Title of Document: AERODYNAMIC MODELING OF A FLAPPING MEMBRANE WING USING MOTION TRACKING EXPERIMENTS Robyn Lynn Harmon, Masters of Science, 2008 Directed By: Langley Distinguished Professor, Dr. James E. Hubbard Jr., Department of Aerospace Engineering An analytical model of flapping membrane wing aerodynamics using experimental kinematic data is presented. An alternative to computational fluid dynamics, this experimental method tracks small reflective markers placed on two ornithopter membrane wings. Time varying three dimensional data of the wing kinematics and the corresponding aerodynamic loads were recorded for various flapping frequencies. The wing shape data was used to form an analytical aerodynamic model that uses blade element theory and quasi-steady aerodynamics to account for the local twist, stroke angle, membrane shape, wing velocity and acceleration. Results from the aerodynamic model show adequate correlation between the magnitude of lift and thrust produced but some phase errors exist between the measured and calculated force curves. This analytical model can be improved by comparison with a RANS CFD solver which provides insight into the fluid behavior. Implications on the membrane wing design are also presented. AERODYNAMIC MODELING OF A FLAPPING MEMBRANE WING USING MOTION TRACKING EXPERIMENTS By Robyn Lynn Harmon Thesis submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Masters of Science 2008 Advisory Committee: Professor James E. Hubbard Jr., Chair Dr. James Baeder, Associate Professor Dr. Inderjit Chopra, Gessow Professor © Copyright by Robyn Lynn Harmon 2008 Acknowledgements This research is dependent on the support of the University of Maryland, the National Institute of Aerospace and NASA Langley. A special thanks to Joe Conroy at the University of Maryland for providing insight and assistance in operating the Vicon Motion Tracking System. ii Table of Contents Chapter 1. Introduction...........................................................................................1 1.1 Introduction to UAVs...................................................................................2 1.1.1 Historical Overview..............................................................................2 1.1.2 UAV Mission Definition and Motivation.............................................3 1.1.3 Comparison of Fixed, Rotary, and Flapping Wing UAVs....................5 1.1.4 Low Reynolds Number Aerodynamics.................................................9 1.2 The Ornithopter Research Platform............................................................13 1.2.1 Ornithopter Wing Design and Dynamic Behavior..............................14 1.2.2 Ornithopter Flight Systems.................................................................18 1.3 Previous Work............................................................................................20 1.3.1 Operational UAVs..............................................................................21 1.3.2 Flapping and Membrane Wing Research............................................28 1.4 Thesis Outline.............................................................................................34 Chapter 2. Avian Flight and Biomimetics............................................................36 2.1 Historical Influence of Avian Flight Research...........................................36 2.2 Wing Structure............................................................................................41 2.3 Wing Kinematics........................................................................................46 2.4 Flight Modes...............................................................................................49 2.5 Aerodynamic Parameters............................................................................52 2.5.1 Reduced Frequency.............................................................................52 2.5.2 Strouhal Number.................................................................................53 2.6 Experimental Research in Avian Flight Theory.........................................54 2.6.1 Empirical Results................................................................................54 2.6.2 Aerodynamic Models..........................................................................56 2.6.3 The Power Curve................................................................................64 Chapter 3. Review of Aerodynamic Theory.........................................................66 3.1 Fundamentals of Fixed Wing Aerodynamics.............................................66 3.1.1 Aerodynamic Coefficients..................................................................67 3.1.2 Two-Dimensional Airfoil Theory.......................................................68 3.1.3 Finite Wing Aerodynamics.................................................................71 3.2 Membrane Aerodynamics...........................................................................76 3.2.1 Thwaites Two-Dimensional Sail Theory............................................76 3.2.2 Modern Membrane Aerodynamics.....................................................87 3.2.3 Nonlinear and Computational Membrane Models..............................91 3.3 Blade Element Theory................................................................................93 3.4 Unsteady Aerodynamics.............................................................................94 3.4.1 Quasi-Steady Thin Airfoil Theory......................................................95 3.4.2 Lift Deficiency Function.....................................................................97 3.4.3 Apparent Mass Effect.........................................................................98 3.4.4 Induced Flows...................................................................................100 3.4.5 Dynamic Stall....................................................................................102 3.5 Conclusions...............................................................................................103 Chapter 4. Wing Tracking Experiments.............................................................104 iii 4.1 Experiment Objective...............................................................................104 4.2 Experiment Setup and Procedure..............................................................105 4.2.1 Vicon Motion Tracking System........................................................105 4.2.2 Wing Marker Placement...................................................................106 4.2.3 Test Setup..........................................................................................107 4.2.4 Test Matrix and Procedure................................................................112 4.3 Post-processing.........................................................................................113 4.3.1 Labeling and Formatting...................................................................113 4.3.2 Data Synchronization........................................................................116 4.4 Kinematic Results.....................................................................................116 4.4.1 Wing Tip Paths.................................................................................117 4.4.2 Leading Edge Spar Bending.............................................................119 4.4.3 Membrane Shape..............................................................................120 4.5 Force Measurement Results......................................................................125 Chapter 5. Aerodynamic Modeling Theory........................................................134 5.1 Assumptions..............................................................................................134 5.2 Algorithm..................................................................................................135 5.3 Nomenclature, Inputs, Constants, and Conversions.................................137 5.4 Wing Geometry and Blade Element Definition........................................138 5.4.1 Wing Geometry.................................................................................138 5.4.2 Blade Element Selection...................................................................139 5.4.3 Blade Element Geometry..................................................................142 5.5 Blade Element Orientation and Kinematics..............................................144 5.5.1 Quasi-Steady Kinematics..................................................................145 5.5.2 Kinematic Calculations.....................................................................147 5.6 Application of Aerodynamic Equations....................................................150 5.6.1 Reference Quantities.........................................................................150 5.6.2 Drag Estimates and Power Requirements.........................................158 5.6.3 Induced Velocity...............................................................................164 5.6.4 Quasi-Steady Circulatory Force........................................................170 5.6.5 Quasi-Steady Non-Circulatory Force...............................................173 5.6.6 Vertical and Horizontal Force Components.....................................173 5.6.7 Blade Element Force Summation.....................................................174 Chapter 6. Aerodynamic Modeling Results.......................................................175 6.1 Comparison of Modeled and Measured Forces........................................175 6.1.1 Blue Ornithopter Results...................................................................176 6.1.2 White Ornithopter Results................................................................180 6.1.3 Conclusions.......................................................................................184 6.2 Comparison with Computational Fluid Dynamics...................................185 Chapter 7. Conclusions.......................................................................................189 7.1 Summary of Research...............................................................................189 7.2 Impact on Design......................................................................................191 7.3 Future Work..............................................................................................193 iv List of Tables Table 1.1: Ornithopter geometry, weight and flight specifications. Table 1.2: Operational Fixed Wing UAV Specifications Table 1.3: Rotary UAV System Specifications. Table 3.1: Aerodynamic coefficients for 2D and 3D bodies. Table 3.2: Flow unsteadiness level based on reduced frequency. Table 3.3: Fourier coefficients for AOA, plunging and pitching airfoils. Table 4.1: Force and stroke angle measurement channels. Table 4.2: Completed test matrix for each ornithopter Table 5.1: Wing geometric values. Table 5.2: Algorithms for determining blade element length and width of the blue ornithopter. Table 5.3: Algorithms for determining blade element length and width of the white ornithopter. Table 5.4: Methods for taking time derivatives. Table 5.5: Vertical and horizontal force components. v List of Figures Figure 1.1: Lift and drag performance with Reynolds number, [3]. Figure 1.2: Blue ornithopter with 1.07m (42”) span and white ornithopter with 1.22m (48”) span. Figure 1.3: Blue wing structure with leading edge and diagonal spars and trailing edge fingers. Figure 1.4: White wing has a similar structure to the blue wing. Figure 1.5: High speed photography of the stroke cycle of the blue ornithopter. Down stroke is presented on the left column, starting at the top of the figure and ending at the bottom. Upstroke begins at the bottom of the right column and continues to the top of the right column. Figure 1.6: Front view of ornithopter shows drive gear and crank arms that flap the wing.. Figure 1.7: Right hand side of ornithopter. Components from left to right include RC receiver, speed controller, electric motor, drive gear and crank arm. Figure 1.8: Left side of ornithopter. Components from right to left include lithium polymer battery, pinion gear from electric motor, transmission gear and shaft, and crank arm assembly. Figure 1.9: Ornithopter tail assembly, right servo controls elevator, left servo controls roll. Figure 1.10: (Clockwise from top left) Aerovironment’s Raven, Dragon Eye, Wasp 3 and Wasp 2. Figure 1.11: Naval Research Laboratory's Micro-Tactical Expendable UAV (MITE). Figure 1.12: Theiss Aviation Ferret UAV. Figure 1.13: Buster UAV from Mission Technologies Inc (MiTex). Figure 1.14: Applied Research Associates Nighthawk Micro Air Vehicle. Figure 1.15: Nascent Technologies Helicopter UAV. Figure 1.16: Honeywell Ducted Fan UAV model and demonstrated in active flight tests. Figure 1.17: Aurora Flight Sciences GoldenEye 50 transitions from vertical to forward flight. Figure 1.18: Micro sized ornithopters. Top row left to right: Aerovironment/Caltec's Microbat, University of Florida MAV, University of Toronto Mentor. Bottom row left to right: Technical University of Delft’s Delfly, Nathan Chronister’s Hummingbird and Petter Muren’s MAV. Figure 1.19: Cybird (left), Kinkade Parkhawk (right). Figure 2.1: Leonardo da Vinci’s human powered ornithopter design. Figure 2.2: Otto Lilienthal's successful gliding attempt. Figure 2.3: First high speed photographs of bird flight, a stork, taken by Marey, [8]. Figure 2.4: Marey's experiment setup to examine birds in flight, [8]. Figure 2.5: Schematics for (a), (b) a bird wing, (c) bat wing, (d) human arm, [9]. Figure 2.7: Hummingbird in hover mode. Figure 2.8: Soaring flight of a red tailed hawk with separated primary feathers. Figure 2.9: A pigeon airfoil versus a conventional wing at the root, midspan and wing tip, [9]. vi Figure 2.10: Three angular motions of the wing: flapping β, pitching θ, lead-lag ξ. Figure 2.11: Forces generated by a flapping wing during a) upstroke and b) downstroke, [10]. Figure 2.12: Tip paths for (a) albatross, fast gate; (b) pigeon, slow gate;. Figure 2.13: Tip path's of a hovering hummingbird, [8]. Figure 2.14: Representation of induced velocities and forces, [10]. Figure 2.15: Vortex ring gate of a chaffinch flying through a cloud of dust. Figure 2.16: Two trailing vortices of constant circulation from a kestrel in flight, [62]. Figure 2.17: Spedding’s model of the concertina wake, [62]. Part A shows the amplitude h of the wake which matches the stroke amplitudeφ. Part B, the side view, shows the length and angles of the vortex during downstroke (L and ψ ) and upstroke (L and ψ ). Part C shows the top 1 1 2 2 view and indicates the lateral separation of the vortices with 2b for 1 downstroke and 2b for upstroke, where the bird’s wingspan is 2b. 2 Also U is the velocity, T is the stroke period, and τ is the ratio of time spent during downstroke over the total stroke period. Figure 2.18: Power required for flight, [57]. Figure 3.1: Direction of aerodynamic forces, [64]. Figure 3.2: Effect of camber from trailing edge flap on lift curve, [64]. Figure 3.3: Delayed stall effect of leading edge device, such as a flap, on lift curve; [64].. Figure 3.4: Representation of downwash, w, with induced AOA and induced drag indicated, [64]. Figure 3.5: Lifting line with three horseshoe vortices showing superposition of circulation, [64]. Figure 3.6: Representation of the downwash solution for lifting-line theory, [65]. Figure 3.10: The first three critical shapes, λ =5.507,λ =11.78,λ =18.08, [27]. 2 4 6 Figure 3.11: Sail shape solutions for 3<λ<8, [27]. Figure 3.12: Solution curve for varying , [27]. α c l Figure 3.13: Relationship between αλ c l and λ, [27]. Figure 3.14: Concave sail shapes showing shift of maximum camber, [27]. Figure 3.15: Example of lift hysteresis of a flexible airfoil with 1.4% slack, [68]. Figure 3.16: Blade element diagram of a flapping wing with eight sections per semi- span. Figure 3.17: (A) – The plunging and pitching motion of an airfoil, (B) – The resulting vertical velocity, w(x), acting on the airfoil due to its motion, (C) – The equivalent angle of attack. Figure 3.18: The lift deficiency function C(k) versus F and G, [71]. Figure 3.20: The dynamic stall process and its effect on forces and moments, [71]. Figure 4.1: Wing marker placement on the blue wing (42” span), to be tracked visually. Figure 4.2: Locations of reflective marker on white wing with blade elements marked. Figure 4.3: Setting the tracking coordinate system. Figure 4.4: Vicon system testing setup. Figure 4.5: Test mount setup with 6-DOF force transducer. Figure 4.6: Magnetic potentiometer placed behind wing root to track wing angle. vii Figure 4.7: DAQ module and force observation station. Figure 4.8: Labeling of marker points on blue wing. Figure 4.9: Post-processing of tracking data. Figure 4.10: Normalized tip paths x vs z and x vs y for the blue ornithopter, R = 0.533m.. Figure 4.11: Normalized tip paths x vs z and x vs y for the white ornithopter, R = 0.599m. Figure 4.12: Leading edge bending of the blue ornithopter at 5.0 Hz flapping rate. Figure 4.13: Leading edge bending of the white ornithopter at 4.67 Hz flapping rate. Figure 4.14: Locationof blade element four for both ornithopterwings. Figure 4.15: Blue ornithopter: Downstroke behavior of blade element four’s membrane airfoil. Figure 4.16: Blue ornithopter: Upstroke behavior of blade element four’s membrane airfoil. Figure 4.17: White ornithopter: Downstroke behavior of blade element four’s membrane airfoil. Figure 4.18: White ornithopter: Upstroke behavior of blade element four’s membrane airfoil. Figure 4.19: Blue ornithopter forces measurements during a frequency sweep from 6Hz to 2Hz. Figure 4.20: White ornithopter force measurements for a frequency sweep from 3.5 to 4.7 Hz. Figure 4.21: Magnitude and phase angle with respect to beginning of downstroke of measured vertical and horizontal force as a function of frequency for the blue ornithopter. Figure 4.22: Magnitude and phase angle with respect to beginning of downstroke of measured vertical and horizontal force as a function of frequency for the white ornithopter. Figure 4.23: Blue ornithopter measured forces at 6.17Hz. The horizontal force is out of phase with the middle of the downstroke due to resonant structural Figure 4.24: Blue ornithopter measured forces at 5 Hz, where the structural resonance dissipates and the horizontal force is maximum near the middle of downstroke as expected. Figure 4.25: White ornithopter measured forces at 4.545 Hz, where the vertical force is exactly at the middle of downstroke. The horizontal force is phased - 30˚ from the start of downstroke, as frequency decreases both forces shift back in phase to 70˚ and -65˚ respectively. Figure 4.26: Blue ornithopter forces vs stroke angle at 5Hz. Figure 4.27: White ornithopter forces vs stroke angle at 4.545Hz. Figure 5.1: Blade element identification for blue ornithopter. Figure 5.2: Blade element identification for white ornithopter. Figure 5.3: Blade nine length and width approximation. Figure 5.8: Reynolds number of the blue ornithopter at the mean chord, wing root, and wing tip for 2, 5 and 8 m/s cases. RE variation is between 20,000 and 260,000, with a mean at 100,000. viii