. Uncertainty of342. GULL WING MORPHINGthe results are displayed as error bars in Figure 2.12A, B, C and Figure 2.14A. The uncertaintyis minimal for all results except for the maximum coefficient of lift.The induced drag in our experiment is overestimated due to the gap between the root of thewings and the tunnel walls (Fig. 2.15). We estimated this effect by using the standard planarwing equation (Eq. 1.7) to compute the amount of induced drag that would occur if the halfmodel was truly a full model (using an span efficiency factor of 1) [37]. In this simplifiedcase we assume that the induced drag over the root is equivalent to that over the wing tip. Weremoved that value from the measured coefficient of drag and re-computed the aerodynamicefficiency (Fig. 2.15 5A). We found that the relative difference between our estimation andmeasured value was 5-20% (Fig. 2.15 5B). Additionally, wings were tested at varying distancesfrom the wall to allow us to ensure that the hand wing remained approximately perpendicularto the freestream flow (Fig. 2.15 5C). As such, this method should provide a conservativeestimate since the presence of the wall in proximity to the root will have a damping effectcompared to the wing in an infinite environment, which is assumed in our model. This effectmay be further reduced due to the geometry of the wings, as span-wise camber improves thespan efficiency factor above 1 and reduces the effects of induced drag compared to their planarcounterparts [61]. Finally, it is possible that the porous feather structure may allow air to passthrough the wing to interact with the boundary layer and impact the induced drag [62]. As aresult of this analysis, we expect that our results will hold, despite the potential over-estimationof drag.352. GULL WING MORPHING30 50 70 90 110 130 15023456Elbow Angle (°)5101520Elbow Angle (°)Error (%)Distance from Body (m)Corrected for additional induced dragMeasured ACLCmaxDBC30 50 70 90 110 130 1500. 2.15. Investigation of induced drag over the wing root. Size constraintsof the wind tunnel allowed only a single wing to be tested at a time. This set-upallowed for additional induced drag to be incurred due to airflow around the root ofthe wing. (A) This effect is estimated using the standard fixed wing induced dragequation. (B) This analysis revealed that 5-20% relative error in the aerodynamicefficiency was possible. (C) The wings were tested at varying distances from the wallto allow correct positioning of the leading edge. The wall would have a dampeningeffect on the induced drag and lessen the error.The pitch stability derivative (Fig. 2.14) was determined by fitting a linear model to thelinear range of the data pre-stall and computing the slope of the line. 95% confidence intervalswere computed and displayed. We used linear mixed-effects models from R package nlme toaccount for repeated measures on the same wings over different turbulence intensities [63].We first selected the models by comparing different linear, quadratic, and cubic fits using theAkaike information criterion and Akaike weights (Table 2.2). The best fit was a linear exponenton elbow angle for the maximum coefficient of lift and coefficient of pitch at the aerodynamiccenter. We found that the quadratic fit best explained the minimum coefficient of drag and thecubic model best predicted the aerodynamic efficiency and pitch stability derivative.362. GULL WING MORPHING∼ ElbowAngle− + TI + (1|WingID)1 2 3CLmaxAIC -74.96 -73.05 -71.05AIC differences 0.00 1.91 3.91Relative likelihood of model 1.00 0.38 0.14Akaike weights 0.66 0.25 0.09C LDmaxAIC 47.71 42.67 41.92AIC differences 5.79 0.76 0.00Relative likelihood of model 0.06 0.69 1.00Akaike weights 0.03 0.39 0.57CDminAIC -157.44 -162.99 -161.76AIC differences 5.55 0.00 1.23Relative likelihood of model 0.06 1.00 0.54Akaike weights 0.04 0.62 0.34dCmdCLAIC -124.90 -124.05 -125.90AIC differences 0.99 1.84 0.00Relative likelihood of model 0.61 0.40 1.00Akaike weights 0.30 0.20 0.50Cm0AIC -171.71 -169.73 -170.03AIC differences 0.00 1.98 1.68Relative likelihood of model 1.00 0.37 0.43Akaike weights 0.55 0.21 0.24Table 2.2. AIC Model selection for aerodynamic parameters. Using the Akaikeinformation criterion (AIC) and Akaike weights we investigated the best linear poly-nomial fit. Columns represent the different exponents on elbow angle for each modeltested.We next used an ANOVA test to compare a reduced model (signifying the null hypothesis)to the full model to determine the association between our explanatory variables (elbow angleand turbulence intensity) and our response variables (aerodynamic characteristics) (Table 2.3).All comparisons (except for the effect of turbulence intensity on the minimum drag) allowedus to reject the null hypothesis and find that there is a significant probability that there is anassociation between our tested explanatory and response variables. The medians of these mod-372. GULL WING MORPHINGels were visualized for Figure 2.12 and 2.14 using a model-based parametric bootstrap methodwith 100 simulations from the lme4 package [64].Model χ2 Df Pr(> χ2)Elbow angleC LDmax∼ 1 + TI + (1|WingID)13.48 3 0.0037 **C LDmax∼ ElbowAngle3 + TI + (1|WingID)CLmax ∼ 1 + TI + (1|WingID)5.003 1 0.0253 *CLmax ∼ ElbowAngle+ TI + (1|WingID)CDmin ∼ 1 + TI + (1|WingID)10.29 2 0.0058 **CDmin ∼ ElbowAngle2 + TI + (1|WingID)dCmdCL∼ 1 + TI + (1|WingID)18.48 3 0.0003 ***dCmdCL∼ ElbowAngle3 + TI + (1|WingID)Cm0 ∼ 1 + TI + (1|WingID)4.39 1 0.0362 *Cm0 ∼ ElbowAngle+ TI + (1|WingID)Turbulence intensityC LDmax∼ ElbowAngle3 + 1 + (1|WingID)5.942 1 0.0147 *C LDmax∼ ElbowAngle3 + TI + (1|WingID)CLmax ∼ ElbowAngle+ 1 + (1|WingID)12.9 1 0.0003 ***CLmax ∼ ElbowAngle+ TI + (1|WingID)CDmin ∼ ElbowAngle2 + 1 + (1|WingID)0.172 1 0.6781CDmin ∼ ElbowAngle2 + TI + (1|WingID)dCmdCL∼ ElbowAngle3 + 1 + (1|WingID)34.03 1 <0.0001 ***dCmdCL∼ ElbowAngle3 + TI + (1|WingID)Cm0 ∼ ElbowAngle+ 1 + (1|WingID)18.68 1 <0.0001 ***Cm0 ∼ ElbowAngle+ TI + (1|WingID)Table 2.3. ANOVA analysis of full vs reduced model. Using the model selectedby AIC (Table S2) we used ANOVA to compare the linear mixed-effect models to areduced model (gray font) to determine the statistical significance of the explanatoryvariable (either elbow angle or turbulence intensity). A p- value of less than 0.05indicates that the explanatory variable has a significant effect on the response variable.382. GULL WING MORPHING2.5 DISCUSSIONGiven the strong influence of elbow angle on aerodynamic efficiency, and on the trade-offin maneuverability and stability, we next examined the coupling of the aerodynamic parametersacross the natural range of wing morphing behavior. As elbow angle increases within the invivo range, wing morphology transitions from configurations with high spanwise camber tobeing nearly planar (Fig. 2.16A and Fig. 2.7). These two extremes in spanwise camber wereassociated with divergent characteristics of efficiency (Fig. 2.16B) and stability (Fig. 2.16C).This is consistent with the hypothesis that an increase in aerodynamic efficiency shifts theaerodynamic center, and thus couples the aerodynamic efficiency to the established trade-offin maneuverability and stability. The same coupling has been observed in stimulations wherewinglets were added to aircraft wings [46]. When we consider the relationship of the elbowangle with wind speeds and maximum wind gust speeds we find that the lower elbow anglesused in windier and gustier conditions are associated with a reduction of passive stability andincreased aerodynamic efficiency (Fig. 2.16D).Our results found no association between the aspect ratio and aerodynamic efficiency ofour wings (χ2 = 1.7024, DF = 1, p-value = 0.192). This is initially counterintuitive becauseanalytical equations developed for planar wings (Eq. 1.7) predict that aerodynamic efficiencywill increase as the aspect ratio of the wing increases. However, our results agree with previousstudies that investigated gull-like non-planar wings. These studies developed the hyper-ellipticcambered-span (HECS) wing and found improved aerodynamic efficiency over an equivalentelliptical planar wing with an identical aspect ratio [47, 65]. Particle image velocimetry re-vealed that the curvature of the wing relocated the wing tip vortex to a more distal location andreduced the induced drag thus improving the aerodynamic efficiency [47]. It should be notedthat there was a significant effect of wing twist on the final aerodynamic efficiency.The aerodynamic efficiency of bird wings has been well studied through prepared speci-mens, computational simulations, experimental measurement of live birds gliding, in either awind tunnel or in free flight (Fig. 2.17) [19, 20, 25, 48, 61, 66–98]. The results from the best392. GULL WING MORPHING0. (m)34°49°52°75°80°82°101°113°115°138°139°149°Spanwise camber Aerodynamic efficiencyPassive pitch stabilityHeight (m)0.05Elbow angle 2.1 5.0 -0.03 -0.760.041.424.61Turbulence intensity (%)A B C0.00Wind speed (m/s)Maximum gust (m/s)DWing center of gravityBehaviour 2 10 18 2 10 18 26Figure 2.16. Summary of morphometrics, performance, stability, and behaviour.(A) Across the in vivo range (gray band) the spanwise camber reduces as the elbowangle increases. Wings with the highest elbow angles (138◦-149◦) have (B) reducedaerodynamic efficiency but, (C) increased passive pitch stability. In contrast, wings withintermediate elbow angles (101◦-115◦) have opposing aerodynamic characteristics. (D)Gulls use lower elbow angles during glides as wind speeds and gusts increase.performing folded, intermediate and extended wing in our study (at 4.61% turbulence inten-sity) are included in Figure 2.17 (folded - AR = 6.26 C LDmax = 4.41; intermediate - AR = 7.28,C LDmax = 5.02; extended - AR = 7.54, C LDmax = 3.28). The data in Figure 2.17 was collectedfrom several authors and nomenclature has been verified to ensure consistency but each methodof data acquisition will have different errors. It is commonly agreed that the error of glider-based observational studies is too large for accurate measurements, however these results wereincluded in Figure 2.17 for completeness [86]. Additionally, there are other published aero-dynamic efficiencies of birds that were determined using analytical models which were notincluded in this figure. These equations are based on planar wing aerodynamic theory, andas such we have only included direct observational measurements of sink speed to airspeed(corrected for external flows), wind tunnel results and simulations.Bird wings have been found to span a vast range of aerodynamic efficiencies from as low402. GULL WING MORPHINGas 2.8 for a prepared swept merlin wing to as high as 17 for swifts [67,70]. This range is largerthan the range for insect wings (0.8-6.5) and bats (4-6) but comparable to that of modeleddinosaurs (4.1-13). Powered aircraft are capable of aerodynamic efficiencies around 17-20while gliders that have been specifically engineered for aerodynamic efficiency can have lift-to-drag ratios over 70. There is a trend of increasing performance as flight speeds increase.Birds often fly in a low/intermediate regime (70, 000 ≤ Re ≤ 200, 000) where performanceis impacted by the formation, size and hysteresis effects of the laminar separation bubble. Ingeneral, reducing the Reynolds number reduces the efficiency of the wing [34, 99, 100].Interestingly, multiple studies on prepared bird wing specimens (including the current one)have found aerodynamic efficiencies nearly half of those reported by studies done on live birdsgliding in wind tunnels (5.3± 2.9 compared to 10.3± 3.2, disregarding Raspet’s 1960 observa-tions). This discrepancy could be a result of the many differences between prepared specimensand live birds. This includes but is not limited to: the additional induced drag over the wingroot, birds not gliding at an equilibrium, the effects of additional lifting surfaces on live birds,and different material properties. This result warrants further investigation to fully decouplethe aerodynamic efficiency of birds from their testing methods.412. GULL WING MORPHING0204060800 20 40 60Aspect ratioAerodynamic EfficiencyBirdDinosaurAircraftInsectBatMethod of data acquisitionaircraftlive animalmodelprepared specimensimulationFlyerBlack vulture primary featherSHK sailplaneEta sailplaneConcordia sailplaneNorth American XB-70A ValkyrieFruit flyBlack vulture (glider-based observation)510152025Aerodynamic Efficiency051015205 10 15Aspect ratioAerodynamic Efficiency0250ABCFigure 2.17. Aerodynamic efficiency by aspect ratio of varied flyers (A) Reportedaerodynamic efficiency of birds (blue), model dinosaurs (yellow), aircraft (black), in-sects (green) and bats (red). (B) Zoom view of the reported values in panel (A) (aspectratios under 15). (C) Bird only view of the data in panel (B), highlighting the differencein reported values based on the method of data acquistion that was used.422. GULL WING MORPHINGCompared to the multitude of prior investigations into bird aerodynamic performance onlya few studies to date have experimentally investigated bird longitudinal stability. One suchstudy compared extinct taxa and the extant Larus taxa using 3D printed models [40]. Thistechnique allows an evaluation of the full body contribution to stability. The authors found thatextinct long tail taxa were passively stable but the short tail taxa (including gulls) are unstable.Observations of gliding gulls do not suggest that they are unstable, as they do not constantlyadjust their wing shape or other control surfaces in flight as would be necessary to maintain asteady path with an unstable configuration. In fact, the posed models had a uniform density andthus their center of gravity would not be similar to a live gull. This would directly affect thestability results as the center of gravity was most likely moved to a more posterior location dueto the uniform weight distribution even for light structures such as feathers. Thomas and Taylorfound that for 11 of 15 species tested, the center of gravity was in front of the wing’s proposedaerodynamic center which means that the wings would increase the passive stability of theflyers [15]. Of note, Withers measured the pitching moment on a prepared red shoulderedhawk wing about the humerus attachment (as was done in the current study) and found anunstable pitch stability derivative contrary to our results. Further comparative analysis may benecessary to better understand these differences [101].Withers also provided a measure for the zero-lift pitching moment which was 0.56 for thered shouldered hawk [101]. This value is much larger than the values calculated analyticallyfrom bird wing cambers (-0.20 to -0.08) [15]. Additionally, it is surprising that the zero-lift pitching moment would be positive, because bird wings have positive chordwise camberand for rigid wings this necessarily implies that the zero-lift pitching moment will be negative[15,38]. We found that the zero-lift pitching moment is negative for the folded and intermediatewings but becomes increasingly positive as the elbow extends. It even moves into positivevalues for the most extended wings at low turbulence intensity (range: -0.08 to 0.02) (Fig.2.14A). Our most positive result is still significantly lower than the zero-lift pitching momentthat Withers reported [101]. The positive contribution of the wings to the zero-lift pitchingmoment means that birds would need less input from the tail to properly trim the aircraft. An432. GULL WING MORPHINGaircraft uses the horizontal tail control surface (elevator) to adjust the zero-lift pitching momentto trim at varied flight conditions. Our finding that the elbow angle is associated with a changein the zero-lift pitching moment indicates that birds may be able to use their elbow angle togain similar benefits as an aircraft elevator. Further research into similar morphing mechanismsmay provide insight into future flying wing or tailess UAV designs.We found that the pitch stability derivative becomes more negative and more staticallystable as the elbow extends (Fig. 2.14B). Our results confirm that lower elbow angles wouldallow the flight path to be less dominated by restorative forces and may allow increased activecontrol. This finding is also supported by the visual observation that gulls flying in extremelygusty environments will frequently and abruptly shift their wing shapes unlike birds glidingin calmer conditions. This observation requires more robust testing in the future includingan investigation of the dynamic stability of gulls. However, we found that the pitch stabilityderivative is still negative at these lower elbow angles and there will still be some passivestability contribution. Our results only allow us comment on the contribution of the wing tothe pitch stability of the full bird. However, a more complete analysis should also includethe contributions of the tail, body, etc. Additionally for a full bird it would be important tocalculate the pitching moment about the exact center of gravity rather than the humerus headas is done in our study. This means that our results may be affected by relocating the originfrom the humerus head to the center of gravity for a full bird. However, the center of gravityshould not be significantly displaced along the birds body axis (x axis, Fig 1.2) and, therefore,the humerus head provides an acceptable reference point for the current work [15].Collectively, our results indicate that by lowering their elbow angle in challenging aerialconditions, gulls reduce their passive stability and increase their maneuverability. This agreeswith the hypothesis that birds use active control in unsteady conditions to steady their flight pathbut may use a combination of passive and active stability [15]. We have found that the abilityto morph their wings permits gulls to navigate trade-offs in efficiency, maneuverability, andstability. These findings suggest that UAVs may benefit from the implementation of a similarmorphing mechanism that would steady their flight path in variable flow environments.443 CONCLUSIONThe important thing is not to stop questioning.– Albert Einstein, 1955Aircraft design has advanced substantially since the first powered aircraft flight in 1903,but we still are unable to reproduce some of the desirable qualities of bird flight. This in-cludes their seemingly effortless ability to fly in turbulent flow environments. In this thesiswe have shown that gulls reduce their passive pitch stability in windy and gusty environmentsby actively morphing their wings. We began by determining the wing shapes used by glidinggulls in varied environmental conditions which we then compared to cadaver wing shapes withknown skeletal joint angles. This comparison allowed us to predict joint angles from the wingshapes used by freely gliding gulls. We found gliding gulls were using lower elbow angles aswind speed and gusts increased. We then explored the aerodynamic performance and stabilityconsequences over the range of observed elbow angles. This revealed that lower elbow angles(characterized by increased spanwise camber) had reduced passive pitch stability but increasedaerodynamic efficiency. Our finding agrees with rigid wing studies that showed that the addi-tion of spanwise camber into a wing can increase the aerodynamic efficiency [47]. In addition,our result supports a previous hypothesis that reduced static stability would be advantageousin unsteady conditions as birds would benefit from more active control to steady their flightpath [15]. We also found support for the hypothesis that birds use a combination of static andactive stability rather than solely relying on active stability [39]. Interestingly, we found thatfully extended gull wings do satisfy the two necessary conditions for passive pitch stabilityunlike rigid cambered wings. In all, our results suggest that further exploration of an avian-likewing morphing mechanism may allow active control of aerodynamic trade-offs in efficiency,maneuverability and stability to improve UAV adaptability in unsteady environments.453. CONCLUSION3.1 PURE SCIENCE TO APPLIED SCIENCE AND BACK AGAINTo advance bio-inspired adaptive UAV designs, it will be necessary to focus on robust testsof an avian-like morphing mechanism. A major challenge in bio-inspired work is transitioningbasic or fundamental research into functional applied designs. In avian biomechanics this chal-lenge has been simplified since the advent of the UAV because both birds and UAVs fly in sim-ilar Mach and Reynolds number flow regimes. This allows researchers to robustly investigateavian morphology in biologically-relevant flight conditions. Yet, there still are major obstaclesto overcome in pursuit of avian-like flight including the development of multi-functional mate-rials, integrated system design, actuation, control and how to correctly apply our fundamentalunderstanding of bird flight.3.1.1 MULTI-FUNCTIONAL MATERIALS AND STRUCTURAL DESIGNConventional aircraft design utilizes rigid, fixed wings to reduce the potentially detrimentaleffects of wing flutter. However, it is now known that passive deformation due to aerody-namic wing loading (aeroelasticity) can advantageous if properly implemented. Additionally,advances in composite materials have improved the strength-to-weight ratio of our wings andreduced the overall weight of recent aircraft designs. These light-weight, flexible wings arebecoming a reality and are implemented on planes already in operation such as the Boeing787 Dreamliner [102, 103]. Despite their impressive design, modern aircraft wings are stillsignificantly more rigid than those seen in natural flyers. Conceptual work including the Elas-tically Shaped Aircraft Concept has suggested that drag can be reduced by actively tailoringthe flexibility of the wing in flight [104]. Further exploration of bird wing material proper-ties, composition and birds’ ability to actively modulate their wing’s aeroelasticity may inspirefuture advances that improve aircraft performance.Bird wings are composites of multi-functional biological materials that have complex struc-tures and are difficult to reproduce. For example, the feather rachis has dorsal ridges that resistdorsal-ventral flexion but is also capable of resisting local buckling due to the fibrous internal463. CONCLUSIONmedullary foam that fills the rachis [105]. Although replicating this complex structure maybecome possible as additive manufacturing technology advances, it may not be necessary toexactly copy feather design to gain similar flight benefits. However, it is possible that futureconceptual work would benefit if they were informed by the known structural and materialproperties of bird wings. Continued research into avian wing structure and material propertieswill provide inspiration for efficient aeroelastic wing designs and multi-functional materials.3.1.2 INTEGRATED SYSTEM DESIGN, ACTUATION AND CONTROLAside from passive deformations, birds can contract their muscles to actively control theirwing shape in flight. Muscles are impressive natural systems due to their large force poten-tial despite their small size. Natural musculo-skeletal systems are also capable of fine tunedmotions because they use a ”chain of actuators” [106]. There have been many attempts tomimic muscle properties, though none of these have been implemented in morphing wings todate. However, the rise of artificial muscles and other smart materials has begun to make theimplementation of morphing structures in UAVs a reality [26].Smart materials integrate the actuator and the structure into one solid-state structure, whichis capable of responding to external stimulation including electricity, heat or strain [107, 108].Implementation of an actuator in a wing requires a detailed understanding of the external inputsand internal limitations of the mechanism. This includes how aerodynamic loading will affectthe actuator’s stroke, binding and friction, and the range of motion [26, 109]. Recent workto refine and implement smart materials has led to bio-inspired morphing structures. This in-cludes a tail fabricated from customized macro fiber composites that is capable of bio-inspiredshape morphing, and an airfoil that uses shape memory alloy and macro fiber composites tomorph the camber [108, 110]. In addition, a morphing UAV capable of varying its wing poly-hedral (a discrete version of spanwise camber) already exists [26, 48]. However, these aircraftare still a long way from the fully integrated wing morphing that is seen in bird flight. Thenext steps will include further analytical, computational and experimental validation of theperformance, stability and control of integrated morphing structures that can couple multiple473. CONCLUSIONmorphing parameters [111].Morphing wing technology must also be simple and inexpensive to be useful to industry.If a mechanism improves efficiency but increases cost, then the design is unlikely to provecommercially successful as the aerodynamic benefits will be negated [26]. One way to ensurethe practicality of a morphing mechanism is to streamline designs to allow for large-scale cost-effective manufacturing.3.1.3 ACCURATE IMPLEMENTATION OF FUNDAMENTAL KNOWLEDGEAn important distinction between natural and man-made flyers is that a bird is not necessar-ily optimized for flight. When observing or analyzing birds it is tempting to ascribe a meaningor an optimal condition to a morphology. However, there are many selective pressures actingon a bird’s morphology and it is important to remember that bird wings are used for moreapplications than just flight. In fact, there is the possibility that some avian wing features arenon-beneficial or even detrimental to flight. Identifying and distinguishing how specific com-ponents of bird morphology contribute to flight performance may serve to narrow the focus ofbio-inspired UAV design.It is also important to not remove the biological system from the design process. This canbe done by including robust behavioural studies of the chosen study organism. In this studywe focused mainly on the active wing morphing capabilities of gulls through the flexion andextension of their elbow joint angle. By studying their behaviour we were able to isolate anin vivo range of angles and identify a trend with environmental conditions. This has given usfurther insight into how and why birds may morph their wings given an environmental input.Investigating how the local environment affects bird behaviour is important not only for devel-oping our understanding of their natural history and ecology, but can also serve to moderatethe potential impacts of man-made installations, such as wind turbine farms or buildings [112].Similar work has begun in labs equipped with facilities that allow birds to fly in controlledenvironments while exposed to controlled and repeatable inputs such as a visual stimulus orwind gust [113, 114]. This research is promising as it may improve collision avoidance and483. CONCLUSIONgust alleviation algorithms in UAVs, but can also provide a concrete idea of how a changingenvironment affects birds foraging, roosting, migrating and their overall success as a species.3.1.4 SUMMARYIn summary, investigating bird flight through a behaviour, mechanism and the aerodynamicconsequences can contribute to both a biological knowledge base and engineering design. De-veloping our understanding of bird wing morphing allows us to begin to define a biologically-relevant design space that may promote new discoveries in aeronautical engineering. Our studyidentified that an adjustment to only one joint in a gull wing may steady their flight path in un-steady conditions. The elbow plays a key role in avian flight by allowing gulls to adjust theirperformance and stability in response to environmental variations. This finding suggests that anavian-inspired morphing wing UAV design could launch a new generation of multi-functionalaircraft capable of using a single joint to actively adjust their aerodynamic characteristics toadapt to their environment. Further integration of bird behaviour and functional anatomy toexplore the aerodynamic consequences of their morphology will allow us to begin to under-stand the mystery of bird flight, and may transform fundamental research into innovative UAVdesigns.49BIBLIOGRAPHY[1] Hallion, R. Taking Flight: Inventing the Aerial Age, from Antiquity through the FirstWorld War (Oxford University Press, 2003).[2] Reay, D. A. The History of Man-Powered Flight (Elsevier, 2014).[3] Wright, W. What Mouillard did. The Aeronautical Journal 20, 107–110 (1916).[4] Anderson Jr, J. D. The Airplane, a History of Its Technology (American Institute ofAeronautics & Astronautics, 2002).[5] Wada, D. et al. 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