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Wind Tunnel Testing of Load-Alleviating Membrane Wings

Permanent Link: http://ufdc.ufl.edu/UFE0041340/00001

Material Information

Title: Wind Tunnel Testing of Load-Alleviating Membrane Wings
Physical Description: 1 online resource (62 p.)
Language: english
Creator: Abudaram, Yaakov
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aerodynamic, aeroelastic, alleviating, anisotropic, attack, batten, camber, carbon, chord, deformation, drag, elongation, epoxy, fiber, hyperelastic, latex, leading, lift, mav, membrane, mold, pitching, reynolds, scallop, silicone, stall, sting, trailing, tunnel, vic, vortex, wind, wing
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work is concerned with wind tunnel testing of elastic latex and silicone membrane wings intended for micro air vehicles. Erratic flow conditions are a particular problem for the smooth controllability of such vehicles, and so stiff batten structures are imbedded into the trailing edge of the membrane wing, intended to passively washout under aerodynamic loading. Several disparate wing structures are fabricated, with varying batten thicknesses and spacing. Another wing with an anisotropic membrane skin is fabricated mimicking the wing skins of biological flyers, such as bats and pterosaurs. In this work an artificial anisotropic membrane skin was utilized on a wing with different orientations to observe and analyze various deformations and loadings in the wind tunnel at low Reynolds Numbers. These passive deformations are not always effective however, particularly at higher angles of attack or higher speeds and so this work is intended to provide some understanding of the complex role of wing structure and flight speed upon aerodynamic performance of membrane wings. Data, in terms of measured aerodynamic loads and structural deformation, is given for a wide range of relatively low Reynolds numbers. Drastic changes in lift slopes, stalling conditions and deformation patterns are found for certain combinations of flight speed and wing structure.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yaakov Abudaram.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041340:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041340/00001

Material Information

Title: Wind Tunnel Testing of Load-Alleviating Membrane Wings
Physical Description: 1 online resource (62 p.)
Language: english
Creator: Abudaram, Yaakov
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aerodynamic, aeroelastic, alleviating, anisotropic, attack, batten, camber, carbon, chord, deformation, drag, elongation, epoxy, fiber, hyperelastic, latex, leading, lift, mav, membrane, mold, pitching, reynolds, scallop, silicone, stall, sting, trailing, tunnel, vic, vortex, wind, wing
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work is concerned with wind tunnel testing of elastic latex and silicone membrane wings intended for micro air vehicles. Erratic flow conditions are a particular problem for the smooth controllability of such vehicles, and so stiff batten structures are imbedded into the trailing edge of the membrane wing, intended to passively washout under aerodynamic loading. Several disparate wing structures are fabricated, with varying batten thicknesses and spacing. Another wing with an anisotropic membrane skin is fabricated mimicking the wing skins of biological flyers, such as bats and pterosaurs. In this work an artificial anisotropic membrane skin was utilized on a wing with different orientations to observe and analyze various deformations and loadings in the wind tunnel at low Reynolds Numbers. These passive deformations are not always effective however, particularly at higher angles of attack or higher speeds and so this work is intended to provide some understanding of the complex role of wing structure and flight speed upon aerodynamic performance of membrane wings. Data, in terms of measured aerodynamic loads and structural deformation, is given for a wide range of relatively low Reynolds numbers. Drastic changes in lift slopes, stalling conditions and deformation patterns are found for certain combinations of flight speed and wing structure.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yaakov Abudaram.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041340:00001


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1 WIND TUNNEL TESTING OF LOAD-A LLEVIATING MEMBRANE WINGS By YAAKOV JACK ABUDARAM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009

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2 2009 Yaakov Jack Abudaram

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3 To my mother, who has given me her unconditional love, and has s hown me the way to success.

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4 ACKNOWLEDGMENTS The m ost special thanks to Dr. Peter Ifju for being a great advisor by giving the best possible and practical solutions to the most challenging problems I have encountered during the time I had spent at the MAV lab, and, of course for funding me throughout the entire time I spent in the graduate school. His intelligence le vel is proportionate to his compassion toward people, which makes him an exceptional being. T hose who work for him are the most fortunate students, and he is an ideal boss everybody would wish for. Thanks go out to Kyuho Lee for teaching me th e skills to manufacture airplanes, being a good friend and a supervisor at the same time, and al so trying to teach me how to fly. I learned it from the best, and without him this thesis would not have been possible. I owe my deepest gratitude to Dr. Bret Stan ford, who taught me the most fundamental and important concepts about the flexib le wings. He is the one who sugge sted the hot topics that I am presenting in this thesis, and he is the mastermind behind most of the ideas covered in this work. He has answered every single email I sent and every question I asked promptly, diligently, and patiently to the full extent. Thanks go out to Dr. Rick Lind and Dr. Da vid Jenkins for accepting to be in my committee. I also would like to th ank Albert Lin and Vijay Jagdale for helping me a great deal in visual image correlation te sting and post-processing. Thanks go out to my future wife, Eda, for feeding me while I was spending extensive hours at the wind tunnel; conseque ntly, keeping my mind fresh to keep the tunnel running. She has also been a wonderful emotional help in writing my thesis. It is said every successful man has a woman behind him. The woman behind me ha s been my mother; therefore, I thank her from the bottom of my heart for be ing a great support in my life.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........6 LIST OF FIGURES.........................................................................................................................7 NOMENCLATURE......................................................................................................................10 ABSTRACT...................................................................................................................................11 CHAP TER 1 INTRODUCTION..................................................................................................................12 2 EXPERIMENTAL TECHNIQUES........................................................................................16 2.1 Wind Tunnel................................................................................................................ .....16 2.2 Sting Balance....................................................................................................................17 2.3 Visual Image Correlation..................................................................................................18 2.4 Membrane Wings............................................................................................................. .20 2.4.1 Latex Membrane Wing........................................................................................... 20 2.4.2 Crinkled Silicone Membrane Wing........................................................................ 21 3 RESULTS...............................................................................................................................25 3.1 Latex Membrane Batten Reinforced Wing Results.......................................................... 25 3.1.1 Effect of Reynolds Number....................................................................................27 3.1.2 Effect of Batten Stiffness........................................................................................ 33 3.1.3 Spanwise Stiffness Gradient................................................................................... 38 3.1.4 Batten Spacing and Trailing Edge Shape............................................................... 41 3.2 Silicone Perimeter Reinforced Membrane Wing Results................................................. 42 3.2.1 Crinkled Silicone Membrane Specimen.................................................................44 3.2.1.1 Visual image correlation (VIC) testing........................................................ 45 3.2.1.2 Aerodynamic load testing............................................................................. 51 3.2.2 Test for Surface Effects..........................................................................................54 3.2.3 Test for Geometrical Effects.................................................................................. 55 4 CONCLUSIONS AND FUTURE WORK ................................................................... 57 APPENDIX EXTRA VISUAL IMAGE CORELATION IMAGES......................................... 59 LIST OF REFERENCES............................................................................................................... 60 BIOGRAPHICAL SKETCH.........................................................................................................62

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6 LIST OF TABLES Table page 3-1 The relationship between angle of attack ( ), crinkle angle ( ), and the highest defor mation value experienced by the membrane (w). ............................................... 46

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7 LIST OF FIGURES Figure page 2-1 Closed loop wind tunnel with th e large test se ction installed. ..................................... 162-2 Sting balance mounted on model arm. ..................................................................... 182-3 Schematic of the wind tunnel setup. ........................................................................ 202-4 Load-alleviating membrane wing. ........................................................................... 212-5 Aluminum and epoxy molds for silicon rubber. ........................................................ 222-6 Steps to fabricate the crinkled silicone membrane for the wing.. ................................. 232-7 Four parts of the wing that will be assembled together. ............................................. 242-8 Fully assembled crinkled silicone membrane wing. ................................................... 243-1 Load alleviating membrane wing. ........................................................................... 253-2 Wing structure definitions. ..................................................................................... 263-3 Wing deformation parameters of interest: wing twisting ( ), cambering (z), and bending ( ). .......................................................................................................... 273-4 Chord normalized out-of-plane disp lacement (w/c) along semi-wing of wing1 =10. .. 283-5 Spanwise strain ( yy) along the semi-wing of wing 1, = 10. ................................... 283-6 Local angle of attack along the semi-wi ng of wing 1 at 7 m/s (left) and 12 m/s (right). ................................................................................................................. 303-7 Local maximum camber along the semi-wi ng of wing 1 at 7 m/s (left) and 12 m/s (right). ................................................................................................................. 313-8 Local bending along the semi-wing of wing at 7 m/s (left) and 12 m/s (right). ............. 323-9 Lift coefficients of wing 1: angle of attack is measured at the rigid root. ..................... 333-10 Chord -normalized deformed semi-wing shape (z/c), = 10. .................................... 353-11 Local angle of attack along the semi-w ing at 7 m/s (left) and 12 m/s (right), = 10. ... 353-12 Local maximum camber along the semiwi ng at 7 m/s (left) and 12 m/s (right), =10. .. 363-13 Local bending along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. ............. 37

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8 3-14 Lift coefficients: angle of att ack is measured at th e rigid root. .................................... 383-15 Local angle of attack along the semi-w ing at 7 m/s (left) and 12 m/s (right), = 10. ... 393-16 Local maximum camber along the semi-w ing at 7 m/s (left) and 12 m/s (right), = 10. ...................................................................................................................... 393-17 Local bending along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. ............. 403-18 Lift coefficients: angle of att ack is measured at the rigid root. .................................... 413-19 Lift coefficients: angle of att ack is measured at the rigid root. .................................... 423-20 Specimens sandwiched in the wing apparatus.. ......................................................... 433-21 Crinkle angle notation for both the sili cone membrane wing and the silicone membrane with a rigid carbon-fiber plate beneath. .................................................... 443-22 Elliptical silicone membrane wing and notation for showing the angle of the ellipse. ... 443-23 Uniaxial stretch test with the crinkle pattern normal to, and parallel to, the loading. ..... 453-24 Deformation on the left side of the wing at =0 and =10. ....................................... 473-25 Deformation on the left side of the wing at =0 and =15. ....................................... 473-26 Deformation on the left side of the wing at =45 and =10. ..................................... 483-27 Deformation on the left side of the wing at =45 and =15. ..................................... 483-28 Deformation on the left side of the wing at =90 and =10. ..................................... 493-29 Deformation on the left side of the wing at =90 and =15. ..................................... 493-30 Deformation on the left side of the wing at =135 and =10. ................................... 503-31 Deformation on the left side of the wing at =135 and =15. ................................... 503-32 Lift curves of four different cr inkle angles and ri gid wing at 15 m/s. .......................... 513-33 Lift over drag curves of all tested an gles of specimen and rigid wing at 15 m/s. ........... 523-34 Pitching moment slope for crinkled me mbrane versus crinkle angle at 15 m/s. ............ 533-35 Lift over drag ratio versus crinkle angle at =6 and 15 m/s. ...................................... 533-36 Lift over drag ratio curve tested at 15 m/ s for four different crinkle angles with the specimen shown in 3-20B. ..................................................................................... 55

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9 A-1 Deformation on the left side of the wing at =105 and =10 ................................... 59A-2 Deformation on the left side of the wing at =105 and =15. ................................... 59

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10 NOMENCLATURE angle of attack b wing span c chord CL lift coefficient CL lift curve slope yy spanwise strains N image correlation grid spacing Re Reynolds number u, v, w Cartesian displacements U free-stream velocity x, y, z Cartesian coordinates leading edge displacement crinkle angle ellipse minor axis angle

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11 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Master of Science WIND TUNNEL TESTING OF LOAD-A LLEVIATING MEMBRANE WINGS By Yaakov Jack Abudaram December 2009 Chair: Peter Ifju Major: Mechanical Engineering This work is concerned with wind tunnel testing of elasti c latex and silicone membrane wings intended for micro air vehicles. Erratic flow conditions are a particular problem for the smooth controllability of such vehicles, and so stiff batten structures are imbedded into the trailing edge of the membrane wing, intended to passively wa shout under aerodynamic loading. Several disparate wing structures are fabricated, with varying ba tten thicknesses and spacing. Another wing with an anisotropic membrane skin is fabricated mimicking the wing skins of biological flyers, such as bats and pterosaurs. In this work an artificial anisotropic membrane skin was utilized on a wing with different or ientations to observe and analyze various deformations and loadings in the wind tunne l at low Reynolds Numbers. These passive deformations are not always effective however, part icularly at higher angles of attack or higher speeds and so this work is intended to provide some understanding of the complex role of wing structure and flight spee d upon aerodynamic performance of membrane wings. Data, in terms of measured aerodynamic load s and structural deformation, is given for a wide range of relatively low Reynolds numbers. Drastic cha nges in lift slopes, stalling conditions and deformation patter ns are found for certain combina tions of flight speed and wing structure.

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12 CHAPTER 1 INTRODUCTION The controllability and range of operation of sm all micro air vehicles (MAVs) can be greatly diminished in the presen ce of unsteady, gusty conditions. Indoor flight (envisioned for very small flapping vehicles) may suffer from si milar problems, due to air vents and ducting, for example. While several complex, active mechan isms may be envisioned to maintain smooth level flight in unsteady conditions 1[1], the energy budgets onboard MAVs are limited [2], and sim ple passive mechanisms may suffice. Extrem ely compliant wings have been used for MAV platforms [1], where the wing structure is predic ated by som e combin ation of carbon fiber composites (wing skeleton), and a la tex rubber membrane skin, sealed to the suction side of the aforementioned skeleton. The wing topology can be tailored to obtain th e desired change in aerodynamic performance through passive shape adaptation 1[4]. Load-alleviation is of obvious interest here (through, for example, uns teady gust alleviation, delayed stall, shallow lift-alpha slopes, minimized drag, etc.), and may be obtained with a very flexible trailing edge. The tr ailing edge deflects upwards due to aerodynamic loading, resulting in a nose-down geometric twist of the flexible wing section. Th is adaptive washout decreases the wings disturbance to the flow field, and thus the loads. For example, as the vehicle hits a head-on wind gust the overall airspeed suddenly in creases. The larger dynamic pressure causes the wing to twist and decrease the lifting efficiency. Because the airspeed is higher however, the wing maintains a near-constant lift history: the result is a wing that flies with exceptional smoothness, even in gusty conditions. However, such a relationship between dynami c pressure and elastic wing compliance may not always be so straightforward. Increasing th e flight speed accentuates the positive deflection of the trailing edge described above for load alle viation, but alters the Reynolds number as well.

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13 Reynolds numbers for typical fixed wing micro air vehicles are between 104 and 105, a span that sees extremely complex and mutable flow fields develop over a wing [5]: flow separation, transition, and reattachm ent [6], periodic vortex she dding, swirling, and pairing [7], and strong inte ractions with threedimensional tip vortices [8] have all been reported. The underlying physics, as discussed by Young and Horton [9], depend on many fact ors including Reynolds num ber and wing shape, the latter of which is not pre-determined for an elastic membrane wing. Though many suitable aeroelastic computational tools exist [3] for membrane micro air vehicle wings, they cannot always be expect ed to faithfully reproduce the com plex physics described above, particularly in post-stall regimes. Experimental wind tunnel testing can provide an initial link between wing structure, Reynolds number, and load alleviation, which can in turn be used to tune the aeroelastic models for a de tailed exploration of the design space. Existing literature on wind tunnel testing of membrane wings generally discuss up to three facets of the underlying physics: loads measurements (lift, dr ag, etc.), shape measurements (displacements and strains of the elastic memb rane under aerodynamic loading) and flow measurements. Shape measurements for membrane wings ar e typically non-contact optical methods, as strain gages and load cells are too intrusive. Song et al. [10] use stereo photogrammetry for displacem ent measurements of a membrane shee t stretched between two rigid posts, with a reported resolution between 35 and 40 m. Data is available at discrete markers placed along the wing. Projection moir interferometry requires no such marker placement (a fringe pattern is projected onto the wing surface), and the resulting data set is full-field. However, displacement resolutions reported by Fleming et al. [11] for micro air vehicle wo rk are relatively poor (250 m ), the dual-camera system mu st be rotated during the -sweep, and only out-of-plane data is available, making strain calculations (if needed) impossible. Stanford et al. [3] utilize a visual

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14 image correlation system for membrane wings, which is a full-field speckl e-based technique with a displacement resolution of 10 m. This method is utilized in the current work as well, and will be described below. Wu et al. [12] have extended the image correlation m ethod for high speed deformation measurements of flapping membrane wings. Experimental flow measurements for membrane wings include recent work with particle image velocimetry (PIV) by Hu et al. [13] and Rojratsirikul et al. [14] concerning an aspect ratio5 m embrane wing. The former is able to show that trailing edge was hout can keep the flow attached to the flexible surf ace up to 14 angle of attack, while a rigid wing under similar conditions shows a very large se paration bubble. The latter find that mean membrane shape is insensitive to angle of attack, though time-averaged flow is not, through the development of flow separation and vortex shedding. The authors are also able to show a strong time-dependent correlation between membrane vibration and the height of the shear layer [14]. A similar wing is studied by Mastram ico and Hubner [15] to correlate the elastic membrane structure with the velocity def icits within the wake. The current work is concerned with experime ntally establishing a general relationship between shape deformation measurements and load measurements of load-alleviating membrane wings, for a variety of wing struct ures, Reynolds numbers, and angles of attack. When possible, results will be further compared to existing flow measurement data in the literature. The outline of the current work is as follows: a general descri ption of the experimental setup will be given, in terms of the wind tunnel facility, sting balance, and image correla tion system. A description of the array of wing structures used for testing is discussed, followed by the first part of results: cambering, twist, wing bending, in-plane strains, a nd lift coefficients are given for a variety of cases. Second part of results elaborates the im ages that were provided by the VIC system, then

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15 shows a relationship between crinkle angle, lift, drag, lift over drag, pitc hing moment, and finally analyzes the effects of surface and different orient ations of geometrical effects. Load-alleviating wings generally present a trade-off in aerodynami c performance: the comp liant nature of the wing allows for gust rejection, delaye d stall, etc, but the lift in stea dy flight typically degrades as well, diminishing the payload capacity and the minimum cruise speed. The ability of a wing structure to decrease the lift slop e or delay the onset of stall, as compared to a nominally rigid model, is of particular interest.

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16 CHAPTER 2 EXPERIMENTAL TECHNIQUES 2.1 Wind Tunnel Experim ental testing is facil itated by wing deformation and f light load measurements, both conducted within a wind tunnel. The test facility used for the entirety of this work is an Engineering Laboratory Design 407B closed loop wind tunnel, with the flow loop arranged in a horizontal configuration. The te st section has an inner dimensi on of 0.84 m on each side, and is 2.44 m long (Figure 2-1). Also, the section has glass side walls a nd ceiling for observation of the model and visual imaging, which wi ll be explained in detail in Section 2.3. The velocity range is between 2 and 45 m/s (maximum Re of 2.7 million), provided by a 250 HP motor and a 2-stage axial fan. Centerline turbulence le vels have been measured on th e order of 0.2%. Optical access is available on the sidewalls and the ceiling. A Heise model PM di fferential pressure transducer is attached to a pitot-static t ube located at the center of the se ctions entrance, while a four-wire RTD mounted to the wall of the test sect ion measures the airflow temperature. Figure 2-1. Closed loop wi nd tunnel with the large te st section installed.

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17 2.2 Sting Balance An Aerolab 01-15 6-component strain gage stin g balance is used to m easure the aerodynamic forces and moments of the wind tunnel models. E ach of the six channels is in a full Wheatstonebridge configuration, with 5 channels dedicated to force, and 1 to a moment. Data acquisition is done with a NI SCXI 1520 8 channel programma ble strain gage module with full bridge configuration, 2.5 excitation vol ts, and a gain of 1000. A NI 6052 DAQ PAD fire wire provides A/D conversion, multiplexing, and the PC connecti on. For a given flight condition, the output signals from the six components are sampled at 1000 Hz for 2 seconds. The average of this data is sent to a LabVIEW-based module for the calcu lation of the relevant aerodynamic coefficients, and the standard deviation of the data is stored for an uncertainty analysis. Corrections are applied to the ae rodynamic coefficients to acc ount for blockage (solid, wake and streamline curvature) and flexibility effects. The latter is chiefly caused by the wind tunnel models slightly flexible suppor t (strain gage sting balance). Wind loads cause the model to pitch up in the wind tunnel. Visual image correla tion (described below) is used to measure the small rigid body movement in orde r to correct the angle of attack. The sting balance is mounted to a custom-fabricated aluminum model arm within the test se ction (Figure 2-2). The arm extends through a hole in the section wall, and is then attached to a gearbox and a brushless servomotor system for angle of attack control (r ates on the order of 1 /s). Tunnel speed, model inclination, and force/moment measurements are set/acquired using a dedicated PC and in-house LabVIEW-based software. The drag data that was gotten from sting balance for wings that have larger spans was seen to be bogus, in which this result may be caused by the 3-D effects since the tips are too close to the walls of the test section. Howeve r, for shorter spans, like the on e that is shown in Figure 3-21, the drag coefficients converge d to result logical values.

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18 Figure 2-2. Sting balance mounted on model arm. 2.3 Visual Image Correlation W ing deformation is measured with visual image correlation (VIC ), a non-contacting fullfield measurement technique orig inally developed by researchers at the University of South Carolina. The underlying principle is to calcul ate the displacement fiel d of a test specimen by tracking the deformation of a random sp eckling pattern applied to the surface [16]. Two precalibrated cam eras digitally acquire this patt ern before and after loading, using stereotriangulation techniques. The VIC system then tries to find a region (in the image of the deformed specimen) that maximizes a normalized cross-correlation function corresponding to a small subset of the reference image (taken when no load is applied to the structure). The image space is iteratively swept by the parameters of the cross-correlation function to transform the coordinates of the original reference frame to c oordinates within the defo rmed image. As it is unlikely that the deformed coordinates will direc tly fall onto the sampling grid of the reference image, accurate grey-value interpolation schemes are implemented to achieve optimal sub-pixel accuracy without bias [17].

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19 In order to capture the three-dimensional feat ures and deformation of a wind tunnel model, twin synchronized cameras, each looking from a di fferent viewing angle, are installed above the wind tunnel ceiling. As the cameras must rema in stationary throughout the experiment, a mounting bracket straddles the tunnel to preven t the transmission of vibration. Optical access into the test section is through a glass cei ling. Two continuous 250 W lamps illuminate the model, enabling the use of exposure times of 5 to 10 ms. The energy emitted from the lights, a potential hazard for the specimen (particularly the thin membrane skin, whose elastic properties are known to degrade in adverse conditions), was not a concern due to the cooling effect of the wind tunnel flow. A schematic of the final wind tunnel setup can be seen in Figure 2-3. The twin cameras are connected with a PC via an IEEE 1394 firewire cable, and a specialized unit is used to sync hronize the camera triggers for inst antaneous shots. A standard acquisition board installed in the computer carries out digitalizati on of the images, and the image processing is carried out by custom software, provided by Correlated Solutions, Inc. Typical data results obtained from the VIC system consist of geometry of the surface in discrete coordinates (x y z ) and the corresponding displacements ( u, v w ). The VIC system places a grid point every N pixels, where N is user defined. A final post-processing option involves calculating the in-plane strains ( xx, yy, and xy). This is done by mapping the displacement field onto an unstructured triangular mesh, and conduc ting the appropriate nu merical differentiation (the complete definition of fi nite strains is used). The general procedural steps used in this work are: 1) Take a picture of the wind tunnel model at the set angle of attack, with the wind off. 2) Start the wind tunnel, and wait for stable conditions. 3) Take a picture of the deformed wing, and record the aerodynamic loads. 4) Stop the wind tunnel, move the mode l to the next angle, and repeat.

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20 Each pair of images is then sent to the VIC system for processing. The acquired displacement field is composed of both the elastic deformation of the wing and the rigid body motions inherent within the wind tunnel setup. These motions are thought to primarily originate from the flexibility of the sting balance, and must be filtered out. The computed strain field is, theoretically, unaffect ed by these motions. Figure 2-3. Schematic of the wind tunnel setup. 2.4 Membrane Wings 2.4.1 Latex Membrane Wing The latex membrane wing under consideration for this work can be s een in Figure 2-4. It is a rectangular wing, with a 10 cm chord and a 4.8 aspect ratio. The maximum camber is 3.2% (at x/c = 0.3). The wing is built up from a T at the leading edge an d root, constructed from four layers of bi-directional pl ain-weave graphite/epoxy. Ten batte ns (strips of uni-directional carbon fiber) extend from the leading edge to the trailing edge of each semi-wing. A thin latex rubber skin (0.1 mm thick) is glue d to the suction side of this carbon fiber skelet on. The battens Wind Tunnel Incoming Flow Mounting Bracke t VIC Model Ar m Sting Balance Speckled Win g

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21 can potentially be excluded for enhanced flexib ility, but the membrane sk in alone is prone to excessive vibration above a critical dynamic pressure [18], resulting in a severe drag penalty. The procedures outlined by Albertani et al. [19] are used to facilitat e visual im age correlation testing. The carbon fiber skeleton is painted white a random black speckle pattern is applied to the translucent latex membrane, and the skin is then affixed to the skeleton with a spray adhesive. The result presents a nearly-homogeno us image for the VIC cameras, which should be unable to discern the location of the skeleton beneath the speckle pattern. Figure 2-4. Load-alleviating membrane wing. 2.4.2 Crinkled Silicone Membrane Wing The crinkled silicone m embrane wing is a rectangular wing with a 10cm chord and 2.0 aspect ratio (Figure 2-8). The maximum camber is same as the latex membrane wing since the same mold was used to manufacture the wing. Two rigid parts were constructed from four layers of bi-directional plain-weave gr aphite/epoxy; afterward, a hole of 73mm was carved out on each side of the upper and lower pa rts of the wing symmetrically and simultaneously to ensure the same geometry for both parts. To fabricate the cr inkled silicone membrane an aluminum mold is manufactured my milling with a fly-wheel crea ting equally spaced grooves. Another mold is formed by pouring epoxy on the top of the aluminum mold to create an identical match for the other side of the silicone r ubber as seen in Figure 2-5. plain-weave carbon fiber latex membrane skin carbon fiber batten

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22 Figure 2-5. Aluminum and epoxy molds for silicon rubber. Following steps are applied for the fabricati on of the crinkled silicone membrane: 1) Two parts of silicone rubber are mixed thoroughly. 2) The mixture is transferred into the two test tubes to be put in the centrifuge machine to remove the entrapped air bubbles. 3) The liquid silicone is pooled onto the surf ace corner of the epoxy mold that was applied a thin release film previously to make the de-bonding process easier. 4) Aluminum mold is started to be pressed fr om the corner at an angle and pushed down until the desired thickness is achieved, which is dictated by a thin indenter [27]. 5) After the silicone is cured, the molds are separated for the final product to be used (Figure 2-5). The crinkled silicone membrane has a wa velength of 0.8mm, amplitude of 0.17mm, and thickness of 0.1mm [26]. Finalized crinkled silicone membrane is speckled for visual image correlation test and glued onto a carbon-fiber ring with zero tens ion (Figure 2-7). Four small holes were drilled around each one of the 73mm holes to keep the entire structure intact with screws. Button-head screws were used for a more aerodynamic design. Finally, the apparatus was sandwiched between the upper and lower surfaces of the wing at the desired crinkle angle (Figure 2-8). Whenever the crinkle angle wanted to be adjusted, the screws were loosened and the specimens were rotated to the new desired an gle. This angle was measured with a digital inclinometer that is sensitive to 0.1.

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23 A B C D Figure 2-6. Steps to fabricate the crinkled silicone me mbrane for the wing. A) pouring the liquid silicone at the corner of the epoxy mo ld, B) pushing down the aluminum mold by slowly decreasing the angle between the tw o molds, C) pressing the aluminum mold to squeeze out the excess silicone with tw o indenters in the middle, D) finalized fabrication of the crinkled silicone membrane. The fabrication was initially done by utilizing five clamps at various locations of the two pieces of molds that had the liquid silicone in between; however, because the pressure was not exactly the same at each clamp, uniform thic kness was not achieved. Another manufacturing process was tried by sandwiching the liquid silicone between the molds under hydrostatic pressure by placing the entire assembly into the vacuum bag, which theoretically would yield a membrane that would have a constant valu e of thickness along each direction. However, vacuuming caused air bubbles inside the membrane.

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24 Figure 2-7. Four parts of the wing th at will be assembled together. Figure 2-8. Fully assembled cri nkled silicone membrane wing.

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25 CHAPTER 3 RESULTS 3.1 Latex Membrane Batten Reinforced Wing Results This work seeks to elucidate the relationship between lift, lift slope, a nd stall behavior of a m embrane wing through wind tunnel testing. While the number of relevant design variables for this problem is large (including planform shap e, ply layup schedule of the plain-weave, pretension within the membrane ski n, among others), only two are cons idered in this work: flight speed and batten thickness. Flight speed (t hrough the Reynolds number) directly impacts the behavior of the flow structures, and (through the dynamic pressure ) impacts the deformation of the structure as well. The battens are allowed to have between 1 and 4 layers of carbon fiber each, or can be removed entirely. The carbon fiber T is fixed at four layers of plain-weave oriented at 45 to the flow, and the membrane skin is slack for the entirety of the experiments. The resulting array of experiments is of course very large (5 desi gn variables for each of the ten battens, and wind speed is allowed to vary betwee n 5 and 15 m/s in increments of 2 m/s), and so a select number of interesting cases are presented for membrane wing characterization. Figure 3-1. Load alleviating membrane wing. The array of wing structures considered in this work is defined in Figure 3-2. The numbers beneath each wing denote the number of layers of carbon fiber used to construct each batten. Plain-weave carbon fiber Latex membrane skin Carbonfiber batten

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26 Only the semi-wing is shown, though of course each wing will be built symmetrically. Wing 1 utilizes single-layer battens th roughout the structure, while wings 2-4 simply increase the thickness of each batten, uniformly throughout the wing. Wings 5, 6, and 7 explore the effect of adding a spanwise stiffness gradie nt to the wing, by either tailori ng stiffness gradually toward the root (wing 5) or toward the wi ngtip (gradually with wing 6, or suddenly with wing 7 which has a very stiff outer batten). Finally, wings 8 and 9 will provide information on the effect of batten spacing, with every other batten removed from the membrane structure. As the large amount of un-reinforced membrane is expected to vibrate along the trailing edge (and detrimentally affect the aerodynamic performance), a scalloped traili ng edge is introduced in wing 9 to potentially offset this behavior. Figure 3-2. Wing structure definitions. The visual image correlation system is capable of providing full-field data along the wing, as discussed above, but comparisons between disparate wing structures is occasionally enhanced by compressing the data into three parameters of interest. Assuming that the spanwise motion of 1 1 1 1 1 1 1 1 1 1 2222222222 3333 3 3 3 3 33 Wing 1 Wing 2 Wing 3 4 4 4 4 4 4 4 4 4 4 3332222111 1112 2 2 2 3 33 Wing 4 Wing 5 Wing 6 1 1 1 1 1 1 1 1 4 1 22222 22 2 2 2 Wing 7 Wing 8 Wing 9

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27 each wing section is negligible compared to chordwise and transverse movements, these parameters are given in Figure 3-3. Wing twist is quantified by the local angle of attack, measured with respect to the free-stream veloci ty. The maximum camber of each flexible wing section is reported, as well as the transverse disp lacement of the leading edge. All three metrics can be measured as a function of the spanwise position along the wing. 3.1.1 Effect of Reynolds Number The range of tested flight speeds (5 to 15 m/s) equates to fairly low chord-based Reynolds numbers between 3.34 and 105. The flow structures pres ent throughout this range of Reynolds numbers should show subs tantial variations, and thus aerodynamic performance will as well. As reviewed by Carmichael [20]: for Reynolds numbers below 54, the laminar separated flow may not have time to reattach to the surface. Above 54, the flow may reattach, forming a long separation bubble over the wing. Fo r increased Reynolds numbers, the size of the bubble decreases, generally resulting in a decrease in form drag. Figure 3-3. Wing deformation parameters of interest: wing twisting ( ), cambering (z), and bending ( ). Results in this section are given solely in terms of wing 1, tested between 5 and 15 m/s in increments of 2 m/s as discussed above. An -sweep between 0 and 40 in increments of 1 is conducted for each speed, and aerodynamic loads are measured for each case. Elastic

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28 deformation is measured at select pre-stall cond itions. Deformation is sampled at 1 Hz for 10 seconds, and loads are sampled at 1000 Hz for 2 seconds. The chord-normalized out-of-plane displacements and spanwise strains that develo p over the semi-wing of wing 1 can be seen in Figure 3-4 and Figure 3-5, at 10 angle of attack and both 7 m/s and 12 m/s. The deformation at the root is close to zero (as this portion of the wing is attached to the wind tunnel sting balance, as seen in Figure 2-3), and each subsequent flexib le wing section sees a substantial trailing edge washout, upwards of 30% of the root chord. Figure 3-4. Chord normalized out-of-plane displacement (w/c) along semi-wing of wing1 =10. Figure 3-5. Spanwise strain ( yy) along the semi-wing of wing 1, = 10. The resolution of the VIC system (estimated at 10 m for displacements) is evident from Figure 3-4, as the carbon fiber areas of the wing (battens) can be clearly differentiated from the membrane skin. Aside from the nose-down twis t of each flexible wing section, the membrane

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29 portions of the wing show a local inflation towa rd the leading edge, and an overall wing bending deformation pattern is visible as well. The majo rity of the deformation is located toward the center of the semi-wing; this is a result of the loading pattern. Although th e structure is weakest at the wing tip (due to a uniformly distributed load, for example), th e sectional lift is estimated to be largest at the root and decrease to zero at the wing tip (from simple lifting line theorems [21], for exam ple). For higher speeds (12 m/s in Figure 34) substantial twisting is seen at the tip as well. Only the spanwise strain is reported here (F igure 3-5), as the batte ns prevent appreciable chordwise stretching [3]. The strain resolution of the VIC system is estimated to be 500 a relatively high value (compared to strain gages, fo r exam ple) due to the fact that the data is obtained by appropriately differentiating the di splacement fields. The VIC system is not expected to have the resolution to capture accurate strain information in the carbon fiber areas of the wing: any non-zero data in th ese areas is probably due to the spatial smoothing algorithm employed by the VIC system. At 7 m/s, ~0.5% stretching is measured between each batten toward the leading edge, where the local inflation is largest. Higher values are seen toward the root and the tip. At higher wi nd tunnel speeds, a large stress c oncentration develops between the rigid root and the first batten, resulting in 3% stretching. I ndeed, potential de-bonding of the membrane skin from the carbon fiber skeleton at this location on the wi ng had to be closely monitored during testing. Local angles of attack measured along the semi -wing of wing 1 are given in Figure 3-6 for a variety of wind speeds and global wing angles of a ttack (measured at the rigid root). At 7 m/s and 0 angle of attack, the major ity of the wing has twisted such that the flexible wing sections have a negative angle of incide nce. Though there app ears to be no appreciable relationship

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30 between twist and span location for this flight condition, a clear trend is seen for the remaining cases in Figure 3-6. The nose-down twist peak s between 40% and 60% of the semi-span, and recovers some of its original (undeformed) inci dence at the wing tip. The twist gradients are fairly large at this lo cation, potentially indicating the effect of the tip vortex swirling [15]. For higher speeds (12 m/s), a substantial portion of the wing at 5 and 10 is twisted to a negative incidence. At the higher angle of attack (15) the twist recovery at the wingtip is less than seen in previous cases. Results for higher angles of attack (which will be discussed in terms of loads measurements) are unavailable with the low-speed VIC system available for the current research: periodic vortex shedding [16] at these a ngles leads to a substantial wing vibration. Figure 3-6. Local angle of attack along the semi-wing of wing 1 at 7 m/s (left) and 12 m/s (right). Similar data is given in Figure 3-7 for the maximum camber at each spanwise station, as defined in Figure 3-3. The camber at 2y/b = 0 is th at of the rigid wing. As before, trends at 0 are unclear: the wing shows a slight increase in camb er (due to inflation) toward the root and the wingtip, but elsewhere slightly de-cambers. For the remainder of the cases considered in Figure 3-7, a clear undulation in the curve distinctly separates areas of me mbrane and carbon fiber. The adaptive washout noted in Figure 3-6 is not a rigid twisting of each section, but instead is

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31 facilitated by chordwise bending of each batten. This causes the wing to de-camber in a global sense, though local increases in camber are seen due to the inflat ion of the membrane skin in Figure 3-7. This behavior follows a similar trend to that seen above: the greatest deformation is between 40% and 60% of the semi-s pan, the wing recovers some of its original shape toward the wingtip, and deformation generally increases with angle of attack and flight speed. Unlike the adaptive washout however, the camb ering of the wing (for a give n flight speed) is relatively independent of angle of attack up to 30% of the semi-span. Similar data is given in Figure 3-8, for the span wise bending of the wing (defined in Figure 3-3). Deformations are fairly large (upwards of 15% of th e root chord), and monotonically increase with angle of attack and flight speed (pre-stall). The slope of the curve decreases toward the wing tip, indicative of the fact that that aerodynamic loading becomes very small in this area, as previously noted. Figure 3-7. Local maximum camb er along the semi-wing of wing 1 at 7 m/s (left) and 12 m/s (right). Lift coefficients for wing 1 and a rigid wing, for the entire sweep of speeds and angles of attack, are given in Figure 3-9. The resolution of the force bala nce in estimated to be 0.01 N, and error bars (not shown) are es timated to be 5% of the mean reported value. No substantial

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32 dependence upon the Reynolds number is noted for the lift of the rigid wing in the pre-stall regime; the extreme Reynolds numbers are reported in Figure 3-9. The rigid wing at the lower speed stalls slightly earlier (12), and shows a larger drop in lift af ter stall. This process repeats itself again at 21 (presumably after the boundary layer vortex sepa rates from the wing and convects into the wake), after which the lift of the rigid wing does not change substantially, regardless of Reynolds number. Figure 3-8. Local bending along the semi-wing of wing at 7 m/s (left) and 12 m/s (right). For the membrane wing, a large variation in the lift curve can be seen with different flight speeds, evinced by the drastic changes in shape seen in Figure 3-6 Figure 3-8. All of the flexible cases have a shallower lift slope and a larger stalling angle than the rigid wing, though the lowest speed (and hence the smallest deviations in wing shape) approaches the rigid case. The large stalling angles are further verified by the results of Hu et al. [13], who find attached flow over load-alleviating m embrane wings at high angles of attack. In general, both CL and CL decrease with higher speeds, due to the adaptive washout and the de-cambering of the wing. The latter metric decreases to the very low value of 1.98 rad-1 for high flight speeds. The angle of attack at zero lift generally increases (from -2 to 5), and

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33 negative lift is seen at positive angles of attack for a number of the cases in Figure 3-9. Even though the un-deformed wing is positively-camber ed, a substantial portion of the semi-wing elastically twists to a negative angle of attack, as seen in Figure 3-6. Wing stall is delayed as well, from 15 at 5 m/s to 32 at 13 m/s. Differences in aerodynamic performance between 13 m/s and 15 m/s are minimal (with th e exception of stalling angle, as the latt er stalls about 5 earlier), which may indicate that th e wing has reached an elastic limit. Figure 3-9. Lift coefficients of wing 1: angle of attack is measured at the rigid root. 3.1.2 Effect of Batten Stiffness Having ascertained in the previous section how a single m embrane structure (wing 1) behaves under a variety of flight conditions, attention is now turned to differing wing structures. Specifically, a comparison of wings 1, 2, 3 and 4 (as seen in Figure 3-2), wh ich alter the stiffness of the wing uniformly along the span by increasi ng the number of plies used to construct each carbon fiber batten. VIC results are given in Figure 3-10, in terms of the chord-normalized

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34 deformed wing shape (z/c) at 10 angle of attac k, and 7 and 12 m/s flight speed. It should be noted that the plots show the deformed wing sh ape, rather than the displacement contours of Figure 3-4. Corresponding wing twist, cambering, a nd bending data is given in Figure 3-11, Figure 3-12, and Figure 3-13, respectively. The most striking feature of the comparison be tween wings 1-4 is the extremely large wing bending of the stiffer structures. Under the same flow conditions, wing 1 bends to 8% at the tip, while wing 4 bends to 72%. This is due to the load-alleviating properties of the thinner battens, which adaptively washout along the trailing edge to decrease the sectional lift. The thicker battens do not washout as much, and so the wing responds to the load by bending along the span. This is emphasized by the contour lines of Figu re 3-10, which progress ively shift from being parallel to the trailing edge (w ashout) to perpendicular (spanw ise bending), as the number of layers in each batten is increased from 1 to 4. Furthermore, as seen in Figure 3-11, wings 2 and 3 show some degree of adaptive wash-in at 7 m/s (particularly wing 3), though this motion is gone at the high dynamic pressure. It is not clear from Figure 3-10 if the positive twist of each wing section (which is just measured by comparing the leading and trailing coordinates) is due to a specifi c wash-in of the battens, or a more global wing shaping behavior. This la tter phenomenon may arise from a bend-twist coupling behavior, perhaps due to the nonhomoge nous wing structure. Though the leading edge T is constructed of orthotropic carbon fiber, all of the layers of the plain weave laminate are oriented in a orientation, which will not contribute to the bend-twist coupling [3]. On a second note, in Figure 3-11 for the 12 m /s case, th e contour lines are angl ed, which is once again caused by the bend-twist coupling. However, this angle is not observed in the other wings.

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35 Figure 3-10. Chord -normalized deformed semi-wing shape (z/c), = 10. Figure 3-11. Local angle of attack along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. Additional aeroelastic load augmenting is ev ident in Figure 3-12, where wings 2-4 show positive adaptive cambering, as opposed to the general de-cambering deformation seen by wing

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36 1. At 12 m/s, the amplitude of the local undulations is much larg er as well (though the pattern is unobservable in Figure 3-10, as the displacements are dwarfed by the global spanwise bending). This is to be expected, as the stiffer battens provide a more rigid boundary condition for the local membrane inflation. Though not explicitly discusse d in this section, the spanwise strains that develop within the membrane skin (as seen in Figure 3-5, for example) grow with the spanwise bending, as expected. Wing 4 at 12 m/s sees 12% stretching at the traili ng edge of the root, a figure which is well above the validity of a lin ear stress-strain relati onship; a hyperelastic constitutive equation governs the response [3]. Figure 3-12. Local maximum camber along the se mi-wing at 7 m/s (left) and 12 m/s (right), =10. The measured lift coefficients for the four membrane wings, as well as the rigid wing, are given in Figure 3-14, for wind spee ds of 5, 9, and 13 m/s. At the lowest Reynolds number (3.34), wings 2, 3, and 4 all have a higher pre-stall lift than the rigid wing, as evidenced by the load augmenting passive shape deformation trends seen above: trialing edge wash-in (Figure 311) and positive cambering (Figure 3-12). As wi ng 4 shows a smaller amount of wash-in than

PAGE 37

37 wings 2 and 3, the increase in lift is also smaller. Only wing 1 is able to appreciably delay stall, and all 5 structures show si milar post-stall behavior. Figure 3-13. Local bending along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. At the median Reynolds number (correspond ing to 9 m/s), the results are strikingly different. Wing 3 stalls at roughly the same location seen at the lower speed, but past this angle of attack the lift continues to monotonically grow through the largest tested angle of 40, reaching an impressive coefficient of 2.2. Wing 4 shows similar behavior, but has a drastic drop in lift at 37. Similar post-stall behaviors for me mbrane micro air vehicle wings are noted in the work of Waszak et al. [22] The reasons for these striking results are as of yet unclear. The passive deformation may provide sm ooth attached flow at large angl es of attack, as noted in the PIV work of Hu et al. [13] Alternatively, static and/or dyna m ic mechanisms (i.e., wing vibration) may be at work to keep a leading edge vortex attached to the wing, as seen in classic dynamic stall studies [23]. The abrupt drop in lift of wing 4 at high angles would i ndica te the latter, potentially caused by a sudden detached vortex. As substantial as these resu lts are, the beneficial post-stall performance is very mutable and frag ile. At the highest Reynolds number seen in Figure 3-14, the phenomenon is gone: the stal led region is very flat, as before.

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38 Figure 3-14. Lift coefficien ts: angle of attack is m easured at the rigid root. 3.1.3 Spanwise Stiffness Gradient This section studies a comparison of wings 5, 6, and 7; each provides a spanwise gradient of batten stiffness. As above, wing twist, cambering, and bending are given in Figure 3-15, Figure 3-16, and Figure 3-17, respectively, along with data from wing 1 for comparisons. In terms of spanwise twist and cambering distributions, wings 5 and 6 are mirror images of each other. The battens of wing 5 are very stiff toward the root, resulting in adaptive wash-in and positive cambering (data for this wing is not available at the higher dynamic pressure, due to excessive vibrations). Toward the wing tip, the battens are very thin, leading to washout and decambering. Opposite trends are seen for wing 6, whose stiffness is clustered at the tip. Differences in wing bending (Figure 3-17) between wings 5 and 6 are marginal, with the former showing a slightly la rger tip deflection. The structures of wings 1 and 7, as reviewed above, are identic al with the exception of the wingtip batten: a single layer of carbon fiber is used for wing 1, while four are used for wing 7. As expected then, twist and camber trends show little difference up to 50% of the semispan. At the wing tip, the shape of wing 7 generally recovers to the undeformed shape: the local incidence returns to 10, and the camber returns to 3%: the wi ng is too stiff to either alleviate or augment

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39 the flight loads. The bending curves of wings 1 and 7 (Figure 3-17) are coincident, due to the fact that adaptive pressure redistributions from wing 1 to wing 7 primarily occur at the wing tip, where the forces may be too small to make much of a difference. Figure 3-15. Local angle of attack along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. Figure 3-16. Local maximum camber along the se mi-wing at 7 m/s (left) and 12 m/s (right), = 10.

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40 Figure 3-17. Local bending along the semi-wing at 7 m/s (left) and 12 m/s (right), = 10. Coefficient of lift data for the three wings, as well as the rigid wing and wing 1 for comparisons, are given in Figure 3-18, for three f light speeds of 5, 9, and 13 m/s. Wings 1 and 7 show substantial differences, a surp rising fact given that the majority of the wing structure is identical. Pre-stall, the lift curves are very simi lar, but wing 7 stalls at a significantly higher lift coefficient (at 9 m/s), and at 13 m/s, the wing neve r appears to stall. This result would almost certainly indicate the strong role of tip vortex swirling in the aeroelastic behavior of the membrane wing. Wing 6, which shares a similar ( however more gradual) stiffness gradient to wing 7, shows a comparable trend, though muted. Par ticularly at 9 m/s, the maximum attainable lift is very large, but occurs (stalls) 10 before wing 7. For the opposite stiffness gradient provided by wing 5, the lift behavior is similar to wings 1 and 7 fo r very small angles of attack (at 9 and 13 m/s), but then shows an extremel y steep lift slope and moderately non-linear behavior (pre-stall). Compared to the rigid wing, wing 5 stalls very early, and has a relatively low maximum lift coefficient. The reasons for th is behavior are unclear, nevertheless as noted by Ormiston [24], the steep lift slopes may make cont rollab ility of the membrane wing very difficult.

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41 Figure 3-18. Lift coefficien ts: angle of attack is m easured at the rigid root. 3.1.4 Batten Spacing and Trailing Edge Shape This section studies the effect of removing ba ttens from the wing structure; specifically a comparison of the lift-producing ab ilities of wings 2, 8, and 9 (as s een in Figure 3-2). All three wings have two-layer battens, but the latter two only have five evenly-spaced strips of carbon fiber, rather than ten. An excessive amount of un-constrained membrane skin will, as the dynamic pressure increases, lead to a large-amp litude vibration along the trailing edge, similar to the flapping motion of a flag. Such motions precl ude the used of the VIC system used in this work. Potential reasons for this complex phenomenon are discussed by Fitt and Pope [18]; experim ental observations are given by Mastramico and Hubner [15], who suggest the use of a scalloped tra iling edge (commonly seen in a bats membrane wing [10]) to remove the portion of the wing that is prone to excessive vibration. As discussed above, scalloping is present in wing 9. A genera l lift coefficient comp arison is seen in Figure 3-19. Scalloping generally provides a larger pre-sta ll lift coefficient than wing 8 for all flight speeds; at the lowest speed c onsidered (below the critical dynamic pressure that leads to vibration), the wing has highe r lift than wing 2 as well. Mastramico and Hubner [15] indicate that a scalloped wing has consistently lower drag than other tested wing structures (potentially

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42 due to a favorable tuning between the shear la yer and the membrane skin), suggesting a high aerodynamic efficiency. The un-scalloped wing 8 t ypically has the shallowest pre-stall lift slopes of the wings compared in Figure 3-19, but the largest maximum post-stall coefficients as well. This latter point may be a beneficial resu lt of the wing vibration, which has been shown by Munday and Jacob [25] to decrease the size of separation bubbles at low Reynolds numbers for certain reduced frequencies. Figure 3-19. Lift coefficien ts: angle of attack is m easured at the rigid root. 3.2 Silicone Perimeter Reinfo rced Membrane Wing Results This research docum ents the correspondence be tween the crinkle angle, lift, drag, lift over drag ratio, pitching mome nt, and pitching moment slope. Though so many different combinations are possible, such as using altere d specimens with varying thicknesses of silicone, any kind of desired materials, or various geomet rical shapes (ellipses, rectangles, or random patterns), three different specimens are taken und er consideration for th is research: crinkled silicone membrane, another crinkled membrane with a rigid carbon-fi ber plate beneath, and isotropic thin silicone elliptical membrane (Figure 3-20). For lower speeds (5 m/s 13 m/s),

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43 results were very similar to rigid wings sinc e the material deformations were not significant; therefore, the tests were conducted so lely at a higher speed of 15 m/s. A B C Figure 3-20. Specimens sandwiched in the wing appa ratus. A) crinkled silicone membrane glued on a carbon-fiber ring, B) crinkled silicone membrane glued on a two layer circular carbon fiber plate, C) isotr opic silicone membrane glued on a two layer carbon-fiber plate that has an elliptical hole. The notation used for the wing structures are shown in Figure 3-21 and Figure 3-22. The crinkle angle is measured with respect to the x-axis of the wing along the chord line. As an example, in Figure 3-21, 45 crin kle angle is drawn while for th e elliptical wing apparatus, the angle between the minor axis and x axis is m easured; therefore, in Figure 3-22 the angle, is equal to 135. The reason for this notation is because under hydrostatic pressure at a crinkle angle of 135, an exaggerated elliptical shape in Figure 322 is expected although loads experienced by the wing are not hyd rostatic in the wind tunnel. As shown in Figure 3-20, specimen A was used on the wing apparatus to explore the aerodynamic loads and deformation at different cr inkle angles, specimen B was installed to see the surface effects, and finally specimen C was pl aced in the wing apparatus to examine if the elliptical angle has an effect on the wing performance. Afterward al l the results were discussed in detail showing images from visual image correlation system (VIC) measurements and wind tunnel experiments.

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44 Figure 3-21. Crinkle angle nota tion for both the silicone membra ne wing and the silicone membrane with a rigid car bon-fiber plate beneath. Figure 3-22. Elliptical silicone membrane wing and notation for showing the angle of the ellipse. 3.2.1 Crinkled Silicone Membrane Specimen Before the wind tunnel and visual im age corre lation experimentations, the properties of the fabricated anisotropic material were studie d by Stanford et al. [26] Two specimens of

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45 membrane were cut to be subjected to a tension test under different loads in two directions, one direction being in the lin e of crinkles and the other perpendi cular to the crinkles. The elongations were measured, recorded, and analyzed. The resu lt was crinkles aligned with the load provided 3.6 times higher stiffness (Figure 3-23). Image Courtesy by Stanford, Bret and Ifju, Peter Figure 3-23. Uniaxial st retch test with the crinkle pattern nor mal to, and parallel to, the loading [26] 3.2.1.1 Visual image correlation (VIC) testing This experiment was first tried with no carbon-fiber ring around th e specimen; however, only a slight tension difference caused a large disc repancy on the drag data. Therefore, to keep the tension exactly as the same as the previous trial of crinkle angle, a ring was glued around the membrane. Afterward, the wing apparatus was ready to be tested under visu al correlation system (VIC) for crinkle angles of 0, 45, 90, and 135 at angles of attack of 10and 15. For every crinkle angle, a higher angle of attack caused a slightly larger deform ation along with a more defined and eccentric elliptical bu lge. The larger deformation is caused by larger loads at 15, and the more eccentric ellipse is caused by th e anisotropic material properties though this F/w = F/w =

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46 geometrical shape was not necessarily expected before the experimentation since the loads are higher toward the leading edge a nd lower at the trailing edge; ther efore, reducing the effects of hydrostatic pressure (Figur e 3-24 Figure 3-31). The most eccentric elliptical geometry is expe rienced at the crinkle angle of 90 because the higher loading toward the leading edge is al igned normal to the crinkles, which causes the material to stretch even more in the direction of the chord line (Figure 3-29). On a second note, the epicenter of all the elliptical deformations is closer toward the leadi ng edge, which is a clear indication that the loads are higher toward the fron t. On the other hand at the crinkle angle of 0 when the crinkles are dir ectly aligned with the higher loading th at is toward the leading edge, the bulging is nearly spherical because the tension al ong the stiffer direction may be similar to the tension in the weaker directi on (Figure 3-24 and Figure 3-25). Also, the highest deformation among this set of trials is expe rienced when the crinkle angle is set to 0 (Table 3-1). The maximum deformation values are also very si milar for crinkle angles of 45 and 135 though these two configurations behave differently in terms of aerodynamic performance, which will be discussed in the next section. Table 3-1. The relationship between angle of attack ( ), crinkle angle ( ), and the highest deformation value experienced by the membrane (w). AOA, Crinkle Angle Highest Deformation (mm) =10, =0 13.50 =15, =0 15.40 =10, =45 12.75 =15, =45 13.40 =10, =90 12.70 =15, =90 13.05 =10, =135 12.80 =15, =135 13.50 Another trial of VIC testing wa s done at the crinkle angle of 105 since this configuration provided an interesting result in the lift over drag data (Appendix).

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47 Figure 3-24. Deformation on th e left side of the wing at =0 and =10. Figure 3-25. Deformation on th e left side of the wing at =0 and =15.

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48 Figure 3-26. Deformation on th e left side of the wing at =45 and =10. Figure 3-27. Deformation on th e left side of the wing at =45 and =15.

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49 Figure 3-28. Deformation on th e left side of the wing at =90 and =10. Figure 3-29. Deformation on th e left side of the wing at =90 and =15.

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50 Figure 3-30. Deformation on th e left side of the wing at =135 and =10. Figure 3-31. Deformation on th e left side of the wing at =135 and =15.

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51 3.2.1.2 Aerodynamic load testing The crink le angle, on the wing apparatus was changed every 15 at 15 m/s for all tests and the data was recorded to be analyzed at an a ngle of attack array of 0-30 with increments of 2. In comparison to rigid wing, every crinkle angl e of the silicone membrane provided a much higher lift curve because the inflation on the wi ng caused an increase in camber, thereby increasing the lift coefficients. Ho wever, at different crinkle angles the lift history variation is negligible as seen in Figure 3-32. The data for only four different specimen angles are shown since plotting all crinkle angles in the same graph would cause the curves to coincide, thereby creating a chaotic image, which expresses the clos eness of all the lift coefficient values. Only when the specimen is set to 90, slightly aggr essive lift curve is observed in the beginning; however, this effect is muted as the stall angle is approached. Figure 3-32. Lift curves of four different crinkle angles and rigid wing at 15 m/s.

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52 Though lift curves were very similar, drag da ta varied substantially between the different angles of the crinkled specimen (Figure 3-33). More flexibility gives higher lift and better static stability since steeper pitching moment curves are observed in Figure 3-34, but more drag and much worse lift over drag coefficients; therefor e, there is a trade-o ff (Figure 3-35). Among the different angles of the specimen when the angle is set to 105, lift ove r drag gives the best performance while 90 gives the worst although nu merical values of deformation were similar for both cases; however, the shape was closer to a spherical shape when the crinkle angle was set to 105 (Appendix). So, it was susp ected that geometrical effect s might have been playing a critical role on drag. Figure 3-33. Lift over drag curves of all tested angles of specimen and rigid wing at 15 m/s.

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53 The stall angle for every trial changed very sl ightly in such a way that one may assume stall angle remains the same fo r all configurations, which corr esponds to 17.5 (Figure 3-32). Figure 3-34. Pitching moment slope for crinkled membrane versus cri nkle angle at 15 m/s. Figure 3-35. Lift over drag ra tio versus crinkle angle at =6 and 15 m/s.

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54 Maximum lift over drag ratio was achieved at approximately 6 angle of attack for most configurations while for crinkle a ngles of 60 and 120 th is angle corresponds close to 4 (Figure 3-33); also, for these two angles pitching moment s slope values were th e highest (Figure 3-34). The reasons of CL/CD and pitching moment slope variations between the different trials are not clear. For instance, looking at Figure 3-35 at crinkle angles of 75 and 105 high and similar lift over drag ratios are seen, and at the crinkle angle of 90 a very si gnificant lower ratio is observed, which cannot be explaine d only by analyzing the data fr om VIC; in other words, a direct relationship between the load test and VI C images cannot be made. Other parameters, such as surface effects, the geometry of deformations (area, volume), or a number of unknowns could be affecting the data. 3.2.2 Test for Surface Effects To understand the nature of the data, a quick test was conducted to seek the effects of the surface, which was to block the air to prevent deformation on the anisotropic silicone membrane. To avoid the membrane to be vacuumed by the lower pressure on the uppe r surface, the entire bottom area of silicone membrane was glued on the circular carbon-fiber plate (Figure 3-20B). The new specimen was rotated every 45 at 15 m/s with an angle of attack a rray of 0-30; hence, the data was analyzed for f our different configurations. The silicone rubber acts very similar to brakes causing an immense amount of drag on the wing in comparison to the smooth surfaced rigid wing (Figure 3-36); however, the lift curves are similar to the rigid wing. Rotation of crinkles had very little aff ect on the lift over drag plot when compared to the differences observed in Figure 3-33; thus, the surface effects can be assumed negligible, particularly looking at the curves for crinkle angl es of 45 and 135 that match perfectly. Therefore the curves seen in Fi gure 3-33 could not have been caused by surface effects.

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55 Figure 3-36. Lift over drag ratio curve tested at 15 m/s for four different crinkle angles with the specimen shown in Figure 3-20B. 3.2.3 Test for Geometrical Effects The test bed constructed for this work is not necessarily intended to imitate the exact geometrical deformations that o ccurred during the crinkled membrane test, but to seek an answer to how much difference would the orientation of an exaggerated geometrical deformation would make, such as the highly eccentric ellipse that was carved on a carbon-fiber plate shown in Figure 3-20C. Basically, the objective of this experiment is similar to simulate the deformations that were observed in the VIC testing and then relate it to the earlier results. Initially, the minor axis angle, was set equal to zero; then the angle was increased 45 for every trial creating four differe nt configurations (Figure 3-22). Each test was conducted at 15 m/s with an angle of attack array of 0-30.

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56 A drastic difference between the lift over drag curves is observed (Figure 3-37); however, the same order of magnitude could not have been expected from the crinkle membrane experiment since the geometrical deformations were entirely diffe rent for every crinkle angle. Discussion of why one minor axis angle provides better performance th an another is beyond the scope of this test though flow vi sualization would give an idea a bout the different drag curves. The objective of the test reached its target by proving that the or ientation of the geometric shape matters while it has no effect on the lift curves as expected since the surfac e area is the same for all configurations. Figure 3-37. Lift over drag ratio curves at f our different minor axis angles at 15 m/s.

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57 CHAPTER 4 CONCLUSIONS AND FUTURE WORK This work has detailed a series of experi m ental wind tunnel test s aimed at obtaining a relationship between structural makeup and aerodynamic performance for fixed flexible micro air vehicle wings. The first wing structure is predicated by a th in latex rubber skin, with stiffer batten structures imbedded within. Th e battens are designed to was hout along the trailing edge in response to an aerodynamic load, meant to alleviate th e flight loads: decreased lift slope, delayed stall, etc. Extensive testing of nine disparate membrane/batten structures and one rigid wing for a wide range of (relatively low) Reynolds num bers reveals a significantly more complex relationship: 1) Extremely thin battens can provide a subs tantial trailing edge washout, with peak twist at 50% of the semi-span. Conversel y, thicker battens are unable to alleviate these flight loads through twist, and show a sizeable spanwise bending whose severity increases with batten thickness and dynami c pressure. Perhaps due to the bending motion, these wings also tend to ad aptively wash-in, for some cases. 2) Wings with thin battens alleviate flight lo ads as the speed increases: delayed stall, shallow lift slopes. 3) Wings with thicker battens can augment th e flight loads (from the aforementioned wash-in as well as cambering via membrane inflation), and may show extremely large values of lift at high angles of attack: stall is delayed, but pre-stall lift is not drastically reduced. 4) A positive spanwise stiffness gradient (thicker at the tip) produces a similar, though muted, result. The wings aeroelastic response is particularly sensitive to the stiffness of the batten at the wing tip. 5) Increasing the distance between battens l eads to a sustained vibration along the membranes trailing edge once a critical dynamic pressure is crossed. This generally decreases the pre-stall lift, but for some cases, shows higher post-stall lift spikes. Scalloping the trailing edge removes the vi bration, and, at lower speeds, can recover some of the pre-stall lift. The second wing structure is configured by embedding three various specimens at different angles to seek the e ffect on aerodynamic performance: one specimen was an anisotropic membrane glued onto a carbon-fiber ring, the sec ond was the same membrane glued onto the

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58 surface of a carbon-fiber plate, and the third wa s an isotropic silicone membrane glued on a carbon-fiber plate that had an ellip tical shape carved in. An inclus ive testing of a total twenty wing configurations yielde d the following results: 1) Changing the crinkle angle on the first spec imen had an effect on the lift over drag ratio data while the lift curves for diffe rent orientations remained unchanged. 2) VIC testing clarified some of the unknowns to why the crinkle angle affects the drag curves. 3) Utilizing the second specimen at different configurations showed surface effects had no influence on the lift over drag plots; al so, this experiment has shown that using silicone membrane increases the drag. 4) Changing the orientation of the geometrical deformation on the wing have proven an immense effect on the drastic changes obs erved in the first specimen results. Future work will utilize various flow vi sualization techniques to obtain further understanding of the unresolved issu es evident in the above result s. Specifically, the underlying physics behind the drastically reduc ed stalling behavior shown by some of the wing structures, as well as the role wing tip vortices pl ay in the aeroelastic behavior, pa rticularly at higher angles of attack, where a close interaction with the longitudinal flow sepa ration seems likely.

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59 APPENDIX EXTRA VISUAL IMAGE CORELATION IMAGES Figure A-1. Deformation on the right side of the wing at =105 and =10. Figure A-2. Deformation on the right side of the wing at =105 and =15.

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60 REFERENCES [1] Pisano, W ., Lawrence, D., Autonomous Gust Insensitive Aircraft, AIAA Guidance, Navigation, and Control Conferen ce, Honolulu, HI, August 18-21, 2008. [2] Kajiwara, I., Haftka, R., Simultaneous Optim al Design of Shape and Control System for Micro Air Vehicles, AIAA Stru ctures, Structural Dynamics and Materials Conference, St. Louis, MO, April 12-15, 1999. [3] Stanford, B., Ifju, P., Albert ani, R., Shyy, W., Fixed Membrane Wings for Micro Air Vehicles: Experimental Char acterization, Numerical Modeli ng, and Tailoring, Progress in Aerospace Sciences, Vol. 44, No. 4, pp. 258-294, 2008. [4] Stanford, B., Ifju, P., Aeroelastic Topology Optimization of Membrane Structures for Micro Air Vehicles, Structural and Multidisciplinary Optimization, DOI: 10.1007/soo158-008-0292-x. [5] Gad-el-Hak, M., Micro-Air-Vehicles: Can They be Controlled Better? Journal of Aircraft, Vol. 38, No. 3, pp. 419-429, 2001. [6] Mueller, T., The Influence of Laminar Separation and Transition on Low Reynolds Number Airfoil Hysteresis, Journal of Aircraft, Vol. 22, No. 9, pp. 763-770, 1985. [7] Lin, J., Pauley, L., Low-Reynolds-Number Separation on an Airfoil, AIAA Journal, Vol. 34, No. 8, pp. 1570-1577, 1996. [8] Tang, J., Zhu, K., Numerical and Experimental Study of Flow Struct ure of Low-Aspect Ratio Wing, Journal of Airc raft, Vol. 41, No. 5, pp. 1196-1201, 2004. [9] Young, A., Horton, H, Some Results of Inve stigation of Separation Bubbles, AGARD Conference Proceedings, No. 4, pp. 779-811, 1966. [10] Song, A., Tian, X., Israeli, E., Galvao, R., Bishop, K., Swartz, S., Breuer, K., Aeromechanics of Membrane Wings with Implications for Animal Flight, AIAA Journal, Vol. 46, No. 8, pp. 2096-2106, 2008. [11] Fleming, G., Bartram, S., Waszak, M., Jenki ns, L., Projection Moir Interferometry Measurements of Micro Air Ve hicle Wings, SPIE Paper 4448-16. [12] Wu, P., Stanford, B., Ifju, P., Structural Deformation Measurements of Anisotropic Flexible Flapping Wings for Micro Air Vehicles, AIAA Structures, Structural Dynamics, and Materials Conference, Schaumburg, IL, April 7-10, 2008. [13] Hu, H., Tamai, M., Murphy, J., FlexibleMembrane Airfoils at Low Reynolds Numbers, Journal of Aircra ft, Vol. 45, No. 5, pp. 1767-1778, 2008.

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61 [14] Rojratsirikul, P., Wang, Z., Gu rsul, I., Unsteady Aerodynamics of Membrane Airfoils, AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 7-10, 2008. [15] Mastramico, N., Hubner, P., A Study of Wa ke Characteristics for Membrane Flat and Cambered Plates, AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Seattle, WA, June 23-26, 2008. [16] Sutton, M., Cheng, M., Peters, W., Chao, Y., McNeill, S., Application of an Optimized Digital Correlation Method to Planar Analysis, Image and Vision Computing, Vol. 4, No.3, pp. 143-151, 1986. [17] Schreier, H., Braasch, J., Sutton, M., Systema tic Errors in Digita l Image Correlation Caused by Intensity Interpolation, Optical Engineering, Vol. 39, No. 11, pp. 2915-2921, 2000. [18] Fitt, A., Pope, M., The Unsteady Motion of Two-Dimensional Flags With Bending Stiffness, Journal of Engineering Mechanics, Vol. 40, No. 3, pp. 227-248, 2001. [19] Albertani, R., Stanford, B., Hubner, J ., Ifju, P., Aerodynamic Coefficients and Deformation Measurements on Flexible Micro Air Vehicle Wings, Experimental Mechanics, Vol. 47, No. 5, pp. 625-635, 2007. [20] Carmichael, B., Low Reynolds Number Airf oil Survey, NASA Contractor Report, CR 165803, 1981. [21] Katz, J., Plotkin, A., Low-Speed Aerodynamics, Cambridge University Press, Cambridge, UK, 2001. [22] Waszak, M., Jenkins, N., Ifju, P., Stability and Control Properties of an Aeroelastic Fixed Wing Micro Aerial Vehi cle, AIAA Atmospheric Flight Mechanics Conference and Exhibit, Montreal, Canada, August 6-9, 2001. [23] Birch, J., Dickinson, M., Spanwise Flow and the Attachment of the Leading-Edge Vortex on Insect Wings, Nature, Vol. 412, pp. 729-733, 2001. [24] Ormiston, R., Theoretical and Experimental Aerodynamics of the Sailwing, Journal of Aircraft, Vol. 8, No. 2, pp. 77-84, 1971. [25] Munday, D., Jacob, J., Active Control of Separation on a Wing with Oscillating Chamber, Journal of Aircraft, Vol. 39, No. 1, pp. 187-189, 2002. [26] Stanford, B., Ifju, P., An Anisotropic Elasto mer Membrane University of Florida, FL, August, 2008. [27] Post Daniel, Han Bongae, and Ifju Peter. Production of Silicone Submasters. High Sensitivity Moire. New York: Spinger-Verlag, 1994. 432-434.

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62 BIOGRAPHICAL SKETCH Yaakov Jack Abudaram was born in Istanbul, Turkey in 1981. As a curious child would fall apart every single little ca r or toy he had instead of play ing with them. Throughout all of his life, he was very much into building model ships, airplanes, and buildings. Having been under the influence of his father he had always wanted to become a medical doctor; though, during the last year of high school realizing he could not stay away from numbers, he chose to study a major that would fulfill his desire : he studied physics for two years at the University of Kocaeli in Izmit, Turkey. Afte rward, took the opportunity to come to the United States, then learn English, and continue on his education at a community college aiming to study aerospace engineer ing at the University of Fl orida. He earned his dual Bachelor of Science Degree in Mechanical a nd Aerospace Engineering. During the last two semesters of his college years his enthusiasm toward airplanes pushed him to the doors of Micro Air Vehicle Laboratory. After working th ere for a few weeks, he felt like this laboratory was where he belonged to having seen the opportunity to combine his interest of building models with academia. He spent ex tensive hours at the la b building wings and fuselages, installing servos, li nkages, motors, cameras, and ta lking to his supervisor, Kyuho Lee, about airplanes and life. Finally, he found himself studying under Dr. Peter Ifju as a graduate student, and now he has come to one of the crossroads of his life by having written a thesis and looking for a job in the industry. He wants to get a PhD in the future, but only if it is possible to do so under Dr. Peter If ju at the Micro Air Vehicle Laboratory.