Flapping Wing Vehicles: Numerical and Experimental Approach [1 ed.] 036723257X, 9780367232573

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Flapping Wing Vehicles

Flapping Wing Vehicles Numerical and Experimental Approach

Lung-Jieh Yang Balasubramanian Esakki

First edition published 2022 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2022 Taylor & Francis Group, LLC First edition published by CRC Press 2022 CRC Press is an imprint of Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 9780367232573 (hbk) ISBN: 9781032074139 (pbk) ISBN: 9780429280436 (ebk) DOI: 10.1201/9780429280436 Typeset in Times LT Std by KnowledgeWorks Global Ltd.

TO My Beloved Father, Mother, Wife, and Children

Contents Preface��������������������������������������������������������������������������������������������������������������������� xv Acknowledgments��������������������������������������������������������������������������������������������������xvii Authors��������������������������������������������������������������������������������������������������������������������xix Chapter 1 Introduction to Micro Aerial Vehicles..................................................1 1.1 1.2

1.3

1.4 1.5

1.6

Flapping Motion.........................................................................1 Aspects of Fluid Mechanics and ­Aerodynamics in the Study of Flyers.................................................................4 1.2.1 Governing Equations of Fluids.....................................5 1.2.2 Ideal Fluid Potential Flow.............................................7 1.2.3 Dimensional Analysis................................................... 8 1.2.4 Viscous Flow ~ Boundary-Layer Theory..........................11 1.2.5 Compressibility........................................................... 12 1.2.6 Drag and Flight Power................................................ 13 1.2.6.1 Induced Drag............................................... 13 1.2.6.2 Total Drag.................................................... 16 1.2.6.3 Flight Power................................................. 16 Flight Mechanics...................................................................... 18 1.3.1 The Dynamic Control of the Flapping Wing MAVs................................................................. 18 1.3.2 Equations of Motion for Rigid Aircrafts.....................20 1.3.3 Steady-State and Perturbation State............................... 21 1.3.4 Steady-state EoM........................................................ 22 1.3.5 Linearized EoM.......................................................... 23 1.3.6 Aerodynamic Forces and Moments............................24 1.3.7 Numerical Example for Longitudinal Modes.............25 1.3.8 Numerical Example for Lateral Modes.......................28 1.3.9 Plate-Body Stability.................................................... 31 Scaling Laws of Flapping Wings............................................. 33 1.4.1 Geometry Similarity................................................... 33 1.4.2 Scaling Laws of Bio-natural Flyers............................. 33 Lift Mechanisms of Flapping Flight........................................ 37 1.5.1 Dimensionless Parameters of Flapping Wings........... 37 1.5.2 Unsteady Lift Mechanisms......................................... 38 1.5.3 Rotational Lift of Flapping Wings..............................40 1.5.4 Added Mass................................................................. 41 1.5.5 Wing-Wake Interaction............................................... 41 Stability Issues of a Flapping Wing......................................... 42 1.6.1 C. G. of a Flapping Wing............................................ 42 1.6.2 Preliminary Review on Flight Dynamics Model of a Flapping Wing..........................................44 vii

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1.6.3 1.6.4

Time-Averaging of Inertia for Flapping Wings.......... 45 New Definition of Stability Derivatives Related to Flapping Frequency................................... 45 1.6.5 New Control Way Other Than Elevator, Aileron, and Rudder.................................................... 45 1.7 Summary.................................................................................. 47 References........................................................................................... 47 Chapter 2 In-Situ Lift Measurement Using PVDF Wing Sensor........................ 49 2.1 2.2 2.3 2.4

Lift Measurement Using Wind Tunnel..................................... 49 Inertial Force Effect on Lift..................................................... 53 Principle of Polyvinylidene Fluoride (PVDF).......................... 55 Fabrication of Flapping Wings with PVDF Lift Sensors............................................................................... 57 2.4.1 Fabrication of Flapping Wing..................................... 57 2.4.2 Introduction of Parylene.............................................. 61 2.5 Preliminary Wind Tunnel Test of Titanium-Parylene Wing.......................................................... 61 2.6 PVDF Sensor in Measuring the Lift Force of Flapping Wings....................................................................64 2.7 Flight Test................................................................................. 68 2.8 Summary.................................................................................. 71 References........................................................................................... 73

Chapter 3 Flapping Wing Mechanism Design..................................................... 77 3.1

3.2 3.3 3.4 3.5

Golden-Snitch Ornithopter....................................................... 77 3.1.1 Design of the Transmission Module........................... 77 3.1.2 Aerodynamic Performance of the Golden-Snitch............................................................. 79 3.1.3 Flight Test.................................................................... 83 Impact of Flapping Stroke Angle on Flapping Aerodynamics........................................................................... 85 Aerodynamic Characteristics of Golden-Snitch Pro...............90 Watt-Stephens Mechanism..................................................... 100 Evans Mechanism................................................................... 105 3.5.1 Preliminary Design................................................... 106 3.5.1.1 Phase Lag................................................... 106 3.5.1.2 Force Transmission Angle......................... 106 3.5.2 Improved Design of Evans Mechanism.................... 107 3.5.3 Comparison of Stephenson Mechanisms and Evans Mechanism............................................... 111 3.5.4 Measurement of Flapping Frequency............................112 3.5.5 Aerodynamic Performance Measurement of Evans Mechanism................................................. 116

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3.5.6

Mass Distribution of FWMAV with Evans Mechanism............................................. 122 3.6 Flight Test of Evans-Based FWMAV..................................... 123 3.7 Summary................................................................................ 127 References......................................................................................... 128 Chapter 4 Fabrication of Flapping Wing Micro Air Vehicles........................... 131 4.1

Electrical Discharging Wire Cutting (EDWC)...................... 131 4.1.1 Gold-Snitch Four-Bar Linkage (FBL) Mechanism by EDWC............................................... 132 4.1.2 EDWC of Evans Flapping Mechanism.......................134 4.2 Injection Molding................................................................... 137 4.2.1 PIM of FBL Mechanism for Golden-Snitch........................................................... 137 4.2.2 Development of Golden-Snitch Outer Body Using PIM.............................................. 141 4.2.3 PIM of Evans Flapping Mechanism.......................... 146 4.3 Additive Manufacturing (3D Printing)................................... 154 4.3.1 Fused Deposition Modeling (FDM).......................... 154 4.3.2 Parylene Coating as a Solid Lubricant...................... 156 4.3.3 Multijet Printing........................................................ 158 4.3.4 Polyjet Printing.......................................................... 158 4.3.5 Stereolithography...................................................... 159 4.4 Performance Comparison of Flapping Mechanisms by Different Manufactures..................................................... 160 4.4.1 Torque of Evans Mechanism by PIM........................ 160 4.4.2 3D Printing Evans Mechanism’s Performance Evaluation............................................ 161 4.5 Summary................................................................................ 168 References......................................................................................... 168 Chapter 5 Flapping Wing Design...................................................................... 173 5.1

5.2 5.3

Strengthening of Leading-Edge in Flapping Wings............... 173 5.1.1 Aerodynamic Enhancement of the Leading-Edge Tape on Flapping Wings.................... 173 5.1.2 Effect of Leading-Edge Tape on Power Consumption............................................................. 176 Carbon-Fiber Rib Effect on the Flapping Wings................... 179 Effect of Materials and Stiffness on the Flapping Wings...................................................................... 184 5.3.1 Aerodynamic Performance of Various Wing Membranes................................................................ 185 5.3.2 Power Consumption in Various Wing Membranes...................................................... 187

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5.4

Bionic Flapping Wings with Check Valves............................ 193 5.4.1 Working Principle of Flapping Wings with Check Valves............................................................. 193 5.4.2 Design of the Flapping Wings with Check Valves..................................................... 194 5.4.3 Wind Tunnel Testing of a Flapping Wing with Check Valves........................................... 196 5.5 Bionic Corrugated Flapping Wings........................................202 5.5.1 Dragonfly Wing and Corrugations............................203 5.5.2 Thickness Effect for Corrugated Wing.....................203 5.5.3 Design and Fabrication of a Corrugated Wing.......................................................204 5.5.4 Aerodynamic Performance Evaluation of a Corrugated Wing.......................................................208 5.5.5 Performance Evaluation at Cruising.........................208 5.6 Wing Stiffness of Different Flapping Wings......................... 213 5.7 Summary................................................................................ 215 References......................................................................................... 215 Chapter 6 Clap-and-Fling Flapping................................................................... 219 6.1 Introduction............................................................................ 219 6.2 Mechanism Design for Clap-and-Fling Motion..................... 220 6.2.1 CF-50 Mechanism Design with 50° Stroke Angle....................................................... 220 6.2.2 CF-51 and CF-72 Mechanism Design....................... 221 6.3 High-Speed Photography Test (Zero Wind Speed)................ 225 6.3.1 CF-50......................................................................... 225 6.3.2 CF-51......................................................................... 226 6.3.3 CF-72......................................................................... 226 6.4 Wind Tunnel Testing.............................................................. 227 6.4.1 CF-50......................................................................... 227 6.4.2 CF-51......................................................................... 229 6.4.3 CF-72......................................................................... 230 6.5 Aerodynamic Performance Comparison................................ 232 6.6 Summary................................................................................ 235 References......................................................................................... 236 Chapter 7 Computational Fluid Dynamics Analysis of Flapping Wings................................................................................. 239 7.1 Introduction............................................................................ 239 7.2 Numerical Simulation of Single Flapping Wing.................... 239 7.2.1 Governing Equations.................................................240 7.2.2 Boundary Conditions................................................ 241 7.2.3 Mesh Setting and Testing.......................................... 242

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7.2.4

Flow Pattern Comparison for Single Flapping Wing...........................................................244 7.2.5 Aerodynamic Force Comparison for Single Flapping Wing................................................246 7.2.6 Comparison of 3D Trajectory Using Stereo-Photography for Single Flapping Wing...........................................................248 7.2.7 Major Observations from CFD Analysis of Single Flapping Wing................................................ 252 7.3 Formation Flight of Flapping Wings...................................... 253 7.4 CFD Analysis of Formation Flight of FWMAVs...................254 7.4.1 Model Generation...................................................... 254 7.4.2 CFD Analysis for Single Flapping Wing.................. 255 7.4.3 CFD Analysis for V-Formation with 3 Flapping Wings...................................................... 256 7.4.4 Comparison of Averaged Lift Per Wing for V-Formation and Single Wing.................................. 256 7.4.5 Lift Comparison for Leading Wing of V-Formation and Single Wing.................................. 257 7.4.6 Lift Comparison for Leading Wing and Follower Wing of V-Formation................................. 258 7.4.7 Comparison of Dimensionless Lift Coefficients........................................................ 258 7.5 Summary on the V-Formation Flapping Flight...................... 261 Summary........................................................................................... 263 References......................................................................................... 263 Chapter 8 Soap Film Flow Visualization of Flapping Wing Motion................. 267 8.1 Introduction............................................................................ 267 8.2 Methodology........................................................................... 268 8.2.1 Working Principle..................................................... 268 8.2.2 Differential Approach about a Soap-Film................. 269 8.2.3 Integral Approach about a Soap-Film Using Stokes Theorem.............................................. 269 8.2.4 The Integral Approach of a Soap-Film Using Gauss Theorem.......................................................... 270 8.2.5 Soap-Film Thickness Interpreted to 3D Downwash of a Wing...................................... 270 8.3 Soap-Film Imaging Experiment of a 10 cm-Span Flapping Wing........................................................................ 272 8.3.1 10 cm-Span Flapping Wing....................................... 272 8.3.2 Experiment Setup...................................................... 274 8.3.3 High-Speed Photography for Capturing Soap-Film of a Flapping Wing Motion..................... 275 8.3.4 RGB-Thickness Field Conversion............................. 275

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Contents

8.3.5

Calculation of 3D Downwash, Lift, and Induced Drag of a Flapping Wing............................. 277 8.4 Summary................................................................................ 279 References.........................................................................................280 Chapter 9 Dynamics and Image-Based Control of Flapping Wing Micro Aerial Vehicles............................................................. 283 9.1 9.2

Introduction to Stereovision System....................................... 283 Simplified Dynamic Model.................................................... 285 9.2.1 Equations of Motion.................................................. 285 9.2.2 Averaging Theory and Formulation of Forces.................................................................... 286 9.2.2.1 Applicability of Averaging Theory........................................................ 286 9.2.2.2 Formulation of Forces and Moments.................................................... 289 9.2.2.3 Coefficients of the Main Wing..................290 9.2.2.4 Coefficients of the Horizontal Wing.......................................................... 291 9.3 Control Law Design................................................................ 292 9.3.1 Linearized Dynamics................................................ 292 9.3.2 Formulation of the Transfer Function....................... 294 9.4 Numerical Simulations........................................................... 294 9.5 Experiments and Discussion.................................................. 296 9.6 Vision-based Control.............................................................. 299 9.7 Experimental Studies Using Developed Image Processing Algorithms................................................302 9.8 Development of Graphical User Interface.............................. 303 9.8.1 Manual Mode............................................................ 303 9.8.2 Hardware Setting.......................................................304 9.8.3 Vision-Based Control Mode......................................304 9.9 Vision System for FWMAV...................................................304 9.10 Motion Estimation Using Frequency Domain Approach..................................................................306 9.11 Group Actuation and Control.................................................307 9.12 Summary................................................................................309 References.........................................................................................309 Chapter 10 Arduino-Based Flight Control of Ornithopters................................. 311 10.1 Estimation of Attitude, Altitude, and Direction of FWMAV............................................................................. 311 10.2 Directional Control of FWMAV with Microcontroller and On-Board Avionics................................ 313

Contents

xiii

10.3 Flight Test............................................................................... 317 10.3.1 Altitude Measurement............................................... 318 10.3.2 Measurement of Flight Data...................................... 318 10.4 Design of Printed Circuit Board............................................. 321 10.4.1 Uploading Firmware................................................. 324 10.4.2 Sensor Data............................................................... 324 10.5 Flight Test............................................................................... 326 10.6 Bionic Actuators for FWMAVs.............................................. 328 10.6.1 Working Principle of Bionic Actuators..................... 329 10.6.2 Design of Bionic Actuator......................................... 329 10.6.3 Fabrication and Testing............................................. 331 10.7 Summary................................................................................ 334 References......................................................................................... 334 Chapter 11 Servo Driven Flapping Wing Vehicles.............................................. 337 11.1 Introduction of Servomotors................................................... 337 11.2 Design of Servo Mount........................................................... 339 11.3 Flight Control of Servo-Driven Flapping Wings...................................................................... 341 11.4 Tethered Flight.......................................................................344 11.5 Attitude Control of Servo-Driven Ornithopter.............................................................................348 11.6 Experimental Analysis........................................................... 350 11.7 Design of Long Wingspan Servo-Driven Ornithopter...................................................... 354 11.8 Lightweight Batteries for FWMAVs...................................... 355 11.9 Summary................................................................................ 357 References......................................................................................... 357 Chapter 12 Figure-of-Eight Motion and Flapping Wing Rotation...................... 359 12.1 Introduction............................................................................ 359 12.2 Passive Wing Rotation of Flapping........................................ 359 12.2.1 Review on Tamkang’s Golden-Snitch....................... 359 12.2.2 Joint Wearing of Flapping Mechanism..................... 362 12.2.3 Oblique Figure-of-8 Flapping Characteristics of Golden-Snitch.............................. 365 12.2.4 Symmetry Breaking of Flapping Dynamics.................................................................. 367 12.3 Active Wing Rotation of Flapping......................................... 370 12.3.1 Lift-Generation Principle for Wing Rotation of Flapping.................................................. 370 12.3.2 Flapping Mechanisms with Wing Rotation........................................................... 372

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Contents

12.3.3 Type A: All Servo Mechanism.................................. 372 12.3.4 Type A1: Normal Servo Mechanism......................... 372 12.3.5 Type B: Servo-Bevel Gear Hybrid Mechanism.................................................... 378 12.3.6 Type B1: Hybrid Servo-Bevel Gear Mechanism with Stoppers................................ 383 12.3.7 FBL-Bevel Gear Hybrid Mechanism................................................................ 386 12.3.8 Major Inferences....................................................... 394 12.4 Power Consumption of Flapping-Wing Flight............................................................. 394 12.5 Summary and Final Conclusion............................................. 397 References......................................................................................... 399 Index....................................................................................................................... 401

Preface The flight of birds and insects has attracted the attention of scholars and engineers for millenniums. In the Chou Dynasty of China (~400 BC), Luban, who was a famous craftsman, fabricated a wooden magpie for surveillance and it was flown for three days. In Greek mythology, Daedalus and Icarus wore wax wings and soared over the Aegean Sea. The wings melted and he died after falling to the ground. Even though it was a tragic myth, the development of bionic aircraft was not halted. During the 15th  century, Leonardo da Vinci sketched a flapping flying machine and it encouraged scientists to design a bird-mimicking structure. In 1870, Gustave Trouvé made a flapping wing vehicle, or ornithopter, propelled by dynamite, and created a successful flight of 70 s. Further, Alphonse Pénaud developed a rubber-bandpowered ornithopter in 1872. From records of the late 19th century, many of the flight pioneers witnessed a number of adventurers to emulate birds flapping, but, unfortunately, all of them failed. In 1983, R. Feynman said in his famous lecture, “Infinitesimal Machinery,” that “one always looks at biology as a kind of a guide, even though it never invents the wheel, and even though we don’t make flapping wings for airplanes because we thought of a better way.” It was a good interpretation of pragmatism on developing the artificial air-vehicles based on the Wright Brothers’ success in fixed wing aircrafts. In the early 1990s, ornithopters were considered toys so there is not much research progress in the development of flapping wing vehicles. After the first Gulf War, ornithopters were used by the US Army for ultra-shortrange surveillance investigations. In 1996, the US Defense Advanced Research Projects Agency (DARPA) funded a three-year micro-air-vehicle (MAV) program. DARPA was to inspire and create artificial flyers of wingspan less than 15 cm for military surveillance. During that period, most of the researchers were focused on the development of fixed-wing and rotary-wing vehicles. After 1999, DARPA supported Caltech and AeroVironment Inc. to develop palm-size flapping wing micro-air-vehicles (FWMAVs). Thanks to the technology of microelectromechanical systems (MEMS), such as microsensors and other small parts like micro-cameras, wireless communications, pager motors, and lithium-polymer batteries, all of them were created thin, lightweight, and easily accessible. Based on miniaturization technology, Microbat of California Institute of Technology (Caltech) and Delfly of Delft University of Technology (TU Delft) appeared one after the other. Subsequently, research focused on increasing the flight endurance from several seconds to 30 minutes. On-board video transmission using a micro camera to a ground station made the research available for surveillance and reconnaissance missions. In 2011, AeroVironment Inc. announced the successful hovering of their NanoHummingbird MAV. The US Army had thought of an artificial hummingbird as a scout in real street fighting for each soldier. Also, in Taiwan, the first research on flapping wings was initiated by Prof. Fei-Bin Hsiao and Prof. Wen-Pin Young of National Cheng Kung University. They have successfully measured the lift characteristics of flapping wings. From 2007–2009, Prof. Jing-Tang Yang from xv

xvi

Preface

National Taiwan University, Prof. Chyi-Yeou Soong from Feng Chia University, and Prof. J. Andrew Yeh from National Tsinghua University implemented a multidisciplinary research project sponsored by the Ministry of Science and Technology (MOST) and developed the Porter Bee ornithopter. It was intended for indoor applications to monitor the safety of the elderly at home. In addition, a 48-cm wingspan flapping wing vehicle was developed and it has achieved the longest flight record of 247 seconds. Similarly, the authors’ research team developed three generations of FWMAVs, namely Initiator, Eagle-II, and Golden-Snitch, from 2003–2009, sponsored by MOST, Taiwan. Various research groups across Taiwan universities were involved, including Prof. An-Bang Wang of National Taiwan University, Prof. Jr-Ming Miao of National Pingtung University of S&T, Prof. Yung-Kang Shen of Taipei Medical University, Prof. Chin-Kwang Huang of Longhua University of S&T, Prof. ChienChun Hung, Prof. Fu-Yuen Hsiao, and Prof. Lung-Jieh Yang (the author) of Tamkang University. They have fabricated an FWMAV structure which had a mass of 5.6 grams for the wingspan of 20 cm. The longest flight endurance of 480 seconds is achieved by the modified Golden-Snitch. Their goal was to develop an FWMAV kit for industrial technology transfer and educate the students on ornithopters. In addition, through the Indo–Taiwan cooperation project during 2013–2016, a vertical take-off and landing (VTOL) FWMAV was developed by the authors and an imagebased control of SWARM of FWMAVs was also attempted. This book is intended as a resource to share the knowledge gained during the course of these two major projects to give better understanding to the readers in developing FWMAVs.

Acknowledgments Many people contributed to this book. First of all, we express our sincere thanks to our beloved families. Secondly, we express our heartfelt acknowledgments and gratitude to many colleagues especially Prof. F.-Y. Hsiao, Prof. W. He, Prof. Rama Bhat, Prof. U. Chandrasekhar, Dr. R. Velu, Dr. D. Rajamani and others, and students, especially Dr. C.-K. Shu, Mr. C.-Y. Kao, Mr. K.-C. Hung, Dr. A.-L. Feng, Mr. S. Marimuthu, Mr. N. Panchal, Mr. N. Kapri, Mr. S. Kompala, Mr. W.-C. Wang, Ms. R. Waikhom, Mr. V. Jabaraj, Mr. N. K. Unnam, Mr. Surendar, Mr. Tesfae, Mr. Mesfin, Mr. Madhu, and others. They helped us greatly in preparation of this book. We thank all students, research scholars, and junior research fellows who have contributed in one way or another to research works during various epochs. We would like to thank the funding agencies, MOST, DST, DRDO, Tamkang University, and Vel Tech Institute for their wonderful support. We are thankful to our friends who have supported us directly and indirectly at various points in the preparation of this book. The outstanding CRC Press team, especially Dr. Gangandeep Singh, Mr. Lakshay Gaba, Ms. Aastha Sharma, and others who helped us by providing valuable and deeply treasured feedback. Many thanks to all of them for their invaluable help and support for completion of this book. Lung-Jieh Yang Department of Mechanical and Electromechanical Engineering, Tamkang University, Taiwan [email protected] Balasubramanian Esakki Department of Mechanical Engineering, Vel Tech Rangarajan Dr Sagunthala R & D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, India [email protected]

xvii

Authors Prof. Lung-Jieh Yang received a PhD from the Institute of Applied Mechanics, National Taiwan University in 1997 and had a one-year sabbatical at Caltech for learning MEMS technology from 2000–2001. He is now a full professor and the former department chair of the Mechanical Engineering Dept, Tamkang University, and is also the former editor-in-chief of Journal of Applied Science and Engineering (an EI/Scopus/ESCI journal with ISSN 1560-6686). Prof. Yang has been devoted to the research of polymer microelectromechanical systems (polymer MEMS, especially parylene and gelatin techniques) and flapping wing micro air vehicles (FWMAVs) for 20 years and has published 66 journal papers, more than 100 conference papers, 2 textbooks about MEMS, and 17 US/Taiwan patents about polymer MEMS and micro ornithopters. He was the Taiwan side’s PI of the Indo-Taiwan project, “Design, Development and Formation Control of Micro Ornithopters (102-2923-E-032-001-MY3)” from 2013–2016. In this project, he built up not only the technical cooperation between India and Taiwan but also coauthored several international journal papers with Indian scholars and institutes. Prof. Yang hosted two international conferences including “The International Conference on Biomimetic and Ornithopters (ICBAO-2015)” and “The International Conference on Intelligent Unmanned Systems (ICIUS-2017).” He has also been one of the vicepresidents of the International Society of Intelligent Unmanned Systems (ISIUS) since 2017. Dr. Balasubramanian Esakki received a PhD in the field of robotics and control at Concordia University, Montreal, Canada. He has published 2 books, more than 100 journals and conference papers, and applied 7 patents. He received grants from various Indian government funding programs supported through DST, DRDO, ISRO, and DBT. He has collaborated with Taiwan scientists under the Indo-Taiwan schema (2013–2016) for the development of micro aerial flapping wing vehicles and formation control through image processing techniques. He has designed a tabletop test rig integrated with two load cells to measure the aerodynamic forces of flapping wing vehicles funded by DRDO – AR and DB. He has also collaborated with Canadian scientists in development and deployment of UAVs for railway bridge inspection. He developed amphibious UAVs for collection of water samples in remote water bodies under Indo-Korea research schemes funded by DST, Govt. of India. His team developed UAVs for diverse applications including power line inspection, telecom tower inspection and radiation measurement, environmental monitoring, surveillance and traffic monitoring, etc. His team won the first prize for Rs 5 lakhs in a national competition organized by Power Grid Corporation Limited and the prestigious telecom sector’s Aegis Graham Bell Award in the category of Best Innovative Business Model 2014. His research interests are UAVs, robotics, control, and sensors with online data acquisition systems. xix

1

Introduction to Micro Aerial Vehicles

The flapping wing is a bionic concept where humans learned from birds to design flying machines in the early days. Looking back at the centuries’ old evolution of modern aeronautical engineering, one can see tremendous technological development of various aircraft structures. Be it a propeller power to jet power, aircraft flying at diverse speeds, increased payload capacity, and enhanced operations ranges, these are a few of the operating characteristics. Basically, in response to air transportation needs, civil-aviation aircrafts are quite big and need a long landing/take-off lane. The invention of flapping wing micro-air-vehicles (FWMAVs) is an attempt to make the aircrafts small and compact. The areas of application have also widened to surveillance on the battlefield and hazardous environments. Similar to unmanned air vehicles (UAVs or drones), FWMAVs extend the reach and thus the physical presence of human beings. This book aims to enable one to study the design, construction, and workings of FWMAVs. This chapter introduces the flapping motion and explains the basic concepts from fluid mechanics, aerodynamics, flight mechanics, and scale laws to better understand the FWMAVs.

1.1  FLAPPING MOTION A kite is an example of a simple flying body. Its surfaces are simultaneously subjected to lift, drag, and the tether string’s tension, as shown in Figure 1.1(a). These three forces create a static force balance enabling the kite to fly in the air. Figure 1.1(b) shows a glider where the tether tension is replaced by a self-weight (mg) of the flyer to have the static balance along with the other two forces like the lift and drag. Gravity-induced velocity tilts the glider down by a glide angle ϕ (2.5° for an albatross). Although the flying body is in static equilibrium, the flight height or altitude of it gradually decreases. To maintain the altitude and a level-flight, natural flyers spend power by flapping their wings to generate a thrust that overcomes the drag. At this moment, lift L is defined as L=

1 ρU 2 SC L , 2

(1.1)

where ρ = Density in kg/m3 U = Air velocity in m/s S = Wing area CL = Lift co-efficient. DOI: 10.1201/9780429280436-1

1

2

Flapping Wing Vehicles

FIGURE 1.1  Powerless steady flight: (a) kite and (b) gliding.

Lift is equal to the gravitational force W acting on the flyer. The horizontal cruising speed U is given by

U=

2W (1.2) ρSC L

In general, a bird’s flapping action can be split into a downstroke and an upstroke [1]. A positive lift is generated during the downward stroke, and a negative lift is generated during the upstroke. The upstroke is also called recovery. Normally, the duration of the downstroke is longer than that of the upstroke. Thus, the positive lift of the downstroke exceeds the negative lift of the upstroke. This ensures an overall positive net lift, which is sufficient to counter the flying body’s weight. Thus the flying body keeps itself airborne. Figure 1.2 shows the flapping wing posture of a bird. When a bird cruises horizontally, its wingtip appears to have a negative angle of attack (AOA) during the downstroke. According to the general rule, a lift is positively related to the AOA (Section 1.2.2). This may be leading us to think that the flapping wing produces a negative lift during the downstroke. Nevertheless, this is not true. The relative flow velocityUr is expressed as

    Ur = U ∞ + U f + wi , (1.3)

where  U ∞ = Forward velocity in m/s U f = Local flapping velocity in m/s  wi = Induced downwash in m/s. The lift needs to consider its relative flow velocity, the forward velocity, the local flapping velocity, and the so-called induced downwash (discussed in Section 1.2.6). A wing-root section shown in Figure 1.2(a) is a fixed-wing with no flapping speed. Hence it exhibits a traditional positive AOA, resulting in a positive lift L, and its drag D (that compose into the resultant force, F has deflected afterward).

Introduction to Micro Aerial Vehicles

3

FIGURE 1.2  Flapping wings posture of a bird: (a) forces at wing root, (b) forces at the middle of the wing, (c) forces at wingtip.

However, regarding the middle wing position of Figure 1.2(b) or the wingtip position of Figure 1.2(c), the local flapping velocity is getting larger. The relative wind velocity is obtained by combining the forward velocity, and the flapping velocity is also rising. Therefore, even the AOA at the middle wing or wingtip seems to be negative relative to the forward velocity, but the actual AOA is positive with respect to the relative flow velocity. In other words, the more the wing section moves toward the wingtip, the more the lift generation and thus resultant force deflected forward is higher. During downstroke, the wing’s inner part produces lift and drag, while the outer part produces lift and thrust. This thrust is the main source for propelling the flyer forward. The concept of relative wind velocity is also used to explain the magnitude of lift during the upstroke. In general, the lift is negative during upstroke that can be resolved into two components: the horizontal component contributes to a positive thrust (whatever is the stroke, whether downstroke or upstroke, a flapping wing always generates thrust) and the vertical component contributes to a negative lift. However, after considering the overall wing surface subjected to downstroke and upstroke, the net lift force generated will balance the gravity and maintain flight. Of course, under the alternating influence of positive lift and negative lift, the flight trajectory may not be a horizontal straight line. It appears like an up-and-down wave, as shown in Figure 1.3. Usually, the upstroke flapping takes place near the peak of the flight trajectory to reset the wing position and allows a slight fall due to negative

4

Flapping Wing Vehicles

FIGURE 1.3  (a) Flight path of Golden-Snitch during forward flight and (b) the time-varying trajectory of the center of mass of Golden-Snitch [2].

lift at the next moment. However, the downstroke flapping happens at the trajectory’s trough to generate a positive lift to restore the ascent.

1.2 ASPECTS OF FLUID MECHANICS AND AERODYNAMICS IN THE STUDY OF FLYERS Fluid mechanics describes how a solid object influences the surrounding fluid into a particular flow field and how much force the fluid flow field acts on the object. The solid object may be stationary so that the surrounding flow field is in a steady state. However, in the case of moving objects, the surrounding flow field tends to be unsteady. Consider the blade of a wind turbine. At the cut-in speed, the blade begins to move, and the flow field around the blade is unsteady until it reaches the rated speed and generates maximum power [3]. Initially, the wind turbine’s flow field is unsteady, and once the blade attains constant speed, the flow observed from the blade is almost similar to that of the surrounding flow field on a fixed-wing surface. The main differences between the flow fields of aircraft wings and turbine blades are (Figure 1.4) as follows: a. The airplane lift during level flight is to resist gravity and let the airplane floating in the air. The air drag was simultaneously generated and it tells us how much minimum thrust the engine should generate to maintain a level flight, as shown in Figure 1.4(a).

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5

FIGURE 1.4  (a) Level flight of an airplane and (b) force components in a turbine blade.

b. The lift FL and drag Fd generated by the turbine blade shown in Figure 1.4(b) are due to the combined velocity used to form a total force FT, whose horizontal component generates a torque to the power generator. The combined velocity is the sum of the freestream velocity and the blade’s rotating speed as represented. In addition to aerodynamic lift and drag, gravity also acts on the turbine blade. For horizontal cruising of the aircraft wing, the direction of gravity is fixed. The steadystate condition of the whole aircraft is maintained without any ambiguity. However, in the case of a single turbine blade rotating at a constant speed along the horizontal axis, the direction of gravity is vertical, as shown in Figure 1.4(b). It varies as a sinusoidal function of time. Hence, in the applied force condition, the turbine blade’s flow field appears to be non-stationary. When a turbine rotates at a constant angular speed and the turbine system is assumed to be a linear dynamic system, the gravity direction’s sinusoidal time-­changing causes a periodic flow field. After deduction of the cyclical factors using Fourier transform, the turbine blade flow field can still be treated as a conventional steady-state aerodynamic problem. The wind turbine analysis can help analyze the case of up-and-down flapping wing motion in its steady state. One can simulate the force analysis of the wind turbine blade shown in Figure 1.4(b) to the flapping wing’s case and understand the relationship between the flapping forces and the relative velocities.

1.2.1  Governing Equations of Fluids The conservation laws and constitutive equations in fluid mechanics are recalled to analyze the flapping wings [4]. Continuity equation (or the conservation of mass)

 ∂ρ + ∇ ⋅ ( ρu ) = 0 (1.3a) ∂t

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Flapping Wing Vehicles

Navier–Stokes equation (or the conservation of linear momentum) ρ



    ∂u + ρ ( u ⋅ ∇ ) u = ∇ ⋅ σ + ρf (1.3b) ∂t

Energy equation (or the conservation of energy)

ρ

   ∂e + ρ ( u ⋅ ∇ ) e = ( σ ⋅ ∇ ) ⋅ u − ∇ ⋅ q (1.3c) ∂t

Constitutive equation

e = cv T



p = ρRT



 q = − k∇T



σ ij = − pδ ij + λδ ij

 ∂u ∂u j  ∂uk + µ i + (1.4a–d) ∂ xk  ∂ x j ∂ xi , 

where u = velocity field, p = pressure field, T = temperature field, ρ = density field, e = inner energy, q = heat flux, σ = stress tensor, f = external force field, cv = specific heat, k = thermal conductivity, λ = viscosity coefficient, μ = viscosity coefficient, and δij  = Kronecker delta. A three-dimensional (3D), unsteady, viscous, compressible flow, and moving solid boundary situation is the most complicated to solve. The complexity of these partial differential equations (PDEs) implies coupling various fields, such as velocity, pressure, temperature, and density. The dependent variable fields include inner energy, heat flux, and stress tensor. The PDEs’ solution needs to well-propose the appropriate boundary conditions (in spatial coordinate) or initial conditions (along time coordinate). Since the actual fluid mechanics problem is too complicated, we simplify the mathematical model from an engineering perspective. The most concise and useful simplification of fluid mechanics is developing an analytical framework with an ideal fluid or potential flow. It has four assumptions: two-dimensional (2D), steady-state, inviscid, and incompressible flow, as shown in the central part of Figure 1.5. We can analyze the ideal fluid part from this and justify the assumptions one-by-one to know the extra effect more accurately than the ideal fluid. For example, the turbine blade’s function block can be represented by combining 3D, viscous flow, periodic quasi-steady, ideal fluid, and compressible flow. Another example is the flapping wing, which can be represented by combining the 3D, viscous flow, periodic quasi-steady, steady, inviscid, incompressible, and aeroelastic.

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Introduction to Micro Aerial Vehicles

FIGURE 1.5  Fluid mechanics and analytical framework.

1.2.2 Ideal Fluid Potential Flow With the above stated four major assumptions, the governing equations of fluid mechanics are greatly simplified. For example, the continuity Equation (1.3a)  becomes a Laplace Equation (1.5) of velocity potential u = ∇ϕ. This Laplace equation is the simplest PDE and is used to solve the 2D velocity field and much easier than solving the Navier–Stokes Equation (1.3b). ∇2ϕ =



∂2 ϕ ∂2 ϕ + = 0 (1.5) ∂ x 2 ∂ y2

Solving the Laplace equation boundary value problem involves the superposition of the basic Laplace solutions and confirms them to the solid boundary shape. The mathematical methods used here include complex variables and conformal mapping. The Navier–Stokes Equation (1.3b) is transformed into the Bernoulli Equation (1.6), which still retains the nonlinear property and is used to solve for the pressure field. ptotal = pstatic +



1 ρ u 2 + v 2 (1.6) 2

(

)

Once the pressure field is solved, the object’s applied force in the flow field can be obtained from the pressure field’s surface integral along the solid boundary. Potential flow theory analytically derives the lift force by applying the Kutta-Joukowski law. Consider a Joukowski airfoil (Figure 1.6) represented by three variables such as AOA (α), thickness (t), and wing camber (h). The 2D lift coefficient CL predicted by potential flow theory is positively correlated with these three parameters as given in Eq. (1.7).

CL =

L t  2h   = 2π 1 + ( 0.77 )    sin  α +  (1.7) 1  c   2 c   ρU A 2

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Flapping Wing Vehicles

FIGURE 1.6  Joukowski airfoil.

Given free stream velocity, chord length, camber angle, and thickness, one can calculate the lift coefficient using Eq. (1.7) for varied AOA, for example, 5°, 10°, and 15°.

1.2.3 Dimensional Analysis When subjected to any fixed solid boundary conditions, the governing equations’ analytical solution is very hard to find. This is due to the varying nature of PDEs and their nonlinearity. Unless few justifiable assumptions are made to convert the PDEs as simplified linear models, they may not be solved. This is also the case of the flow fields of wind turbines and flapping wings. Therefore, it is necessary to adopt a simple and qualitative analytical method like the dimensional analysis. The dimensional analysis helps to find the qualitative relationship of the complicated physical problems directly from the fundamental units like mass (M), length (L), and time (T). The aerodynamic forces are utilized to derive the power law of possibly related physical quantities or even dimensionless parameters. a. Steady-state fixed solid object Let us start with a fixed solid object subject to a steady-state flow [5,6]. Assume that aerodynamic force F (lift or drag) is related to the viscosity coefficient μ, air density ρ, flow velocity U, and the characteristic size D of the object with the following power equations where a, b, c, and d are undetermined coefficients.

F = µ a ρ bU c D d (1.8) Then, to introduce the factors of each physical quantity, which is expressed using M, L, and T as given by the following relations:



F   =   MLT −2

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Substituting Equation. (1.9) in Equation (1.8) and comparing the respective powers of M, L, and T, we obtain the relationship b = 1 − a; c = d = 2 − a. We are still left with an unknown component from the relationship, a, whose value needs to be found using wind tunnel experiments or to be defined theoretically. Equation (1.8) is then rewritten as per the similarity law, which is given by F   = ρU 2 D 2 (



ρUD − a ) (1.10) µ

The term ρU2 represents the dynamic pressure of airflow and the term D2 represents the wetting surface area of the object in the fluid. The dimensionless parameter ρUD/μ is known as the Reynolds number. The Reynolds number is the most important dimensionless parameter of viscous flow. b. Unsteady state flow moving object with periodic motion Consider the case of unsteady flow on turbine blade rotation or flapping wing motion. Because the blades rotate at a constant speed or a constant-frequency flapping, the flow field exhibits an unsteady characteristic that eventually changes with time. The aerodynamic force F has given in Equation (1.8) can be rewritten by multiplying the speed of the blade or flapping frequency n with the power of e, F = µ a ρ bU c D d n e, (1.11)

where F = MLT −2 m = ML−1T −1 r = ML−3 U = LT −1 D = L

n = T −1 . (1.12) Again, by substituting Eq. (1.12) in Eq. (1.11) and comparing the respective powers of M, L, and T, we obtain the relationship b = 1 − a; c = 2 − a − e; d = 2 − a + e. This relationship has two unknown components a and e. Equation (1.11) is then rewritten as Eq. (1.13) as per the revised similarity law.



 ρUD  F = ρU 2 D 2   µ 

−a

 U    nD 

−e

(1.13)

The second dimensionless parameter (U/nD) here is called the advance ratio J. Similarly, a and e are the undetermined coefficients that can be found using theory or experimentation.

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Flapping Wing Vehicles

c. Dimensionless parameter Dimensional analysis always leads to many interesting dimensionless parameters like the Reynolds number and advance ratio. The physical meaning of these two is mentioned below:



Re =

ρUD ρU 2 dynamic pressure inertial force = = = . (1.14) U µ shear stress viscous force µ D

J=



U wind spreed = . (1.15) nD wind turbine tangential speed

Reynolds number is very helpful to know whether the flow characteristic is turbulent or laminar. Usually, we use critical Re as a borderline value. (This critical value for Reynolds number is 100,000 for external flows; 2,300 for internal flows.) If Re is less than the critical value, then the flow is in the laminar regime, and if Re is much larger than the critical value, then the flow is considered to be turbulent. The movement of general aircraft, large-scale wind turbines, and flapping wing vehicles with a wingspan of more than 1 m is considered a turbulent regime. Keeping the Reynolds number constant to maintain similar physical phenomena is important. For example, during the wind tunnel experiment, we may not use a full-scale model in the wind tunnel test but only a reduced model (1/5 of the original size). In order to ensure a constant Reynolds number and compensate for the reduction, the wind speed of the wind tunnel should be appropriately increased by five times accordingly (of course, if the original problem is incompressible, the wind-tunnel speed cannot exceed to compressible flow regime). Another factor to adjust the Reynolds number is to change the wind tunnel to the water tunnel or oil tank. For wind turbines, the advance ratio J represents the ratio of wind speed to the blade rotation’s tangential speed (i.e., how far the air travels once the blade makes one revolution). For flapping wings, J represents the ratio of wind speed to the tangent speed of flapping motion (i.e., how far the air travels once the flapping wing makes a full up and down stroke). The dimensionless parameter (U/nD) can also be interpreted as the ratio of the inertial force to the Coriolis force, also called the Rossby ratio (RO), which is expressed as



RO =

( dynamic pressure )( wing area ) (1.16) U ρU 2 ⋅ D 2 = = 3 nD n ⋅ U ⋅ ρD (angualr velocity )( velocity ) ( mass )

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FIGURE 1.7  Schematic of boundary layer.

1.2.4 Viscous Flow ~ Boundary-Layer Theory The potential flow theory only predicts lift rather than drag. The inviscid assumption that regards the solid boundary as one streamline and allows fluid particles to slip along the solid boundary is not true. Fluid molecules contact solid boundaries and stagnate there without slipping. In other words, there is a boundary layer near the solid object, as shown in Figure 1.7. At the boundary, fluid has zero velocity, and the velocity gradually increases until the outer edge of the boundary layer thickness approaches 99% of free velocity. The velocity gradient in this hidden boundary layer is the source of drag force.



 ∂u ∂ v + =0  ∂ x ∂y  GE  (1.17) 2  u ∂u + v ∂u = U ∞ dU ∞ +  µ  ∂ u  ∂x ∂y dx  ρ  ∂ y 2 



 u( x ,0) = v( x ,0) = 0 (1.18) BC  u ( x , ∞) = U ∞ 

The solution of the velocity distribution u(y) in the boundary layer depends on the boundary layer theory. Assuming that the thickness of the boundary layer in the y-direction is very small, the vertical velocity v is also much smaller than the horizontal velocity u. The Navier–Stokes equation of a 2D, steady-state, incompressible flow subject to a flat plate is simplified as the boundary layer Eq. (1.18). In order to facilitate the solution, a stream function is introduced to make the boundary layer equations. From two PDEs of velocity field to a third-order PDE of a streamline function ψ y ψ xy − ψ x ψ yy = νψ yyy. By similarity transformation, ψ = νUx f ( η) with similarity variable η = y / νx / U , the third-order PDE is transformed into a

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Flapping Wing Vehicles

third-order ordinary differential equation (ODE) f ′′′ + (0.5) ff ′′ = 0 using the chain rule technique. The overall deduction process is detailed as the Blasius solution [7]. Finally, the ODE f ′′′ + (0.5) ff ′′ = 0 is numerically solved. The drag coefficient CD and the boundary layer thickness are successively obtained. The relationship with the Reynolds number Re is given by:

CD =

1.328 D ρU ∞ x , Rex = = (1.19a) 1 2 Re µ x ρU A 2 δ 5.0 = (1.19b) x Rex



The above results show that viscous drag decreases as Re increases in the laminar flow region. Beside the viscous drag, other sources are given below that contribute to the actual drag, such as: • Form drag produced by flow separation or stall • The induced drag from the 3D wingtip vortex • The wave drag caused by high-speed shock waves

1.2.5 Compressibility The compressibility of an object in a flow field is usually judged by Mach number:

Mach Number ( M ) =  

Free Stream Velocity U (1.20) Speed of  Sound ( a )

Generally, M = 0.3 is used as the judgment criterion. If the Mach number is greater than 0.3, it is said to be a compressible flow. The study of compressible flow is common in high-speed aircraft design, such as subsonic, transonic, supersonic, or hypersonic vehicles. However, in the case of a flapping-wing vehicle, the flapping frequency is not high. The flow velocity is usually less than 20 m/s and the compressibility is not obvious. However, in order to have a comprehensive view, compressibility is briefly dealt with here. When discussing compressibility, for simplicity, assuming no viscosity, the Navier–Stokes equation gets simplified into Euler equation as given below:

 ∂ρ + ∇ ⋅ ( ρu ) = 0 (1.21) ∂t    ∂u ρ + ρ ( u ⋅ ∇ ) u = −∇p (1.22) ∂t

For the Euler equation, the solid boundary is a streamline similar to that of the ideal flow. Since the density is no longer constant incompressible flow, it is necessary

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to combine the energy equation and gas-state equation to complete the solution. Although the Euler equation is much simplified than the Navier–Stokes equation, still it is a nonlinear PDE, whose exact solution is difficult to find. A perturbation method is therefore required for the linearized approximation. In terms of the perturbation form of the full velocity potential ϕ = U ∞ x + Φ, the linear governing equation for the perturbed velocity potential after removing the higher-order nonlinear terms is given by [8].

(1 − M ) ∂∂ xΦ + ∂∂ yΦ = 0 (1.23) 2 ∞



2

2

2

2

By observing the governing equation of the perturbed velocity potential, we state that it is similar to the Laplace equation of potential flow, except that the Φ is multiplied by a factor 1 − M ∞2 . According to the Prandtl–Glauert rule, as long as x-coordinate is replaced by a new variable x* that satisfies x = 1 − M ∞2 x* (which is called the 2 2 affinity transformation) [9], Eq. (1.23) becomes the Laplace equation ∂∂x*Φ2 + ∂∂ yΦ2 = 0 . Then the analytical results of the potential flow theory can be directly applied to the compressible case herein. * represents the result of the potential flow theory. After adding the compressibility effect due to Mach number M∞, both the pressure coefficient and lift coefficient increased substantially relative to the potential flow case.

(

)

(

Cp =



C p* 1− M

2 ∞

; CL =

CL * 1 − M ∞2

)

(1.24)

An increase in lift is due to the shortened chord x by multiplying 1 − M ∞2 and is equivalent to the thickening of the airfoil. We can understand this increase in the lift by the lift coefficient of the Joukowski airfoil is given in Eq. (1.7). One example of applying the Prandtl–Glauert rule is shown here. Consider a 4 MW offshore wind turbine with a diameter of 120 m. If its blade speed reaches n = 1/3 rev/s), the blade tip speed is above M∞ = 0.38. By the Prandtl–Glauert rule,

(

)

the correction factor 1 / 1 − M ∞2 is found to be 1.08, which means that the lift increases by 8% due to the compressibility effect.

1.2.6 Drag and Flight Power 1.2.6.1  Induced Drag Generally, a 2D wing is considered to have an infinitely long wingspan. Airflows around the 2D wing in a streamlined manner. The airflow is divided so that some quantity flows above the wing and the remaining below it. While 3D wing has a finite span and a wingtip, it allows the airflow around the wing to stagger up and down. During the maneuvering of flight, higher static pressure under the wing causes more air to flow above the wing. The upward flow combines the free stream to form a wingtip vortex, as shown in Figure 1.8 that causes an induced drag in all air vehicles. Kutta–Joukowski law defines a bound vortex with strength Γ∞ in the 2D potential flow theory. According to Kelvin’s theorem, there is a starting vortex with the

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FIGURE 1.8  Flow conditions around a 3D wing with finite span (a) wingtip vortex and (b) horseshoe vortex system.

same strength but with a negative downstream of infinity (–Γ∞). A horseshoe vortex system is constructed by combining bound vortex, starting vortex, left and right wingtip vortices. There is a downwash speed in the surrounded area of the horseshoe vortex system. The downwash can bring a time changing rate of the vertical flow momentum to manifest as a lift. Meanwhile, the streamwise kinetic energy of airflow is partially consumed by the wingtip vortex pairs that can further interpret the induced drag. The relationship between the induced drag and the downwash can be explained using Figure 1.9. Consider a wing with a freestream velocity U and a wingspan b. Assume that only the circular cross-sectional area Sb whose diameter is b is affected by the wing with a uniform downwash speed w.

FIGURE 1.9  Front view and top view of the downwash.

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Introduction to Micro Aerial Vehicles

Then, the mass flow rate m cross the circular cross-sectional area is given by [10,11], m = ρUSb =



ρUπb 2 (1.25) 4

The time changing rate of the vertical momentum is lift. We can establish the relationship between downwash and lift L as:

L=

d  = wρUSb [ m ( 0 + w )] = mw dt ⇒w=



L (1.26) ρUSb

The downwash power P due to the average induced drag Did is the time-changing rate of the kinetic energy about downwash. A relationship is derived as given below when the mass flow rate Eq. (1.25) is substituted.

P = Dind ⋅ U =

d 1 w 2 ρUSb  L  mw 2  = m =  2 2  ρUSb  dt  2  ⇒ Dind =



2

L2 (1.27) 2ρU 2 Sb

Since the above derivation is the first-order estimation based on a uniform downwash and circular influenced domain, the actual induced drag needs to be multiplied with an induced drag factor k. Therefore, the average induced drag is given by: Dind =



kL2 (1.27a) 2ρU 2 Sb

In general, k = 1 for an elliptic wing varies from 1.1 to 1.2 for other types of wings. The induced drag coefficient C D ind is derived, as shown below:





C D ind =

kL2 S  = kC L 2  2  2 1  2 2 ρ U S π b  b ρU S 2 1

⋅

where

AR =

⇒ C D ind = k

b2 S

CL 2 (1.28) π ⋅ AR

It can be seen from Eq. (1.28) that larger the aspect ratio AR, smaller is the induced drag.

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TABLE 1.1 Drag Coefficients of Different Ground Vehicles and Airliners Road Vehicle (year) Flat plate (1930) Cylinder (1960) Elliptic body (2010)

CD 0.65–0.80 0.45–0.55 0.25–0.30

Airliner (year) B747 (1970) A380 (2005) B787 (2013)

CD 0.0310 0.0265 0.0240

1.2.6.2  Total Drag At least four types of drag act on a fixed-wing aircraft during the forward flight or cruising condition. They are • • • •

Profile drag due to skin friction or the viscous effect; Pressure drag or form drag due to boundary layer flow separation or stall; Induced drag or 3D effect due to the finite wingspan; and Wave drag or compressibility effect due to a high Mach number.

Typical drag coefficients for different objects are listed in Table 1.1. It may be seen that the state-of-art of airliners are designed to have better drag reduction than that of ground vehicles. 1.2.6.3  Flight Power The Mach number of MAVs is much less than 0.3, and hence no shock wave is observed. Besides, assuming that the wing airfoil is well-designed without the occurrence of stall or boundary layer separation, the pressure drag can be ignored. The total drag is only induced drag and profile drag, which comes from the friction drag Dpro and Dpar of the wing and the fuselage. Since flight power = drag × flight speed, we multiply all the above drags by the flight speed U to get corresponding powers. Thus

P = Pind + ( Ppro + Ppar ) = 2K

( Mg)2 1 + ρU 3 SC D f (1.29) ρUπb 2 2

The induced power Pind changes with U−1, and the profile drag (Dpro+Dpar) changes with U3. When both the powers of U are synthesized, we get a Smile curve that is shown in Figure 1.10. • Maximum flight endurance (minimum power velocity Ump) The flight speed is relatively straightforward and easy to understand. Differentiating P with respect to U and equating to zero, we can find Ump. The maximum flight

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Introduction to Micro Aerial Vehicles

FIGURE 1.10  Relationship between flight power and flight speed.

power value in Figure 1.10 is provided at the lowest point (Ump, Pmp) of the Smile curve. ⇒



dP =0 dU

 4 K ( Mg)2 = 2 2  3ρ πb SC D f

⇒ U mp

  

0.25

(1.30)

• Maximum range velocity UMr The range is “flight speed times flight time,” similar to “flight speed times flight time provided per unit fuel energy (or reciprocal of flight power),” which is the range per unit fuel energy U/P. In other words, finding the maximum value of range U/P is no different from finding the minimum value of P/U. Therefore, as we differentiate P/U with respect to U and equate to zero, then UMr is obtained inversely. The meaning of maximum range in Figure 1.10 is easy to understand: P/U is the slope of the straight line passing through the origin. We just adjusted the straight line’s minimum slope passing through the origin and found the lowest tangent point (UMr, PMr) of the Smile curve.



 1   Range : Y   = U  ⇒ (1.31)  P  max  Range  min P d   U ⇒ =0 dU ⇒ U Mr

 4 K ( Mg)2 = 2 2  ρ πb SC D f

  

0.25

(1.32)

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The drag coefficient can refer to the flat plate model Eq. (1.19) of the other airfoils’ boundary layer theory.

CD f =

1.328 ρUc ,Rec = (1.33) Rec µ

Comparing the two speeds in Eqs. (1.30) and (1.32), it is found that the difference is only 30.25 = 1.32 times. That is, UMr = 1.32 Ump. This process is employed for the power estimation of fixed-wing aircraft. When applied to the power estimation of the flapping wings, it is more suitable for forward flight at a higher cruising speed than for hovering. In the case of hovering, estimation of the downwash speed and thrust is needed.

1.3  FLIGHT MECHANICS FWMAV or ornithopter design involves different domains of physics. Since an ornithopter’s wings are flapped and twisted with respect to time, the flow is considered unsteady and encounters a 3D problem with moving wing boundary and flexible deformation of the wings. Hence, there is an essential consideration of the so-called fluid-structural interaction (FSI) for flapping wings.

1.3.1 The Dynamic Control of the Flapping Wing MAVs A mathematical model of the dynamics control of flapping-wing is more complicated. We divide the mechanics of the entire wing shown in Figure 1.11 into four domains to discuss. a. Motion trajectory of the leading edge of the flapping wing  The trajectory of flapping-wing motion is defined as x 0 ( t ) a function of time, t. This trajectory considers translational plugging, wing rotation, and thrust reaction motions. The final flapping motion is due to the up-and-down flapping cycle, which generates one waveform of lift and two waveforms of thrust. However, both upstroke and downstroke can produce thrust. Besides, flapping motion produces an oblique Figure-of-8 depicts a flapping or a streamwise oscillation motion. This type of motion was observed using 3D high-speed stereo-photography [12] from the Golden-Snitch FWMAV constructed by Tamkang University, Taiwan. b. Flexural deformation of the rear half of the flapping wing Due to the time-varying phenomenon, the overall flapping wing is regarded as a structural dynamic problem with flexural deformation. The sum of inertial force, damping force, and structural reaction force constituted the aerodynamic external force [13]. Mathematically,





[ m ] ⋅ x¨ + [c ] ⋅ x˙ + [ k ] ⋅ x = f A ( p,U ) (1.34) 





 It can be seen from Figure 1.11 that x 0 ( t ) for the given motion of wing leading    edge u ( x 0 ) control, the wing location x ( t ) is defined by considering deformation, vibration, inertial, damping, structural dynamics, and aerodynamic loading.

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Introduction to Micro Aerial Vehicles

FIGURE 1.11  Modeling of an ornithopter.

c. Time-varying incompressible flow field around a flapping wing

      DU ∂U ρ = ρ  + U ⋅ ∇ U  = −∇p + µ∇ 2U (1.35) Dt ∂t  

(

)

Solving Navier-Stokes (N-S) Equation (1.35) is relatively difficult since the flapping wing’s solid boundary is a moving boundary, including the leading   edge displacement x 0 ( t ) and the wing deformation x ( t ). These two parts sum up to be FSI problem. At present, few commercial software, such as COMSOL Multiphysics, using finite element method (FEM), have shown converging 3D solution of a flapping wing for at least ten flapping cycles even though it is time-consuming to calculate [14]. d. Governing equation of flight mechanics of flapping wings   Field variable X is different from the aforementioned displacement x 0 ( t ) or  deformation x ( t ). It denotes the velocity, angular velocity, and Euler angles of the air vehicle relative to its body coordinate. The linearized model of the ornithopter without external force is given by:

˙  X = [ A ] ⋅ X (1.36)   If a feedback control u ( x 0 ) is added to the linearized model, the dynamic model becomes



˙    X = [ A ] ⋅ X + [ B ] ⋅ u ( x 0 ) (1.37)

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Flapping Wing Vehicles

FIGURE 1.12  Dynamic model of flapping wing air vehicles.

  The aerodynamic force f A p,U , an output from the N-S equation, can be  applied to the flapping wing boundary to solve the x ( t ) FSI analysis’s defor mation. On the other hand, it x ( t ) is also assigned as the input to execute the   flapping air vehicle’s aerodynamic feedback control u ( x 0 ).

(

)

1.3.2 Equations of Motion for Rigid Aircrafts Combining these four mathematical functions, the overall solution process is shown in  Figure 1.12. The solution lies with respect to the flapping wing input x 0 ( t )’s trajectory function to determine the flight velocity and attitude. The FSI block shown in Figure 1.12 is a very time-consuming finite element solution for the fluid and solid domains. When we derive the equations of motion (EoM) of an aircraft (Figure 1.13), the following are assumptions made [15]: 1. The aircraft is located in an inertial coordinate system X, Y, and Z, where Newton’s second law is valid. 2. Impact due to the rotation of the earth is negligible. 3. Aircraft mass is constant. 4. Mass distribution is uniform with the passage of time. Newton’s second law is interpreted as below. Force and moment EoM for the aircraft in Figure 1.14 are as below:

( ) m (V + UR − WP ) = mg sin ϕ cos θ + F m (W − UQ + VP ) = mg cos ϕ cos θ + F

m U − VR + WQ = − mg sin θ + FAx + FTx Ay Az

+ FTy + FTz (1.38)

21

Introduction to Micro Aerial Vehicles

FIGURE 1.13  Coordinates in an aircraft.



I xx P − I xz R − I xz PQ + ( I zz − I yy ) RQ = L A + LT



I yyQ + ( I xx − I zz ) PR + I xz P 2 − R 2 = M A + M T



I zz R − I xz P + ( I yy − I xx ) PQ + I xz QR = N A + N T (1.39)

(

)

Kinematic equations of the aircraft:

P = ϕ − ψ sinθ



Q = θ cosϕ + ψ cosθ sinϕ



R = ψ cosθ cosϕ − θ sinϕ



(1.40)

1.3.3 Steady-State and Perturbation State The motion equations (Eqs. (1.38)–(1.40)) of the rigid body aircraft deduced in the previous section are completely nonlinear and coupled differential equations. They generally lack mathematical, analytical solutions and rely on numerical methods to solve them. In other words, the linearized approximation still needs engineering. The process of linearization divides the original nonlinear velocity field into the steadystate and perturbation. Total quantity = steady-state quantity + perturbed state quantity. Assume that the time-varying terms of velocity and angular velocity are both zero: Because the time-varying terms have disappeared U1 = V1 = W1 = 0; P1 = Q1 = R1 = 0. Equations (1.38)–(1.40) are simplified into algebraic equations that are relatively easier to solve.

22

Flapping Wing Vehicles

FIGURE 1.14  Definition of Euler angles.

1.3.4 Steady-state EoM:

m ( −V1 R1 + W1Q1 ) = − mg sinθ1 + FAx 1 + FTx 1



m (U1 R1 − W1 P1 ) = mg sinϕ1 cosθ1 + FAy1 + FTy1



m ( −U1Q1 + V1 P1 ) = mg cosϕ1 cosθ1 + FAz1 + FTz1 (1.41)



− I xz PQ 1 1 + ( I zz − I yy ) R1Q1 = L A1 + LT1



( I xx − I zz ) P1 R1 + I xz ( P12 − R12 ) = M A



( I yy − I xx ) PQ 1 1 + I xz Q1 R1 = N A

1

1

+ M T1

+ N T1 (1.42)

Introduction to Micro Aerial Vehicles

23



P1 = ϕ 1 − ψ 1 sinθ1



Q1 = θ 1 cosϕ1 + ψ 1 cosθ1 sinϕ1



R1 = ψ 1 cosθ1 cosϕ1 − θ 1 sinϕ1 (1.43)

Assumptions made in the analysis for most of the aircraft dynamic models: • No initial side velocity: V1 = 0 • No initial bank angle: φ1 = 0 • No initial angular velocities: P1 = Q1 = R1 = ψ 1 = θ 1 = ϕ 1 = 0 The above assumptions mean that Eq. (1.43) can be dropped. Equations (1.41) and (1.42) are related to the force balance or moment balance of gravity, aerodynamic forces, and thrust. They do not directly relate to velocity, rotation, and inertia. Therefore, it is sufficient to perform the computational analysis only on the perturbation-state equations. Three cases of steady-state flights are: • Steady-state rectilinear flight (straight line flight): P1 = Q1 = R1 = 0  • Steady-state turning flight (steady level turn): ω = k1ψ 1 • Steady symmetrical pull-up: V1 = 0; P1 = R1 = 0; φ1 = 0

1.3.5 Linearized EoM When the field variables such as velocity, angular velocity, and Euler angle are brought into a complete nonlinear motion equation in the form of “steady-state + disturbance dynamics,” the steady-state’s magnitude is much larger than the disturbance dynamics. As far as the terms of the second-order disturbance dynamics are concerned, the perturbed dynamic motion equations usually appear as purely disturbing dynamic linear differential terms or multiplied by a known steady-state linear term. The higher-order terms, which are much smaller than the steady-state or the linear disturbance term, can be ignored for the time being from Eq. (1.41) to Eq. (1.43) and they can be rewritten as,

m ( u + W1q ) = − mgθ cosθ1 + f Ax + fTx



m ( v + U1r − W1 p ) = mgϕ cosθ1 + f Ay + fTy



m ( w − U1q ) = − mgθ sinθ1 + f Az + fTz (1.44a–c)



I xx p − I xz r =  A +  T



I yy q = m A + mT



I zz r − I xz p = n A + nT (1.45a–c)



p = ϕ − ψ sinθ1



q = θ



r = ψ cosθ1 (1.46a–c)

24

Flapping Wing Vehicles

The perturbed vertical velocity w and side velocity v in the Eq. (1.46) are usually replaced by the AOA α = w / U1 and the yaw angle β = v / U1. We could check the linearized perturbed-state EoM Eqs. (1.44)–(1.46) and find them split into two decoupled parts, including: 1. The longitudinal direction Eqs.: (1.44a ) + (1.44c ) + (1.45b ) + (1.46b ) 2. The lateral direction Eqs.: (1.44b ) + (1.45a ) + (1.45c ) + (1.46a ) + (1.46c )

1.3.6 Aerodynamic Forces and Moments Aerodynamic forces and moments are divided into two parts: normal state dynamics and disturbance dynamics. To provide a simplified treatment, this book discusses disturbance dynamics only. Longitudinal perturbed aerodynamic force, moment, and thrust are given by:  f Ax + fTx   qS     f + f  Az Tz =   qS     m A + mT   qSc 

 −(C Du + 2C D1) + (CT xu + 2CTx1) −C Dα +C L1 0 −C DδE 0  − + − − − − C C C C C C ( 2 ) Lu L1 Lα D1 Lα Lq −C LδE   −(C + 2C ) + (C + 2C ) C +CmTα Cmα Cmq −CmδE mu m1 mTu mT 1 mα 

           

u α α c 2U1 qc 2U1 δE

      (1.47)     

Lateral perturbed aerodynamic force, moment, and thrust are given by:



 f Ay + fTy  qS    A +  T   qSb  n A + nT  qSb 

      =    C   nβ  

C yβ

0 C yp

C yr

C yδA

C yδR

Cβ

0 C p

C r

C δA

C δR

+CnTβ

0 Cn p

Cnr

CnδA

CnδR

              

 β  β b  2U1   pb   2U1  (1.48) rb   2U1  δA   δ R,  

25

Introduction to Micro Aerial Vehicles

where C L1 =



W (1.49) qS

α = w / U1, Angle of attack δE = Elevator angle β = v / U1, Side slip angle δ A = Aileron angle δR = Rudder angle.

1.3.7 Numerical Example for Longitudinal Modes We can show the longitudinal and dimensional stability derivatives as given below: − q1 S (C Du + 2C D1 ) ; sec −1  mU1

Mu =

X Tu =

q1 S (CTxu + 2CT x1 ) ; sec −1  mU1

M Tu =

q1 Sc (CmTu + 2CmT1 ) ;  ft −1 sec −1  I yyU1

Xα =

− q1 S (C Dα − C L1 ) ;  ft ⋅ sec −1  m

Mα =

q1 ScCmα ; sec −2  I yy

M Tα =

q1 ScCmTα ; sec −2  I yy

M α =

q1 Sc 2Cmα ; sec −1  2 I yyU1  q1 Sc 2Cmq ; sec −1  2 I yyU1 

XδE = Zu =

− q1 SC DδE ;  ft ⋅ sec −2  m

− q1 S (C Lu + 2C L1 ) ; sec −1  mU1

− q S (C Lα + C D1 ) ;  ft ⋅ sec −2  Zα = 1 m



q1 Sc (Cmu + 2Cm1 ) ;  ft −1 sec −1  I yyU1

Xu =

Zα =

− q1 ScC Lα ;  ft ⋅ sec −1  2mU1 

Mq =

Zq =

− q1 ScC Lq ;  ft ⋅ sec −1  2mU1 

MδE =

ZδE =

…

q1 ScCmδE ; sec −2  I yy

− q1 SC LδE ;  ft ⋅ sec −2  m



(1.50)

Longitudinal small perturbation is given by:

u = − gθ cosθ1 + ( X u + X Tu ) u + X α α + X δ E δ E



w − U1q = − gθ sinθ1 + Zu u + Zα α + Zα α + Z q q + Zδ E δ E



q = ( M u + M Tu ) u + ( M α + M Tα ) α + M α α + M q q + M δ E δ E (1.51)

26

Flapping Wing Vehicles

Take the Laplace transform on Eq. (1.51) and express in the following matrix form, we get:  (− X − X ) − X gcosθ1 u Tu α   − Zu s (U1 − Zα ) − Zα − ( Z q + U1 ) s + gsinθ1   − ( M u + M T ) − M α s − ( M α + M T ) s ( s − M q ) u α 

 u (s) / δE (s)  ×  α (s) / δE (s)  θ(s) / δ (s) E 

  Xδ E   Z = δ   E   Mδ E  

      (1.52)

    

We can input the specification of a real aircraft given in Table 1.2. W = 13,000 lbs Iyy = 18,800 slug-ft2 c = 7.04 ft θ1 = 0 h = 40,000 ft U1 = 675 ft sec−1 Xcg = 31.5% α1 = 2.7° ρ = 0.000588 slug ft−3 M = 0.7 S = 232 ft2. TABLE 1.2 Longitudinal Perturbed-state Derivatives of an Aircraft Dimensionless Derivatives

Dimensional Derivatives

Dimensionless Derivatives

Dimensional Derivatives

C Du = 0

X u = −0.0075(sec −1 )

C Lδ E = 0.556

Zδ E = −0.746( ft ⋅ sec −2 )

Cmu = 0.05

M u = 0.0011( ft −1 ⋅ sec −1 )

C D1 = 0.033 CTxu = 0.066

−1

Cm1 = 0.007

X Tu = 0(sec )

CTx1 = 0.033 C Dα = 0.3

CmTu = 0.0034 −2

X α = 8.48( ft ⋅ sec )

C L1 = 0.41 −2

C Dδ E = 0

X δ E = 0( ft ⋅ sec )

C Lu = 0.40

Zu = −0.139(sec −1 )

CmT1 = −0.007 Cmα = −0.64

M α = −7.448(sec −2 )

CmTα = 0

M Tα = 0(sec −2 )

Cmα = −6.70

M α = −0.407(sec −1 )

C Lα = 5.48

Zα = −451.7( ft ⋅ sec )

Cmq = −15.5

M q = −0.941(sec −1 )

C Lα = 2.20

Zα = −0.882( ft ⋅ sec −1 )

Cmδ E = −1.52

M δ E = −0.308(sec −2 )

C Lq = 4.70

−2

M Tu = −0.0003( ft −1 ⋅ sec −1 )

−1

Z q = −1.885( ft ⋅ sec )

27

Introduction to Micro Aerial Vehicles

Based on the elevator control, the linear transfer functions are shown as given below. The characteristic equation is given by Eq. (1.53).







u (s) = δE (s)  s2  2  ( 2.836 )

s s + 1  + 1 −0.872   781.4  2 ( 0.076 ) s  2 (.355) s   s 2 + 1 + + 1  2 + 0.091 2.836   ( 0.091) 

( 5500 ) 

 s2 2 ( 0.078 ) s  s + 1  + 1 2 +  0.081 279.2  ( 0.081)  2 ( 0.076 ) s  2 (.355) s   s 2 + 1 + + 1  2 + 0.091 2.836   ( 0.091) 

( −1.74 ) 

α (s) = δE (s)  s2  2  ( 2.836 )

s s + 1 + 1  ( −3.07 )  θ(s) 0.018   0.640  = (1.53) δE (s)  s2 2 ( 0.076 ) s  2 (.355) s   s 2 + 1 + 1   2 + 2 + 0.091 2.836  ( 2.836 )   ( 0.091) 

There are two motion modes in the longitudinal transform functions, as shown below in Table 1.3: (5 5 We assign δ E = 5° = 57.3 radian. By substituting δ E ( s ) = 57.3) / S Eq. (1.53) and using the inverse Laplace transform, we can obtain the transient responses of u(t), α(t), and θ(t). For example, the transient form of side angle u(s) can be expressed as: u (s) =

A ( s + 1.007 ) + B 2 2 2 [s + (0.355)(2.836)] 0.355 ]   + (2.836) [1 − 1.007



+

(2.651)2

C ( s + 0.007 ) + D (1.54) 2 2 2 [s + (0.076)(0.091)] (0.091) [1 0.076 ] + −    0.007

(0.091)2

Inverse Laplace transform is given by: u ( t ) = e −1.007t { A ⋅ cos ( 2.651t ) + B ⋅ sin ( 2.651t )} + e −0.007t {C ⋅ cos ( 0.091t ) + D ⋅ sin ( 0.091t )} + E   Short − period Phugoid



TABLE 1.3 Vibration Parameters Based on Table 1.2 Mode Short period Long period (phugoid)

Natural Frequency ωn 2.836 0.091

Damping Ratio ζ 0.355 0.076

(1.55)

28

Flapping Wing Vehicles

Equation (1.55) depicts that besides the steady part of E, u(t) includes short-period mode and the phugoid mode. Both modes are transient sinusoidal oscillation whose amplitude decays exponentially. It means that after actuating an elevator angle of δE, the horizontal perturbed speed u(t), AOA α(t), and pitch angle θ(t) all oscillate exponentially and approach to their individual steady values. The oscillation of the first several seconds was dominated by the short period mode and gradually added with the long-period mode later on. The transient overshoot and the long-term oscillation are uncomfortable to the passengers inside the aircraft. Therefore the FAA of USA regulated some rules and practical values about the transient oscillation about the civil aviation airliners and termed them as the airworthiness.

1.3.8 Numerical Example for Lateral Modes We can show the lateral, dimensional stability derivatives using Eq. (1.56).

Yβ = Yp = Yr =

q1SC yβ ;  ft ⋅ sec −2  m q1SbC y p ;  ft ⋅ sec −1  2mU1 

Lp =

q1SbC yr ;  ft ⋅ sec −1  2mU1 

Lr =

Yδ A = Yδ R

Lβ =

q1SbCβ ; sec −2  I xx 2

q1Sb C p ; sec −1  2 I xxU1  q1Sb 2C r ; sec −1  2 I xxU1 

q1SC yδ A q1SbC δ A ;  ft ⋅ sec −2  Lδ A = ; sec −2  m I xx

q1SC yδ R q SbC δ R = ;  ft ⋅ sec −2  Lδ R = 1 ; sec −2  m I xx

Nβ =

q1SbCnβ ; sec −2  I zz q1SCnTβ

N Tβ =

I zz

q1Sb 2Cn p ; sec −1  2 I zzU1 

Np = Nr =

; sec −2 

q1Sb Cnr ; sec −1  2 I zzU1 

Nδ A =

q1SbCnδ A ; sec −2  I zz

NδR =

q1SbCnδ R ; sec −2  I zz

We can input the specification of a real aircraft as given in Table 1.4. W = 13,000 lbs U1 = 675 ft sec−1 b = 34.2 ft θ1 = 0 h = 40,000 ft M = 0.7 Xcg = 31.5% α1 = 2.7° ρ = 0.000588 slug ft−3 S = 232 ft2 c = 7.04 ft

(1.56)

2

In body axes Ixx,B = 28,000 slug-ft2 Izz,B = 47,000 slug-ft2 Ixz,B = 1,350 slug-ft2 In stability axes Ixx,S = 27,915 slug-ft2 Izz,S = 51,380 slug-ft2 Ixz,S = 450 slug-ft2



29

Introduction to Micro Aerial Vehicles

TABLE 1.4 Lateral Perturbed-state Dimensionless Derivatives and Dimensional Derivatives of an Aircraft Dimensionless Derivatives

Dimensional Derivatives

Dimensionless Derivatives

Dimensional Derivatives

C yβ = –0.73

Yβ = −56.1

Cδ A = 0.178

Lδ A = 6.77

Cyp = 0

Yp = 0

Cδ R = 0.0172

Lδ R = 0.747

C yr = 0.40

Yr = 0.779

Cnβ = 0.127

N β = 2.627

C yδ A = 0

Yδ A = 0

CnTβ = 0

N Tβ = 0

C yδ R = 0.138

Yδ R = 10.65

Cn p = 0.008

N p = 0.0042

Cβ = –0.110

Lβ = −4.188

Cnr = –0.201

N r = −0.105

C p = –0.453

L p = −0.437

Cnδ A = –0.0172

N δ A = −0.0414

Cr = 0.163

Lr = 0.157

Cnδ R = –0.0747

N δ R = −1.55

Lateral small perturbation equations are given by:

v + U1r = gϕ cos θ1 + Yββ + Yp p + Yr r + Yδ A δ A + Yδ R δ R



p − A1r = Lββ + L p p + Lr r + Lδ A δ A + Lδ R δ R



r − B1 p = Nββ + N Tβ β + N p p + N r r + N δ A δ A + N δ R δ R ,



where

A1 =

I xz I xx

and

B1 =

I xz (1.57) I zz

Take the Laplace transform on Eq. (1.57) and express them in the following matrix form:  sU − Y ( 1 β ) − ( sYp + g cosθ1 ) s (U1 − Yr )   β ( s ) / δ ( s )   Yδ        −L s (s − Lp ) − s ( sA1 + Lr )   ϕ ( s ) / δ ( s )  =  Lδ  (1.58) β    −N − N   ψ ( s ) / δ ( s )   N δ ,  − s sB + N s s − N ( ( 1 p) β Tβ r)     where δ can be either δ A or δR. Based on the aileron control (δ A is input), the transform functions are given by:



s s + 1  + 1   β (s) 0.0685 1.267  = δ A (s)  s  s2 2 ( 0.036 ) s  s + 1 + 1  + 1   2 +    1.618 0.001 0.507  (1.618 ) 

( 23.2 ) 

2 ( 0.058 ) s  s2 + 1 2 + 1.539 1.539 ( ) ϕ (s)   = 2 δ A (s)  s  2 ( 0.036 ) s  s s + + 1 + 1  + 1   2 1.618 0.001   0.507   (1.618 )  

(12,000 ) 



30

Flapping Wing Vehicles

 s2 2 ( 0.80 ) s  s + 1  + 1 2 +  1.380 1.132 1.380 ( ) ψ (s)   = (1.59) 2 δ A (s)  2 ( 0.036 ) s  s s s     + + 1 s +1 +1  0.001   0.507   (1.618 )2 1.618 

( −579 ) 



Based on the rudder control (Dr is input), the transform functions are:



s s + 1 + 1  ( 23.2 )  β (s) 0.0685   1.267  = δ A (s)  s  s2 2 ( 0.036 ) s  s + + 1 + 1  + 1   2 1.618 0.001   0.507   (1.618 ) 



2 ( 0.058 ) s  s2 + 1 2 + 1.539 (1.539 ) ϕ (s)   = 2 δ A (s)  s  s 2 ( 0.036 ) s  s + + 1 + 1  + 1   1.618 0.001   0.507   (1.618 )2 



 s2 2 ( 0.80 ) s  s + 1  + + 1 2 1.380 1.132   (1.380 ) ψ (s)  = (1.60) 2 δ A (s)   2 0.036 s s s s ( )     + + 1 s +1 +1  0.001   0.507   (1.618 )2 1.618 



(12,000 ) 

( −579 ) 

There are three motion modes in the lateral transform functions that are given below: 1. Roll mode: its time constant TR for exponential decay is 1 / TR = 0.507 2. Spiral mode: its time constant TS for exponential decay is 1 / TS = 0.001 3. Dutch roll mode: the natural frequency ωn and damping ratio ζ are ω n = 1.618 ς = 0.036 We can assign δ A = 5°  = 5/57.3 radian into Eq. (1.59), and obtain the transient responses of β(t), ϕ(t), and ψ(t). For example, the transient form of side angle β(s) is given by: β(s) =

 Aˆ Cˆ ( s + 0.058 ) + Dˆ Eˆ + + + 2 2 2 s + 0.001 s + 0.507 [s + ( 0.036 )(1.618 )] + (1.618 ) 1 − 0.036  s    0.058

(1.61)

(1.617)2

Inverse Laplace transform is given by:

{

}

t −.507 t −.058 t β (t ) =  Aˆ ⋅ Bˆ ⋅ e Cˆ ⋅ cos (1.617t ) + Dˆ ⋅ sin (1.617t ) + Eˆ (1.62) e −.001  +  +e    spiral rolling Dutch − roll

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ˆ β(t) includes exponential Equation (1.62) depicts that besides the steady part of E, decaying roll mode, spiral mode, and a sinusoidal decaying oscillation called Dutch roll. It means that after actuating an aileron angle of δ A or a rudder angle of δR, the perturbed side slip speed β(t), roll angle ϕ(t), and yaw angle ψ(t) all exponentially approach to their individual steady values. Different from the longitudinal direction, there is only one oscillation of Dutch roll mode which causes uncomfortable overshoot and the long-term oscillation to the passengers inside the aircraft. Therefore the FAA of USA regulated some rules and practical values about the transient oscillation about the civil aviation airliners and termed them as the airworthiness.

1.3.9  Plate-body Stability The Golden-Snitch FWMAV has two kinds of fuselages. Real flight maneuver shows that the plate-like fuselage of Figure 1.15 is more agile but unstable. The bird-like fuselage of Figure 1.16 is more stable but not agile. Let us discuss the flight performance difference between the two FWMAVs using the rigid-body flight dynamics model in this section. Characteristic equation (longitudinal) is given by:

D1 = As 4 + Bs 3 + Cs 2 + Ds + E



A = U1 − Zα



B = − (U1 − Zα )( X u + X Tu + M q ) − Zα − M α (U1 + Z q ) (1.63)

For the coefficient B, there are only Mq and Mα including Iyy, which relates to the geometry of the aircraft body. Under detailed observing, even the inertia Iyy is almost

FIGURE 1.15  Fuselages of the Golden-Snitch: plate-like fuselage.

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Flapping Wing Vehicles

FIGURE 1.16  Fuselages of the Golden-Snitch: bird-like fuselage.

nothing to do with the thick body or thin body of the aircraft. Therefore, the pitching stability behaviors of the two bodies are similar and it matches the flight testing result of the Golden-Snitch. Characteristic equation (lateral) is given by:

(



D2 = s As 4 + Bs 3 + Cs 2 + Ds + E



A = U1 (1 − A1 B1 )

)

B = −Yβ (1 − A1 B1 ) − U1 ( L p + N r + A1 N p + B1 Lr ) (1.64)



Some inertia information about the above two fuselages is given by: I xz ∫ xzdm I ∫ xzdm ; B1 = xz = = I xx ∫ ( y 2 + z 2 )dm I zz ∫ ( x 2 + y 2 )dm A1,plate > A1,bird

A1 =

B1,plate > B1,bird

(1.65)

( y ~ 0)plate On the lateral stability of the plate-body, y ~ 0, For example,

A1 = 0.048 | B1 = 0.029 |plate

vs.

A1 ≈ 0.0 | B1 ≈ 0.0 |Bird

We substitute the above coefficients into the lateral characteristic equation for comparison. Routh stability criterion reveals that all the coefficients are positive herein. The absolute values Aplate and Bplate of the plate-body is smaller than the case of a bird-like body. Therefore, it is less stable for the plate-like case or less agile maneuver for the plate-like case.

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1.4  SCALING LAWS OF FLAPPING WINGS Based on the observation of geometric similarity, we can predict the size, overall weight, flight speed, and frequency of FWMAV from the regression analysis of bird crickets, bats, and insects. We use this correlation and fly according to the wing area, speed, aspect ratio, and weight, which can be conceptually designed for the performance characteristics of the FWMAV [16].

1.4.1  Geometry Similarity The following parameters are directly deduced from the definition of a physical quantity. We know that the physical law changes with the size or mass m and the power law, which is also called geometric similarity. Different parameters are defined as given by: • • • • •

Wing loading Wingspan Wing area Aspect ratio Wing-beat frequency



W 3 = k 2 = k = k1m −3 S 



b ∝  ∝ m3



S = k 2  2 = k3 m 3



AR =



fw ,max = k5 −1 = k6 m 3



fw ,min =

1 2

b2 = k4 m 0 S −1

−1

−1

ω 1 2W = = k7 −1+(3− 2)/ 2 = k7  2 = k8 m 6 2π 2π ρSC L

(1.66a–f)

1.4.2 Scaling Laws of Bio-natural Flyers In fact, the power law of the physical quantities of natural creatures as a function of size or mass m will not be as ideal as the above-mentioned geometric similarity. However, they evolve and adjust according to geographical living conditions. As shown in Table 1.5, their exponential figures of the laws are different from those of the geometric similar laws [17,18]. The following sub-items are briefed. a. Wingspan In the study of flapping creatures and flapping wing vehicles’ design, the variations in power-law due to the flying vehicle’s varying weights are quite

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TABLE 1.5 Scaling Law for General Birds and Hummingbirds Correlation Based on All Birds Based Geometrical on Empirical Animal Group Dimensions Similarities Data Wingspan [m] m0.33 — Wing area [m2] m0.67 — Wing loading [N/m2] m0.33 — Aspect ratio [1] 0 — Wingbeat [Hz] m−0.33 3.87m−0.33 frequency

All Birds Except Hummingbirds Hummingbirds Based on Based on Empirical Data Empirical Data 1.17m0.39 2.24m0.53 0.16m0.72 0.69m1.04 62.2m0.28 17.3m−0.04 8.56m0.06 7.28m0.02 −0.27 3.98m 1.32m−0.60

interesting to go through. In view of the accuracy of the geometric similarity law, Greenewalt’s [17] early research found that as the bird’s weight increases, the bird’s actual wingspan is larger than the value estimated by the geometric similarity law. Norberg [18] calculated that the power exponent of the general bird’s wingspan versus body mass as close to 0.4, which is different from the geometric similarity law of 0.33. The power index varies with species, and Norberg finds that most birds are very close to 0.28–0.42 (preferably 0.39) except for hummingbirds. The regression analysis of wingspan vs. body mass is shown in Figure 1.17. It can be found that the dotted diagonal line for

FIGURE 1.17  Regression analysis of wingspan and body mass of flying creatures.

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hummingbird is much steeper than the general scale law (preferably 0.53), which means that the hummingbird wingspan is not only larger than the law of geometric similarity but is also larger than the predicted value of the scale law of the bird wingspan. b. Wing area In the Norberg study, it is noticeable that the wingspan is varied for different bird species. Hummingbirds are an obvious example of this feature. Under the same body mass, hummingbird (~m1.04) has a larger wing area than other birds’ wings (~m0.72). c. Wing loading In many cases of the flying creatures, the mass obtained from the relationship between wing load and weight (m0.28~m−0.04) is much lower than that obtained from the trend expected by the law of geometric similarity (~m0.33). d. Aspect ratio Under normal circumstances, the agility and maneuverability of the aircraft increase with the reduction of the aspect ratio. The general military fighter or acrobatic aircraft has a smaller aspect ratio than the conventional traditional aircraft has. However, the aspect ratio is not closely related to body mass (m0.06~m−0.02) in particular. e. Flapping frequency Norberg’s statistical resources also addressed the relationship between wingbeat frequency and body mass. The wings of flying birds and insects are composed of muscles and bones, and their strengths are limited. Through the geometric similarity law, the structural upper limit of the flapping frequency can be defined as [19].

fw ,max ~ m −1/ 3 (upper limit) (1.67) It can also be seen from Eq. (1.67) that the wing flap frequency decreases with weight. When large bird crickets fly at their maximum speed, most of the wing-flapping speeds are very low, and their wingtip speed is usually lower than the fly wing speed. For small birds or large insects, the wing tip speed is often greater than the flying speed. Few insect species can reach a frequency of more than 100 Hz. Besides, the scale law’s data point depicts a lower limit, called the aerodynamic lower limit.



fw ,min ∼ m −1/ 6 ( lower limit ) (1.68) When we compare the scale law values of the flapping frequency, we can come across the following conclusions: a. As body mass m is much larger than 1, the law of geometric similarity (natural frequency of the body) of (3.87) · m−0.33 is greater than the general bird flap frequency of (3.98) · m−0.27 holds good. It means that

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Flapping Wing Vehicles

the general bird’s body structure is softer than the flapping wing, and the high-frequency vibration of the more rigid flapping wings will be absorbed by the bird body, which helps to stabilize the head or eyes of birds when they fly. b. As body mass m is much larger than 1, like that of hummingbirds, the flapping frequency (1.32) · m −0.60 less than the law of geometric similarity (natural frequency of the body) (3.87) · m −0.33. It still means that the body structure of the hummingbird is softer than that of the flapping wings and absorbs the high-frequency flapping vibration. Using the scale laws of Table 1.5 of general birds and hummingbirds, Table  1.6 lists the corresponding values of body mass (kg) and flapping frequency (Hz) within the mass range of 3–20 g. When the body’s total mass is in the range of 6–11 g, the wingspan limit is reduced to 16–20 cm (Figure 1.18). The flapping frequency must be as high as 13.4–15.8 Hz for performing a horizontal forward flight. The total body mass includes flaps, fuselage, tail, main motor, tail rudder, transmission mechanism, battery, and remote control chip.

TABLE 1.6 Calculation Data of Flying Biological Scale Law (Mass 3–20 g) Wingspan b (m) Body Mass, M (kg) 0.020 0.019 0.018 0.017 0.016 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003

Bird b = (1.17) m0.39 0.254 0.249 0.244 0.239 0.233 0.227 0.221 0.215 0.208 0.202 0.194 0.186 0.178 0.169 0.159 0.148 0.136 0.121

Hummingbird b = (2.24) m0.53 0.282 0.274 0.266 0.258 0.250 0.242 0.233 0.224 0.215 0.205 0.195 0.185 0.173 0.161 0.149 0.135 0.120 0.103

Flapping Frequency f (Hz) Bird f = (3.98) m−0.27 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.9 13.1 13.4 13.8 14.2 14.7 15.2 15.8 16.6 17.7 19.1

Hummingbird f = (1.32) m−0.60 13.8 14.2 14.7 15.2 15.8 16.4 17.1 17.9 18.8 19.8 20.9 22.3 23.9 25.9 28.4 31.7 36.3 43.1

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FIGURE 1.18  Specification of the Golden-Snitch of Tamkang University.

1.5  LIFT MECHANISMS OF FLAPPING FLIGHT In flapping wings, the birds use appropriate feedback control to change the wings into various geometric shapes. The flapping flight can be unstable in the 3D field. However, none could accurately analyze the flapping wing characteristics so far. The complete wing-flapping system model can predict the unsteady state and describe the  overall geometric shape over time due to the interaction between the wings and the field. Therefore, we will discuss a few important dimensionless parameters related to flapping.

1.5.1 Dimensionless Parameters of Flapping Wings The unsteady flow can be decided by the reduced frequency K, which is expressed as:

K = ωc / 2V , (1.69)

where ω is the angular velocity (frequency) of the flapping wing, c is the chord length at the wing root, and V is the forward flight speed. The reduced frequency is the ratio of the flapping speed to the forward flight speed. When the value of K increases, the flow field tends to be unsteady. For fixedwing, during hovering mode (V = 0), K-value approaches infinity or undefined. In addition, the advance ratio can also be used to evaluate the unsteady flow as:

J = U / ( φbf ) , (1.70)

where U, ϕ, f, and b represent flight speed, stroke angle, wing frequency, and span, respectively. J is the ratio of flight speed to flapping speed that can also be interpreted as the distance advanced per up-and-down flapping stroke in a full cycle. The advanced distance divided by the flapping stroke length is J. The border between the

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Flapping Wing Vehicles

unsteady state and the quasi-steady state is at J = 1. When J > 1, it is a quasi-steady state, and when J < 1, it is considered as an unsteady state. Most insects such as the bumblebee, black fly, and fruit fly are in the unsteady state category. Other commonly used dimensionless parameters are Reynolds number (Re), Strouhal number (St), lift coefficient (CL), and thrust coefficient (CT ).

Re   = ρU ∞ lref / µ, (1.71)

where ρ is the air density, 1.225 kg/m3 μ is the air viscosity of 1.79 × 10 −5 kg/ms U∞ is the freestream velocity lref is the characteristic length (chord for general aircraft). Strouhal number is also a dimensionless parameter given by:

St =   fA / U∞, (1.72)

where f is the flapping frequency, A is the amplitude stroke from the upper position to the lower position for a wingtip, and U∞ is the free stream velocity. Value of St between 0.2 and 0.4 represents the best cruise mode.

1.5.2 Unsteady Lift Mechanisms In the unsteady lift mechanism for flapping flight, the vortex generation is first introduced as follows: a. Von Kármán vortex street In 1935, Von Kármán [20] proposed a phenomenon of vortex streets. First, the phenomenon of drag and push due to vortices was explained. Clockwise vortices are generated above the centerline of the fixed-wing, and anticlockwise vortices are generated below the centerline as depicted in Figure 1.19(a). The vortex pairs are generated from left to right, and these vortices cause the centerline of the composite velocity to move forward and thus cause obstruction. Anticlockwise vortex is generated above the flap’s centerline, and a clockwise vortex is generated below, as shown in Figure 1.19(b). These vortices cause the composite velocity of the centerline to move backward, which results in a push. b. Clap and fling mechanism In 1973, Weis-Fogh [21,22] studied the flapping wing of Encarsia Formosa. It has a high-lift mechanism at very low Reynolds numbers, named clap and fling or Weis-Fogh mechanism. When the insect’s wings are close to the back but have not yet entered the downstroke, this action is called clap. At the beginning of the clap, the wings’ leading edge will gradually approach, and the wings will rotate around the leading edge of the wings. The leading edge will contact first than the wing’s trailing edge, and finally, the distance between the wings is very close to each other. At

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FIGURE 1.19  Von Kármán vortex: (a) drag of fixed wings and (b) thrust of flapping wings.

this time, a large jet will be pushed and the vortex generated at the leading edge of the wing during the approach of the wing. During the fling, the wing’s leading edge begins to split and rotates around the wing’s trailing edge. A low-pressure area is generated between the leading edge of the wings. Bound vortex circulation attached above the wing will produce lift. This mechanism can generate a considerable lift, but generally, insects do not use this way when flying freely. c. Leading-edge vortex of unsteady flapping wings The quasi-steady blade element theory can describe an unsteady flapping lift. Different kinds of lift sources include translational lift Fs, lift, rotational force Fr, and added mass force Fa, shown in Figure 1.20(a). In 1998, Ellington [23–25] pointed out that the vortex bubble in the unsteady state is caused by the flow separation at the wing’s leading edge. It is called a leading-edge vortex (LEV) that is shown in Figure 1.20(b). This can also help in explaining the characteristics of the flapping wing. This kind of flow separation is not harmful to the flapping wing. The flapping action is shown in Figure 1.20(b) is with a high inclined angle or high AOA. The airflow separates at the leading edge, and the shedding LEV is firmly attached above the flapping wing. LEV reattached to the wing at the trailing edge is different from the other separation case of fixed-wing at high AOA, where the boundary explodes into a chaotic wake without regular patterns. Therefore, the flapping wing with high AOA causes no stall issue but generates LEV and needy downwash for lift. The stabilization of the unsteady LEV without stall is the most dominant lift mechanism during the upstroke, and the upstroke translation flapping is called a delayed stall [26]. The centrifugal acceleration and Coriolis acceleration cause the stabilization of LEV during flapping. LEV is continuously maintained at the leading edge of the wing and extended along the wingspan direction to the wingtips on both sides. LEV combined with the wingtip vortex keeps on providing the main contribution to the flapping lift. LEV is widely found in the fruit fly, hawkmoth, dragonfly, bumblebee, and FWMAV.

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Flapping Wing Vehicles

FIGURE 1.20  (a) Quasi-steady flapping model and (b) the smoke line of the Golden-Snitch in the wind tunnel.

According to the blade element theory, the quasi-steady translational lift Fs lift is given by:

1  2 Fs ,lift = ∑ ρ ue ⋅ C L ( α ) ⋅ c∆r , (1.73) 2  where ue, the blade element’s velocity relative to the air, a combination of freestream velocity and flapping velocity. C L ( α ) can adopt the potential flow solution Eq. (1.7).

1.5.3 Rotational Lift of Flapping Wings In 1999, Dickinson [27] used a Drosophila melanogaster wing model to study the wing rotation between the downstroke and upstroke. A rotation mechanism is proposed with several stages. In the first stage, the wings are almost translated at a fixed AOA (greater than the fixed AOA 15° of a fixed-wing) and fixed speed. The second stage is a supination wing-rotation at the stroke reversal. The third stage is pulled back at another fixed AOA (almost vertical) and fixed speed. Finally, it reaches the other stroke reversal to perform the wing-rotation pronation.

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Wing rotation has three possibilities: advanced rotation, symmetric rotation, and delayed rotation. Dickinson found that both the advanced rotation and the symmetric rotation can use the Magnus effect to explain lift improvement, but the delayed rotation negatively affects lift. Dickinson’s fruit fly model experiment revealed that the wing rotation could contribute an additional 35% to lift. Hoverfly model experiment found that lift generation by wing rotation is increased by 50%. However, an insect model experiment cannot exactly simulate the real insects. Lift generation by wing rotation will be discussed more in Chapter 12. According to the blade element theory, the quasi-steady rotational force Fr is given by:  Fr = ∑ ρ ⋅ Cr α c 2 ⋅ ue ∆r , (1.74)



where α is the angular acceleration of AOA, Cr α c 2 is the rotational circulation, Cr is the wing rotation force coefficient with the theoretical value of π ( 0.75 − xˆ 0 ), x 0 is the axis of rotation (from 0 to 1). The experimental value Cr is 1.55.

1.5.4 Added Mass When a wing starts to accelerate from rest or decelerates before the stroke reversal, it should agitate or push the surrounding air to exhibit the largest acceleration or deceleration. Therefore, it deduces an additional pressure that increases from the air mass on the wing surface. This effect can theoretically be equivalent to an added wing mass and the wing’s time-varying inertia increment. The added mass is associated with the wing acceleration as the inertial force increases the flapping wings’ aerodynamic forces. According to the blade element theory, the quasi-steady added mass force Fa is given by [16]:

Fa = ∑

    ρπc  ue ⋅ u e   sinα + u e α ⋅ cosα  c∆r (1.75) 4  ue 

 where u e is the velocity of the blade element relative to air.

1.5.5 Wing-Wake Interaction At the moment of stroke reversal, the wing can capture the vortex shed by the previous flapping stroke, and the vortex stays in the wake region. This action partially captures some energy that has been spent in the previous flapping stroke, thus improving the efficiency of the aerodynamic force generation. This unsteady effect is called wake capture or wing–wake interaction. The lift-incremented pulse just follows after each stroke reversal or appears at the beginning of each flapping stroke. The magnitude and the direction of the lift pulse depend on the phase relationship between the wing rotation and the flapping translation. Combined with a clap-and-fling mechanism, the lift contribution of the wake capture can be up to 25% of the total lift during a hovering flight. It will be even more if

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Flapping Wing Vehicles

the duration of flapping stroke increases. In 2003, wake capture was observed in the butterfly experiment [28]. Many used the particle-image-velocimetry (PIV) to investigate the vortex wake and the velocity distribution field of flying creatures. However, rare cases can isolate the wake capture effect from the whole flow field [29].

1.6  STABILITY ISSUES OF A FLAPPING WING An FWMAV consists of various components, such as a flapping wing, fuselage, tail, main motor, tail rudder, flapping mechanism, battery, a remote-control chip, and so on. There are many limitations in the positioning of these components in the vehicle. For example, the main motor must be placed close to the flapping mechanism and cannot be placed at the tail. The center of gravity (C. G.) influences the position of the aerodynamic center (A. C.)

1.6.1 C. G. of a Flapping Wing The location of C. G. in an unstable general aircraft is shown in Figure 1.21. Herein the C. G. is behind the A. C. about 1/4 chord position from the leading edge of the wing. In order to balance the moments, the tail must provide an upward force to generate a pitching moment opposite to the one generated by the main wing. The advantage here is that the tail lift is positive against gravity like the main wing lift, and the flight maneuver is excellent. However, it also leads to instability due to the chance of the aircraft suddenly increasing its AOA due to some external disturbances causing a nose-to increase the main wing lift. Although the tail lift increases too, yet it is not enough to balance the main wing lift. The AOA and lift keep on increasing until a stall happens. In order to prevent the divergence of this nose-up and stall, the computer needs to assist in adjusting the tail (elevator) control immediately (so-called fly-by-wire), otherwise resulting in a crash. A stable design of the aircraft is shown in Figure 1.22, where the C. G. precedes the A. C. In order to balance the overall moment (taking a moment about the C. G.), the tail must provide a negative lift to generate a pitching moment opposite to the main wing. The disadvantage is that the tail lift acts in the opposite direction to the one generated by the main wing. The advantage is that it is inherently stable. When the aircraft suddenly increases the AOA due to some external disturbances, causing the nose to increase the main wing lift. The tail’s

FIGURE 1.21  Location of C. G. in a general unstable aircraft.

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FIGURE 1.22  C. G. location for a general stable aircraft.

negative lift is still not enough to balance the increased torque from the main wing. However, the main wing moment automatically generates a nose-down, making the aircraft return to its original level (this action is known as “trim”). Therefore, this type of design does not require a computer to assist in adjusting the tail control. The aircraft can easily maintain a small AOA for stable flight, and it is not prone to stalling. Hence, a question arises as to adopt which one of the C. G., as mentioned earlier, positions for the FWMAV. Figure 1.23 shows the FWMAV flight trajectory of different C. G. found to differ from fixed-wing aircraft’s behavior. If the stable design (Figure 1.22) is adopted (C. G. in front), then the FWMAV will slowly land due to insufficient lift and hard to continue its level flight. Of course, C. G. cannot be pushed too far to the rear (C. G. in rear), either. That will make the FWMAV quickly pull up the drive down for a crash. Both C. G. designs, that is, C. G. in front or C. G. in the rear, are not advisable for an FWMAV. In fact, a flapping wing allows a higher AOA or fuselage inclination. The AOA is about 60°–70°, much higher than the upper limit 15° of a fixed-wing aircraft. The unstable C. G. assignment after A. C. (Figure 1.23) is a more appropriate way. Because of the instability at the initial flight condition, FWMAV has a nose-up. However, the flapping wing can resist stall and can keep the FWMAV to maintain a level flight at a higher AOA. When the inclined angle is high, the original C. G. position produces a nose-up rotation and moves C. G. forward until a “trim” state and a level flight. Actually, C. G. is very close to A. C. at this “neutral-point,” as shown in

FIGURE 1.23  Flight trajectories of FWMAVs with different C. G.

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Flapping Wing Vehicles

FIGURE 1.24  C. G. location of an FWMAV meets with A. C. at the neutral point for level cruising flight.

Figure 1.24. Meanwhile, the tail acts as a C. G. adjuster rather than the aerodynamic force balancer. From our real-flight observation of FWMAVs, tail AOA during level cruising is almost zero and provides very little lift to FWMAV. Based on the above observation, we can directly place its C. G. at the A. C. when designing a flapping-wing aircraft. The C. G. is located using the relation

 M i ( g ) × X i ( l ) C. G.( l ) = ∑  = A. C. i=0 M all ( g )

(1.76)

where M is mass, X is the distance between the centroid of the part and the origin, and i is the part number.

1.6.2  Preliminary Review on Flight Dynamics Model of a Flapping Wing For more than 40 years, many people have extensively researched insect flight mechanics and stability. They assumed the wing-beat frequency to be much lower than the natural frequency of the wing. The unsteady state aerodynamic forces and moments of flapping wings can be averaged over a while and brought into the traditional fixed-wing flight mechanics [30] EoM in Eqs. (1.38)–(1.40). In those articles about flapping wings, most of them are for insects, hummingbirds, and hovering MAVs [31,32]. The analytical method still linearizes the original nonlinear dynamic equations using the traditional small disturbance technique to simplify Eqs. (1.44)–(1.46). A few examples [33,34] deal directly with nonlinear dynamic equations. (The right side of Eqs. (1.44)–(1.46) represents the aerodynamic forces of flapping wings.) Most of the existing flapping-wing literature uses FEM CFD software (Fluent or COMSOL) to calculate unsteady lift and thrust and apply them into EoM Eqs. (1.44)–(1.46). However, the standard EoM has not been reviewed and checked for their accuracy.

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1.6.3 Time-averaging of Inertia for Flapping Wings Again, reviewing the basic derivation given by Roskam for flight mechanics, the four basic assumptions of fixed-wing aircraft with EoM Eqs. (1.44)-(1.46) in Section 1.3.2 are: 1. It is in the inertial coordinate system X, Y, and Z, which applies Newton’s second law; 2. Ignore the Earth’s rotation; 3. The total weight of the aircraft does not change with time; 4. Mass distribution does not change over time. For flapping wings, the fourth assumption is doubtful. According to general practice, when the flapping frequency is much lower than the flapping wing’s natural frequency, it is approximated as a steady-state case. Also, the aerodynamic forces and moments can be processed by a time-averaged method. However, the time-averaged processing for the mass distribution definition of flapping wings, including the centroids and various moments of inertia, should be reconsidered since the centroids and various moments of inertia will eventually affect the stability derivatives in the left-hand side of EoM Eqs. (1.44)–(1.46). The changing of the center of mass and all inertia quantities is based on the experimental observation. One such center of a flapping wing’s mass trajectory is seen from a high-speed photograph shown in Figure 1.3. Therefore, reconsideration of all the time-averaged quantities should be based on the flapping wings’ actual flight in the EoM given by Eqs. (1.44)–(1.46). For example, regarding the time history, downstroke accounts for about 60% of a flapping cycle, and the upstroke accounts for about 40%.

1.6.4 New Definition of Stability Derivatives Related to Flapping Frequency There are many stability derivatives in Eqs. (1.50) and (1.56), which need to be reviewed one by one. Some exclusive aerodynamic parameters for flapping-wing should also be appropriately added. Subsequently, a full set of either a wind tunnel or numerical wind tunnel (computational fluid dynamics) experiments can collect all the values for stability derivatives. The flapping wings possess the conventional aerodynamic parameters of fixed wings C Lα , CTα , C Mα and have other parameters related to flapping frequency, for example C Lω = ∂C L / ∂ω , CTω = ∂CT / ∂ω , and C Mω = ∂C M / ∂ω.

1.6.5 New Control Way Other Than Elevator, Aileron, and Rudder The tailless flapping wing found in the hovering FWMAVs seldom uses the conventional control like elevator angle δE, rudder angle δR, and aileron angle δ A in the fixed-wing case. New control variables such as the flapping frequency ω, the wing rotation angle ζ, and the phase-lag angle Δ between two wings can take the place

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Flapping Wing Vehicles

of the above control variables (δE, δR, and δ A) [35–40]. In principle, the three new control variables (ω, ζ, and Δ) provide enough function and degrees-of-freedom as compared to (δE , δR, and δ A). The new control variables (ω, ζ, and Δ) for flapping wings may no longer be true for the decoupling of the longitudinal and lateral EoMs in a fixed-wing aircraft (again, the decoupling means δE only related to the longitudinal pitch control and lift; and δA related to lateral roll and yaw control). All variables (ω, ζ, and Δ) are directly related to lifting for flapping wings. Therefore, the disadvantage of adopting a tailless control strategy for the flapping wing is that the EoM becomes highly coupled, and the calculation becomes more complicated than for the fixed-wing. However, the advantage is that it is possible to control the overall flight with only one variable, for example, flapping frequency. This has been verified in the actual flight of the Tamkang Golden-Snitch. The aerodynamic derivatives or parameters for flapping stability control are given in Table 1.7. The new dimensionless derivatives for flapping wings are provided in the third column. The establishment of these parameter databases in Table 1.7 includes the fixedwing part (Columns 1 and 2) and the new part of flapping wings (Column 3). Regarding the original part of the fixed-wing, we just use the DACOM database to establish the numerical library. For the new part of the flapping wing, it is felt that the source data will be insufficient and must be collected from the experiments in a wind tunnel or from the numerically simulated wind tunnel (CFD). TABLE 1.7 Aerodynamic Parameters for Flapping Stability Control Conventional Longitudinal Dimensionless Derivatives

Conventional Lateral Dimensionless Derivatives

New Dimensionless Derivatives for Flapping Wings C Lω

C(T − D )1

C yβ

C ( T − D ) xu

C yr

C Lς

C(T − D )x1

C β

C L∆

C( T − D ) α

C p

C( T − D ) ω

C L1

C r

C( T − D ) ς

C Lu

Cnβ

C( T − D ) ∆

C Lα

Cn p

Cmω

C Lα

Cmς

C Lq

Cnr ×

Cmu

×

Cm1

×

CmTu

×

CmT1 Cmα Cmα Cmq

C m∆ C y∆ C ∆

×

C n∆ ×

×

×

×

×

×

×

Introduction to Micro Aerial Vehicles

47

1.7 SUMMARY This chapter initially discussed the flapping motion phenomenon and its fluid mechanics with the governing equations. Further, dimensional analysis and similarity rule pertaining to the flapping wing aerodynamics and their relationships are discussed. The concept of boundary layer theory and compressibility of air is outlined. Estimation of power through considering various types of drag is discussed. The flight mechanics of FWMAV with reference to steady and unsteady state flight are elaborated with appropriate governing equations and EoM. Numerical examples are provided for the lateral and longitudinal modes of flight. The scaling laws of flapping wings with respect to various wingspans and flapping frequencies are discussed. Von Kármán vortex street phenomenon during unsteady lift behavior is explained. Finally, the stability issues on flapping wings through balancing their C. G. positions are discussed in detail.

REFERENCES

1. Shyy, W. (2013) An Introduction to Flapping Wing Aerodynamics, Cambridge. 2. Shu, C. K. (2008) The Preliminary Design, Fabrication, and Testing of Flapping Micro Aerial Vehicles, Ph.D. Dissertation, Mechanical & Electromechanical Engineering, Tamkang University (Chinese version), Taiwan. 3. Dixon, S. L. (1998) Fluid Mechanics, Thermodynamics of Turbomachinery, 4th edition, Butterworth-Heinemann. 4. Currie, I. G. (1974) Fundamental Mechanics of Fluids, McGraw-Hill. 5. Fox, R. W. and Mcdonald, A. T. (1973) Introduction to Fluid Mechanics, 2nd edition, John Wiley & Sons, 305–312. 6. Norberg, U. M. (1990) Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution, Springer, 16. 7. Incropera, F. P. et al. (2017) Incropera’s Principles of Heat and Mass Transfer, 8th edition, John Wiley & Sons, 403–405. 8. Van Dyke, M. (1975) Perturbation Methods in Fluid Mechanics, Academic Press, 46 and 106. 9. Bertin, J. J. and Smith, M. L. (1979) Aerodynamics for Engineers, Prentice-Hall, 287. 10. Anderson, J. D. JR. (1984) Fundamentals Aerodynamics, McGraw-Hill, Chapter 5. 11. Norberg, U. M. (1990) Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution, Springer, 20–24. 12. Yang, L. J. (2012) The micro-air-vehicle Golden-Snitch and its figure-of-8 flapping. Journal of Applied Science and Engineering, 15(3), 197–212. 13. Ogata, K. (1970) Modern Control Engineering, Prentice-Hall. 14. Yang, L. J., Feng, A. L., Lee, H. C., Balasubramanian, E. and He, W. (2018) The 3D flow simulation of a flapping wing. Journal of Marine Science and Technology, 26(3), 397–308. 15. Roskam, J. (1979) Airplane Flight Dynamics and Automatic Flight Control, Roskam Aviation and Engineering Corp. 16. Tennekes, H. (1996) The Simple Science of Flight (from Insects to Jumbo Jets), MIT Press. 17. Greenewalt, C. H. (1962) Dimensional relationships for flying animals. Smithsonian Miscellaneous Collections, 144(2), 1–46. 18. Norberg, U. M. (1990) Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution, Springer, 166–177.

48

Flapping Wing Vehicles

19. Shyy, W., Berg, M. and Ljungqvist, D. (1999) Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, 35, 455–505. 20. Von Kármán, T. and Burgers, J. M. (1935) Aerodynamic Theory: General Aerodynamic Theory – Perfect Fluids, Springer, 308. 21. Weis-Fogh, T. (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. Journal of Experimental Biology, 59, 169–230. 22. Weis-Fogh, T. and Jensen, M. (1956) Biology and physics of locust flight. Philosophical Transactions of the Royal Society of London, B239, 415–584. 23. Ellington, C. P. (1984) The aerodynamics of hovering insect flight. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 305, 1. 24. Van Den Berg, C. and Ellington, C. P. (1997) The vortex wake of a ‘hovering’ model hawkmoth. Philosophical Transactions of the Royal Society of London, 352, 317–328. 25. Wang, Z. J. (2000) Vortex shedding and frequency selection in flapping flight. Journal of Fluid Mechanics, 410, 323–341. 26. Chin, D. D. and Lentink, D. (2016) Flapping wing aerodynamics: From insects to vertebrates. The Journal of Experimental Biology, 219, 920–932. 27. Dickinson, M., Lehmann, F. and Sane, S. (1999) Wing rotation and the aerodynamic basis of insect flight. Science, 284, 1954–1960. 28. Srygley, R. B. and Thomas, A. L. R. (2003) Unconventional lift-generating mechanisms in free-flying butterflies. Nature, 420, 660–664. 29. Bomphrey, R. J. (2012) Advances in animal flight aerodynamics through-flow measurement. Evolutionary Biology, 39, 1–11. 30. Etkin, B. and Reid, L. D. (1996) Dynamics of Flight: Stability and Control. John Wiley & Sons. 31. Xu, N. and Sun, M. (2013) Lateral dynamic flight stability of a model bumblebee in hovering and forward flight. Journal of Theoretical Biology, 319, 102–115. 32. Xiong, Y. and Sun, M. (2008) Dynamic flight stability of a bumblebee in forward flight. Acta Mechanica Sinica, 24, 25–36. 33. Orlowski, C. T. and Girard, A. R. (2011) Modeling and simulation of nonlinear dynamics of flapping-wing micro air vehicles. AIAA Journal, 49, 969–981. 34. Liang, B. and Sun, M. (2013) Nonlinear flight dynamics and stability of hovering model insects. Journal of the Royal Society Interface, 10, 1–11. 35. Straw, D., Lee, S. and Dickinson, M. H. (2010) Visual control of altitude in flying Drosophila. Current Biology, 20(17), 1550–1556. 36. Medici, V. and Fry, S. N. (2012) Embodied linearity of speed control in Drosophila melanogaster. Journal of The Royal Society Interface, 9(77), Art. no. 77. 37. Muijres, F. T., Elzinga, M. J., Melis, J. M. and Dickinson, M. H. (2014) Flies evade looming targets by executing rapid visually directed banked turns. Science, 344(6180), Art. no. 6180. 38. Muijres, F. T., Elzinga, M. J., Iwasaki, N. A. and Dickinson, M. H. (2015) Body saccades of Drosophila consist of stereotyped banked turns. Journal of Experimental Biology, 218(6), 864–875. 39. Whitehead, S. C., Beatus, T., Canale, L. and Cohen, I. (2015) Pitch perfect: How fruit flies control their body pitch angle. Journal of Experimental Biology, 218(21), Art. no. 21. 40. Dickinson, M. H. and Muijres, F. T. (2016) The aerodynamics and control of freeflight manoeuvres in Drosophila. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1704), Art. no. 1704.

2

In-Situ Lift Measurement Using PVDF Wing Sensor

2.1  LIFT MEASUREMENT USING WIND TUNNEL Caltech and UCLA developed, using MEMS, an FWMAV named Microbat (Figure 2.1) weighing 10.6 g [6]. It has a parylene wing weighing 0.3 gf. Motor and power unit weighs about 5 gf. The support structure is built using titanium alloys. The maximum flapping frequency and the flight endurance achieved are 30 Hz and 6 min, respectively. Stanford Research Institute (SRI) developed an FWMAV and focused on employing piezoelectric polymer materials called artificial muscles to drive the flapping wing (www.sri.com). This arrangement can simulate more complex flight movements. The strain of electrical materials can reach even up to 100%. Researchers at Vanderbilt University incorporated similar piezoelectric technology to eliminate the gear-linkage parts and simplified the piezo-driven flapping mechanisms. (research. vuse.vanderbilt.edu/cim/research_flyer.html). UC Berkeley [7,8] has developed a micromechanical flying insect (MFI) shown in Figure 2.2 that helps emulate the flight feature of insects and blowflies. They designed the FWMAV based on a multidimensional thorax mechanism. It has a wingspan of 25 cm and weighs about 100 gf. It is driven by piezoelectric materials as well. The specially designed thorax performed a complex flapping motion and attained a flapping frequency of 150 Hz. A dragonfly-like MAV developed by Georgia Tech [9] uses two pairs of flapping wings, driven by reciprocating chemical muscle. Weighing about 50 gf, it has a wingspan of 15 cm. Besides the artificial muscles and MEMS technology applied to MAV researches, in recently years the most famous ones are the MAV Delfly Nimble as Figure 2.3 developed by TU Delft, Netherland [10], and developed the MAV KU Beetle as Figure 2.3 by Konkuk University, Korea [11]. They used their precision flapping mechanisms and the tailless control techniques to make great progress. The aerodynamic characteristics of the FWMAVs as mentioned above are measured using small wind tunnels. Since FWMAVs are smaller in size, they can be directly kept inside the wind tunnel for testing without scaling down. Figure 2.4(a) shows a blow-down wind tunnel with a test cross-section of 300 × 300 × 1000 mm 3. The inlet section’s contraction ratio is 6.25, and wind speed can be varied between 0 and 7 m/s. A Hot-wire anemometer is used to calibrate the wind speed. Figure 2.4(b) demonstrates the flapping wing’s installation in the test section of a wind tunnel. The wind tunnel’s turbulence intensity is about 0.05–0.028%, which is one order-of-magnitude smaller than the suggested value of 1% by Mueller [12]. DOI: 10.1201/9780429280436-2

49

50

Flapping Wing Vehicles

FIGURE 2.1  Microbat developed by Caltech/UCLA using MEMS technology [6].

The cross-section of the flapping wing placed in the wind tunnel should not affect the wind flow, and it is evaluated using a terminology called blockage ratio. It is defined as,

Blockage ratio =

Front – view area of MAV × sinα × 100% (2.1) Cross section area of wind – tunnel

The blockage ratio should be small to avoid the wall effect of a wind tunnel. The Wall effect affects the accuracy of aerodynamic force measurements. According to Rae [13], the wall confinement effect can be ignored if the blocking ratio is less than 7.5%. It is evident from Figure 2.5 that FWMAV kept at an inclined angle of less than 30° meets the thumb rule. The aerodynamic force generated by the flapping wing for diverse wind speed conditions and inclination angles is measured using a six-axis force gauge (Bertec, OH, USA) shown in Figure 2.6(a). It provides forces and moments (6 degrees of

FIGURE 2.2  MAV Delfly Nimble [10].

In-Situ Lift Measurement Using PVDF

51

FIGURE 2.3  MAV KU Beetle [11].

freedom) along and about the Cartesian frame. The force measurement specifications are as follows: maximum lift FL along the Z-axis is 200 gf, maximum thrust or drag FT along the Y-axis is 100 gf. Because of the non-linearity and hysteresis, the maximum measurement error of the force gauge’s full scale is 0.2% for 1,000 points of data for each degree of freedom. Since the flapping motion is up-and-down and unsteady, the lift is measured along the (-Z) vertical direction. The typical lift force signal waveform generated for a 20 cm wingspan kept at 20˚ inclination angle, 3.7 V driving voltage, and at three m/s wind speed is shown in Figure 2.7(a). However, the thrust force is measured as a net thrust force along the horizontal direction. The flapping wing experiences drag (D) along the +Y axis and produces thrust (T) along the –Y-axis. These two forces are coupled together, and it is not easy to measure them separately. The net thrust force (FT = T – D) is calculated, and its signal is shown in Figure 2.7(b).

FIGURE 2.4  (a) Open blow-down wind tunnel and (b) flapping wing mounted on the wind tunnel.

52

Flapping Wing Vehicles

FIGURE 2.5  Blockage ratio.

The magnitude of these two forces varies concerning wind speeds, inclined angle, and flapping frequency. The DC motor’s input driving voltage is varied between 0 and 3.7 V to obtain various flapping frequencies. Hence, for each measurement condition of a waveform, time-averaging should be performed to facilitate the subsequent discussion of the correlation between the average lift/net thrust and individual experimental parameters. The time-averaging of 12,000 data points collected from the force gauge is shown in Figure 2.7, which is an average aerodynamic data point [14]. Since the flapping frequency is about 13–15 Hz, the average aerodynamic data point is calculated using the time-averaging of 156–180 flapping cycle data. However, the transient response due to unsteady state signals will not affect the wind tunnel measurement’s credibility resulting from the timeaveraging data.

FIGURE 2.6  (a) Six-axis force gauge and (b) wind tunnel experimental setup.

53

In-Situ Lift Measurement Using PVDF

FIGURE 2.7  Typical signals of unsteady aerodynamic forces of flapping wings: (a) lift and (b) net thrust.

2.2  INERTIAL FORCE EFFECT ON LIFT The inertial force is one of the crucial factors influencing the average lift force of a flapping-wing vehicle. Chapter 1 discussed Dickinson’s three important insect wing lift mechanisms, including delayed stall, rotation lift, and wake capture. Among them, the discussion on wake capture was questioned. Sunada et al [15,16]. Believed that the rotation lift pulse initiated at the upstroke or downstroke of a horizontal figure-8 motion was due to the wing acceleration reaction or the so-called added-mass effect. Sun and Tang [17] have identified three wing-lifting mechanisms similar to Dickinson’s theory [18–20]. However, they have replaced the wake capture with the rapid acceleration of the wings at the beginning of the upstroke or downstroke. It is tedious to calculate the inertial force when assessing the added mass of the flapping flow field. It necessitates the flow field information from unsteady CFD and particle image velocimetry (PIV) experimental techniques [21]. High-speed stereo photography is utilized to capture the three-dimensional (3D) trajectory of designated mass points on the flapping wings with respect to time to obtain the flow field information. The following mathematic relations are used to calculate the inertial force of the flapping wing: The time-varying trajectory obtained based on high-speed stereo photography is relative to the fixed coordinate system (similar to fixing the flapping wing in a wind tunnel). The following relation is used to calculate the time-varying inertial force,

 Finertial ( t ) =

∫ dm

 a (t ), (2.2)

wing  where a ( t ) represents the instantaneous acceleration vector of infinitely small mass dm on the flapping wing. Integrating the time-varying inertial force with time for a period T and dividing by the period is the time-averaged inertial force. The integral expression is



 1 Fave = T

t =T

∫ dt

t=0

 Finertial ( t ) (2.3)

54

Flapping Wing Vehicles

 Substituting Eq. (2.2) into Eq. (2.3) Fave becomes





 1 Fave = T 1 = T =

1 T

t =T

∫

dt

∫ dm

 a (t )

wing

t=0

t =T

∫

dm

∫

dm



∫ a (t ) dt

t=0

wing

  V ( t = T ) − V (t = 0), 

(2.4)

wing

 the instantaneous velocity vector of infinitely small mass dm where, V ( t ) represents   on the flap. a ( t ) V ( t ) Both from time-varying data from a winged stereo high-speed photography experiment. From Eqs. (2.2)–(2.4), the following observations are made: 1. For theperiodic flapping motions of cruising or hovering flight, the start speed V ( t = 0 ) is the same as the end  speed V ( t = T ) of the cycle, and hence, the time average inertial force Fave is zero. It means that, whether it is  a wind tunnel or oil tank experiment, the measured inertial force Finertial ( t ) of the periodic flapping motion affects the lift or thrust waveform locally. Nevertheless, there is no substantial contribution from the time-averaged inertial force Fave for the overall time-averaged lift or thrust. 2. Based on the fact that there is no contribution of inertial acceleration to the time-averaged lift of periodic flapping motion and the force contribution from the added mass does not affect the global lift. The non-zero lift pulse at the beginning of the hovering stroke measured in the wind tunnel experiments is independent of the inertial acceleration or added mass of flapping motion. In other words, from the logic of the exclusion, returning to Dickinson’s theory on hovering lift of insects, the wake capture or wingwake interaction may be a more convincing argument than the added mass acceleration.   3. If the initial speed V ( t = 0 ) and final speed V ( t = T ) are different, then the time-averaged inertial force of Eq. (2.4) is no longer zero and substantially affects the flapping motion. For example, a butterfly, a bat, or a buzzard has a high wing-to-body ratio (the wing mass occupies a high percentage of the total mass of the flying body). As the difference increases, the non-zero  time-averaged inertial force Fave may dominate the flapping motion. Using wind tunnel experiments, the measured lift/thrust signal or waveform shown in Figure 2.7 has the contribution of inertial force rather than pure aerodynamic force. Based on the above derivation that the average inertial force of periodic flapping motion time is zero. Hence the time-averaging of lift and thrust forces measured from the wind tunnel experiment is purely based on aerodynamic force.

55

In-Situ Lift Measurement Using PVDF

However, the traditional wind tunnel measurements may not perform the insitu measurement of flapping wing aerodynamic forces. These measurements may help develop intelligent onboard flight technology of FWMAVs and enhance flight endurance. Hence, the polyvinylidene fluoride (PVDF)-based in-situ measurement is needed that is discussed in the following sections.

2.3  PRINCIPLE OF POLYVINYLIDENE FLUORIDE (PVDF) Based on the outstanding achievements in the field of fluid mechanics by Professor Ho’s team at UCLA and the superior micromachining capabilities of Professor Tai’s team at Caltech, together initiated the in-situ measurement of low Reynolds-number FWMAVs. They have employed a discrete check-valve micro-actuator array to enhance the lift and thrust of flapping wings, and it was significantly improved by 50% [22,23]. It is the research counterpart of the famous tailless aerodynamic control of the fixed-wing MAVs. However, the present idea is providing distributed sensors and actuators adapted from Lee [24]. Polyvinylidene fluoride (PVDF) piezoelectric material is utilized as a sensing unit because of its flexibility and its ability to be bent into any shape. It is integrated into the flapping wings, and the real-time signal output is measured during the flapping motion that provides the global lift force of a flapping wing. A mathematical model for measuring lift using PVDF piezoelectric materials is described below. We assume a pressure difference distribution Δp(x,y,z) due to aerodynamic action on the surface of the flapping wing. The lift L generated from the wing surface S is given by, L=



∫ ∫∆p ⋅ dA (2.5) S

When Δpacts on the PVDF piezoelectric film mounted on the wing, it is equivalent to applying a non-uniformly distributed load on the shell or plate’s surface. Due to this load, the film and wing may be deformed or stretched. Assume that the everyday stresses σx(x,y,z) and σy(x,y,z) of a plane stress problem are generated on the wing surface. The correlation between these normal stresses and Δp(x,y,z) is given by (Hooke’s Law) ∆p = k x ⋅ σ x = k y ⋅ σ y , (2.6)



where k x and k y are assumed stiffness functions (similar to spring elastic coefficients). Regarding the PVDF piezoelectric film as an aerodynamic sensor for lift measurement, we obtain the charge density ρi (i = x, y, z) through the transformation matrix of piezoelectric theory [25] as follows:  ρx     ρy  ρz 

  0   = 0   d31  

0 0 d32

0 0 d33

0 0 0

0 0 0

0 0 0

   σ σ σ τ τ τ T (2.7)   x y z xy yz zx  

56

Flapping Wing Vehicles

The non-zero piezoelectric coefficients of PVDF piezoelectric film is given by,  d31 = 20 pC / N     d32 = 2 pC / N (2.8)  d = −30 pC / N  33



It is reiterated here that the flapping force is regarded as a plane stress problem (σz = 0), and the charge density along the z-direction is therefore derived as, ρz = d31 ⋅ σ x + d32 ⋅ σ y (2.9)



Utilizing Eqs. (2.6)–(2.9), the total charge Q can be obtained, which is expressed by the pressure difference distribution Δp and the stiffness function k as follows:

Q=

 d31

∫ ∫ρ dA = ∫ ∫∆p ⋅  k z

S

S

x

+

d32   dA (2.10) ky 

Because the stiffness functions k x and k y are not uniform on the wing surface, the lift cannot be directly picked up from Eq. (2.10). As an approximation, we equivalently replace the terms in the bracket of Eq. (2.10) with d*, so that the lift from Eq. (2.5) can be substituted into Eq. (2.10) as mentioned below. Q = d * ⋅ L (2.11)



However, from Eq. (2.11), the total charge Q can also be expressed as the product of voltage V and the capacitance C. Since the piezoelectric material is also a dielectric material, it is an open circuit for the electrode of the sandwich piezoelectric material PVDF. Hence, there is a capacitor across the PVDF. Total charge is given as, Q = C ⋅ V (2.12)



Relating Eqs. (2.11) and (2.12), the lift establishes a linear relationship with the voltage as

L=

Q C =   V (2.13) d*  d* 

Equation (2.13) is a simplified relationship between the piezoelectric output voltage and the generated lift. It provides a simple and concise guideline to represent the in-situ lift force, electrical output from the PVDF piezoelectric film embedded on the flapping wing. Besides, this PVDF film’s output signal needs to be calibrated or quantitatively compared with the standard wind tunnel force gauge in advance. The force gauge and the PVDF piezoelectric wing sensor must be integrated with a flapping wing in the wind tunnel measurement.

57

In-Situ Lift Measurement Using PVDF

2.4  FABRICATION OF FLAPPING WINGS WITH PVDF LIFT SENSORS In the early days of development of the FWMAVs at Tamkang University, Caltech’s Microbat and MEMS technology [26] was learned. The frame of the flapping wing is made of titanium-alloy whose properties are given in Table 2.1. A twin-wing shown in Figure 2.8 has a half-span of 7 cm, the central chord of 5.5 cm, and an area of 64.5 cm2. The angle between the wing root and span skeleton is 90°. A 4-cm wing rib is provided to maintain the airfoil film’s strength and shape to limit excessive deformation and avoid irregular change in the lift during the up-and-down stroke of flapping. The thickness of the titanium alloy component is 250 μm, and its width is 2 mm. However, the single-wing shown in Figure 2.8 has a half-span of 9.5 cm, a center chord of 8.5 cm, and an area of 108.8 cm2. The left and right-wing frames share the same membrane surface. The wing root and the rib are connected to increase the central effective wing area, and correspondingly lift increases.

2.4.1 Fabrication of Flapping Wing The fabrication of the two wings, as mentioned earlier, using the MEMS process is depicted in Figure 2.9. The step-by-step procedure for fabricating flapping wings using the MEMS process is given below: Step (a): Clean the titanium-alloy plate’s surface with acetone, isopropanol alcohol (IPA), and DI water. Blow-dry it with nitrogen gas. Step (b): AZ4620 photoresist is spin-coated on the front and backside of the titanium-alloy plate. The thickness is not more than ten μm and softbake it. Step (c): After the front side is UV-exposed and then developed by AZ400K, hard-bake it. Step (d): Etching the titanium-alloy plate with five wt% hydrofluoric (HF) acid for 60 min to obtain the titanium-alloy skeletons shown in Figure 2.10(a). Step (e): Remove the photoresist on the skeleton using acetone. Step (f): Adhere the titanium skeletons on a temporary substrate as the coating base of parylene.

TABLE 2.1 Mechanical Properties of Titanium Grade 4 Density Elastic modulus Tensile strength Yield strength Hardness

4.54 g/cm3 104 GPA 552 MPa 482 MPa HV 240

58

Flapping Wing Vehicles

FIGURE 2.8  Skeletons of twin-wing (A-type) and single-wing (B-type).

Step (g): Deposit the 1st parylene layer on the titanium skeletons with the temporary substrate as electrical insulation. Step (h): Soak the parylene skeleton in an ultrasonic cleaner with IPA to remove the temporary substrate. Finally, deposit the 2nd parylene film, as shown in Figure 2.10(b). The MEMS-based parylene wing has a thickness of 33 μm (thickness adjustable), and two types of FWMAV Initiator with parylene wing are shown in Figure 2.11.

FIGURE 2.9  MEMS process (a) cleaning titanium-alloy plate, (b) double-sided coating of photoresist, (c) UV exposure and developing, (d) titanium alloy etching by HF solution, (e) removing the photoresist, (f) pasting a temporary substrate, (g) depositing the 1st layer of parylene and removing the temporary substrate and (h) depositing the 2nd layer of parylene.

In-Situ Lift Measurement Using PVDF

59

FIGURE 2.10  (a) Titanium-alloy skeletons after HF etching and (b) the parylene coated single-wing.

The Type-A (Microbat-like) twin-wing assembly has a mass of 7.91 g, and Type-B (Initiator) single-wing assembly has 7.52 g. When lithium batteries are integrated into the structure, the weight increases from 13.91 gf to 13.52 gf. The assembly includes a flapping mechanism, DC motor, fuselage carbon rods, and tail. The ­lithium battery-powered DC motor rotates at high speed to provide torque for driving the flapping mechanism and to achieve the flapping motion. The MEMS process for coating the PVDF-parylene on the composite flapping wing is depicted in Figure 2.12. The only difference between the MEMS process shown in Figures 2.12 and 2.9 is that, in step (f), the 1st layer of parylene was coated on the titanium skeleton surface to prevent a short-circuit between the titanium skeleton and the PVDF electrode. The PVDF film is similar to the role of a temporary substrate in Figure 2.9. However, it need not be removed at the end, and the 2nd parylenecan be directly deposited for the final package. The Step (a) to Step (e) given in Figure 2.9 of the MEMS process is similar for the case of PVDF-parylene coating on the composite wing. However, additional procedures are given below: Step (f): To prevent the short-circuit between the titanium-alloy skeleton and PVDF electrode, the 1st parylene layer is coated on the surface of ­titanium-alloy skeletons using SCS PDS-2010 parylene coater, parylene

FIGURE 2.11  The airframe and wing assembly according to the design of Figure 2.8 (a) Type A twin-wing and (b) Type B single-wing.

60

Flapping Wing Vehicles

FIGURE 2.12  MEMS process for PVDF-parylene coating on the composite flapping wing: (a) cleaning titanium-alloy plate, (b) double-sided coating of photoresist, (c) UV exposure and developing (d) titanium alloy etching by HF solution, (e) removing the photoresist, (f) depositing the 1st parylene layer on both sides of skeletons, (g) paste the skeletons on the PVDF film, and (h) depositing the 2nd parylene layer to package the PVDF.

dimer powder is about 15 g to achieve effective insulation. The thickness of the parylene layer is about 11.5 μm. Step (g): Paste the PVDF piezoelectric film about 9 μm thick on the titaniumalloy skeletons and connect the signal wire. Step (h): Adding the 2nd parylene layer about 5-10 μm thick on the surface of PVDF to protect and insulate PVDF. The final PVDF–parlyne coated composite flapping wing (Type A twin-wing) is shown in Figure 2.13(a), which is mounted on a wind tunnel, as shown in Figure 2.13(b).

FIGURE 2.13  PVDF-parylene composite wing: (a) the PVDF-parylene coated composite wing and (b) fabricated wing installed in the wind tunnel.

In-Situ Lift Measurement Using PVDF

61

FIGURE 2.14  Parylene coating machine: (a) American SCS company PDS-2010 and (b) Taiwan Lachi Company LH-300.

2.4.2 Introduction of Parylene Poly-para-xylylene (parylene) is a polymer, and 20 varieties of fluorene are known. However, only N, C, and D are commercially available (http://parylene.com). Parylene coating is a kind of chemical vapor deposition (CVD) realized at room temperature. It is performed using a PDS-2010 parylene coating machine (American SCS Company; https://scscoatings.com/) shown in Figure 2.14(a) or LH-300 model coater shown in Figure 2.14(b) (Taiwan La-Chi Company; http://www.corecn.tw/). The parylene dimer powder is initially heated to 150°C to vaporize and then further heated to 690°C to pyrolyze into monomer gas. Finally, the monomer gas is supplied into a vacuum chamber under room temperature to begin the polymerization, and parylene film coating is made on the solid object. The residual monomer gas continued to be pumped out from the chamber by a vacuum system and collected in the final cold-trap tube. Parylene has excellent properties with respect to the coating wherein the thickness of the deposited film is controlled easily. There will not be any residue after the layer, and it has good dielectric and biocompatible properties. It is almost transparent. In 2001, Caltech’s Micromachining group used parylene as the wing skin material for their FWMAV Microbat.

2.5 PRELIMINARY WIND TUNNEL TEST OF TITANIUM-PARYLENE WING The effect of wind speed on the lift force for Type-A and Type-B wings is studied using wind tunnel experiments. They are mounted at 20° inclined angle with respect to the test-rig of the wind tunnel, and the wind speed is varied from 1 to 7 m/s. Without flapping conditions, the lift force’s increasing trend is observed in Figure 2.15 as the wind speed increases. The experimental results show that Type-B generates more lift than type-A. It is due to the fact that the area of the Type-B is much larger than that of Type-A. In the

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FIGURE 2.15  Effect of wind speed on lift force.

absence of flapping motion, the lift is proportional to the square of the wind speed; i.e., the lift is proportional to the dynamic pressure. Generally, the lift and thrust coefficient is defined as:

CL =

2L (2.14) ρ ⋅ A ⋅U 2



CT =

2T , (2.15) ρ ⋅ A ⋅U 2

where L, T, ρ, U, and A represents lift, (net) thrust, air density, wind speed, and wing area, respectively. Under the flapping condition, the flapping frequency is controlled by the voltage of the driving motor. When the input voltage is varied from 3 to 7V, the flapping frequency varies from 7 to 16 Hz. Also, the wind speed is varied from 1 to 5 m/sec. To measure the aerodynamic performance of these two wings, the advance ratio is used. It is defined as the ratio of freestream wind speed to the local speed of flapping wing tip which is given by the following relation:

J=

U , (2.16) ϕ⋅ f ⋅b

where ϕ, f, b the flapping stroke angle, flapping frequency, and wingspan. Under the dynamic condition, the flapping frequency and wind speed can be adjusted to obtain various advance ratio. When J < 1, it is an unsteady state, and when J approaches infinity (no flapping), it is a steady-state or a constant wing flow field [27,28]. Wind tunnel experiments are conducted on the flapping wings kept at a 20° inclined angle. The average lift and net thrust are measured under different wind

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FIGURE 2.16  The aerodynamic characteristics of the twin-wing (Type A) and single-wing (Type B) in the flapping state: (a) lift force, (b) net thrust force.

speeds, and flapping frequencies and corresponding lift and net thrust coefficients are calculated in Figure 2.16. It can be seen from Figure 2.16 that, as J approaches 0 (denoting an obvious flapping situation), CL gradually increases. With an increase in J > 4 (the flapping case is not obvious), CL approaches a convergent value of 0.13, which is almost equal to the lift experienced without flapping, as observed in Figure 2.15. It is also evident from Figure 2.16 that, Type-A wing is better than the Type-B wing with respect to both lift and net thrust coefficients. Especially when J is less than 1, a lift of Type-A wing is always slightly larger than that of Type-B wing. The Type-A twin-wing has a stronger structure of leading-edge spar, wing root, and wing rib than the Type-B single wing. It is also observed in Figure 2.16 that the force data are slightly scattered near J = 1, which may be due to fluctuation in measurements due to the prolonged time of performing the experiments. At this condition, the flapping mechanism structure

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may have an aging problem to deviate many parts from their original assembly position, which will affect the aerodynamic performance accordingly.

2.6 PVDF SENSOR IN MEASURING THE LIFT FORCE OF FLAPPING WINGS In this section, the use of piezoelectric PVDF sensors to study a flapping wing’s aerodynamic characteristics is explained [29–33]. The left and the right wings of FWMAV are made of the composition of parylene and PVDF. During the wind tunnel testing, the onboard PVDF sensors mounted on both the wings got an individual lift and also simultaneously. The lift force is measured using the force gauge. The difference in the lift force measured by PVDF and force gauge is calculated and used to modulate the aerodynamic phase lag between the right and left wings during flapping. The PVDF piezoelectric film has a size of 120 mm × 120 mm (Figure 2.17) with a thickness of 9 μm. Both the sides are sputtered with chrome-aluminum as a conductive layer. It is then carved into the required shape and size, and two wires are silver-glued to get the output signal. The FWMAV considered for evaluating the PVDF sensor’s performance has the transmission mechanism unit, which is mainly composed of a reduction gear set and dual four-bar linkage (FBL), which is driven by a DC motor of 7 mm-diameter. The transmission unit shown in Figure 2.18 has a driving rod OA and driven rod BC connected to the leading edge spar and wing skeleton. The motor, gear reduction unit, and connecting rod set are firmly fixed on an

FIGURE 2.17  PVDF piezoelectric film.

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FIGURE 2.18  Flapping mechanism.

aluminum base. The gear reduction ratio of 26.7 can generate a flapping frequency of 17 Hz for the given input maximum voltage of 3.7 V. When OA continues to rotate, the BC imparts up and down motion to the wings. Even though these two wings are designed with the same flapping stroke angle, due to the dimensional constraint of dual FBL, there is a phase difference between the left and right wings, as shown in Figure 2.19. By adjusting the lengths of OA, AB, and BC, different flapping stroke angles and corresponding phase lag can be measured. The following dimensions are considered for the simulation studies to examine the phase lag: OA = 4 mm, AB = 21.5 mm, and BC is varied from 8 to 12 mm, and corresponding flapping stroke angle and phase lags are

FIGURE 2.19  Flapping stroke history of the left and right wings.

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measured. It is evident from Table 4.2 that an increase in the length of link BC reduces the phase lag. However, the phase lag is inevitable, leading to a reduction in the transmission module’s life due to the uneven cyclic loading acting on the linkages. To understand the aerodynamic characteristics of such FWMAV, wind tunnel experiments are conducted. The flapping wing model is firmly fixed on the force gauge to obtain the aerodynamic signal directly, and the PVDF piezoelectric film is provided an output signal in real-time. In this study, a 4 V DC power supply is given to achieve the flapping motion, and FWMAV is kept at an inclined angle of 45°. Wind tunnel test results show (Figure 2.20) that the flapping wing’s aerodynamic signals (BC = 11 mm) can be successfully captured in real-time using PVDF and force gauge. Even though the waveforms are apparently similar, a phase difference is observed. It is due to the lift signal of the left-wing measured using PVDF does not include the right-wing lift contribution. However, the force gauge includes the global lift signal of both the wings. With different lengths of the rod BC, the left and right wings generated different mechanical phase lag due to the inherent shortcomings of the FBL. Accordingly, the lift signals from the PVDF sensor and the force gauge have different aerodynamic phase lag degrees.

FIGURE 2.20  Lift signal of FWMAV: (a) PVDF signal, (b) force gauge signal.

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FIGURE 2.21  Comparison of “pseudo” PVDF lift signal (pink curve) and force gauge signal (blue curve).

In order to get the left-wing lift component alone from the twin-wing force gauge signal, a signal processing technique is adopted. Initially, the waveform shown in Figure 2.20(a) is superimposed on another identical waveform with a phase lag of 11° and a “pseudo” waveform curve shown as a thin pink line in Figure 2.21 is produced. However, the “pseudo” PVDF signal and the global twin-wing lift waveform from the force gauge are of a similar trend. In order to determine the phase lag between these two signals, a statistical method is employed. The phase lag varies from 0° to 27°, and the wave signal’s superimposition is carried out. The corresponding standard deviation is calculated and shown in Figure 2.22. It is observed that, at the phase lag of 11°, the minimum standard deviation is observed, and hence it is considered as the phase lag between these two signals. To understand the effect of phase lag on PVDF-based lift signal, the length of BC is varied as given in Table 2.2, and the phase lag is measured using a high-speed

FIGURE 2.22  Identification of phase lag.

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TABLE 2.2 Phase Lag of Flapping Mechanism Length of Link BC (mm) 8 9 10 11 12

Flapping stroke angle 60.5° 53.0° 47.2° 42.7° 39.0°

Phase lag (max) 13.3° 9.4° 6.4° 4.1° 2.5°

camera. It is observed that the phase lag varied from 2.5° to 13.3°. A similar procedure for processing the PVDF lift signal is carried out, and the phase lag of aerodynamic lift as shown in Figure 2.23 can be obtained. It is found that the mechanical phase lag of the flapping wing is not avoidable. It must be properly controlled within 4.1° to ensure that the lift phase lag between the twin wings is within the range of 11°. However, an increase in the mechanical phase lag beyond 9.4°causes an increase of lift phase lag in a rapid manner to 58° that affects the flapping flight stability.

2.7  FLIGHT TEST The FWMAV assembly shown in Figure 2.11 can be tested for its performance in an indoor environment. The list of components of the FWMAV Initiator is given in Table 2.3. During the test flight, the Type-A twin-wing model flew only about 4 m, and it did not have enough stability to soar the indoor. It is due to the minimal strength of central fuselage, which deteriorates due to leading-edge vortex (LEV) as well as the flapping lift generation. It was unable to overcome the total weight of

FIGURE 2.23  Measurement of lift phase lag from the PVDF signal.

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TABLE 2.3 Weight of Each Component of the FWMAV Initiator Component Wing weight Motor (including wire) The base for flapping mechanism Gears Acrylic (PMMA) rods Ti alloy connecting rods Batteries Fuselage and tail Total weight

Weight (g) 1.62 (Twin-wing)

1.22 (Single-wing) 2.75 0.80 0.75 0.25 0.15 5.60 1.60

13.51

13.12

FWMAV. As far as the Type-B single-wing is concerned, it was also without the apparent central body. However, the single-wing did not deteriorate due to the continuous LEV and flapping lift. The wing area of Type B is larger than Type A was also an added advantage. The test flight for the Type-B single-wing Initiator was conducted, and it flew horizontally up to a distance of 10–15 m. Hence, it is evident that the single-wing geometry and larger wing area are beneficial to FWMAV flight’s stability. Figure 2.24 shows the flight test of Type-B single-wing FWMAV Initiator. The flight test of the Initiator revealed two issues that affect flight performance. Firstly, the lithium battery required to drive the flapping frequency up to 16 Hz weighed 5.6 gf, too heavy. Secondly, the 2 gf flapping mechanism (including base, gear, rods in Table 3.3) runs at high speed, the FWMAV vibrates severely, and it changes the flying attitude or may even crash. Since both of these issues are related to reducing the weight of FWMAV, lightweight materials have to be chosen, and all the parts need to be re-designed. The titanium alloy-parylene wing has a wingspan of 28 cm and a chord of 8 cm, as shown in Figure 2.11. The 45° rib of titanium-alloy is replaced by a light-weight Balsa wood that reduces the weight of Initiator from 13 gf to 11 gf, which necessitated a single lithium battery of 2.8 gf instead of two batteries. Also, a lighter remote-control receiver chip (0.9 g) and an electromagnetic tail actuator (1.1 g) shown in Figure 2.25 can be used for the flight control. The remote-control receiver has two channels. One channel controls the speed of the BLDC motor and varies the pitch angle. The other channel adjusts the swing direction of the tail so that the FWMAV can make turns. The selected parts, including the remote control receiver, the tail actuator, and lithium battery, are integrated into an assembly of modified FWMAV shown in Figure 2.26 and named as Eagle-II. It weighs about 10.67 gf. The flight test is conducted in the outdoor, as shown in Figure 2.27. The designed flapping-wing structure followed the desired flight trajectory with an endurance of 10 mins, and the flight distance improved to 40 m.

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FIGURE 2.24  Test flight of the Type-B single-wing FWMAV initiator: (a) horizontal throw (b) after flying 5 m.

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FIGURE 2.25  The electromagnetic actuator is controlling the direction of the tail.

FIGURE 2.26  Eagle-II – Modified version of Type-b single-wing FWMAV.

2.8 SUMMARY This chapter introduced the various developments of FWMAVs and lift force measurements using wind tunnel experiments [34–40]. The obtained time-averaged lift data was not having much influence on the inertial force of periodic flapping motion. Besides, traditional wind tunnel measurements may not provide accurate aerodynamic force data. Hence, a PVDF-based in-situ measurement was considered. PVDF-parylene composite wings were fabricated using MEMS technology [32,41]. The experimentation was performed by varying the flapping stroke angles, and phase lag was measured. As far as the unsteady flapping is concerned, the lift

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FIGURE 2.27  Outdoor flight test of the Eagle-II and its trajectory.

coefficient of the twin-wing configuration is higher than that of the single-wing configuration related to its high flapping stiffness. However, in actual flight, the singlewing design is relatively stable and easy to test because the fuselage is fixed at the wing centerline. During the wind tunnel experiments, the PVDF sensor and force gauge waveforms were simultaneously captured and compared [42]. Since the flapping mechanism is not symmetrical, the lift from the twin wings attained a phase lag phenomenon. A pseudo waveform of PVDF signal is produced through identical waveform superimposition with a phase lag of 11°. To understand the effect of phase lag on PVDF-based lift signal, the linkage length of BC was varied, and the phase lag was measured using a high-speed camera. The inference made from the amplification of phase lag contributes to the futuristic aspects of developing the flapping wing mechanism in the next chapter. The Initiator flight tests suggested few modifications on the FWMAV components to reduce the weight of the structure. The consequence was reduced from 13 gf to 11 gf, horizontal flight travel was increased from 15 m to 40 m, and 10 s flight endurance was achieved.

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There are still a few applications wherein in-situ lift measurement is paramount of interest: • Academic research field: Different motions of FWMAVs can be monitored in real-time. The flapping wing motions include forward flight, hovering, soaring, formation flight, and so on. The time history of the lift force is beneficial to understand the unsteady lift generation of flapping wings. • Production field: Development of new actuators for FWMAV flight control is exemplified through bio-mimicking the energy-saving and long-duration soaring of crested serpent eagles using the surrounding lifting-up airflow. The in-situ lift measurement will be useful to fine-tune the feather position of the wingtip.

REFERENCES

1. Shyy, W., Berg, M. and Ljungqvist, D. (1999) Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, 35(5), 455–505. 2. Norberg, U. M. (2012) Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution (Vol. 27), Springer Science and Business Media. 3. DeLaurier, J. D. (1994) An ornithopter wing design. Canadian Aeronautics and Space Journal, 40(1), 10–18. 4. Sane, S. P. (2003) The aerodynamics of insect flight. The Journal of Experimental Biology, 206, 4191–4208. 5. Sun, Y., Fry, S. N., Potasek, D. P., Bell, D. J. and Nelson, B. J. (2005) Characterizing fruit fly flight behavior using a microforce sensor with a new comb-drive configuration. Journal of Microelectromechanical Systems, 14(1), 4–11. 6. Pornsinsirirak, T. N. (2003) Parylene MEMS Technology for Adaptive Flow Control of Flapping Flight. Ph.D. Dissertation, EE, California Institute of Technology. 7. Sitti, M. (2001, May) PZT actuated four-bar mechanism with two flexible links for micromechanical flying insect thorax. Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No. 01CH37164) (Vol. 4, pp. 3893–3900). 8. Sitti, M. (2003) Piezoelectrically actuated four-bar mechanism with two flexible links for micromechanical flying insect thorax. IEEE/ASME Transactions on Mechatronics, 8(1), 26–36. 9. Howse, J. R., Topham, P., Crook, C. J., Gleeson, A. J., Bras, W., Jones, R. A. and Ryan, A. J. (2006) Reciprocating power generation in a chemically driven synthetic muscle. Nano Letters, 6(1), 73–77. 10. Narásek, M., Muijres, F. T., De Wagter, C., Remes, B. D. W. and de Croon, G. C. H. E. (2018) A tailless aerial robotic flapper reveals that flies use torque coupling in rapid baked turns. Science, 361, 1089–1094. 11. Phan, H. V. and Park, H. C. (2020) Mechanisms of collision recovery in flying beetles and flapping-wing robots. Science, 370, 1214–1219. 12. Mueller, T. J. (2000) Aerodynamic Measurements at Low Reynolds Numbers for Fixed Wing Micro-Air Vehicles, Notre Dame University, Dept. of Aerospace and Mechanical Engineering. 13. Barlow, J. B., Rae, W. H. and Pope, A. (1999) Low-Speed Wind Tunnel Testing, John Wiley and Sons. 14. Yang, L. J., Hsu, C. K., Han, H. C. and Miao, J. M. (2009) Light flapping micro aerial vehicle using electrical-discharge wire-cutting technique. Journal of Aircraft, 46(6), 1866–1874.

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15. Sunada, S. and Ellington, C. P. (2000) Approximate added-mass method for estimating induced power for flapping flight. AIAA Journal, 38(8), 1313–1321. 16. Shyy, W., Aono, H., Kang, C. K. and Liu, H. (2013) An Introduction to Flapping Wing Aerodynamics (Vol. 37), Cambridge University Press. 17. Sun, M. and Tang, J. (2002) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. The Journal of Experimental Biology, 205(1), 55–70. 18. Dickinson, M. H., Lehmann, F. O. and Sane, S. P. (1999) Wing rotation and the aerodynamic basis of insect flight. Science, 284(5422), 1954–1960. 19. Birch, J. M. and Dickinson, M. H. (2003) The influence of wing–wake interactions on the production of aerodynamic forces in flapping flight. The Journal of Experimental Biology, 206, 2257–2272. 20. Wang, Z. J., Birch, J. M. and Dickinson, M. H. (2004) Unsteady forces and flows in low Reynolds number hovering flight: Two-dimensional computations vs robotic wing experiments. The Journal of Experimental Biology, 207, 449–460. 21. Lua, K. B., Lim, T. T. and Yeo, K. S. (2011) Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing. Experiments in Fluids, 51(1), 177–195. 22. Pornsinsirirak, N., Liger, M., Tai, Y. C., Ho, S. and Ho, C. M. (2002, January) Flexible parylene-valved skin for adaptive flow control. Technical Digest of 15th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2002) (Cat. No. 02CH37266), 101–104. 23. Pornsinsirirak, T. N., Tai, Y. C., Nassef, H. and Ho, C. M. (2001) Titanium-alloy MEMS wing technology for a micro aerial vehicle application. Sensors and Actuators A: Physical, 89(1-2), 95–103. 24. Jiang, F., Lee, G. B., Tai, Y. C. and Ho, C. M. (2000) A flexible micromachine-based shear-stress sensor array and its application to separation-point detection. Sensors and Actuators A: Physical, 79(3), 194–203. 25. Lee, C. K. (1992) Piezoelectric laminates: Theory and experiments for distributed sensors and actuators Intelligent Structural Systems, ed. by Tzou, H. S. and Anderson, G. L., 75–167. 26. Liu, C. (2006) Foundations of MEMS, Pearson/Prentice Hall, 1st ed., 256. 27. Wu, J. H. and Sun, M. (2004) Unsteady aerodynamic forces of a flapping wing. The Journal of Experimental Biology, 207(7), 1137–1150. 28. Lugt, H. J. (1983) Vortex Flow in Nature and Technology, John Wiley and Sons. Inc., 52. 29. Seminara, L., Capurro, M., Cirillo, P., Cannata, G. and Valle, M. (2011) Electromechanical characterization of piezoelectric PVDF polymer films for tactile sensors in robotics applications. Sensors and Actuators A: Physical, 169(1), 49–58. 30. Wang, Y. R., Zheng, J. M., Ren, G. Y., Zhang, P. H. and Xu, C. (2011) A flexible piezoelectric force sensor based on PVDF fabrics. Smart Materials and Structures, 20(4), 045009. 31. Mizuno, Y., Liger, M. and Tai, Y. C. (2004, January) Nanofluidic flowmeter using carbon sensing element. Technical Digest of the 17th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2004), Maastricht (pp. 322–325). 32. Yang, L. J., Hsu, C. K., Ho, J. Y. and Feng, C. K. (2007) Flapping wings with PVDF sensors to modify the aerodynamic forces of a micro aerial vehicle. Sensors and Actuators A: Physical, 139(1-2), 95–103. 33. Shirinov, A. V. and Schomburg, W. K. (2008) Pressure sensor from a PVDF film. Sensors and Actuators A: Physical, 142(1), 48–55. 34. Yang, L. J., Esakki, B., Chandrasekhar, U., Hung, K. C. and Cheng, C. M. (2015) Practical flapping mechanisms for 20 cm-span micro air vehicles. International Journal of Micro Air Vehicles, 7(2), 181–202. 35. Yang, L. J. (2012) The micro-air-vehicle Golden–Snitch and its figure-of-8 flapping. Journal of Applied Science and Engineering, 15(3), 197–212.

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36. Hsiao, F. Y., Yang, L. J., Lin, S. H., Chen, C. L. and Shen, J. F. (2012) Autopilots for ultra light weight robotic birds: Automatic altitude control and system integration of a sub-10 g weight flapping-wing micro air vehicle. IEEE Control Systems Magazine, 32(5), 35–48. 37. Yang, L. J., Kao, A. F. and Hsu, C. K. (2012) Wing stiffness on light flapping micro aerial vehicles. Journal of Aircraft, 49(2), 423–431. 38. Yang, L. J., Hsiao, F. Y., Tang, W. T. and Huang, I. C. (2013) 3D flapping trajectory of a micro-air-vehicle and its application to unsteady flow simulation. International Journal of Advanced Robotic Systems, 10(6), 264. 39. Yang, L. J., Feng, A. L., Lee, H. C., Esakki, B. and He, W. (2018) The three-­dimensional flow simulation of a flapping wing. Journal of Marine Science and Technology, 26(3), 297–308. 40. Yang, L. J., Kao, C. Y. and Huang, C. K. (2012) Development of flapping ornithopters by precision injection molding. Applied Mechanics and Materials, 163, 125–132. 41. Hsu, C. K., Ho, J. Y., Feng, G. H., Shih, H. M. and Yang, L. J. (2006) A flapping MAV (Micro Aerial Vehicle) with PVDF-parylene composite skin. Proceedings of AsiaPacific Conference of Transducers and Micro-Nano Technology (APCOT 2006). 42. Yang, L. J. (2009) Flapping wings with micro sensors and flexible framework to modify the aerodynamic forces of a micro aerial vehicle (MAV). Aerial Vehicles, edited by Lam, T. M., INTECH Open Access Publisher, 691–718.

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3.1  GOLDEN-SNITCH ORNITHOPTER The first model of FWMAV, named Eagle-II has a total mass of 11 g and a wingspan of 30 cm. It could have a total flight time of 11 s, and a make a flight distance of 40 m. However, its wingspan exceeded the requirement set by Defense Advanced Research Projects Agency (DARPA). In view of this, an improved mechanism is designed by modifying the flapping mechanism of Eagle-II. The modified FMMAV assembly was named Golden-Snitch [1]. Norberg’s scaling law has been followed to reduce the wingspan from 30 cm to 20 cm [2,3]. Figure 3.1(a) shows the four-bar linkage (FBL) mechanism driven by gears designed for the Golden-Snitch MAV. The base frame in the mechanism acts as the holder for the transmission gears and a base for the mechanism. An exploded view of the entire setup is shown in Figure 3.1(b) to provide the details [4]. Didel brushless DC motor with 6 mm outer diameter (http://www.didel.com) is rigidly fixed to the base frame. The pinion is attached to the shaft of the motor and drives the gear train set. A reduction ratio of 26.6 provides sufficient torque to flap the wings. A Lithium – Polymer battery of 50 mAh is used as the power source. Initially, the base of Eagle-II was made of polyoxymethylene (POM), and the connecting rod weighing 3.756 gf was made of bamboo. Due to the modification of the mechanism, the mechanism assembly’s weight is reduced to 1.2 gf. Figure 3.2 shows the flying sequence of the Golden-Snitch flapping mechanism during the upstroke and downstroke motion.

3.1.1 Design of the Transmission Module Major geometric parameters of the FBL mechanism are shown in Figure 3.3(a). The crank length (a), connecting rod length (b), rocker length (c), width (w), and height (h) of the FBL mechanism are varied, and their effects on stroke angle or flapping angle as well as the phase lag are brought out. In Eagle-II, the width is 24 mm, whereas, in the Golden-Snitch, it is reduced to 20 mm, which is shown in Figure 3.3(b). A fork shape is introduced to mount a carbon fiber rod at the rocker linkage for attaching the wings. Also, link c is specially designed to have a dihedral angle of 20° to make a stable flight [5–13]. Kinematic simulation studies are performed by varying the FBL mechanism’s geometric parameters, and their effects on the Golden-Snitch flight performance are found [14–16]. A larger value of a, i.e., the longer crank makes a wider stroke angle increasing the phase lag between both the left and right wings and reducing the output torque. The length of the connecting rods and b affects the symmetry of flapping wings and the mechanism’s vibration during operation. The transmission DOI: 10.1201/9780429280436-3

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FIGURE 3.1  FBL gear mechanism: (a) assembly (b) exploded view.

angle between the connecting rod and the rocker is (90°±ψ), where ψ is called an asymmetry angle that needs special attention for stability. Experience shows that ψ must be maintained within 30° for smoother operation of the mechanism. The length of rocker, c must be equal to or less than 0.5 w to avoid collision between linkages. For a typical simulation, the geometric parameters are assigned the values as follows: a = 3 mm, b = 20 mm, c = 9 mm and w = 20 mm. From the simulation, the relationship between the stroke angle w.r.to the driving link angular position is shown in Figure 3.4. It can be seen that the maximum value of the flapping angle is 38.9° with a phase lag of 2°. The asymmetry angle (ψ) changed as per the crank position, as shown in Figure 3.5. The transmission angle is about 23°, which is lesser than the maximum permissible limit of 30°. Table 3.1 provides the results obtained from the simulation by varying the geometric parameters. Table 3.1 shows that a group I category of linkages and their dimensions are realizable for an FBL mechanism. It can be seen that the flapping angle increased from 38.9° to 56.3° by varying the geometric parameters. On the other hand, it can be seen that group II has more failures, as the mechanism is unable to provide full crank rotation. It is observed when the flapping stroke angle approaches 90°, the phase lag is greater than 5.2°, and the asymmetry angle exceeds 40° [17,18]. Furthermore, when ϕ = 70.6°, the Ornithopter flies with a trembling motion, which upsurges the power requirement leading to higher energy dissipation. However, the flapping angle is still less than the stroke angle of common birds and hummingbirds, which are 120° and 180°, respectively.

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FIGURE 3.2  Upstroke and downstroke flapping motion of the Golden-Snitch mechanism.

3.1.2 Aerodynamic Performance of the Golden-Snitch The aerodynamic performance of the Golden-Snitch has been evaluated by conducting an actual flight test. This test has to be carried out after several laboratory experiments, including the wind tunnel and the outdoor environment. During the experiments, the supply voltage has been varied from 0 to 3.7 V to change the speed of the DC motor to get different flapping frequencies. The free stream wind velocity has been measured using a hot-wire anemometer and varied from 0.4 to 3.0 m/s. The lift and net thrust have been measured using load cells of 200 gf and 100 gf capacity attached to the MAV body from the wind tunnel experiments. The load cell error due to hysteresis has been considered to be 0.2% of full-scale measurement [19–21]. The Golden-Snitch is an unsteady aerodynamic system. An advance ratio is used to analyze the system. In general, non-flapping wings or fixed-wing aircraft require a bigger advance ratio. For the case of unsteady flapping flight, the advance ratio is less than or equal to 1. However, two significant dimensionless parameters, lift

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FIGURE 3.3  FBL mechanism (a) geometric parameters (b) fabricated mechanism.

FIGURE 3.4  Relationship between the stroke angle and position of the driving link.

FIGURE 3.5  Crank length vs. transmission angle.

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TABLE 3.1 Linkage Dimensions and Kinematic Parameters

Group I

II

b, 2nd bar (mm) 21 21 21 21 21

a, 1st bar (mm) 3 3.3 3.65 3 3.3

c, 3rd bar (mm) 9 9 9 7 7

Holder width w (mm) 20 20 20 16 16

Flapping angle ϕ (deg) 38.9 43 47.9 50.8 56.3

Phase lag (deg) 2 2.2 2.6 2.7 3.2

Asymmetry angle, ψ (deg) 21.2 23.4 26.5 25.4 28.7

20.3 20.3 20.3 20.3 20

2.4 4 5.2 6.3 4.9

9 9 9 9 7

20 20 20 20 16

30.9 52.8 70.6 89.4 89.2

1.6 3.2 5.2 7.9 6.8

14.9 28.4 40.5, fluttering 54.6, get stuck 52.1, get stuck

coefficient, and net thrust coefficient, are generally used for analyzing the aerodynamic performance of flapping wing vehicles. The lift coefficient shows the relationship between the flight’s geometric form, orientation, and flow conditions [22]. Using wind tunnel experiments, the lift and net thrust coefficients have been determined, and the results are shown in Figure 3.6. About 12,000 data points have been collected from the 6 degree-of-freedom load cell whose data breeding rate is 1,000 points per second. Besides, the time-averaged values of the lift coefficient and the net thrust coefficient are determined. They are useful in influencing the hovering and flapping of the flight. Based on the time-average lift coefficient, one can determine whether the generated lift force is sufficient to support MAV’s weight. It can be seen from Figure 3.6(a) that when the lift coefficient is larger than 3.0, and the advance ratio is

FIGURE 3.6  Wind-tunnel data of the Golden-Snitch (b = 21.6 cm; ω = 10.5-23.6 Hz) (a) lift coefficient CL, (b) net thrust coefficient CT.

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less than 0.4, the lift force is sufficient enough to counterweight the total load of the vehicle. It is also observed from Figure 3.6(b) that, for an advance ratio of less than 0.4, the net thrust coefficient is always greater than zero. This signifies the continuous forward pushing force without decreasing the speed of flight. The lift of the Golden-Snitch has been measured prior to tail installation during 20° inclined angle. From the observation, at the standard atmospheric pressure and wind speed of 3 m/s, the maximum lift is 6.415 gf. It is larger than the weight of the vehicle, which is 5.9 gf. Therefore, it is evident that, for CL value greater than 0.92, sufficient lift is generated to overcome the MAV’s weight. The same can be observed from Figure 3.7 [23,24].

FIGURE 3.7  (a) Lift coefficient; (b) net thrust coefficient for various free stream velocities (b = 21.6 cm; φ = 38.9°; ω = 10.5–23.6 Hz).

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3.1.3 Flight Test Flight tests are conducted in the indoor environment to study the effects of fuselage orientation and to record flight patterns. Figure 3.8(a) shows a tail touch-down flying pattern where the ornithopter violently flaps and gradually descends to the ground even when it is fully powered. It is due to a high inclined angle, which causes the tail to touch the ground. Also, a small stabilizer at the tail region may contribute to the maintenance of the inclined angle. The nose touch-down flying pattern that has been observed is shown in Figure 3.8(b). The MAV plunges head-on and hits the ground quickly. This flying pattern might be due to the shift of C. G. toward the front part of the MAV or inadequate pitch moment that could cause the MAV to behave in such a manner. Figure 3.8(c) shows the stall-and-dive flying pattern, which explains that the MAV stalls and dives continuously until it touches the ground, nose-first. A large pitching moment is responsible for this kind of shaky flight. The spiral turn flight pattern is shown in Figure 3.8(d) is the most frequently seen flight pattern that indicates a flight that takes place for a few meters until it suddenly changes the flight path and dives to hit the ground. Such a flight pattern could result from apparent tensions between the two wings. This inference can be supported by the fact that wrinkles are found on either side of the wings’ membrane. The wrinkles stem from the tensile loads on the wings. Moreover, during the spiral-turn flapping mode, the membrane’s loosening is caused due to the large housing joint of the linkage c (rocker). Being light in weight and flexible, the new configuration of the Golden-Snitch MAV shown in Figure 3.9 provides superior flight efficiency than that of the semirigid Eagle-II MAV. It can attain an endurance (flight duration) of 6 min 7 s during the flight test, which is comparatively much higher than that of the Eagle-II flight time of 11 s. The Golden-Snitch MAV flight test carried out in the outdoor environment is shown in the snapshots in Figure 3.9. It is anticipated that in the absence of gust wind, Golden-Snitch could fly in an imaginary virtual cylindrical barrel surface of several meters diameter. In such a case, the vehicle can be stabilized by the negative lift generated by the tail.

FIGURE 3.8  Flight patterns: (a) tail touch-down, (b) nose touch-down, (c) stall-and-dive, (d) spiral-turn.

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FIGURE 3.9  Snapshots of an outdoor flight test of the Golden-Snitch MAV (http:// tw.Youtube.com/watch?v=YkEoxyWGl_k).

Since the maximum flight speed of the Golden-Snitch MAV is 3 m/s, it is vulnerable to wind speed variation in the outdoor environment. As a result, wind gust factors make the vehicle’s performance in the outdoor environment unpredictable. However, in the indoor environment, the response variables of the Golden-Snitch vehicle are more reliable. The control strategies of the Golden-Snitch model are vital to manipulate the device that is not fully comprehended yet. For instance, the speed of MAV is dependent on an inclined angle. i.e., small inclined angle results in high forward speed while large inclined angle leads to low forward speed. During the feasibility study of hovering the Golden-Snitch, the lift force generated corresponding to various inclined angles at zero forward speed has been measured (; no data shown here.) The result depicts that the lift of 5.1 gf obtained at an inclined angle of 80° can be considered an optimum solution. However, it is lower than the Golden-Snitch weight and confirms that the lift generated at zero forward speed is insufficient to support the flyer’s weight. Therefore, from the investigation, it is concluded that the Golden-Snitch with a single pair of wings is not capable of hovering at zero forward flight speed.

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FIGURE 3.10  Scale law of flapping flying creatures including Tamkang’s Golden-Snitch and Eagle-II [26].

Comparison between Eagle-II and Golden-Snitch with respect to their weight and flapping frequency using the scaling law was discussed in Chapter 1 (Figure 3.10). Eagle-II has a wingspan of 30 cm, weighs about 11 gf, and has a maximum flapping frequency of 16 Hz. However, Golden-Snitch has a wingspan of 20 cm, weighs about 5.9 gf, and a maximum flapping frequency of 20 Hz. In Figure 3.10, Golden-Snitch is located slightly to the left of Eagle-II. Also, it is smaller than the traditional MAV and close to the range of hummingbirds [25].

3.2 IMPACT OF FLAPPING STROKE ANGLE ON FLAPPING AERODYNAMICS The body of the Golden-Snitch is built using expandable polystyrene (EPS), and it has a horizontal tail area of 5.55 mm2. The flapping wing has a wingspan of 20 cm and wing area of 11.40 mm2. The wings are made of polyethylene terephthalate (PET) film material. The inclined angles defined in Figure 3.11 change during 0° to 40°. The magnitude of the flapping stroke angle by Figure 3.12 is controlled by

FIGURE 3.11  Inclined angle.

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FIGURE 3.12  Flapping stroke angle.

adjusting the linkage lengths of the FBL mechanism. The connecting rod is made up of aluminum alloy. 4 various mechanism designs with different flapping stroke angles 30.9°–70.6° by changing the 1st bar length 2.4–5.2 cm of the FBL mechanism are shown in Figure 3.13. Wind tunnel experiments were performed by varying the parameters as given in Table 3.1A. The flapping lift and the net thrust forces can be changed due to the wind speed, driving voltage, inclined angle and the different stroke angles depended on different designs of connecting rod length shown in Figure 3.13. Basically, 1. With the inclined angles of 10°–40°, the lift of the 4 stroke angles (30.9°–70.6°) increases with the flapping frequency. 2. When the inclined angle is 0°, because the instantaneous angle of attack changes sign during the flapping and the wing has a positive dihedral angle, the instantaneous lift is not always vertically upward. Therefore, the lift may reversely decrease as increasing the flapping frequency. 3. When the inclined angle is larger than 10°, the lift restores to the positive increasing trend with the flapping frequency; the net thrust force also has this behavior. 4. Regarding the best driving voltage, there is no doubt the maximum 3.7 V for generating the largest lift. However, the largest net thrust force happens at 2.9 V only. According to the developing experience of the former MAVs, the smallest driving voltage for keeping MAVs for possible flight is 2.9 V. The overall wind tunnel data are massive and not exactly shown herein except the driving voltage case of 2.9 V. The relationship between lift and wing stroke angle at different inclined angles and flight speeds is depicted in Figure 3.14. The general trend found from the graphs is that the lift initially increases with an increase in stroke angle. It can be found that at medium stroke angles the higher amount of lift is generated. When the inclined angle is at 0°, the lift experienced is about ± 0.8 gf, as shown in Figure 3.14(a). More

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FIGURE 3.13  Positions of mechanism under various flapping stroke angles (a) 30.9°, (b) 39°, (c) 52.8°, and (d) 70.6°.

lift at the inclined angle of 10° is produced for the flapping angles of 30.9° and 52.8°, as shown in Figure 3.14(b). However, the higher lift occurs when the flapping stroke angle is 39° firstly and 52.8° secondly as observed from Figure 3.14(c)–(f) with the inclined angle of 20°~50°. This may be due to the higher quantity of air being pushed by wings, and more amount of airflow happens where the flapping wings push the TABLE 3.1A Parameters Performed in the Wind Tunnel Experiments for Golden-Snitch Parameter Wind speed Driving voltage Inclined angle Flapping stroke angles Connecting rod length

Values 0 to 3 m/s in steps of 1 m/s 1.3 V, 2.1 V, 2.9 V, and 3.7 V 0° to 50° in steps of 10o 30.9°, 39°, 52.8°, and 70.6° 2.4, 3, 4, and 5.2 cm

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FIGURE 3.14  Lift vs. Stroke angle for different wind speeds (0–3 m/s) under 2.9 v at different inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°, (f) 50°.

air, and more lift is produced. For larger flapping stroke angles, air swiftly passes, reducing the generation of lift. The relationships between the net thrust forces and the stroke angles for different inclined angles and flight speeds are shown in Figure 3.15. When the inclined angles are at 20°, 40°, and 50° (Figure 3.15(c), (e), (f)) and at various flight speeds, the net thrusts are monotonously larger as increasing flapping stroke angles. (Higher stroke angle is beneficial to the net thrust generation.) However, at higher stroke angles of 30°–50° (Figure 3.15(d)–(f)) and during the speed of 2–3 m/s, the net thrust forces are negative and imply the more drag occurs at a higher inclination angle [26].

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FIGURE 3.15  Net thrust vs. Stroke angle for different wind speeds (0–3 m/s) under 2.9 V at different inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°, (f) 50°.

• Summary about the stroke angle effect on the Golden-Snitch using FBL mechanism (under the same driving voltage of 2.9 V): 1. At the inclined angle of 0°, bigger stroke angle gives smaller lift. The case of 0° is not an ideal flapping condition. 2. When the inclined angle is larger than 10°, the more apparent stroke angle is beneficial to the flapping lift generally. The medium stroke angles of 39° and 52.8° generate better lift values. (70.6° is the worst case.) At the meanwhile, the larger stroke angle is more apparent to the positive generation of net thrust.

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3. From Figures 3.14 and 3.15, Golden-Snitch has better lift at the stroke angle of 39° and 52.8°, and generate the larger net thrust at the stroke angle of 52.8° and 70.6°. The compromise selection about the best stroke angle goes to 52.8° with the additional consideration of the phase lag and the asymmetry angle shown in Table 3.1.

3.3  AERODYNAMIC CHARACTERISTICS OF GOLDEN-SNITCH PRO The first generation FWMAV utilized MEMS technology to make the titanium alloy wing frame and parylene film wing. It combined the non-MEMS process to manufacture the transmission mechanism. The fuselage skeleton and tail wing appeared to be a wing-type MAV with a weight of 22 gf and a wingspan of 30 cm. Figure 3.16 shows the Initiator of the first generation FWMAV. Due to the heavyweight of the mechanism used in the 1st generation FWMAV, the test flight could attain a reach of only 10 m. The 2nd generation FWMAV, Eagle-II flies by the mechanism shown in Figure 3.17(a) has an acrylic base fitted with gears and a simple FBL. The flapping

FIGURE 3.16  Initiator, the 1st generation FWMAV at Tamkang University.

FIGURE 3.17  (a) Flapping mechanism of Eagle-II, (b) Eagle-II.

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wing frame is made of Balsa wood. It is a tapered rectangular column from the wing root to the wingtip. The horizontal rear wing is made of Balsa wood, and the rear wing actuator is fixed on the rear wing frame. A strong and lightweight fuselage skeleton is needed, and hence carbon fiber rod of 1 mm diameter is used to build it. The wing film is made of parylene because of its lightweight and flexibility. The assembled Eagle-II airframe structure is shown in Figure 3.17(b). The main issue in FWMAV Eagle-II is, its base and connecting rod may fail due to the poor rigidity, brittleness, and inadequate strength of acrylic and thus cannot withstand high torque. Therefore, the Golden-Snitch of the 3rd generation FWMAV of Tamkang University utilizes a lightweight and strong aluminum alloy as the flapping mechanism material. It is manufactured using electric discharge wire cutting (EDWC; discussed in Chapter 4.) The 3rd generation flapping-wing skeleton is changed from Balsa wood to a carbon fiber rod, producing completely different flexible flapping wing characteristics. The tip of the wing also outputs an out-of-plane motion at the same frequency as the vertical stroke of the flapping wing (discussed in Chapter 12). The 3rd generation FWMAV Golden-Snitch utilized plastic mold production technology (discussed in Chapter 4) to make the fuselage. This led to low price and small size and established an FWMAV named Golden-Snitch Pro in Figure 3.18 with a full plastic skeleton and an expandable polystyrene (EPS) fuselage body [27]. Wind tunnel experiments are conducted by varying the parameters mentioned in Table 3.1B. It may be noted for the inclined angle, 50° is not used because the fuselage wing’s blocking ratio exceeds 7.5%. The lift data at an inclined angle of 0° is irregular and lacks the trend, as observed in Figure 3.19(a). The lift for the inclined angle of 10° is not significantly varied with respect to input driving voltage in Figure 3.19(b). However, the increase of inclined angle 20° onwards and the increase of wind speed and driving voltage leads to an

FIGURE 3.18  FWMAV Golden-Snitch Pro.

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TABLE 3.1B Parameters of the Wind Tunnel Experiments for Golden-Snitch Pro Parameter Wind Speed Driving voltage Inclined angle Flapping stroke angles Connecting rod length

Values 0, 1, 2, 2.5, 3 and 3.5 m/s 0.9 V and 3.7 V in 0.4 V step 0° to 40° in steps of 10° 52.8° 4

increase in the lift as depicted in Figures 3.19(c)–(e). Therefore, it can be inferred that it is necessary to keep the inclined angle at more than 20° to attain a positive lift as adding an EPS fuselage body to the MAV. Since the maximum lift in Figure 3.19 is more than 11 g, surpassing the body weight of the Golden – Snitch Pro. This MAV seems to have a stable flight. However, this maximum lift should be justified by observing its corresponding net thrust at the same time. If the corresponding net thrust is negative (thrust is less than drag), then the MAV will be retarded to reduce air speed, lift and drag sequentially until reaching an equilibrium state of zero net thrust (thrust is equal to drag). The net thrust measured for various input driving voltage and inclined angles is shown in Figure 3.20(a)–(e). In each case, the net thrust increases with an increase in the driving voltage. However, as the wind speed increases, the net thrust reduces since flapping wings have to face more air drag. Figure 3.20 also can output the maximum forward speed according to different inclined angles by observing the zero net thrust, and output the maximum net thrust corresponding to zero wind speed and the driving voltage of 3.7 V. We summarize the results in Table 3.2. Table 3.2 summarized that under the maximum net thrust range of 4.5~4.9 gf, the flight with higher inclined angle is coupled with low forward speed; the flight with lower inclined angle is coupled with high forward speed. Take the example of the inclined angle 40° case in Figure 3.20(e), the net thrust values at the high speed of 3 m/s are all negative. More increase of the wind speed gives the more negative net thrust and the more non-realistic flight conditions. Therefore, there are no experiment data for the higher speed domain (>3 m/s) at the inclined angle of 40°. We moreover change to co-relate the lift of the Golden-Snitch Pro in terms of the flapping frequency in Figure 3.21 (flapping frequency is not linearly dependent of driving voltage). It can be seen from Figures 3.21 (a) and (b) (at inclination angles 0° and 10°), the lift force decreases during the increase of flapping frequency, which is essentially the same case as shown in Figure 3.19. It is due to the negative lift effect on the Golden – Snitch Pro generated by incorporating the fuselage. However, at higher inclination angles, as seen from Figure 3.21(c)–(e), there is an increase in lift due to the increase in flapping frequency, but still not apparent in the lowspeed region.

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FIGURE 3.19  Lift of the Golden-Snitch Pro vs. driving voltage for different speeds at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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FIGURE 3.20  Net thrust force of Golden-Snitch Pro vs. driving voltage for different speeds at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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TABLE 3.2 Max. Forward Speed and Net Thrust According to Different Inclined Angles Inclined Angle 0° 10° 20° 30° 40°

Max. Forward Speed (Zero Net Thrust) [m/s] 3.5 3 3 2.5 2

Max. Net Thrust (Zero Speed/3.7 V) [gf] 4.6 4.5 4.6 4.9 4.5

The net thrust force for the Golden-Snitch Pro with respect to increase in flapping frequency increases for all the inclination angles as seen from Figure 3.22. However, for an increase in wind speed, more drag is experienced, and the net thrust force becomes negative. Figure 3.22 globally shows the similar trend with Figure 3.20. We can obtain the similar results like Table 3.2 showing the maximum forward speed of zero net thrust according to different inclined angles and the maximum net thrust values at zero speed and the maximum flapping frequency. Restated, under the maximum net thrust range of 4.5~4.9 gf, the flight with higher inclined angle is coupled with low forward speed; the flight with lower inclined angle is coupled with high forward speed. For the Golden-Snitch Pro at different inclined angles, lift force increases as increasing the wind speed in Figure 3.23. At higher inclined angles, the lift force approaches a smooth quadratic curve (dynamic pressure) with respect to an increase in wind speed. Golden-Snitch Pro experiences the maximum net thrust force of about 4–5 gf for all the inclined angles, as seen from Figure 3.24. As wind speed increases, drag increases, and correspondingly the net thrust decreases. The net thrust force is negative due to more drag at higher wind speed, and FWMAV may not move forward. Therefore, the zero net thrust or the cruising conditions should be addressed to conclude the wind tunnel data of the MAV. The lift forces at the zero net thrust and the cruising conditions can be referred as the bodyweight specification of MAVs. We observed the forward speeds corresponding to the possible maximum driving voltages of different inclined angles from Figure 3.24 and found the corresponding lift values at the same cruising conditions (inclined angle, max. driving voltage, max. forward speed) from Figure 3.23, and finally summarize Table 3.3. Table 3.3 shows the cruising conditions of Golden -Snitch Pro using FBL mechanism. When we increase the inclined angle, the max, forward speed will be reduced. The overall best point happens at the inclined angle of 40° to have the maximum lift of 9.8 gf to support the body weight (about 8 gf) of the MAV. There is still some tolerance to load more components like rudders, camera chip, and inertial measurement unit (IMU) in the future to do intelligent control. Generic speaking, MAVs herein generate lift to counterbalance their body weight by creating forward speed

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FIGURE 3.21  Lift of the Golden-Snitch Pro vs. flapping frequency for different speeds at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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FIGURE 3.22  Net thrust force of the Golden-Snitch Pro vs. flapping frequency for different speeds at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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FIGURE 3.23  Lift force of Golden-Snitch Pro vs. wind speed for different driving voltages at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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FIGURE 3.24  The net thrust of Golden-Snitch Pro vs. wind speed for different driving voltages at various inclined angles: (a) 0°, (b) 10°, (c) 20°, (d) 30°, (e) 40°.

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TABLE 3.3 The Cruising Conditions of Golden-Snitch Pro Using FBL Mechanism Inclined Angle 0° 10° 20° 30° 40°

Net Thrust [gf] 0 0 0 0 0

Max. Driving Voltage [V] 2.5 2.9 3.7 3.7 3.7

Max. Forward Speed [m/s] 3.15 3.3 3.42 2.82 2.62

Max. Lift [gf] 68°) and an increased phase lag (the suggested value is within 3°). Some others did not mention about phase lag at all [5,9,31–33,35,37,40]. There is an additional difficulty with the miniaturization. The flapping mechanism of the Nano Hummingbird [43] (with stroke angle >120°) and the Konkuk Beetle [44] (with stroke angle of 92°) have almost achieved zero phase lag and can be qualified as suitable flapping mechanisms in the practical scenario and apt for miniaturization. However, both the Nano Hummingbird and Konkuk Beetle have more connecting rods, requiring a powerful motor to drive. The earlier Golden-Snitch mechanism had a maximum stroke angle of 53° with a phase lag of 3°. It can be improved by adding a straight-line mechanism to minimize or nullify the phase lag. In view of this, Watt’s straight-line mechanism shown in Figure 3.25 is employed to provide a straight-line motion [43]. From mechanism design aspect, it can be seen that if the relationship BC / CD = DE / AB is maintained, then the trajectory of point C, for a portion of the stroke, will be an approximately straight line as the Watt’s mechanism (ABCDE) shown in Figure 3.25(a) [44]. When Watt’s mechanism gets integrated with the modified five-link mechanism as shown in Figure 3.25(b), the resulting one is called the WattStephenson mechanism or, in short, Stephenson mechanism [45,46]. The 2nd linkage

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TABLE 3.4 Phase Lag and Flapping Stroke Angle of Various Flapping Mechanisms Flapping Stroke Angle 53° ±45° 76° 120° 68° 90° 150° ±70° 74° 160° 80° ±60° ±50° ±90° -

Literature Yang [26], 2009 Zbikowski [28], 2005 Ge [5], 2013 Han [29], 2010 McDonald [30], 2010 Fenelon [31], 2010 Fujikawa [32], 2007 Yan [33], 2001 Tanaka [34], 2005 Isaac [35], 2006 Saifuddin [36], 2006 Finio [37], 2009 DiLeo [38], 2007 Khan [39], 2007 Link [40], 2008 Banala [41], 2005

Phase Lag 3° -

Avadhanula [6], 2003

20°

120°

-

0° 20° 20° 180° 0° 5° 90° 7.9°

90°

Yan [8], 2003 Maybury [9], 2004 Kennon [13], 2012

0°

80° 120° 210°

Park [42], 2014

0°

92°

Remarks (Golden-Snitch) FBL mechanism FBL mechanism with figure-8 generator crank-link a pair of FBL mechanism spherical FBL mechanism crank-link Butterfly-type crank-link FBL mechanism FBL mechanism FBL mechanism FBL mechanism FBL mechanism slider crank Six link Pantograph Combination of a 5-bar linkage and FBL mechanism Combination of double FBL mechanism and ball-bearing differential FBL mechanism 2 DOF rigid body dragonfly mechanism (Nano Hummingbird) 2 FBL mechanism in series (Konkuk Beetle) FBL mechanism +slider-crank

FIGURE 3.25  (a) Watt mechanism, (b) Stephenson mechanism design, (c) Stephenson mechanism prototype using EDWC.

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TABLE 3.5 Linkage Dimensions of Stephenson Mechanism Flapping angle Base width; B.E. Base height; OA Linkage width 1st bar; O.P. 2nd bar; PA Control bar; CD = 2CA Sidebar; DE = BC 3rd bar; AF Wing bar; F.G. All dimensions are in mm

70° 20 19 0.7 2 16 4 10 6.5 3 (120°)

144° 30 18.8 1.5 6.5 16.6 4 16.6 6 5 (120°)

PC moves up and down while point C traces an approximate vertical straight line. Watt’s mechanism restricts this to move along the vertical line path. Correspondingly, the left and right linkages CFG and CHI produce the flapping motion symmetrically up and down. A preliminary kinematic analysis shows that the phase lag almost reached zero while the flapping angle is confined to a range of 70°–144°. The reason to confine the flapping angle is to ensure point C only moves up and down vertically and does not travel along the other portions of the coupler curve (8-curve) shown in Figure 3.25(a). Figure 3.25(c) is the Stephenson mechanism prototype using electrical discharge wire cutting (EDWC). Table 3.5 provides the detailed dimensions of each linkage of the Stephenson mechanism wherein flapping angles of 70° and 144° (based on simulation trials) are obtained for a 20 cm-span FWMAV. The Stephenson mechanism’s linkages are fabricated using 7075 aluminum alloy by EDWC (details in Chapter 4) since the alloy provides the mechanism sufficient structural integrity while being light in weight. A view of the fabricated mechanism is shown in Figure 3.25(c). The mechanism has a gear ratio of 26.7 and is assembled using stainless steel pins. The gear ratio can be flexibly changed to 6.67, 8.57, 21.3, 26.67, and 27.43, respectively. High-speed photography measurements using a Phantom V 4.2 high-speed camera are used in order to determine the flapping angle and flapping frequency of Stephenson mechanism-based FWMAV. Figure 3.26 shows high-speed photographs for one cyclic flapping motion of the Stephenson mechanism. Lithium battery provides a driving voltage of 3.7 V. Because of the carbon fiber rod’s flexibility, the same is used as the wing’s leading edge to achieve maximum flapping stroke angle during real flapping. Without adding the flapping wings, the stroke angle measured is 79°, and incorporating the wings is increased to 108° in Figure 3.27(a) for 20 Hz flapping frequency. However, for the flapping frequency of 21.28 Hz, the flapping stroke angle is increased to 115°, as shown in Figure 3.27(b).

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FIGURE 3.26  Single-cycle high-speed photography of FWMAV with Stephenson mechanism.

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FIGURE 3.27  The maximum flapping stroke angle of Stephenson mechanism: (a) gear ratio 26.6, (b) gear ratio 21.3.

For the gear ratio of 26.67, 20 cm wingspan (123.4 cm2 wing area), wind speed of 1.5 m/s, Φ6 mm × 14 mm motor achieved a maximum flapping frequency of 14 Hz to produce a maximum lift of 8.3 gf. Figure 3.28 shows the actual flight test at the height of about 2 m and successfully flew at an inclined angle of 66° for 57 s. The Stephenson mechanism intrinsically has an issue of compactness and poor positioning of C.G. Due to the stroke traveling along a straight line, the mechanism needs a significantly large space in the horizontal direction. To increase the stability of the mechanism during flapping motion, the thickness of the middle rod has to be increased, as shown in Figure 3.29(a). Besides, as shown in Figure 3.29(b), the flapping wing and motor center are not on the same vertical axis. When the FWMAV flew at a higher inclined angle, the motor’s weight will automatically lower the nose and leads to a lower inclination angle. If the motor’s position can be adjusted, for example, if it can be placed on the same axis height as the center of the flapping wing, the mechanism’s size will be effectively reduced, and the MAV is more likely to fly at a high inclined angle.

FIGURE 3.28  Stephenson mechanism test flight and the instantly inclined angle of 66°.

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FIGURE 3.29  (a) Rod thickening, (b) position of motor and flapping center.

3.5  EVANS MECHANISM To overcome the issues of Stephenson mechanism, a compact straight-line mechanism called the Evans mechanism is used in the FWMAV. Evans mechanism shown in Figure 3.30 is divided into two portions: the flapping portion and the phase lag control portion. The flapping portion is based on the Stephenson mechanism. It consists of an output rod (as the 2nd bar PC) connecting two 3rd bars and two wing bars (CFG and CHI). The phase lag control portion uses the approximate linear mechanism of rocking-crank, as shown in Figure 3.30(a). The rocking-crank in

FIGURE 3.30  Evans mechanism: (a) flapping portion; (b) rocking-crank part.

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FIGURE 3.31  (a) Nodes of the mechanism, (b) trajectory of rocking-crank mechanism.

Figure 3.30(b) comprises three rods, and its trajectory is an approximate line. The mechanism obeys the following relationship:

BC = CD = CE = 2.5AB,    AE = 2AB

(CE : BC = BC : BA, CE;  Special case of longer CE  is better). The straight-line motion trajectory of the Evans mechanism is shown in Figure 3.31.

3.5.1  Preliminary Design 3.5.1.1  Phase Lag Using the motion simulation software, the approximate trajectory of the Evans mechanism is determined, which is shown in Figure 3.32. The left and right-wing have a low phase lag of about 0°–0.1° with a maximum flapping stroke angle of 82°, as shown in Figure 3.33. 3.5.1.2  Force Transmission Angle In the Evans mechanism, the force transmission angle α is the angle between the output lever and connecting rod, as shown in Figure 3.34. A mechanism has an efficient transmission of motion when the force transmission angle is 90°.

FIGURE 3.32  X-axis offset of Evans five-bar mechanism.

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FIGURE 3.33  Flapping angle of the Evans mechanism.

During one revolution of the crank, the force transmission angle varies between 31° and 55.8°, as shown in Figure 3.35. Due to a low transmission angle, excessive torque loss occurs, leading to the poor performance of the flapping mechanism. Also, the resulted flapping frequency of 9 Hz was very less, and hence the design needs further improvement.

3.5.2 Improved Design of Evans Mechanism In order to improve the existing Evans mechanism in terms of reducing its weight through miniaturization, crank length, and connecting rod length are varied. A shortened crank can produce more torque, and anincreased crank can impart a higher angular velocity. To compensate for the smaller flapping stroke angle due to the shortened crank, the two-shaft hole distance in the wing rod must also be shortened,

FIGURE 3.34  Transmission angle α in the Evans mechanism.

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FIGURE 3.35  Variation in force transmission angle.

as shown in Figure 3.36(a). The lever principle allows shorter driving stroke to reach a larger flapping stroke angle via the pivot. However, by changing the length of AF, the stroke angle can also be varied, and hovering stability can be obtained by an asymmetrical motion of both the wings. The length of the output rod driven by the crank must conform to the gear-shaft holes’ spacing that effectively maintains an approximately straight line during the flapping motion. The rule followed to achieve it is



Spacing   between   gear − shaft   holes = proportional   spacing   constant × ( number   of   driving   teeth + number   of   driven   teeth) / 2 

For example, consider a gear ratio of 489 ⋅ 605 = 26.67 , where the number of the small gear’s driving teeth is 9, the number of the middle gear teeth is 48, and the number of the middle gear’s driving teeth is 12. Finally, the number of the driven teeth of the big gear is 60. If the proportional spacing constant is 0.3 mm/tooth, the spacing between the small gear and middle gear shaft-holes is 8.55 mm, and spacing between the middle gear and large gear shaft holes is 10.80 mm, as shown in Figure 3.36(b).

FIGURE 3.36  (a) Shortened two-shaft holes distance, (b) gear-shaft hole spacing.

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TABLE 3.6 Dimensions of the Modified Evans Flapping Mechanism Component 1st bar (OP) 2nd bar (PA) 3rd bar (AF) Wing bar (FG) Control short bar (DE) Control medium bar (CB) Control long bar (AC = AD + CD)

Size (mm) 2.5 19 5.516 3.25 2.5 3 11.475 = 7.225 + 4.25

The Evans flapping mechanism’s linkage dimensions for a flapping angle of 82° and a gear ratio of 26.67 are given in Table 3.6 [47]. The wing rod part is designed like a fork shape, and the slot width is made with a negative tolerance, as shown in Figure 3.37. After the carbon fiber rod of 0.8 mm diameter is inserted into the slot and clamped, it is coated with quick-drying adhesive to prevent disengagement. Kinematic analysis is performed to improve the design of Evans flapping mechanism. The exploded view of the Evans mechanism is shown in Figure 3.38(a). The yellow line (Figure 3.38(b) above the center driving rod is used to calculate the X-axis offset of the trajectory, from −0.001 mm to 0.008 mm, as shown in Figure 3.39. Compared to the Stephenson mechanism and the first version of the Evans mechanism, the modified Evans mechanism has improved its straight-line trajectory [48]. Kinematic analysis is performed, and the phase lag between the left and right wings of the modified Evans mechanismis determined. The phase lag of the mechanism is shown in Figure 3.40. It is found that under the maximum flapping stroke angle of 80°, the phase lag is very minimal, i.e., 0.0017°–0.0025°, which meets the design requirement. The Evans mechanism’s force transmission angle was far away from 90° to cause a low flapping frequency of 9 Hz. However, in the modified Evans mechanism that is shown in Figure 3.41, α increases from 75°to 104°, which is very close to the ideal value of 90°. The effect of crank rotation on the modified Evans mechanism’s transmission angle is shown in Figure 3.42.

FIGURE 3.37  Carbon fiber rod inserted into the fork-shaped slot of the wing rod.

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FIGURE 3.38  (a) Exploded view of Evans mechanism (b) straight-line trajectory.

FIGURE 3.39  X-axis offset of the modified Evans mechanism.

FIGURE 3.40  The phase lag of the modified Evans mechanism.

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FIGURE 3.41  Transmission angle in the Evans mechanism.

3.5.3 Comparison of Stephenson Mechanisms and Evans Mechanism Stephenson mechanism is an asymmetrical mechanism that requires a longer space to insert the Watt straight-line rods in the central portion. While the Evans mechanism is an asymmetric mechanism that places the rocking crank on one side portion for achieving straight-line motion so that the overall mechanism size is small and compact. Figure 3.43 shows the length from the bottom-most point to the wing rod in the modified Evans mechanism is 31.30 mm, whereas the length in the Stephenson mechanism is 41.55 mm. The motor is the heaviest part of an FWMAV. If the motor mounting position is close to the flapping center, then the FWMAV may have good flight stability. Figure 3.44 shows the position difference between the motor and flapping center for the two flapping mechanisms. Regarding the size and motor position, the Evans mechanism is similar to the FBL mechanism of Golden-Snitch shown in Figure 3.1. On the contrary, the Stephenson mechanism’s motor position is too far away from the flapping center, and the motor weight automatically pushes the FWMAV nose down. This makes it difficult to hover. To pitch up the FWMAV, the avionics unit and battery have to be shifted to the tail end. Figure 3.45 shows the position comparison.

FIGURE 3.42  Effect of crank rotation on transmission angle of the modified Evans mechanism.

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FIGURE 3.43  Comparison of Stephenson and Evans mechanisms.

3.5.4 Measurement of Flapping Frequency Flapping frequency is a significant indicator to understand the performance of flapping mechanisms. The Evans mechanism integrated with a flapping wing of 21.53 cm span and a wing area of 123.4 cm2 as shown in Figure 3.46 is considered. The DC motor was changed to ϕ7 mm × 16 mm, and the gear-reduction ratio was also fine-tuned as 16, 20, 21.3, and 26.67, which is different from Stephenson’s case of 6.67, 8.57, 21.3, 27.43, and 26.67. A high-speed camera setup (Figure 3.47) is used to capture the flapping motion, shown in Figure 3.48. The driving voltage varies from 0.8 V to 3.7 V with an increment of 0.2 V. The shooting speed of the high-speed camera is set to 1,000 fps (time step of 1 ms). For one flapping cycle, the total number of image frames is calculated, and its reciprocal provides the flapping frequency. The flapping frequency for the driving voltage at the start is not equal to that for the driving voltage at the end or even during the voltage increase. This effect is called hysteresis. For preventing the uncertain frequency measurement due to hysteresis, the measurement was modified. After measuring the flapping frequency using a high-speed camera at a particular driving voltage, we reset the driving voltage to zero and set it to the next higher driving voltage for

FIGURE 3.44  Comparison of Stephenson and Evans mechanisms.

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FIGURE 3.45  Position difference about the motor and wing loading.

FIGURE 3.46  Wing geometry.

FIGURE 3.47  Experimental setup of high-speed photography.

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FIGURE 3.48  Snapshots of one full cycle of flapping of FWMAV fitted with Evans mechanism.

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FIGURE 3.49  Flapping frequency of Evans mechanism (a) load-free case (no wing), (b) with wings.

the next measured point. This method can also avoid the motor aging issue due to continuous motor rotation or even motor burn-off. High-speed photography measurements are performed to identify flapping frequency for the two cases: flapping wings and flapping wings (load-free). A maximum voltage of 3.7 V is provided to obtain maximum flapping motion. Regarding the load-free case shown in Figure 3.49(a), a gear ratio of 16 provided a higher flapping frequency of 53 Hz, and at a higher gear ratio of 26.67, the flapping frequency was reduced to 30 Hz [49]. Moreover, with the attachment of flapping wings in Figure 3.49(b), due to aerodynamic loading, the flapping frequency reduces to 19 Hz for the gear ratio of 26.67. While comparing the gear ratios and corresponding flapping frequencies with and without wings, it is evident from Table 3.7 that, maximum of 62.24% reduction in frequency is obtained. However, the flapping frequency without wings decreases as the gear ratio increases, and in the case of wings, the flapping frequency increases with increasing gear ratio. Comparative evaluation is made for the Stephenson and Evans flapping mechanisms without incorporating wings with reference to two gear ratios 21.3 and 26.67. The Evans mechanism has achieved the highest flapping of 39 Hz for the gear ratio of 21.3, and about 30 Hz was obtained for the gear ratio of 26.67, as shown in Figure 3.50(a). After integration of flapping wings in the mechanisms, flapping frequency is measured. It can be seen from Figure 3.50(b) that the highest flapping frequency of 13.88 Hz is obtained for the gear ratio of 21.3 and 14.29 Hz for the case of 26.67 gear ratio. TABLE 3.7 Comparison of Wingbeat Frequency with and without Wings in Evans Mechanism Gear Ratio 16 20 21.3 26.67

Flapping Frequency without Wings (Hz) 52.63 40.00 38.46 30.30

The Flapping Frequency with Wings (Hz) 13.51 14.49 15.62 18.86

Frequency Achieved Percentage 25.67% 36.23% 40.61% 62.24%

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FIGURE 3.50  Comparison of Stephenson and Evans mechanisms: (a) without wing, (b) with attaching wings.

Comparative studies on these two mechanisms for the two gear ratios 21.3 and 26.67 reveals that (Table 3.8), Evans mechanism has the highest reduction in flapping frequency of about 62.2% for the gear ratio 26.67, which is higher than the Stephenson mechanism. Using high-speed photography measurement [4], Evans’s mechanisms’ maximum wing stroke angle is found to be about 100.43°, as shown in Figure 3.51. Due to the large deformation of the carbon fiber rod at the leading edge of the wing. The test flight depicts that Evans’s flapping mechanism can achieve an instant high inclined angle of 77.94°. Simultaneously, the maximum flapping frequency of 18 Hz with a flight endurance of 120 s was obtained, and it was also flown 20 m in 20 s. From the above, the Evans mechanism is found to be more suitable for a MAV development because of its compact size, maximum flapping angle, higher flapping frequency, and the high inclined angle of flight compared to the Stephenson mechanism. We will now discuss the results of wind-tunnel testing, indoor, and outdoor flight tests.

3.5.5 Aerodynamic Performance Measurement of Evans Mechanism To measure the lift and net thrust force of FWMAV, wind tunnel-based experiments were conducted. The wind tunnel is used to provide airflow at different wind velocity, and a fixture was used with an adjustable mounting to vary the inclination angle. The aerodynamic force generated by the FWMAV was transmitted to the six-axis force gauge. According to actual research and development attempts, the flying attitude of FWMAV is mainly divided into two types. The first one is a forward flight. For TABLE 3.8 Comparison of Flapping Frequency between Evans and Stephenson Mechanisms

Gear Ratio Evans mechanism 21.3 26.67 Stephenson mechanism 21.3 26.67

Flapping Frequency without Wings (Hz) 38.46 30.30 34.48 28.57

The Flapping Frequency with Wings (Hz) 15.62 18.86 13.88 14.29

Frequency Achieved Percentage 40.61% 62.24% 40.26% 50.01%

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FIGURE 3.51  Maximum wing-travel stroke angle of Evans mechanism.

example, the FWMAV Golden-Snitch equipped with FBL mechanism often adopted the forward flight with an inclined angle of about 20°–30°. The flying speed was higher than 1.5 m/s. The second is a hovering-like flight, such as the FWMAV equipped with the Stevenson or Evans mechanism with an inclined angle of about 60°–70°. The flying speed is about 1–1.5 m/s, which is slower than forwarding flight. According to these two flight conditions, the wind tunnel experiments were conducted. Former is with low inclined angles of 20°, 30°and with the wind speed of 1.5, 2.0, 2.5, 3.0 m/s, respectively. The hover-like mode was achieved for higher inclined angles such as 50°, 60°, 70° and with a wind speed of 0.5, 1.0, 1.5 m/s, respectively. In Evans flapping mechanism, the gear ratio was varied as 16, 20, 21.3, and 26.67, respectively, and wind tunnel experiments were conducted to measure the lift and net thrust force. The following are the major inferences made through performing the experimental studies, and the results are shown in Figures 3.52–3.55 [48]. 1. The lift increases significantly with wind speed and an inclined angle. The lift naturally increases with dynamic pressure. The vertical component of net thrust increases with an increase of inclined angle, which is combined to lift, and thus lift force shows an increasing trend with an increase in wind speed. 2. The lift increases with the gear ratio increase (gear ratio 16 generated 5–8 gf and gear ratio 26.67 generated 8–13.67 gf). The flapping frequency increases with the increase of gear ratio, and thus lifts increase. 3. The net thrust decreases during the increase of wind speed and inclined angle. At this condition, the air drag increases with wind speed, and hence the net thrust (thrust minus drag) decreases. In addition, the vertical

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FIGURE 3.52  Lift/net thrust data of gear ratio 16.

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FIGURE 3.53  Lift/net thrust data of gear ratio 20.

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FIGURE 3.54  Lift and net thrust data of gear ratio 21.3.

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FIGURE 3.55  Lift and net thrust data of gear ratio 26.67.

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component of net thrust decreases with an increase of inclined angle. Even though the lift’s horizontal component is also slightly increased simultaneously, the overall net thrust is still getting smaller. Specifically, on the lift/net thrust data of Figure 3.55 subject to the gear ratio of 26.67, the Evans mechanism inclined at 70°, wind speed of 1.5 m/s, and driving voltage of 3.7 V could generate the maximum lift of 13.67 gf and net thrust of 1.9 gf. The fact of this flight condition is to accelerate upward continuously. During a level-cruising flight condition with an inclined angle of 70° and wind speed of 1.5 m/s, the driving voltage was lowered to 3.0 V so that the net thrust decreases to 0 and the lift was still 10 gf. In other words, compared to Golden-Snitch using FBL mechanism driven by 3.7 V, the FWMAV using Evans mechanism needs a lower driving voltage of 3.0 V to perform a level-cruising flight [48]. For example, in Figure 3.55(b2) with an inclined angle of 30°, although the net thrust data is positive, the net thrust may still approach zero, which is another cruising condition. The lift data are shown in Figure 3.55(b1) on cruising condition confirms that about 10–11 gf lift force was generated, which is still larger than the bodyweight of Golden-Snitch, and the stable flight is guaranteed. The aerodynamic performance of the Evans mechanism and Stephenson mechanism were compared. For the gear ratio of 26.67 and the inclined angle of 20°, the maximum lift generated by the Stephenson mechanism is 9.18 g, which is lesser than the maximum lift of 9.93 gf by the Evans mechanism as shown in Figure 3.56. Besides, for the inclined angle of 60°, the maximum lift generated by the Stephenson mechanism is 8.6 g, which is lesser than the maximum lift of 13.02 gf by the Evans mechanism. Hence, it was observed that for the small inclined angle (forward flight) and large inclined angle (hovering-like flight), the Evans mechanism provided better lift than the Stephenson mechanism. The net thrust comparison between the two types of mechanism is shown in Figure 3.57, and it can be seen that Evans mechanism was better than the Stephenson mechanism in generating net thrust force.

3.5.6 Mass Distribution of FWMAV with Evans Mechanism The Golden-Snitch-based FWMAV embedded with a motor of ϕ6 mm × 14 mm, fuselage, wings,18 mAh 25C lithium battery, and IR receiver. Table 3.9 shows each

FIGURE 3.56  Comparison of lift force.

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FIGURE 3.57  Comparison of net thrust.

part’s weight and percentage. The mechanism and motor together contribute approximately half of the weight of the flyer. Hence it is difficult to adjust the C.G. by movingthe position of the receiver and lithium battery. They can only be positioned at the bottom of the FWMAV to obtain better flight control. The weight estimation of Evans-based FWMAV is carried out. Table 3.10 provides an individual component’s weight and percentage. In order to increase the endurance, 70 mAh 20C Lithium battery is selected. The overall weight was 9.62 gf. The receiver and motor position was possible to adjust the overall C.G., and good flight control was achieved.

3.6  FLIGHT TEST OF EVANS-BASED FWMAV Using a lighter IR receiver and 18 mAh 25C lithium battery, the weight of Evans-based FWMAV is around 8.16 g, achieving an 18.86 Hz flapping frequency. The location of the receiver and lithium battery is shown in Figure 3.58(a) (Arrangement 1). The FWMAV took off directly from the ground like a rocket launching, as shown in Figure 3.58(b). Due to its lightweight and generation of more thrust, the flight control was difficult. TABLE 3.9 Mass of Each Part of Golden-Snitch Component Mass (g) Percentage

Motor 1.72 25%

Mechanism 1.24 18%

Body 2.46 36%

Lithium Battery 1.08 16%

IR Receiver 0.4 5%

Total 6.9 100%

Lithium Battery 2.34 24%

IR Receiver 0.6 6%

Total 9.62 100%

TABLE 3.10 Mass of Each Part of Evans Based FWMAV Components Mass (g) Percentage

Motor 2.56 27%

Mechanism 1.78 19%

Body 2.32 24%

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FIGURE 3.58  Arrangement 1: (a) location of receiver and battery, (b) vertical take-off from the ground.

However, by utilizing a 900 MHz receiver and 70 mAh 20C lithium battery, the overall weight was increased to 9.62 gf. The location of the receiver and lithium battery is shown in Figure 3.59(a) (Arrangement 2). The flight test results suggested that it was more stable than Arrangement 1, and the FWMAV has flown at a high inclined angle of 77.94° as indicated in Figure 3.59(b). (This is close to the cruising condition depicted in Section 3.5.5: zero net thrust and lift of 10g under the inclined angle 70°, airspeed 1.5 m/s, and driving voltage 3.0 V). However, due to CG shift, it lifted instantly when accelerating, shaken back and forth, and quickly lost its stability. The receiver and the lithium battery were placed at the front and lower than Arrangement 2, as shown in Figure 3.60(a) (Arrangement 3), the inclined angle was effectively reduced through the shift of CG, with the power control of only half of the Arrangement 2, the FWMAV flown in a stable manner as shown in Figure 3.60(b). (This is close to another cruising condition depicted in Sec. 3.5.5: zero net thrust and lift of 10–11 gf under the inclined angle 30°, airspeed 3.5 m/s, and driving voltage 3.0 V). If there is an increase of output voltage and power output, the FWMAV quickly gets out-of-control due to an excessive net thrust. The influence of airflow in the indoor flight test reduces during flight, and thus the flyer can successfully climb to 20 m in 22 s, as shown in Figure 3.61.

FIGURE 3.59  Arrangement 2: (a) location of receiver and battery, (b) flying with high inclined angle.

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FIGURE 3.60  Arrangement 3: (a) location of receiver and battery, (b) stable flight.

FIGURE 3.61  Indoor flight altitude test (https://www.Youtube.com/watch?v=fbQV0nZqS 6o&t=6s).

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FIGURE 3.62  Outdoor flight altitude test (https://www.Youtube.com/watch?v=fbQV0nZq S6o&t=6s).

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In the outdoor flight height test, flying in a breezy environment, the flyer could reach an altitude of 20 m as shown in Figure 3.62. During the rapid rise, the breeze that leads to a stable flight does not significantly disturb it.

3.7 SUMMARY This chapter discussed the design of novel flapping mechanisms, aerodynamic performance evaluation of designed flapping mechanisms from the perspective of developing prototypes. The design of the flapping mechanism is reviewed to improve the kinematic and aerodynamic performance of Golden-Snitch. 1. Section 3.2 the integration of the FBL mechanism was investigated (using ϕ6 mm × 14 mmDC motor and gear reduction ratio of 26.67) into GoldenSnitch and the maximum flapping stroke angle was found to be 52.8°. 2. The wind tunnel testing and real flight testing of Golden-Snitch using the FBL mechanism were demonstrated. A cruising condition of zero net thrust force was found at the inclined angle of 40°, driving voltage of 3.7 V (with the flapping frequency of 14 Hz), and maximum lift force of 9.8 gf. However, the phase lag between two wings was 3.2°, which induces a non-­synchronized lift difference between two wings that may cause the FWMAV to spiral down. 3. Stephenson mechanism and Evans mechanism effectively increased the flapping stroke angle and the lift and minimized the phase lag close to zero simultaneously. It was found that the aerodynamic performance of the Evans mechanism was better than the Stephenson mechanism. Evans mechanism attained a maximum flapping stroke angle of 80°, and the motor-mechanism configuration was very similar to the FBL mechanism. 4. To generate more net thrust and sufficient power to drive a large stroke angle, a ϕ7 mm × 16 mm motor was used. The Evans mechanism achieved the higher flapping frequency of 18.86 Hz than 13 Hz of Stephenson flapping mechanism for the gear ratio 26.67. Due to the magnified effect through a flexible carbon fiber rod, the wing stroke angle slightly exceeded 100°, and a small phase lag (within 3°) was observed. 5. The wind tunnel experiments of the Golden-Snitch using the Evans mechanism shows a maximum lift of 13.67 gf, which is much greater than its total weight of 9.62 gf. Hence, FWMAV can take off vertically like a rocket. However, flight instability occurred due to the shift in the center of gravity. 6. Masses can be relocated so that the center of gravity can be shifted toward the tail to achieve high inclined-angle and level-turning flight. The FWMAV using the Evans mechanism has a cruising condition of zero-net thrust at an inclined angle of 70°, a driving voltage of 3.0 V, a flight speed of 1.5 m/s (forward flight). The maximum lift force was observed to be more than 10 gf.

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36. Syaifuddin, M., Park, H. C. and Goo, N. S. (2006) Design and evaluation of a LIPCAactuated flapping device. Smart Materials and Structures, 15(5), 1225. 37. Finio, B. M., Eum, B., Oland, C. and Wood, R. J. (2009, October) Asymmetric flapping for a robotic fly using a hybrid power-control actuator. 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 2755–2762). 38. DiLeo, C. and Deng, X. (2007, October). Experimental testbed and prototype development for a dragonfly-inspired robot. 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 1594–1599). 39. Khan, Z. A. and Agrawal, S. K. (2007, April) Design and optimization of a biologically inspired flapping mechanism for flapping wing micro air vehicles. Proceedings 2007 IEEE International Conference on Robotics and Automation (pp. 373–378). 40. Lentink, D., Muijres, F. T., Donker-Duyvis, F. J. and van Leeuwen, J. L. (2008) Vortexwake interactions of a flapping foil that models animal swimming and flight. Journal of Experimental Biology, 211(2), 267–273. 41. Banala, S. K. and Agrawal, S. K. (2005) Design and optimization of a mechanism for out-of-plane insect winglike motion with twist. Journal of Mechanical Design, 127(4), 841–844. 42. Truong, Q. T., Argyoganendro, B. W. and Park, H. C. (2014) Design and demonstration of insect mimicking foldable artificial wing using four-bar linkage systems. Journal of Bionic Engineering, 11(3), 449–458. 43. Cheng, C. M. (2013) The Preliminary Study of Hummingbird-like Hover Mechanisms, Master Thesis, Mechanical and Electromechanical Engineering, Tamkang University. 44. Strandh, S. (1979) A History of The Machine, A and W Pub. Inc. 45. Dijksman, E. A. (1971) Six-bar cognates of a Stephenson mechanism. Journal of Mechanisms, 6(1), 31–57. 46. Liu, C. H. and Chen, C. K. (2015) Kinematic analysis of a flapping-wing micro-aerialvehicle with watt straight-line linkage. Journal of Applied Science and Engineering, 18(4), 355–362. 47. Hung, K. C. (2014) Design and Manufacture of Hummingbird-Like Flapping Mechanisms and Plastic Kits, Master Thesis, Mechanical and Electromechanical Engineering, Tamkang University. 48. Yang, L. J., Esakki, B., Chandrasekhar, U., Hung, K. C. and Cheng, C. M. (2015) Practical flapping mechanisms for 20 cm-span micro air vehicles. International Journal of Micro Air Vehicles, 7(2), 181–202. 49. Yang, L. J., Kao, A. F. and Hsu, C. K. (2012) Wing stiffness on light flapping micro aerial vehicles. Journal of Aircraft, 49(2), 423–431.

4

Fabrication of Flapping Wing Micro Air Vehicles

This chapter deals with various manufacturing methods such as electrical discharge wire cutting (EDWC), plastic injection molding (PIM), and 3D printing for the fabrication of micro mechanism parts of FWMAVs. Detailed discussion on the manufacturing aspects of tiny mechanism parts, assembly of fabricated parts, estimation of flapping frequency, flapping angle, the total mass of mechanism assembly, endurance, and power consumption of Evans and Stephenson mechanisms are discussed. Aerodynamic force measurement of developed FWMAVs using custom build test rig is performed and compared with all the three manufacturing techniques and also various 3D printing materials are elaborated. Various 3D printing methods of fabricating these flapping mechanism components, such as Multijet, Polyjet, stereolithography, and fused deposition modeling (FDM) are explained and their aerodynamic force measurements with comparative evaluation are detailed. The application of the parylene solid lubricant and its influence on the flapping frequency is also mentioned.

4.1  ELECTRICAL DISCHARGING WIRE CUTTING (EDWC) Electrical discharging machining (EDM) is a non-traditional manufacturing method to remove material from the metal workpiece through a high-temperature spark or arc generated by a high-voltage discharge between the workpiece and electrode. Workpiece and electrodes are usually placed in an insulated coolant like deionized water (DI water). Discharging occurs continuously to ensure that the arc temperature is close to 10,000°C, not only to melt or vaporize the workpiece locally but also to splash the debris to pure water for washing away. The electrical discharge wire cutting (EDWC) is a kind of EDM, wherein copper or brass wire is used as the electrode having a wire diameter of about 0.02 to 0.3 mm, for cutting the metal workpiece with respect to the pre-programmed path. The workpiece is moved based on the numerical control (NC) machining path to achieve a two-dimensional (2D) cutting motion [1]. A schematic of EDWC is shown in Figure 4.1, where the cutting wire rolls through the pulley and the guide hole. It is fed into the workpiece’s processing area, which is immersed in the DI water bath. The power supply unit provides high-voltage electrical pulses through which a high-temperature arc between the workpiece and electrode wire is produced. Since this process avoids direct contact between the electrode wire and the workpiece to function smoothly, the workpiece’s hardness or brittleness has no bearing on the material removal. There is no mechanical stress produced, either. Besides, EDWC can also meet the requirement of complex machining contour at high precision. It is a cost-effective way to process hard, brittle materials and to prototype small parts. Comparable to traditional machining such as drilling, milling, and grinding, EDWC has been recognized as a matured processing technology [2]. DOI: 10.1201/9780429280436-4

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FIGURE 4.1  Electrical discharging wire cutting (EDWC).

4.1.1  Gold-Snitch Four-Bar Linkage (FBL) Mechanism by EDWC EDWC is utilized to fabricate the tiny components of FBL flapping mechanism for Gold-Snitch. Aluminum alloy 7075 is selected due to its higher (0.2%) offset yield strength of 455 MPa, a higher tensile strength of 524 MPa, and a light density of 2.73 g/cm3. The linkage parts are made from 1 mm-thick 7075 plates, and the base part is fabricated using a 4 mm-thick plate [3,4]. Aluminum alloy 7075-T6 is machined in submerged type EDWC machine W-B430S (specifications are given in Table 4.1), shown in Figure 4.2. In Submerged type EDWC, both the workpiece and arc head are submerged in water during the cutting process, and copper-plated metal wire is used as an electrode. Water is used for cooling, avoid breaking of copper-plated metal wire, and flushing away the metal debris after high-temperature arc melting. In EDWC, the cutting path is planned before the two-dimensional (2D) object contour. The cutting process is assigned with a starting point and followed by an Eulerian graph for cutting the whole contour of this workpiece. The width of the cutting path is the same as the wire diameter. In the present case, it is 0.25 mm, as shown in Figure 4.3(a) [5]. Due to high cyclic loading at the hinge joints, aluminumalloy may not withstand high stress for a longer duration. Hence, steel injection hollow needles are considered as hinge joints. In this case, all the mechanical parts are

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TABLE 4.1 Specifications of W-B430S Submerged EDWC Machine Model item Machining method Max. artifact size (L×W×H) Simultaneous axis X/Y axis travel Z-axis travel U/V axis travel Wire diameter Max. taper angle The capacity of the water tank

W-B430S Submerge Type 700 mm × 520 mm × 295 mm XYUV (4 axes) 400/300 mm 300 mm 100/100 mm Ø 0.25 mm ±22.5° 570 L

pin-jointed using a 0.9 mm diameter injection steel needle. If the hole diameter is set prior as 0.9 mm, a negative tolerance may occur during the final assembly and may cause interference in the flapping mechanism resulting in improper rotation. After cyclic loading, the actual hole size got enlarged more than the needle diameter as 0.05 mm for the linkage pin joint, 0.04 mm for the motor ring, and 0.13 mm for the multi-stage gear set. This resulted in a positive tolerance and provided the clearance fit. The spacing of 8.68 mm between the 1st stage gear set using 12-teeth/48-teeth with 2nd-stage gear 60-teeth as shown in Figure 4.3(b) has obtained proper meshing of gear teeth smoother running of the flapping mechanism is achieved. Using EDWC, machining tolerance as small as 0.03 mm can be obtained, and hence it is suitable for tiny machining components for the flapping mechanism. Table 4.2 shows the mass of the individual components of the FBL mechanism of Gold-Snitch [6–9]. After assembling all the components, the FBL flapping mechanism of Gold-Snitch, along with gears and DC motor (Figure 4.4), weighed only 2.3 g, which is lighter than

FIGURE 4.2  (a) EDWC machine, (b) machining process.

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FIGURE 4.3  (a) Holes for linkage pin joints, (b) spacing in gear set.

the mass of Caltech’s Microbat of 2.8 g. The 0.9 mm-diameter steel needle extended along with the reduction gear set’s thickness by adding a 4 mm-long Teflon spacer.

4.1.2 EDWC of Evans Flapping Mechanism Unlike CNC machine, three-dimensional (3D) components are not possible to fabricate using EDWC. A-C- Shape spacer can be introduced to compensate for the non-coplanar issues between the base and the wing rod, as shown in Figure 4.5(a). For example, in Figure 4.5(b), a 4 mm spacer is provided. As mentioned previously, the part assembly is made using hollow steel needles of 0.9 mm diameter. Both the left and right ends of the steel needle are cut using a sharp-nose plier to have T-heads, and it acts as rivets. Adding the C-shaped spacers between the T-head and rod can prevent wearing parts at pin joints and avoid the mechanism’s chattering [10,11]. The assembly of Evans flapping mechanism is divided into linkages and base parts. The simulation results confirm that there is no interference between the linkages and gear units. The base part is equipped with two-stage gear sets and combined with the straight-line motion linkage part, as shown in Figure 4.6. The Evans TABLE 4.2 Mass of the Components Fabricated by EDWC Part name Base The first bar (a) The second bar (b) Third bar (c)

Mass (g) 0.261 0.030 0.041 0.040

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FIGURE 4.4  EDWC-based FBL mechanism of Gold-Snitch.

and Stephenson components are fabricated using EDWC assembled using a 0.9 mm needle, as shown in Figures 4.7(a) and (b). However, during the preliminary testing, the gears are stuck when turned to a certain angular position. Therefore, the runningin or grinding-in process at the driving voltage of 3.7 V is required for 1 to 2 hours. The method of testing the appropriate degree of run-in is to measure the current. If the current is found to be decreasing, the grinding-in resistance is decreased as well. In the actual experiment, it is found that the current before the running-in is 0.5A, whereas, after the running-in, it is reduced to 0.1A [12–15]. The performance evaluation between Stephenson and Evans mechanisms is given in Table 4.3.

FIGURE 4.5  (a) C-shaped spacers, (b) fabricated C-shaped spacers.

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FIGURE 4.6  Exploded view of Evans flapping wing mechanism.

FIGURE 4.7  (a) Evans mechanism, (b) Stephenson mechanism.

TABLE 4.3 Comparison between Stephenson and Evans Mechanisms Mechanism Stephenson Evans

Lithium Battery Specifications 60 mAH, 3.7 V max. 60 mAH, 3.7 V max.

Maximum Endurance (s) 57 120

Total Power Consumption (W) 14.02 6.66

The Mass of the Assembly (g) 2.44 1.48

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4.2  INJECTION MOLDING The EDWC method of fabrication is time-consuming, and metal parts alone can be manufactured. To reduce the components’ weight and manufacture the tiny components with high geometric precision, plastic injection molding (PIM) is considered. Plastic injection molding currently dominates the mass production of all plastic products. Plastic raw grains (pellets) are heated up to the melting point of polymers and poured into the mold. Unlike metal casting characteristics, molten plastic is difficult to pour into the mold directly. Hence, huge pressure needs to be applied to inject the plastic into the mold cavity smoothly. A schematic of PIM is shown in Figure 4.8. The use of a variable lead screw (whose pitch and rod diameter are gradually reduced) decreases the volume, thereby increasing pressure. The plastics parts that are formed are often characterized by high strength, complex 3D dimensionality, and high accuracy, making them ideal for mass production. For plastics with tolerances within 10 μm, especially micro-PIM, the processed parts’ size is usually tiny. The mold production is more sophisticated, but the plastic raw grains screening and the injection process control are also more stringent. The necessary amount of raw grains is, of course, less as well. In response to MAVs’ high-speed flapping motion and the extreme gust loading during the real flight, parts of the flapping mechanism must be both delicate and strong. Besides, compared to the EDWC technology, where manufacturing time per part is at least half an hour, PIM takes only 30 seconds to a minute (not including the mold developing time) to finish apart [16–23].

4.2.1  PIM of FBL Mechanism for Golden-Snitch The Moldflow analysis is performed to understand Polyoxymethylene’s flow characteristics (POM) and Polyamide 66 (PA66). POM is a thermal-plastic polymer and has a good hardness and strength comparable to metals. It has good self-lubricating properties, high chemical resistance, anti-wear, and elasticity within a big temperature range. PA66 has good mechanical strength, thermal stability, low friction coefficient, antiwear, self-lubricating, and shock-absorbing. The drawbacks are water-absorbing and dimension instability. PA66 is apt to bind to glass fiber to reduce the water content of the FRP resin material. Table 4.4 shows the material properties of POM and PA66 [24–26].

FIGURE 4.8  Schematic of plastic injection molding (PIM) machine operation.

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TABLE 4.4 Comparison of Material Properties between POM and PA66 Material Property Density (g/cm3) Tensile strength (MPa) Elongation (%) Heat distortion temperature (°C) Tensile modulus (GPa) Flexural modulus (GPa) Water absorption (%) Hardness

POM (DuPont 900P) 1.42 70 17 162 3.3 3.0 1.8–2.0 R120

PA66 (DuPont 101L) 1.14 82 25 200 3.1 2.8 1.5 R108

The mold flow analysis helps us determine PIM’s suitable material by comparing the deflections at linkages, bases, and gear. The deflection values influence the tolerance of the final part assembly of the mechanism and its smooth operation. In general, the material with smaller deflection would be selected for PIM. The entire mold flow analysis process is shown in Figure 4.9.

FIGURE 4.9  Mold flow analysis process.

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FIGURE 4.10  Mold flow analysis (temperature) of gear mold.

Three molds of linkage rods, bases, and gears are placed in the Moldflow analysis software and individually engaged with mold holes, flowing channels, runners, runner gates, cooling pipe, and regulation valves as shown in Figure 4.10. Further, POM and PA66 properties given in Table 4.4 are applied. The deflection of each component is determined, shown in Figure 4.11(a)–(c), and the maximum deflection is given in Table 4.5. Figure 4.11(a) depicts that the largest deflection in the linkage rod is at both ends of the third rod, a key component in the FBL mechanism connecting to the leading edge wing spar. Hence, the deflection has to be minimized. However, the POM deflection is found to be smaller than PA66 in the linkage mold. Similar results are also found in the remaining two molds. Hence, POM is selected as the PIM material for the fabrication of flapping mechanism components.

FIGURE 4.11  Deflection of POM parts in: (a) linkage mold, (b) base mold, (c) gear mold.

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TABLE 4.5 Maximum Deflection from Mold Flow Analysis Connecting rod mold Base mold Gear mold

POM Maximum Deflection (mm) 0.0541 0.1155 0.1376

PA66 Maximum Deflection (mm) 0.1581 0.2433 0.1630

The Arburg 220S PIM machine (Figure 4.12) is considered to produce the plastic kit. The three molds to fabricate base, linkages and gears are shown in Figure 4.13. The linkage mold is a two-plate mold; the base and gear molds are both three-plate molds. PIM process has two stages: • The filling stage is performed through forward driven by the lead screw, squeezes the high-temperature plastic melt into the lower-temperature mold cavity until the melt fills the mold cavity. Because of the compressibility of melt and the polymer melt in the cooling has a considerable degree of contraction, additional melt must be squeezed into the mold to reduce the size error caused by this contraction.

FIGURE 4.12  Arburg 220S PIM machine.

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FIGURE 4.13  Mold of the FBL flapping mechanism part: (a) base mold, (b) the linkage mold, (c) gear mold.

• The post-filling stage can be divided into the packing and cooling process. In the final cooling process, the polymer melt in the mold cavity must continue to cool until the finished product’s center solidifies to a considerable extent, and the final component is produced. Table 4.6 shows the list of parts of the FBL flapping mechanism for base 20 mm and 16 mm wide cases, respectively. The base support is designed as an I-beam to reduce the overall weight without compromising its rigidity. Multiple circular holes are provided for assembling the DC motor, carbon fiber rod, and gear pins. A delta-shaped rib is added to both sides of the base to increase the mechanical strength. The jack position at the bottom of the base is reserved for the anti-collision rods installed in the future [27–31].

4.2.2 Development of Golden-Snitch Outer Body Using PIM The outer body of Golden-Snitch Pro resembling the bionic swallow fuselage shell of a bird’s structure. The interior of the shell is equipped with a flapping mechanism, battery, and receiver. The computer-aided design (CAD) model of the fuselage is shown in Figure 4.14(a), and the cross-sectional view is shown in Figure 4.14(b). For weight reduction, the bird’s head is made as a thin shell design, and an overweighted head may cause instability during the high-inclined flight angle. For mounting the flapping mechanism, a U-groove space for flapping wings is provided at the bird’s head. For the battery module configuration, considering the battery heat dissipation, provisions are made at the shell’s back with 1 mm space tolerance. The receiver module is configured at the shell bottom with an opening, easier for external signal communication and recharging battery. The exterior partition of the fuselage shell is shown in Figure 4.14(b). After the shell enclosures with the flapping mechanism, motor, lithium battery, and receiver, the motor is partially exposed to the outer environment. The shell is made of polystyrene (PS), a colorless transparent thermoplastic with a glass conversion temperature above 100°C. Foamed and heated polystyrene, commonly known as expandable polystyrene (EPS), is a very light material, of which 90% to 95% of the volume is air, and is a good fall-buffer, is selected for the fuselage shell of FWMAV [32,33].

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TABLE 4.6 Four-Bar Linkage (FBL) Flapping Mechanism Parts Component Name Isometric No. 1 20 mm wide base

No. 2 gear

No. 3 Middle gear

No. 4 4 mm large gear

No. 5 20.3 mm 2nd Rod

ICON Look Ahead

Lookup

Right View

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TABLE 4.6 (Continued) Four-Bar Linkage (FBL) Flapping Mechanism Parts Component Name Isometric No. 6 9 mm 3rd Rod

No. 7 16 mm wide base

No. 8 3 mm large gear

No. 9 20 mm 2nd Rod

No. 10 7 mm 3rd Rod

ICON Look Ahead

Lookup

Right View

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FIGURE 4.14  The EPS fuselage of the MAV: (a) 3D fuselage, (b) the exterior partition.

The EPS foam-forming machine is shown in Figure 4.15(a), and the fabricated shell fuselage is shown in Figure 4.15(b), which weighs 1.27 gf. The male and female EPS case molds of fuselage shells are shown in Figure 4.16. The exploded view of FWMAV Golden-Snitch Pro with a wingspan of 20 cm is shown in Figure 4.17. Within the limited EPS fuselage space, the FBL flapping mechanism (No. 3), the wireless receiver chip (No. 4), lithium battery (No. 5), vertical tail (No. 6), and horizontal tail (No. 7), PET/parylene wing (No.  8) and the leading edge carbon fiber rod (No. 9) are mounted inside FWMAV shell. Also, vertical tail (No. 6) and horizontal tail (No, 7 are also made from EPS. Their mass production with two sets of knife molds of mold processing is shown in Figure 4.18. The tail parts are punched by the knife molds directly, as shown in Figure 4.19.

FIGURE 4.15  (a) EPS foam-forming machine, (b) the finished parts weighing 1.27 gf.

Fabrication of Flapping Wing Micro Air Vehicles

FIGURE 4.16  EPS case mold: (a) male mold, (b) female mold.

FIGURE 4.17  Exploded view of 20 cm-wide MAV Golden-Snitch Pro.

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FIGURE 4.18  (a) Horizontal tail knife mold, (b) vertical tail knife mold.

4.2.3  PIM of Evans Flapping Mechanism The prototyping of the FBL flapping mechanism discussed in Section 4.1.1 made through EDWC is a planar cutting wherein the workpiece thickness is maintained as uniform. Hence, the width of the component is adjusted to meet the mechanical strength requirement of different parts. Take the example of the base shown in Figure 4.20(a) where the workpiece contour is simple for EDWC, but the hole sleeves (red circle) of the 3rd bar are extruded and thickened in order to allow the other

FIGURE 4.19  Horizontal tail (left column) and vertical tail wing (right column) molding process: (a) place the blank EPS (pearl) plate on the bottom pad, (b) cover with cap and punch, (c) detach the finished tail parts from the mold.

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FIGURE 4.20  Base of the FBL mechanisms by: (a) EDWC, (b) PIM.

parts to overlap smoothly. In the case of PIM molds as shown in Figure 4.20(b), the extruded hole-sleeves are integrated into the mold design, and without overlapping fully functional flapping mechanism is made [34]. There are up to 8 linkages in the Evans mechanism. The overlapping of linkages is more serious than the case of the FBL mechanism. Therefore, the EDWC base in Figure 4.21(a) is unable to meet the need of the mechanism operation, and it is necessary to use the stacking of C-shaped spacers with different heights as the whole sleeve. In contrast, the PIM base is shown in Figure 4.21(b) has integrated the 3D hole sleeves in the mold design, which fully meets the actual need of the Evans mechanism and convenient to the final assembly. The connecting position between the wing rod and the base, as shown in Figure 4.22(a), needs to be strengthened because of its overhanging structure, and simulation results suggested 0.52 mm deformation. In this regard, a supporter is added as depicted in Figure 4.22(b), where the maximum deformation is reduced to 0.36 mm. Another region that needs to be strengthened in the Evans mechanism base is the crank part shown in Figure 4.23(a), and maximum deflection through simulation is found to be 1.548 mm. After adding a supporter, as shown in Figure 4.23(b), the maximum deflection is reduced to 0.519 mm.

FIGURE 4.21  Base of Evans mechanisms by: (a) EDWC, (b) PIM.

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FIGURE 4.22  Strengthening the connection position of the wing rod: (a) before, (b) after.

The wing rod is the most vulnerable part because it has to bear the load generated by the flapping wing, and it must be much stronger than other parts. The Evans mechanism and FBL mechanism use the same membrane wing of 20 cm span (with wing area 123.4 cm2). However, their flapping frequencies are different. FBL mechanism can generate 15 Hz flapping with a stroke angle of 53°, and Evans mechanism generates 18 Hz flapping with a stroke angle of 80°. Therefore, considering the strengthening of the Evans mechanism’s wing rods, it should be based on the FBL mechanism of Figure 4.24 and to be stout and thick enough. The final design of the wing rod is modified, which is shown in Figure 4.25. The other parts of the Evans mechanism are shown in Figure 4.26 [4,35,36]. As mentioned at the beginning of this section, the motion among the linkages rods is overlapped. It increases the friction between two-rod surfaces during the mechanism’s operation, as shown in Figure 4.27(a). Therefore, the shaft hole position

FIGURE 4.23  Strengthening the shaft hole of crank part: (a) before, (b) after.

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FIGURE 4.24  Wing rod of Golden-Snitch.

FIGURE 4.25  Wing rod of Evans mechanism.

FIGURE 4.26  Evans mechanism parts.

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FIGURE 4.27  (a) Overlapping of shaft hole rod and output rod, (b) separation gap.

is thickened by 0.05 mm, and the overlapping is avoided. Further, the 2nd rod is set apart from the 3rd rod with 0.4 mm spacing; as shown in Figure 4.27(b), surface contact is avoided. The development of mold for PIM is so expensive, and it is hoped to add possible configuration in the mold design of the flapping mechanism. One of which is to adjust the gear ratio: using a different gear ratio is equivalent to adjusting the beat wing frequency suitable for different flight attitudes. For example, hovering requires a very high flapping frequency, and the gear ratio should be small. Therefore, in the PIM base design with the pillar end of Figure 4.28(a) has five gear shaft holes are provided. Coupled with the three holes on the output rod in Figure 4.28(b), these five holes can generate four different gear ratios, such as 16, 20, 21.3, and 26.67, respectively. The gear ratio 16 corresponds to the red and yellow holes in Figure 4.28; the gear ratio 20 corresponds to red and green holes; the gear ratio 21.3 corresponds to orange and green holes; the gear ratio 26.67 corresponding to orange and blue holes. The parts configuration in the PIM mold for the Evans mechanism is shown in Figure 4.29, and its upper cover mold is shown in Figure 4.30. The manufactured Evans mechanism parts using PIM are shown in Figure 4.31.

FIGURE 4.28  For different gear ratios (a) 5 base holes, (b) 3 link holes.

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FIGURE 4.29  Parts configuration in the PIM mold for Evans mechanism.

FIGURE 4.30  Upper cover mold of Figure 4.32.

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FIGURE 4.31  Manufactured PIM parts of Evans mechanism.

FIGURE 4.32  Exploded view of the Evans mechanism assembly.

TABLE 4.7 Comparison of the Two Differently Processed Evans Mechanisms (Wing Flapping Stroke Angle Design Is 80°) (20 Cm Wingspan, 3.7 V Driving) Items Mass (g) Phase lag (design value = 0°) Max. flapping stroke angle Flapping frequency (Hz)

Aluminum Alloy by EDWC 2.44 0.48° 100.43° 18.86

POM by PIM 1.48 0.68° 82.32° 13.51

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FIGURE 4.33  (a) Comparison of different materials, (b) wing stroke angle.

Since the PIM of molded parts is already considered with 3D geometry, there is no need to use stacked spacers at the pin joints, and the assembly job becomes easier. The dismantling can be completed through the exploded view shown in Figure 4.32. The finished PIM/POM Evans mechanism after the assembly is compared with the original mechanism made of aluminum alloy 7075, as given in Table 4.7 and shown in Figure 4.33(a). The aluminum alloy mechanism weighs 2.44 g, and the POM mechanism weighs only 1.48 gf, reduced by 0.96 gf. The stroke angle of the mechanism without a wing is shown in Figure 4.33(b). The POM mechanism’s maximum travel angle is 82.32°, and its phase lag is 0.68°, which is 0.48° higher than the aluminum alloy mechanism. The maximum flapping frequency obtained POM mechanism is 13.51 Hz, which is lesser than the aluminum alloy mechanism of 18.86 Hz. Table 4.8 compares the consuming time of manufacturing the Evans mechanism by EDWC and PIM, respectively. Under the premise of the same assembly time for fuselage and tail, the PIM process time is only one minute, far better than the 45–50 minutes of EDWC. Besides, because there is no C-shaped spacer problem, the assembly time of PIM is only 1/3 of the EDWC. Hence, the overall manufacturing time of PIM is only 1/4 of EDWC. The shortening of the production time is much suitable for mass production. TABLE 4.8 Comparison of Consuming Time of Single MAV with Different Methods Different Ways of Fabrication Stephenson mechanism by EDWC Evans mechanism by EDWC Evans mechanism by POM-PIM

Manufacturing (min) 50

Assembly (min) 35

Body/Tail Assembly Total Fabrication (min) Time (min) 10 95

45

30

10

85

1

10

10

21

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4.3  ADDITIVE MANUFACTURING (3D PRINTING) The previous section discussed the Golden-Snitch FBL mechanism and the Evans mechanism, respectively, using EDWC and PIM for manufacturing. These two methods involve the preprocessing of EDWC, the design challenge of the PIM mold, and the processing and assembly time-evaluation. Therefore for fabricating the tiny components of the FWMAVs, developing a precise mold is cumbersome and timeconsuming. To overcome these difficulties, this section uses additive manufacturing (AM) or 3D printing to prototype the flapping mechanism in an attempt to reduce development cost and time. AM originated from rapid prototyping (RP) is considered one of the most concise and efficient processes of the next generation manufacture because it does not require complicated clamps, molds, and other assembly tools. Since the additive material is non-homogeneous and anisotropic, the product of the 3D printing often has the problem of insufficient bonding strength at the microstructure interface between two accumulation layers [37–40]. It results in the bulky material block becoming more brittle, lacking flexibility, and cannot withstand heavy loads. Regarding the tiny parts of the flapping mechanism discussed in this chapter, if the spatial resolution of the 3D printer is not good enough (with too large line-width), the printed components may all be rendered useless. To solve the problem of insufficient mechanical strength using 3D printing to fabricate the flapping mechanism, properly enlarging the Evans mechanism’s component dimension in Figure 4.34 seems to be a faster and effective way. As shown in Table 4.9, under the premise of no change about all of the linkage length, shaft hole position, the original mechanism’s straight-line motion, large stroke angle, and no linkage interference, we appropriately thicken the base support pillar, the related linkage rods, and the ring diameters of the shaft holes (from 1.9–2.2 mm to 2.4–2.8 mm).

4.3.1 Fused Deposition Modeling (FDM) After completing the dimension thickening, a 3D printing attempt using a commercial machine Inventure (Zortrax), which has a print volume of 135 mm × 135 mm × 130 mm, is made. This model has a dual-nozzle print-head for printing the support

FIGURE 4.34  (a) 3D printed mechanism components (PLA material), (b) improved Evans mechanism after assembly.

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TABLE 4.9 Modified Evans Flapping Mechanism Parts by 3D Printing Component Name Base

2nd rod

Controller rod

Wing rod connector

3rd rod Medium rod Short rod

PIM Component Size

Improve the Size of the Design

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layer Polyvinyl alcohol (PVA) and the structural layer Polylactic acid (PLA) simultaneously. Once printed, the part must be soaked in water with an ultrasonic shaking to dissolve the support layer PVA and leave the PLA’s structural layer. General-purpose 3D printers with a single-nozzle head process a single type of printing material only. For fabricating free-standing structures, few narrow pillars under the product structure are assigned and printed as the support and need to be removed manually after the 3D printing process. Small spikes are left with the part due to improper pillar removal. Sometimes, suspended structures may collapse because of insufficient pillar support. However, with a dual-nozzle printer, the complete supporting block or spacer block instead of the pillars can be printed with fewer issues of insufficient supporting. After the removal of the supporting block, the part surface is also relatively smooth without residual spikes. The entire dual-nozzle 3D printer’s processing concept is similar to the sacrificial layer of surface micromachining in MEMS. At present, a dual-nozzle printer is not popular because of the shortcomings in practice, like the dual-nozzle regime is more prone to being jammed or choked with PVA or PLA. PVA support layer wire is easy to absorb water moisture in the air and gets deterioration. The computer-aided design (CAD) model for the Evans mechanism components given in Table 4.9 is converted to a standard STL format and input to the Z-suite 2.3 software (Zortrax) where the 3D model is sliced into layers with a layer thickness of 400 μm. The bottom of the print area is maintained at 75 °C for uniform curing, while the structural PLA is melted at 180°C and printed out through the nozzle in a toothpaste-squeezing manner with 400 μm in diameter. A typical 3D printer can adjust its printing density (porosity) to avoid using excessive printing material and consuming time. However, the parts in Table 4.9 are pretty small and require high strength and hence the print density can be close to 100% without any pore inside. The layer-to-layer adhesion of 3D printing must be sound enough to ensure the part strength for withstanding the periodic load. The sharp edge design is neither necessary nor printed here, as the tolerance can reach 100 μm for complex exterior processing. Figure 4.34 shows the tiny parts of the 3D-printed modified Evans flapping mechanism. Even with the assistance of support materials, there is still a great need to remove those after printing [41–43].

4.3.2  Parylene Coating as a Solid Lubricant Previously, no lubricant has been used in all the flapping mechanism joints, and hence friction loss is hard to evaluate. Another reason to reduce friction loss is that excessive friction may cause local heating in the joint’s bearing area. The PLA, as mentioned earlier material, is hard but not temperature-resistant. When the operating temperature exceeds 70°C, PLA begins to soften. A new method of using parylene conformal coating to fill in the joint gap of the flapping mechanism is shown in Figures 4.35(a)–(c). Parylene can be regarded as a solid lubricant, similar to graphite, to reduce wear and friction. This process is maskless, and no need for patterning. Figure 4.35(d) shows the PLA flapping mechanism after the parylene coating. As mentioned in Section 2.4, parylene is a room-temperature vacuum coating. Parylene has a fairly good solid mobility on the workpiece’s outer surface during polymerization is not only a pinhole-free growth [44]. However, it also deeply grows into the μm-scaled gap at the flapping mechanism’s inner joint portion.

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FIGURE 4.35  (a) Schematic diagram of rod shaft connection, (b) stereoscopic diagram, (c) parylene coating on the surface including inner gaps, (d) assembly of PLA flapping mechanism after parylene coating.

Parylene’s surface friction coefficient is as low as 0.25 to 0.30 [45,46]. Moreover, it is believed to decrease the friction loss of the flapping mechanism during operation. About 5 µm thickness of the parylene is coated to the Evans mechanism, and the whole processing time is about 6 hours. After coating, to understand the friction loss changes, it is necessary to run the Evans mechanism by applying different driving voltages and monitoring the flapping frequency. Figure 4.36(a) is the case of voltage increasing and depicts that the parylene coating case’s frequency is found 5–10% more than the case without coating. The increasing and decreasing voltage conditions and corresponding flapping frequency measurement as measured revolution per minute (rpm) are shown in Figure 4.36(a) and (b). From Figure 4.36, by comparing the RPM hysteresis, we understand the minor effect of friction loss. Because of the resistance starting and stopping the mechanism, there is a so-called cut-in voltage and cut-off voltage. Figure 4.36(a) shows the cut-in voltage as 1.5 V, and its cut-in RPM is 310 and 284 with and without parylene, respectively. The RPM increases with the voltage until 3.7 V, corresponding to RPM of 569 and 540, respectively. In Figure 4.36(b), the voltage is reversely dropped back

FIGURE 4.36  The flapping frequency (RPM; Vertical axis) of the flapping mechanism with or without parylene coating vs. the driving voltage (v; Horizontal axis): (a) voltage increasing condition (b) voltage decreasing condition.

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to the cut-off voltage of 1.5 V corresponding to its cut-off RPM of 317 and 292 with and without parylene. Cut-off RPM is slightly bigger than the cut-in RPM, and the RPM difference can be quantified as hysteresis here. Using the parylene as the solid lubricant can increase 10% RPM by maximum about the flapping frequency; but at the same time, the incremental RPM percentage of 2.7% drops to 2.2% due to hysteresis. The parylene coating part is a post-process after the 3D printing and assembly, and it is compatible with all kinds of 3D printers.

4.3.3 Multijet Printing The Multijet printing (MJP) with a model of ProJET-2500-Plus uses a piezo print head to print photocurable resin, while the support material is low-density polypropylene is used. The build volume is 294 mm × 211 mm × 144 mm, nozzle diameter is 0.4 mm, with a thickness of 32 μm per layer and an accuracy of about 0.025 to 0.05  mm. The printing substrate temperature is maintained at 24°C and the printing material is warmed at 65°C. This technique is more similar to thermo-bubble inkjet printing with a sharp printing angle and clear hole-size. The fidelity is high, and the surface is smooth. The parts of the aforementioned modified Evans flapping mechanism are fabricated, shown in Figure 4.37(a), and assembled using an injection needle as discussed in the previous section shown in Figure 4.37(b). The processing resolution is good enough to print the gear parts directly, and the shaft-hole machining is also fine [47].

4.3.4  Polyjet Printing The printing technology of Polyjet-Eden-260 VS is to print photopolymer resin by an inkjet method and then irradiate ultraviolet (UV) for curing [48,49]. It can print transparent acrylic (polymethyl methacrylate; PMMA) as the structural material. The ­single-layer print thickness is 17 μm, and the build volume of 355 mm × 305 mm × 305 mm. The spatial resolution along the X-axis and Y-axis direction is 600 dpi,

FIGURE 4.37  ProJET-2500-Plus using Visijet M2G-DUR3D: (a) mechanism parts, (b) Evans mechanism assembly.

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FIGURE 4.38  Polyjet-Eden-260 VS printing (PMMA material): (a) mechanism parts, (b) Evans mechanism assembly.

while along the Z-axis direction is 1600 dpi. Figure 4.38(a) shows the Evans mechanism’s printed parts, and the assembled mechanism is shown in Figure 4.38(b).

4.3.5 Stereolithography Stereolithography (SLA) is the earliest rapid prototyping (RP) [49], and Project 6000  HD model having a build volume of 250 mm × 250 mm × 264 mm with a ­single-layer thickness of 100 µm and an accuracy of 0.025–0.05 mm is considered. The photo-polymerized resin is used as a structural material, and polypropylene is used as the support material. The grid parameters for printing the linkage parts are as follows: penetration length 0.6 mm; contact width 0.5 mm; and base height 0.5  mm. The mechanism parts printed by Visijet-SL-Flex via SLA material are shown in Figure 4.39(a), and Evans mechanism assembly is shown in Figure 4.39(b).

FIGURE 4.39  Visijet-SL-Flex printing: (a) mechanism parts, (b) Evans mechanism assembly.

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4.4 PERFORMANCE COMPARISON OF FLAPPING MECHANISMS BY DIFFERENT MANUFACTURES 4.4.1 Torque of Evans Mechanism by PIM Section 3.5.4 compared the flapping frequency of Evans mechanism with or without flapping wing and discussed gear ratio effect. This section supplements the practical information of the POM mechanism (by PIM) and compares it with the aluminumalloy Stephenson mechanism (by EDWC). The torque is measured from electrical power consumption during flapping. The Evans mechanism has different gear ratios of 16, 20, 21.3, and 26.67, respectively. The torque required for various gear ratio is almost equal for an increase in flapping frequency, as observed in Figure 4.40(a). For the below 19 Hz case, the gear ratio of 26.67 requires the lowest torque and increases positively with the flapping frequency. The highest torque for all the frequencies occurs in the gear ratio of 21.3. For the gear ratios, 21.3 (highest torque) and 26.67 (lowest torque) comparison is made between Stephenson and Evans mechanism as shown in Figure 4.40(b). The Evans POM mechanism is tightly assembled, and hence the required torque is higher than that of the aluminum-alloy-based Stephenson mechanism. However, the required torque with flapping load is at least one order-of-magnitude higher than the load-free case. The effect of gear ratio on torque requirement for the POM-based Evans mechanism with flapping wing exhibits similar characteristics, which is positively correlated with the flapping frequency observed in Figure 4.41(a). When the driving voltage is below 3.7 V and gear ratio 26.67, the highest flapping frequency of 19 HZ is achieved, and the required torque is lower than other gear ratios. The gear ratio 26.67 demands the lowest torque and the gear ratio 21.3 necessitates higher torque for both Evans and Stephenson mechanisms, as seen in Figure 4.41(b). However, the torque requirement for the POM-based Evans mechanism is smaller than that of the aluminum-alloy-based Stephenson mechanism. Hence, the Evans mechanism consumes less power and low friction loss, which causes an increase in flapping frequency [4]. The performance of the Stephenson and Evans mechanism is compared and given in Table 4.10. It is observed that the Evans mechanism with higher stroke angle and flapping frequency consumes 47.5% of the power consumed by the Stephenson mechanism.

FIGURE 4.40  The torque requirement without wing for (a) the Evans mechanism with different gear ratios, (b) comparing Stephenson and Evans mechanisms.

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FIGURE 4.41  The torque requirement with wing for (a) the Evans mechanism with different gear ratios, (b) comparing Stephenson and Evans mechanisms.

4.4.2  3D printing Evans Mechanism’s Performance Evaluation The measurement of lift and net thrust of 3D printed mechanisms is carried out using the wind tunnel test facility available at Vel Tech Institute, Chennai, India, which is shown in Figure 4.42. It is a low-speed subsonic wind tunnel with a crosssectional test area of 600 mm × 600 mm and a length of 2000 mm, a contraction ratio of 1: 3, and a maximum airspeed is 50 m/sec. As mentioned in Section 2.1, the blockage ratio of MAV installed in the wind tunnel must be less than 7.5%. The blockage ratio is calculated for the increase of inclined angle, and it shows an increasing trend, as observed in Figure 4.43. The MAV size is very small, and the cross-sectional area of the wind tunnel is 4 times compared to the earlier used wind tunnel shown in Figure 2.2. For various inclined angles, the blockage ratio is determined and within the maximum limit, and the internal effects of air will not affect the force measurement. A test rig to measure the lift and thrust force of FWMAV is custom made, which is shown in Figure 4.44 (a). The developed test rig can be easily mounted onto the wind tunnel facility available at Vel Tech University. However, the airfoil sections with solid bar attachment connected with load cell arrangement can also be utilized in other wind tunnel facilities provided a proper mounting arrangement to fix the test bench without air disturbance should be readily available. Micro aerial flapping vehicles of any wingspan configurations can be mounted onto the test rig, and experiments can be performed. Since load cell attachments are beneath the test section of the wind tunnel, as shown in Figure 4.44(b), the effect of wind

TABLE 4.10 Performance of Stephenson and Evans Mechanism Measurement at 3.7 V Driving Voltage Flapping angle Flapping frequency Maximum total power consumption

Stephenson Mechanism 82–84° 14.3 Hz 14.02 W

Evans Mechanism 96–100° 18.9 Hz 6.66 W

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FIGURE 4.42  Low-speed subsonic wind tunnel.

disturbance is completely avoided. A six-axis force cell with the minimum force resolution of 0.01 gf is utilized to measure the aerodynamic forces. The data acquisition system is controlled by the LAB VIEW program that collects the force gauge signals, as shown in Figure 4.45. The built-in anemometer calibrates the wind speed [50–52].

FIGURE 4.43  Blockage ratios for various inclined angles.

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FIGURE 4.44  (a) Developed test rig, (b) test rig with MAV mounted in the wind tunnel.

Figure 4.46 shows the lift force generated by the flapping mechanism of different 3D-printing materials at different inclined angles (0–60°). Except for the irregular lift when the inclined angle 0° changes from a positive value to a negative value at high wind speed, the lift at cases of inclined angles is positively correlated with wind speed. The lift saturation at high wind speed may be due to the 3D printing materials’ mechanical strength for the flapping mechanism. It is observed that high tensile strength (Polyjet) material has more resistant to bend, and a minimal amount of lift is generated. However, Multijet material has more flexibility than the other two materials, and hence lift force is increased at higher inclined angle as observed in Figure 4.46 (a)–(f). After the inclined angle 60°,

FIGURE 4.45  Data acquisition below the wind tunnel.

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FIGURE 4.46  Lift force generated by the flapping mechanisms using different 3D printing materials vs. wind speed at inclined angles: (a) 0°, (b) 20°, (c) 30°, (d) 40°, (e) 50°, (f) 60°.

there is a decrease in the trend of lift force, and about 50°–60° inclined angles, the maximum amount of lift force is produced for low tensile strength materials. The maximum value of the lift data alone is not sufficient to represent the superiority of the flapping mechanism, as that maximum lift is not necessarily the operating point of the flapping wing. We still need to make a comprehensive judgment by checking the net thrust data at the same time. Figure 4.47 shows the net thrust generated by the flapping mechanism made of different 3D printing materials versus the wind speed at different inclined angles (0–60°). It is evident from Figure 4.47(a)–(f) that the maximum lift force of about 14 gf at inclined angle 60° and 2.8 m/s wind speed and thrust force of about 7 gf are developed at inclined angle 0° and 0.8 m/sec wind speed conditions. The net thrust (T-D) of inclined angle 0° is positive abnormally, and the net thrust at other inclined angles shows positive and negative. The net thrust for the high-strength Polyjet flapping mechanism’s acrylic material generates a larger net thrust at the inclined angle above 40°. The flexible MJP flapping mechanism generates less net thrust at an inclined angle above 40°. The net thrust data shown in Figure 4.47 reveals that highstrength material’s flapping mechanism helps improve the net thrust.

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FIGURE 4.47  Net thrust generated by the flapping mechanisms using different 3D printing materials vs. wind speed at inclined angles: (a) 0°, (b) 20°, (c) 30°, (d) 40°, (e) 50°, (f) 60°.

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TABLE 4.11 Performance Comparison of Flapping Mechanism of Different Traditional Materials and 3D Printed Materials Parameters Mass (g) Phase lag (design value = 0°) Flapping frequency (Hz)

Al-alloy 7075 by EDWC 2.44 4.53° 19

POM by PIM 1.48 2.05° 14

FDM 1.82 2.8° 21

Polyjet 1.80 1.04° 23

Multijet 1.86 5.22° 22

SLA 1.86 6.34° 20

Like the aerodynamic force study of the Golden-Snitch FBL mechanism and the Evans mechanism in Chapter 3, the net thrust data in Figure 4.47 can also be used to choose the cruising speed of FWMAV. Under cruising conditions, the net thrust is zero (T=D). This cruising speed and corresponding actual lift force shown in Figure 4.46 provides an idea of whether the lift force generated is exceeded the FWMAV weight or not. This observation for determining the operating cruising point combining lift and net thrust force will be discussed in detail for the flapping-wing design in Chapter 5. Table 4.11 shows the performance comparison of flapping mechanisms made using 3D-printing, POM/PIM, and EDWC in terms of weight, phase lag, and

FIGURE 4.48  Lift force for POM/PIM and 3D printed mechanism vs. air speed at different inclined angles: (a) 20°, (b) 30°, (c) 50°, (d) 60°.

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flapping frequency. It is evident that the weight of 3D printed mechanism assemblies marginally increased an average of 0.36 gf compared to the IM process. Due to the highly accurate 3D printing of mechanical components using Polyjet, its mechanism assembly obtained minimal phase lag in comparison with other methods. Also, the low tensile strength of polypropylene (Multijet) material leads to an increase in flapping frequency, and the higher tensile strength of PMMA (stereolithographic) has reduced the flapping frequency. However, the biggest challenge of 3D printing is the long processing time, and mass production is not possible. Besides, the lift and net thrust generated by the Evans mechanisms by injection molding (POM/PIM) and Fused Deposition Modeling (FDM)-based 3D printing using Polylactic Acid (PLA) material is compared, which is shown in Figures 4.48 and 4.49. In the lift shown in Figure 4.48, the mechanism made by the 3D printing mechanism (PLA/FDM) is far superior to the POM/PIM for all wind speeds at an inclined angle of 60°. However, even at the small inclined angle (with a high cruising speed), the lift of the 3D printing (PLA) mechanism also surpasses POM/PIM mechanism. So overall, the lift generated by the 3D printing (PLA) mechanism is better than the POM/PIM mechanism. Looking at the comparison of net thrust in Figure 4.49, it is obvious that the net thrust force is always positive, which means that the Evans flapping mechanism

FIGURE 4.49  Net thrust of POM/PIM and 3D printing mechanism vs. air speed at different inclined angles: (a) 20°; (b) 30°; (c) 50°; (d) 60°.

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produces a greater thrust, which is always greater than the drag. Furthermore, the net thrust generated by the 3D printing (PLA/FDM) mechanism is greater than generated by the POM/PIM mechanism. It should be related to applying the parylene solid lubricant and the increased flapping frequency about 5–10%.

4.5 SUMMARY This chapter dealt with various manufacturing methods such as EDWC, PIM, and 3D printing to fabricate micro mechanism parts of FWMAVs. The assembly of mechanism parts, estimation of flapping frequency, flapping angle, the total mass of mechanism assembly, endurance, and power consumption of Evans and Stephenson mechanisms are discussed. Aerodynamic force measurement of developed FWMAVs using a custom build test rig is performed and compared with all the three manufacturing techniques and various 3D printing materials. The 3D printed mechanism effectively increases the flapping frequency and lift. Especially the application of the parylene solid lubricant increased the flapping frequency by about 5–10%. Although it also increases the mass slightly (1.8 g of PLA mechanism >1.48g of POM mechanism), the overall performance is better than anticipated. If it can overcome the issues such as long processing time of 3D printing and mass production, it is recommended for precise manufacturing of tiny parts and minimize the friction loss, thereby increasing lift and thrust force.

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46. Shin, Y. S., Cho, K., Lim, S. H., Chung, S., Park, S. J., Chung, C. and Chang, J. K. (2003) PDMS-based micro PCR chip with parylene coating. Journal of Micromechanics and Microengineering, 13(5), 768. 47. Raddatz, L., de Vries, I., Austerjost, J., Lavrentieva, A., Geier, D., Becker, T. and Scheper, T. (2017) Additive manufactured customizable labware for biotechnological purposes. Engineering in Life Sciences, 17(8), 931–939. 48. Barclift, M. W. and Williams, C. B. (2012, August) Examining variability in the mechanical properties of parts manufactured via polyjet direct 3D printing. International Solid Freeform Fabrication Symposium (pp. 6–8). University of Texas at Austin, Texas. 49. Kechagias, J. P. A. I., Stavropoulos, P., Koutsomichalis, A., Ntintakis, I. and Vaxevanidis, N. (2014) Dimensional accuracy optimization of prototypes produced by PolyJet direct 3D printing technology. Advances in Engineering Mechanics and Materials, 61–65. 50. Yang, L. J., Kao, A. F. and Hsu, C. K. (2012) Wing stiffness on light flapping micro aerial vehicles. Journal of Aircraft, 49(2), 423–431. 51. Balasubramanian, E., Sasitharan, A., Chandrasekhar, U., Karthik, K. and Yang, L. J. (2018) Low-cost test rig for aerodynamic evaluation of ornithopters. Journal of Applied Science and Engineering, 21(2), 179–186. 52. Yang, L. J., Kapri, N., Waikhom, R. and Unnam, N. K. (2021) Fabrication, aerodynamic measurement and performance evaluation of corrugated flapping wings. Journal of Aeronautics, Astronautics and Aviation, 53(1), 83–94.

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5.1  STRENGTHENING OF LEADING-EDGE IN FLAPPING WINGS The single-wing of 20 cm-span having an area of 11,404 mm2 and an aspect ratio of 3.51 shown in Figure 5.1 is attached to the FBL flapping mechanism has attained a stroke angle of 52.8° [1]. In this type of wing, the leading edge and wing rib spars are attached to strengthen the flapping wing, as shown in Figure 5.2. They are made of carbon fibers having 0.6 mm and 0.5 mm-diameter, respectively, and the wing membrane material is assigned as Polyethylene (PE) or parylene.

5.1.1 Aerodynamic Enhancement of the LeadingEdge Tape on Flapping Wings The wing leading edge reinforcement tape is embedded into the flapping wing, as shown in Figure 5.3. To increase the wing camber; thereby, the lift is increased. Table 5.1 provides various configurations of wing tape attached to the flapping wings and its estimated mass. The wind-tunnel experiments are conducted for the various configurations (S1– S6) of flapping wings with an inclined angle of 20° and various wind speeds. The flapping frequency is varied by changing the input voltage levels, and the results are shown in Figure 5.4(a)–(f). The following are the major observations with respect to enhancement of lift: 1. Lift force increases with the increase of wind speed and flapping frequency. It is because the drag is minimal, and high flapping motion yielded more amount of lift. 2. The lift of S1 (without leading-edge tape) gradually increases with wind speed, and a maximum lift of 3.77 gf is generated. After attaching the leading-edge tape, the lifts for the wings S2–S6 significantly increase at higher wind speeds, and it exceeded above 5.0 gf. The attachment of reinforcing tape at the wing leading-edge has a positive effect on increasing the lift. To understand the lift performance better, the dimensionless lift coefficient and advance ratio J are calculated for the various wing designs, and they are depicted in Figure 5.5. It is observed that when J < 0.6 (unsteady flapping), the lift coefficients for the reinforced wings S3 and S2 are still higher. However, the lightest wing S1 (without leading-edge tape) has attained better performance when J < 0.4. As far as the reinforced wings S4 and S6 are concerned, when J < 0.6, the lift coefficient has a decreasing trend because of more weight (for S4) and improper tape location (for S6). Besides, when J > 1.0 (the quasi-steady state with less obvious flapping), the lift coefficients of S2, S3, and S5 are very close and have achieved a similar trend. DOI: 10.1201/9780429280436-5

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FIGURE 5.1  Single-wing design.

FIGURE 5.2  Single-wing with spars.

FIGURE 5.3  Wing leading-edge reinforcement tape.

TABLE 5.1 Leading-Edge Tape and Design Parameter for PE Wings of 17 μm Thick ID S1

Tape Width 0

Tape Shape

Wing Mass (gram) 0.226

S2

0.5 cm

0.297

S3

1.0 cm

0.330

S4

1.5 cm

0.376

S5

0.5-1.5 cm

0.335

S6

1.5-0.5 cm

0.335

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FIGURE 5.4  Lift performance for various wing configurations (S1–S6).

Similarly, the net thrust force is measured, and the following are the major observations from the Figure 5.6: 1. Net thrust force increases with the increase in flapping frequency. However, the increase in wind speed causes more induced drag, and the net thrust decreases.

FIGURE 5.5  Effect of advance ratio for various wing configurations (S1–S6) in lift.

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FIGURE 5.6  Thrust performance for various wing configurations (S1–S6).

2. At the wind speed of 0 m/s, S5 achieved the maximum net thrust of 3.38 gf. 3. The red dots marked in Figure 5.6 denotes the maximum flying speed that can be reached for the driving voltage of 3.7 V. Among them, S5 reaches the maximum flying speed of 2.81 m/s. At this cruising speed, the net thrust is zero (thrust is equal to drag.) The cruising flight is similar to the speed at which no acceleration and deceleration take place. Similarly, the dimensionless parameters such as net thrust coefficient and advance ratio are calculated, and their relationship is shown in Figure 5.7. The net thrust coefficients for S1–S6 have a similar trend, and S5 has achieved the highest cruising speed (lift 5.6 gf), followed by S3 and S2.

5.1.2 Effect of Leading-Edge Tape on Power Consumption The flapping wing’s required power depends on overcoming the motor torque, wear against the gears and linkages, and inertial effects of flapping wings. The voltage and current are measured during the flapping motion of various wing configurations, and corresponding power is calculated for different wind speed conditions, shown in Figure 5.8. For S1–S6, at the wind speed is 0 m/s, the maximum power corresponding to 3.7 V is 0.5 W. It conforms to the safety specification of DiDEL MK07-3.3 motor of maximum power, which is less than 0.8 W. However, as the wind speed

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FIGURE 5.7  Effect of advance ratio for various wing configurations (S1–S6) in thrust.

increases, the maximum power starts to decrease. At a wind speed of 3 m/s, the maximum power of S5 drops to 0.41 W. The required power of various wing membranes also positively correlates with the wing mass (refer to Table 5.1.) Since the driving voltage is positively related to the flapping frequency, the power consumption is estimated by varying the flapping frequency, shown in Figure 5.9. It is obvious that an increase in power consumption as the flapping frequency increases. The power consumption and lift force are compared, shown in Figure 5.10. It is evident that, during the lower speed of 0, 1, and 2 m/s, the lift force of S2 and S3 are higher than that of other designs. Similarly, the net thrust force and power consumption are compared, which is shown in Figure 5.11. At the wind speed of 0 m/s, the S1–S6 wings achieved similar performance characteristics. As the wind speed increases, the net thrust force for the

FIGURE 5.8  Power requirement for various wing configurations (S1–S6).

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FIGURE 5.9  Power consumption for various wing configurations (S1–S6).

S1–S6 wings decreases due to the continuous increase of air drag. However, S5 has achieved less power consumption in comparison to other wing configurations. Based on the aforementioned wind tunnel data presented for S1–S6 wing configurations, it is observed that S2 and S3 obtained higher lift force and S5 generated more net thrust force. However, S5 requires higher power at low speed and low power at a high wind speed of 3 m/s. The following are the observations for the case of leading-edge tape reinforcement to increase the lift and thrust characteristics of FWMAVs: (1) If the lifting phenomenon is desired, then the width of the tape can be selected either as 0.5 cm (S2) and 1.0 cm (S3). (2) If the thrust generation is more concerned, the wing membrane is strengthened by varying the leading-edge tape width from 0.5 to 1.5 cm (S5).

FIGURE 5.10  Lift trend for various wings (S1–S6) with respect to power.

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FIGURE 5.11  Net thrust trend for various wings (S1–S6) with respect to power.

5.2  CARBON-FIBER RIB EFFECT ON THE FLAPPING WINGS Adding the strengthened ribs to the flapping wing (or rib reinforcement) is believed beneficial to the lift generation if the wing membrane thickness is not very apparent. The various diameters of carbon-fiber ribs and their angle of positioning the rod considered are given in Table 5.2. They are attached to the flapping wings, and the corresponding wind tunnel experiments are conducted. The following observations are made from Figure 5.12 with MAV span of 20 cm and the aspect ratio of 3.51: 1. Lift force increases with the increase of wind speed, and beyond 2.5 m/s, it tends to decrease because of a higher amount of drag. TABLE 5.2 Carbon Fiber Ribs and an Estimated Mass of the Wings Carbon Fiber Diameter and Angle ϕ0.3 mm, 30°

ID S7

Tape Width 0.7 cm

Wing Configure

Weight (gram) 0.360

S8

0.7 cm

ϕ0.5 mm, 30°

0.392

S9

0.7 cm

ϕ0.3 mm, 20°

0.364

S10

0.7 cm

ϕ0.3 mm, 40°

0.366

S11

0.5-1.5 cm

ϕ0.3 mm, 30°

0.394

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FIGURE 5.12  Lift performance for various wings (S7–S11) with carbon fiber rod attachments.

2. As the flapping frequency increases, the lift force also increases significantly. 3. Since the S8 wing rib is thicker and heavier than the S7, the flapping frequency drops, and correspondingly lift force is decreased. 4. S9 wing rib is closer to the leading edge, and due to the large wing area from the wing rib to the trailing edge, the lift force is decreased. The larger wing membrane is too weak to support. 5. S10 wing rib is closer to the trailing edge, and it attains the highest flapping frequency. S11 wing has generated maximum lift force in comparison to other wings (S7–S10). The dimensionless lift coefficient shown in Figure 5.13 depicts that, when J is between 0.4 and 0.8, S11 and S7 have experienced better aerodynamic performance. Similarly, the net thrust force for S7–S11 wing configurations is determined and shown in Figure 5.14(a)–(e). The following are the major observations: 1. Net thrust force increases with the increase in flapping frequency and decreases as the wind speed gradually increases due to the predominant drag effect. 2. At zero wind speed conditions, S11 has attained a maximum net thrust of 4.01 gf to have the greatest acceleration for takeoff.

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FIGURE 5.13  Effect of advance ratio for various wings (S7–S11) in lift.

3. The red dots marked in Figure 5.14 represent zero net thrust conditions at the driving voltage of 3.7 V, and their maximum cruising speeds are 2.85, 2.60, 2.85, 2.75, and 2.94 m/s, respectively, for S7–S11 wings. 4. The maximum lift force of 5.6 gf is experienced by S11 at 2.94 m/s wind speed.

FIGURE 5.14  Net thrust performance for various wings (S7–S11) with carbon fiber rod attachments.

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FIGURE 5.15  Effect of advance ratio for various wings (S7–S11) in net thrust.

Similarly, the thrust coefficient has a predominant effect for J < 0.2 for the S7 to S11 wing configurations, as observed in Figure 5.15. The influence of rib diameter and orientation on power consumption is shown in Figure 5.16. At the zero-wind speed, the maximum power required for S7–S11 wings has not exceeded 0.68 W. As the wind speed increases and power consumption decreases. The S8 and S11 wings necessitate lower power of 0.5 W and 0.43 W at the wind speed of 3 m/s. In general, the power consumption increases with the wing mass. Similarly, for the maximum flapping frequency of 16 Hz at 3 m/s, the power consumption is estimated as 0.43W as depicted in Figure 5.17(a)–(e). The S11 wing achieved a maximum lift of 5.6 gf at 3 m/s compared to others, and the power consumption is estimated as 0.5W, as observed from Figure 5.18.

FIGURE 5.16  Power consumption for various wing configurations S7–S11.

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FIGURE 5.17  Power consumption for various wings (S7–S11) with respect to flapping frequencies. 183

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FIGURE 5.18  Lift trend for various wings (S7–S11) with respect to power.

Similarly, the net thrust force decreases during the increase of wind speed, and correspondingly the power requirement is minimal. The S11 apparently requires a low amount of power to generate high net thrust force, as seen from Figure 5.19(a)–(e).

5.3 EFFECT OF MATERIALS AND STIFFNESS ON THE FLAPPING WINGS The membrane stiffness has a tremendous contribution to enhance the lift force of FWMAVs. As per the earlier observations, S11 wing configurations have achieved superior aerodynamic performance compared to other wing configurations, further considering adopting various wing membrane materials and thicknesses to improve the lift.

FIGURE 5.19  Net thrust trend for various wings (S7–S11) with respect to power.

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TABLE 5.3 Wing Membranes ID Material Wing mass (g) Thickness (μm) Young’s Modulus (GPa)

F1 (S11) PE 0.394 17 1

F2 Tissue 0.581 -

F3 PET 0.564 24 2.95

F4 Parylene 0.575 26 2.41

F5 Parylene 0.730 35 2.41

F6 Parylene 0.837 43 2.41

The S11 wing configuration has the leading-edge spar’s diameters, and wing ribs are 0.6 mm and 0.3 mm, respectively. The rib is placed with a 30° angle to the leading edge, and trapezoidal tape width is maintained as 0.5–1.5cm along the leading edge. Various materials for the wing membranes considered are given in Table 5.3.

5.3.1 Aerodynamic Performance of Various Wing Membranes Wind tunnel experiments are performed by varying the wind speed conditions and flapping frequencies for all the wing membranes attached to the Golden-Snitch FWMAV. The following are the major observations from Figure 5.20: 1. Lift force increases with the increase of wind speed and flapping frequency 2. F6 generated more lift force due to its high stiffness, and a lower lift force is obtained from F1. This phenomenon is similar to Ho’s lift comparison between soft Mylar and high stiffness wings [2] 3. Comparing F4–F6, a higher thickness parylene membrane generated more amount of lift. With reference to the dimensionless parameter, the lift coefficient for F6 is significantly higher than other wings, as shown in Figure 5.21. However, the lift coefficients for F2 to F5 have almost achieved a similar trend. Similarly, the net thrust force is determined for various wing membranes, which is shown in Figure 5.22, and the following are the major observations: 1. Net thrust force increases with the increase in flapping frequency and decreases as the wind speed increases due to larger drag. 2. At zero wind speed, F5 has generated a maximum net thrust of 4.93 gf. 3. The red dots marked in Figure 5.22 denotes the maximum flight speed that can be reached at the given maximum voltage of 3.7 V. Among them, F5 attained the maximum flight speed of 3.41 m/s with a lift of 9.5 gf. As observed from Figure 5.23(a) that, the net thrust coefficient of all the wing membranes have a similar tendency. The quasi-steady net thrust behavior of Figure 5.23(a) is magnified and shown in Figure 5.23(b). It is evident that for the same value of J, F5 outperforms other wing membranes.

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FIGURE 5.20  Lift performance for wing membranes (F1–F6).

FIGURE 5.21  Effect of advance ratio for various wing membranes (F1–F6) in lift.

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FIGURE 5.22  Net thrust force performance for various wing membranes (F1–F6).

The results of Figures 5.20–5.23 show that the thicker parylene wing membrane produces more lift force but increases the wing mass, which in turn causes a reduction in the flapping frequency. The net thrust and the maximum cruising speed are also lowered.

5.3.2  Power Consumption in Various Wing Membranes At zero wind speed, the power requirements for F6 (max), F3 (medium) and F1 (min) observed in Figure 5.24 (a)–(d) are 0.85 W, 0.72 W, and 0.53 W, respectively. As wind speed increases, the required power decreases. At a wind speed of 3 m/s, the maximum power requirements for F6 (max), F3 (medium) and F1 (min) drops to 0.69 W, 0.54 W, and 0.43 W, respectively. Experimental results show that the power consumption is positively correlated with wing mass under the same driving voltage. At the same power, the F1 attained the highest flapping frequency because of less mass. However, since F6 is the heaviest and required larger power to actuate, as observed from Figure 5.25. Besides, even though F2 is heavier than F3 and F4, it has got a higher flapping frequency. The porous fiber material, which is much softer than PET and parylene, can reduce the motor loading.

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FIGURE 5.23  Effect of advance ratio for wing membranes (F1–F6) in net thrust.

It is also observed from Figure 5.26 that lift force increases significantly with the increase of the wind speed, and the required power decreases with an increasing wind speed. Under the same power, the lift force for F6 is higher than other wing membranes. For the same power consumption, the high stiffness membrane S6 produces a lower net thrust, which in contrast to F1 that produces a higher net thrust as observed in Figure 5.27. However, the wing mass of F2, F3, and F4 are comparable to one another, and their net thrust at various wind speeds are also attained a similar trend. Based on the wind tunnel test results of F1–F6 wing membranes, F6 is experienced a higher amount of lift force, and F5 generated more amount of net thrust force. The performance of F2, F3, and F4 are moderate. Also, F5 and F6 demand larger power up to 0.7–0.8W, for which a lithium battery with higher power capacity is needed. It is summarized that by selecting F2–F4 with moderate aerodynamic

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FIGURE 5.24  Power consumption for various wing membranes (F1–F6). 189

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FIGURE 5.25  Power consumption for various wing membranes (F1–F6) with respect to flapping frequencies.

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FIGURE 5.26  Power consumption for various wing membranes (F1–F6) in lift.

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FIGURE 5.27  Power consumption for various wing membranes (F1–F6) in thrust.

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performance but necessitating lower power consumption, about 0.5 W seems to be a better choice. Regarding the material characteristics and fabrication aspects, the paper tissue material of the F2 wing is not water-endurable for a long-term operation, and the F4 wing requires a time-consuming parylene coating process. Hence, F3 (24 μm thick PET) is selected as the final wing configuration for the Golden-Snitch FWMAV. F3 wing generated lift of 9 gf under the flapping frequency of 15 Hz and consumed power of 0.54 W. PET film with thickness specification is a standard roll-to-roll film material which is easy to purchase, and the cutting process for the wing geometry is also simple and fast.

5.4  BIONIC FLAPPING WINGS WITH CHECK VALVES Flapping flight is known for its trending research topic in aerospace, involving all basic bionics and biological sciences, iterative learning control under distributed disturbances [3,4]. Compared with multicopter and fixed-wing airplanes, the function of FWMAV has good maneuverability and low energy consumption [5,6]. Due to the surveillance and reconnaissance applications, many FWMAVs have been developed [7–12]. Most of them used membrane wings made by polymers like Kapton (polyimide), PET (polyethylene terephthalate), parylene, FEP (fluorinated ethylene propylene), and Latex. Generally, aerodynamic analysis is influenced by Reynolds number, thickness, and camber of flapping membrane wings [13]. In contrast to the prior arts, this section focuses on designing a micro actuator to enhance the aerodynamic performance of FWMAVs by incorporating check-valves in the flapping wings, which have not yet been discussed widely. Caltech has developed the parylene check-valves of sub-mm size to actuate micropump in BioMEMS applications [14,15]. Moreover, the adaptive flow control of flapping wings [16].

5.4.1 Working Principle of Flapping Wings with Check Valves The inspiration for the check-valve design comes from observing the functionality of feathers in ornithology [17]. The bird’s feather acts as a key factor of lift enhancement, and the structure of the feather is too complex to manufacture using traditional processing methods [18]. However, by attaching the check-valves on the membrane wing, which function as feathers of the bird and enhance the lift by opening and closing during the upstroke and downstroke, respectively. Figure 5.28 illustrates the opening and closing of the check-valve during the upstroke and down strokes, respectively. The valve-opening action can be effectively reduced the magnitude of the negative lift because its pin hole-opening spoils both the completeness of the wing and smoothen the airflow. On the other hand, it also shows that the check-valve closing during downstroke restores the wing contour completely. It ensures a positive lift similar to the flat membrane wing without valves. The expected lift waveforms for the flapping wings with and without check-valves are shown in Figure 5.29. The local flow passing through the check-valves’ pin-holes effectively mitigates the wing-tip vortex’s growth during the upstroke. Therefore, the induced drag during the upstroke decreases, and the overall flapping period is shortened as well.

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FIGURE 5.28  (a) Check-valve closing during downstroke, (b) check-valve opening during the upstroke.

5.4.2 Design of the Flapping Wings with Check Valves A disc shape with 3 S-beams as the main structure of the check valve, which is shown in Figure 5.30(a), is developed, and the resonance is avoided at the central disc. The annular ring is fixed on the membrane wing, which has its corresponding pin-hole underneath the central disc. However, the deformation of the check-valves during the flapping is considered a dynamic problem, and determining the temporary solution is laborious. However, static solutions are viable enough to perform design optimization instead of performing dynamic analysis. Hence, finite element analysis (FEA) is performed for the designed check-valve shown in Figure 5.30(b), which is made of PET membrane. In general, the structural dynamics phenomenon is dealt with the frequencyresponse, as shown in Figure 5.31. ωn is assumed as the check valve’s intrinsic natural frequency, and ωF is the flapping frequency (external excitation). To avoid the resonance and response decay, the flapping frequency ωF should be much smaller

FIGURE 5.29  Expected lift waveform: (a) without check-valves, (b) with check-valves.

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FIGURE 5.30  FEA analysis of check valve: (a) dimension, (b) modal analysis.

than the natural frequency ωn. Therefore, there is no gain or only 0 dB according to the static solution. On the other hand, the disc motion’s dynamic solution can be reasonably approximated by the check-valve disc’s static solution. The modal analysis is performed to determine the natural frequency of checkvalve under free vibration. The natural frequency of the 1st mode in Figure 5.30(b) is 63.1 Hz subjected to a disc radius of 4.95 mm, which is much higher than the flapping frequency 11–14 Hz. However, the maximum deformation of this check-valve disc is 0.16 mm, and not possible for the valve opening to enhance the flapping lift. A modified design of a larger disc radius of 7.43 mm is proposed and redo the corresponding FEA. The 1st mode natural frequency reduces to 17.86 Hz, and the maximum deformation is now up to 6 mm, ensuring that the valve is effectively opened to enhance the aerodynamic lift. Integration of check-valves on wing membranes is attempted. The 6-pair checkvalves with a radius of 4.95 mm in Figure 5.32(a) and single-pair of check-valves with a radius of 7.43 mm in Figure 5.32(b) are made on the 20 cm-span FWMAV Evans mechanism in Figure 5.32. The arrangement of check-valves is modified based on

FIGURE 5.31  Frequency response of check valve.

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FIGURE 5.32  (a) multiple (12) 6-pair check-valves with a radius of 4.95 mm, (b) single-pair of check-valves with a radius of 7.43 mm on a wing.

the observation made through high-speed photography, and the instantaneous position of the central disc is shown in Figure 5.33. The single-pair of check-valves with a central disc radius of 7.43 mm is deformed to have a maximum deformation of 7.39 mm as Figure 5.33(b), much better than the 6-pair case.

5.4.3 Wind Tunnel Testing of a Flapping Wing with Check Valves According to different wind-tunnel testing conditions, the lift and the net thrust forces are measured for the time-average of more than 100 flapping cycles, which is shown in Figure 5.34 (without check-valve) and Figure 5.35 (with check-valves). We often select the data points with a zero net thrust to determine the cruising conditions of the FWMAV. Under these conditions, the thrust is equal to air drag, and no more acceleration/deceleration will apply on the MAV, and the MAV will keep flying at a constant cruising speed.

FIGURE 5.33  High-speed images showing central disc deformation during upstroke (flapping frequency of 13–14 Hz): (a) pin-hole is opening, (b) central disc detaching with a maximum deformation of 7.39 mm subject to a radius of 7.43 mm.

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FIGURE 5.34  The lift and net thrust vs. wind speed for the flapping wing without check-valves.

The sequence of finding a cruising condition from Figures 5.34 and 5.35 are given below: • Select a curve in Figure 5.34 or 5.35 with respect to specific driving voltage and inclined angle. • Identify the cruising speed by observing the intercepted point with a zero value in the net thrust plot. • Find the corresponding cruising lift by the identified result of the cruising condition (driving voltage, inclined angle, wind speed) in the lift force plot.

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FIGURE 5.35  Lift and net thrust vs. wind speed for flapping wings with check-valves.

Table 5.4 shows the cruising speeds and lifts of all possible cruising conditions deduced from the aerodynamic data presented in Figures 5.34–5.35. As mentioned previously, sometimes there is neither cruising speed nor lift corresponding to the zero net thrust (Wrong thrust trend or All “−/+” net thrust); or the deduced cruising lift is too small (1.5 m/s).

5.5.5  Performance Evaluation at Cruising The sequence of finding the cruising conditions from Figures 5.46 and 5.47 is similar, as explained in Section 5.4. Table 5.7 summarizes the cruising speed and the corresponding lift of all possible cruising conditions shown in Figures 5.46–5.47. As mentioned previously, there is neither cruising speed nor lift corresponding to the zero net thrust force. The deduced cruising lift is too small ( CF-51 > FBL > CF-72. • At 20° inclined angle, for J = 0, the net thrust coefficient is CF-50 > FBL > CF-51 ~ CF-72, and for J = 0.6, the net thrust coefficient of these mechanisms are in the order of CF-50 > FBL ~ CF-51 > CF-72. • At 40° inclined angle, for J = 0.8, the net thrust coefficient is CF-50 > FBL > CF-72, and for J = 0.6, the net thrust coefficient of these mechanisms are in the order of CF-50 ~ FBL > CF-72 > CF-51.

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FIGURE 6.20  Net thrust force vs. wind speed for CF-72 at various inclined angles: (a) 0°, (b) 20°, (c) 40°, (d) 60°.

TABLE 6.2 Cruising Speed and Lift (Zero Net Thrust) for Different MAVs (at Inclined Angle of 40°) FWMAV Cruising speed (m/s) Cruising lift (gf)

FBL, Golden-Snitch 2.62 9.8

CF-50 2.75 9.6

CF-51 1.62 8.1

CF-72 2.25 5.5

TABLE 6.3 Maximum Net Thrust of Different MAVs (at 3.7 V, Inclined Angle 0° and Wind Speed 0 m/s) FWMAV Max. net thrust (gf)

FBL, Golden-Snitch 4.9

CF-50 5.5

CF-51 5.2

CF-72 4.1

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FIGURE 6.21  Net thrust coefficient vs. advance ratio for 4 kinds of MAVs at various inclined angles: (a) 0°, (b) 20°, (c) 40°.

• The lift performance is examined with reference to advance ratio as shown in Figure 6.22. • At 0° inclined angle, for J ≧ 1, all lift coefficients are less than 0.5, and it deviates at J < 1. • At 20° inclined angle, for J ≧ 1, all lift coefficients are less than 2 and increases as J decreasing. For J = 0.8, the lift coefficient of these mechanisms is in the order of CF-51 > CF-50 > FBL = CF-72, and for J = 0.6, the lift coefficient is CF-51 > CF-50 > CF-72 > FBL. • At 40° inclined angle, for J ≧ 1, all lift coefficients are around 2 and increases as J decreasing. For J = 0.8, the lift coefficient of these mechanisms is in the order of CF-50 > FBL > CF-72 (no data for CF-51), and for J = 0.6, the lift coefficient of these mechanisms is in the order of CF-50 > CF-51 > FBL > CF-72. It is evident that, for the case of J ≦ 1, CF-50 has outperformed better on the net thrust generated. Increase of inclined angle, CF-50 behaves similarly to FBL. On the inclined angles between 20° and 40°, the lift coefficient of these mechanisms is in the order of CF-51 > CF-50 > CF-72 ~ FBL. The dimensionless data trend does not match the data given in Tables 6.2 and 6.3 (FBL is the best). The reason is that the lower flapping frequency of the clap-and-fling mechanisms developed in this chapter will increase the value of the advance ratio. Hence, the data of CF-50, CF-51, and

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FIGURE 6.22  Lift coefficient vs. advance ratio for 4 kinds of MAVs at various inclined angles: (a) 0°, (b) 20°, (c) 40°.

CF-72 are move to the right in Figures 6.21 and 6.22, which are almost equal in the performance of the FBL mechanism.

6.6 SUMMARY 1. Aerodynamic performance at cruising: • Based on wind tunnel test data, FBL of Golden-Snitch attained a maximum lift of 9.8 gf, and CF-50 achieved 9.6 gf. Moreover, the cruising speed of CF-50 is 2.75 m/s, and FBL is 2.62 m/s by paying the higher price of power consumption. • For the clap-and-fling mechanisms, the single-pivot flapping performs better than the two-pivot mechanism. The mechanism with larger stroke angle CF-72 has achieved inferior performance than CF-50 and CF-51 with smaller stroke angle. 2. Dimensionless parameter: • When J ≦ 1, CF-50 has attained a better net thrust coefficient. At the increase of inclined angle, CF-50 and FBL have achieved comparable net thrust coefficient. • At 0° inclined angle, the comparison of lift coefficient is unpredictable. During the inclined angles of 20° and 40°, the lift coefficient of CF-51 is apparently better than others, and they are in the order of performance: CF-51 > CF-50 > CF-72 ~ FBL.

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• The lift coefficient of CF-50 is comparable to FBL or even better. However, CF-51 and CF-72 inferior than CF-50 and the order of performance is given by FBL > CF-50 > CF-51 > CF-72. 3. The clap-and-fling effect on 20 cm-span FWMAV seems to be fair and not outstanding as it is compared with simple flapping motion. As observed from nature, the insect with the clap-and-fling phenomenon is much smaller than the currently developed FWMAVs. In the future, developed FWMAVs can be further reduced in size, and a flapping frequency of more than 100 Hz can be achieved with the clap-and-fling effect.

REFERENCES





1. Weis-Fogh, T. (1973) Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. Journal of Experimental Biology, 59(1), 169–230. 2. Palavalli-Nettimi, R. and Sane, S. P. (2018) Fairyflies. Current Biology, 28(23), R1331–R1332. 3. Schroeder, T. B., Houghtaling, J., Wilts, B. D. and Mayer, M. (2018) It’s not a bug, it’s a feature: Functional materials in insects. Advanced Materials, 30(19), 1705322. 4. Lee, S. H. and Kim, D. (2017) Aerodynamics of a translating comb-like plate inspired by a fairyfly wing. Physics of Fluids, 29(8), 081902. 5. Ellington, C. P. (1999) The novel aerodynamics of insect flight: Applications to microair vehicles. Journal of Experimental Biology, 202(23), 3439–3448. 6. Lehmann, F. O., Sane, S. P. and Dickinson, M. (2005) The aerodynamic effects of wing–wing interaction in flapping insect wings. Journal of Experimental Biology, 208(16), 3075–3092. 7. Sun, M. and Yu, X. (2006) Aerodynamic force generation in hovering flight in a tiny insect. AIAA Journal, 44(7), 1532–1540. 8. Takahashi, H., Aoyama, Y., Ohsawa, K., Tanaka, H., Iwase, E., Matsumoto, K. and Shimoyama, I. (2010) Differential pressure measurement using a free-flying insect-like ornithopter with a MEMS sensor. Bioinspiration and Biomimetics, 5(3), 036005. 9. Yan, J., Wood, R. J., Avadhanula, S., Sitti, M. and Fearing, R. S. (2001, May) Towards flapping wing control for a micromechanical flying insect. Proceedings of ICRA. IEEE International Conference on Robotics and Automation (vol. 4, pp. 3901–3908). 10. Ma, K. Y., Chirarattananon, P., Fuller, S. B. and Wood, R. J. (2013) Controlled flight of a biologically inspired, insect-scale robot. Science, 340(6132), 603–607. 11. Sohn, M. H. and Chang, J. W. (2007) Flow visualization and aerodynamic load calculation of three types of clap-fling motions in a WEIS-FOGH mechanism. Aerospace Science and Technology, 11(2–3), 119–129. 12. Lehmann, F. O. (2008) When wings touch wakes: Understanding locomotor force control by wake–wing interference in insect wings. The Journal of Experimental Biology, 211(2), 224–233. 13. Kraemer, K. L. (2012) On the Application of Rapid Prototyping Technology for the Fabrication of Flapping Wings for Micro Air Vehicles, Doctoral dissertation, Carleton University. 14. Nabawy, M. (2015) Design of Insect-Scale Flapping Wing Vehicles, Doctoral dissertation, The University of Manchester, United Kingdom. 15. Yang, L. J., Esakki, B., Chandrasekhar, U., Hung, K. C. and Cheng, C. M. (2015) Practical flapping mechanisms for 20 cm-span micro air vehicles. International Journal of Micro Air Vehicles, 7(2), 181–202.

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16. Yang, L. J. (2012) The micro-air-vehicle Golden-Snitch and its figure-of-8 flapping. Journal of Applied Science and Engineering, 15(3), 197–212. 17. de Croon, G. C. H. E., Perçin, M., Remes, B. D. W., Ruijsink, R. and De Wagter, C. (2016) The DelFly. Dordrecht, Springer. 10, 978–94. 18. de Croon, G. C. H. E., De Clercq, K. M. E., Ruijsink, R., Remes, B. and de Wagter, C. (2009) Design, aerodynamics, and vision-based control of the DelFly. International Journal of Micro Air Vehicles, 1(2), 71–97. 19. de Clercq, K. M., de Kat, R., Remes, B., van Oudheusden, B. W. and Bijl, H. (2009) Aerodynamic experiments on DelFly II: Unsteady lift enhancement. International Journal of Micro Air Vehicles, 1(4), 255–262. 20. de Croon, G. C., Groen, M. A., De Wagter, C., Remes, B., Ruijsink, R. and van Oudheusden, B. W. (2012) Design, aerodynamics and autonomy of the DelFly. Bioinspiration and Biomimetics, 7(2), 025003. 21. Karásek, M., Muijres, F. T., De Wagter, C., Remes, B. D. and de Croon, G. C. (2018) A tailless aerial robotic flapper reveals that flies use torque coupling in rapid banked turns. Science, 361(6407), 1089–1094. 22. Hsiao, F. Y., Yang, T. M. and Lu, W. C. (2012) Dynamics of flapping-wing MAVs: Application to the Tamkang Golden-Snitch. Journal of Applied Science and Engineering, 15(3), 227–238. 23. Yang, L. J., Cheng, C. M., Chiang, Y. W. and Hsiao, F. Y. (2012) New flapping mechanisms of MAV Golden-Snitch. Proceedings of International Conference on Intelligent Unmanned Systems (ICIUS-2012). 24. Norberg, U. M. (2012) Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution, Springer. 25. Raney, D. L. and Slominski, E. C. (2004) Mechanization and control concepts for biologically inspired micro air vehicles. Journal of Aircraft, 41(6), 1257–1265. 26. Sane, S. P. (2003) The aerodynamics of insect flight. The Journal of Experimental Biology, 206(23), 4191–4208. 27. Sane, S. P. and Dickinson, M. H. (2002) The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. The Journal of Experimental Biology, 205(8), 1087–1096. 28. Zhao, L., Huang, Q., Deng, X. and Sane, S. P. (2010) Aerodynamic effects of flexibility in flapping wings. Journal of the Royal Society Interface, 7(44), 485–497. 29. Sane, S. P. and Dickinson, M. H. (2001) The control of flight force by a flapping wing: Lift and drag production. The Journal of Experimental Biology, 204(15), 2607–2626. 30. Kim, D. K., Han, J. H. and Kwon, K. J. (2009) Wind tunnel tests for a flapping wing model with a changeable camber using macro-fiber composite actuators. Smart Materials and Structures, 18(2), 024008. 31. Caetano, J. V., Percin, M. U. S. T. A. F. A., van Oudheusden, B. W., Remes, B., De Wagter, C., de Croon, G. C. H. E. and de Visser, C. C. (2015) Error analysis and assessment of unsteady forces acting on a flapping wing micro air vehicle: Free flight versus wind-tunnel experimental methods. Bioinspiration and Biomimetics, 10(5), 056004. 32. Nian, P., Song, B., Xuan, J., Yang, W. and Dong, Y. (2019) A wind tunnel experimental study on the flexible flapping wing with an attached airfoil to the root. IEEE Access, 7, 47891–47903. 33. Yang, L. J., Hsu, C. K., Hsiao, F. Y., Feng, C. K. and Shen, Y. K. (2009, January) A Micro-Aerial-Vehicle (MAV) with figure-of-eight flapping induced by flexible wing frames. The 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2009–0875. 34. Yang, L. J., Lee, H. C., Feng, A. L., Chen, C. W., Wang, J., Lo, Y. L. and Wang, C. K. (2017) The wind tunnel test and unsteady CFD of an ornithopter formation. Innovative Design and Development Practices in Aerospace and Automotive Engineering, Springer, Singapore, 9–16.

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35. Yang, L. J. (2009) Flapping wings with micro sensors and flexible framework to modify the aerodynamic forces of a micro aerial vehicle (MAV). Aerial Vehicles, edited by Lam, T. M., INTECH Open Access Publisher, 691–718. 36. Yang, L. J., Miao, J. M., Kao, A. F. and Hsu, C. K. (2010) Effect of flexural stiffness on the aerodynamic forces of flapping MAVs. The 28th AIAA Applied Aerodynamics Conference, AIAA 2010–5077. 37. Yang, L.-J. (2012) Wingtip trajectory of a flapping micro-air-vehicle in its forward flight. The 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012), Beijing, China, FS-06-010. 38. Yang, L.-J., Cheng, C.-M., Chaing, Y.-W. and Hsiao, F. Y. (2012) New flapping mechanisms of MAV Golden-Snitch. The 8th International Conference on Intelligent Unmanned Systems (ICIUS 2012), Singapore. 39. Udayagiri, C., Kulkarni, M., Esakki, B., Pakiriswamy, S. and Yang, L. J. (2016) Experimental studies on 3D printed parts for rapid prototyping of micro aerial vehicles. Journal of Applied Science and Engineering, 19(1), 17–22. 40. Yang, L. J., Balasubramanian, E. and Waikhom, R. (2020) Inertial effect on the timeaveraged lift of flapping wings. Journal of Applied Science and Engineering, 23(2), 357–359.

7

Computational Fluid Dynamics Analysis of Flapping Wings

7.1 INTRODUCTION Numerous studies have been performed to investigate the flapping wing motion of two-dimensional (2D) airfoils with low Reynolds number using computational fluid dynamics (CFD) analysis [1–5]. However, the three-dimensional (3D) wing feature of FWMAVs has not been often examined using CFD analysis. A 3D time-varying, flapping-wing profile, and the inherent fluid-structure interaction (FSI) appear to be beyond the simulation capability of conventional finite-element methods (FEM) software such as Fluent, CFDRC, CFX, and StarCD. The flapping wing flow field [6] is analyzed by using Fluent and user-defined function (UDF) to describe the moving boundary of the flapping wing in terms of precisely given functions for time. CFD analysis of flapping-wing through the UDF at time t and (t + Δt) for solving the Navier–Stokes equations toward convergence for varied flapping strokes is difficult and ineffective because it involves preprogrammed UDF that is invariant during the whole CFD computation. Moreover, the analysis can be used only for rigid or prescribed wing shapes. The wings FSI from past iterations may not influence future iterations, which is not the case with the real-time scenario of flapping wing motion. Several CFD computations have been performed to investigate the effect on FSI of 2D flapping wings through experiments such as wind tunnel tests measuring the lift and thrust of flexible flapping wings [7]. 3D stereo photographic analysis of the instantaneous profiles of flexible wings [8], flow visualization involving smoke track experiments, and particle image velocimetry [9,10]. The experimental data obtained from these studies reveal that the developed FWMAVs work successfully. The CFD analysis of 3D flapping wings is still necessary for the accurate evaluation of flapping wing flow characteristics.

7.2  NUMERICAL SIMULATION OF SINGLE FLAPPING WING The 3D, time-varying, and flexible nature of the flapping wing obviously may not be just represented by a 2D structure using a UDF. Therefore, 3D flow simulation of the flexible flapping wing is inevitable. COMSOL Multiphysics with FSI capability is computationally powerful, and earlier studies on 2D flapping flows have proven to be useful in utilizing this software [11–15]. Numerical simulation of the 3D flapping flow phenomenon is realized using COMSOL Multiphysics to approximate the actual flapping situation. The unsteady simulation uses the mesh or grid number test by checking their corresponding convergence. The so-called convergence can DOI: 10.1201/9780429280436-7

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be determined by observing the periodic behavior of numerical results of velocity or pressure field after several flapping cycles. The convergence is also confirmed by taking into account the average lift forces. If the numerical results are converged, they are compared with other experimental data. Comparisons have been made for a 20-cm-span FWMAV named Golden-Snitch and include the following three parts: 1. Comparison of the flow patterns: The existence of reverse Kármán vortex in the flow field around a flapping wing from COMSOL Multiphysics and earlier wind tunnel data results. 2. Comparison of time history or waveforms of lift force obtained from CFD analysis and experimental results. 3. Comparison of the influence of FSI concerning its 3D surface profile of flexible wings over a full flapping cycle due to its aeroelasticity using the results of COMSOL Multiphysics and earlier high-speed stereo photography.

7.2.1  Governing Equations A 20 cm-span FWMAV Golden-Snitch, whose wing membrane having a thickness of 24 μm and is made of polyethylene terephthalate (PET) (the half wing is shown in Figure 7.1), is considered for the CFD analysis. Assuming that the flapping wing is bilaterally symmetrical and only half of the 20-cm span (i.e., 10 cm for the half right-wing) is simulated. The FSI governing equations are given by: For Fluid Part: Mass conservation:  ∂ρ + ∇ ⋅ ρU fluid = 0 (7.1) ∂t

(



)

Momentum conservation:



   ∂U fluid + ρ U fluid ⋅ ∇ U fluid = ρ ∂t       2 ∇ ⋅ −PI + µ ∇U fluid + (∇U fluid )T − µ ∇ ⋅ U fluid I  + F   3

(

)

(

)

(

)

(7.2)

[Solid Part] Eulerian equation of motion

  ∂2U solid ρ − ∇ ⋅ σ = F (7.3) 2 ∂t

  U fluid The fluid velocity vector U solid denotes the solid’s deformation vector; P is  hydrostatic pressure; σ is the stress tensor; I is the identity tensor, and F is the external force vector. r, and are the fluid density and viscosity, respectively [16]. The

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FIGURE 7.1  Right-side half domain of a half flapping wing with its preliminary mesh.

upstream velocity regimes are considered to have a speed of 0–3 m/s and the corresponding Reynolds number is approximately 0–13,380 at a temperature of 300 K.

7.2.2 Boundary Conditions Using COMSOL Multiphysics software, the simulation of a 3D flapping wing is performed. The wing membrane coordinates data are first imported, followed by establishing a rectangular wind tunnel that served as a surrounding boundary. The wind tunnel was 1 m long, 0.3 m wide, and 0.3 m tall, and it is identical to the tunnel used in the previous FWMAV wind tunnel test, depicted in Figure 7.2(a). The flapping wing is bisected together with the wind tunnel (0.15 m wide), whereby the incision site is configured as a symmetrical plane to reduce the computation time. The preliminary mesh of a flapping wing kept in the wind tunnel is shown in Figure 7.2(b).

FIGURE 7.2  Right-side half domain of a single flapping wing in wind tunnel: (a) airfoil model, (b) meshing of domain.

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FIGURE 7.3  Right-side half domain of a single flapping wing with wind tunnel: (a) fine mesh configuration, (b) extra fine mesh configuration.

7.2.3 Mesh Setting and Testing Triangular elements are considered for the meshing of the wing surface. Subsequently, tetrahedral elements are considered for meshing of wind tunnel domain, as shown in Figure 7.2(b). After selecting the different mesh sizes in COMSOL and using the corresponding three sets of mesh number distributions, the meshes are divided into Normal (Figure 7.2(b)), Fine (Figure 7.3(a)), and Extra Fine (Figure 7.3(b)) configurations. The number of elements for each set is listed in Table 7.1 and the complete procedure for CFD analysis followed in COMSOL Multiphysics environment is detailed in Table 7.2. Simulations are performed for the flapping frequency of 14 Hz and upstream wind velocity of 0 m/s with an inclined angle of 20°. The generated lift force for the three types of mesh is shown in Figure 7.4. It is observed that an increase in the number of elements enhances the lift force. Additionally, Figure 7.4 indicates that a minimum of three flapping cycles is required to reveal a periodic lift trend showcasing the changes. The COMSOL simulation does not use the turbulent model because of zero upstream velocity and the fluid’s small Reynolds number.

TABLE 7.1 Number of Elements in Various Mesh Configurations Mesh Location and Shape Tetrahedral elements Triangular elements Boundary elements Endpoint elements Total elements

Normal Mesh 5,498 850 121 22 6,491

Fine Mesh 6,835 3,730 203 22 10,790

Extra Fine Mesh 57,341 9,568 397 22 67,328

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TABLE 7.2 COMSOL Multiphysics Simulation Configuration Process Step 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Task Description Input wing membrane coordinates data Rotate the wing (20°) along its wingspan axis into an inclined angle Construct the wind tunnel Form the right-side half domain of the flapping wing and wind tunnel Select the materials for the wind tunnel and flapping wing Set air as the space material for the wind tunnel Input the flapping wing material parameters Set the flapping wing as a linear elastic material Configure the wind tunnel entrance and wind velocity Configure the wind tunnel exit Configure the fixed constraint for the leading edge (L. E.) of the flapping wing Configure the symmetrical plane of the flow field Configure the predetermined time-varying displacement function for the leading edge of the flapping wing Initiate mesh configuration Construct the triangular meshes of the flapping wing Scan the entire flapping wing Initiate conversion Construct the tetrahedral meshes Configure the fineness of the mesh size Complete configuration and initiate FEM calculation

Notably, the periodic changes increased with the number of meshes, particularly in the extra fine mesh configurations, wherein the lift trend demonstrated the most periodic changes with smaller disturbances to the lift waveforms. Under the multicore computer’s limited computing power, the extra-fine meshes (67,328 elements) required approximately 154 hours and 43 min to perform eight cyclic flapping motions. Using a time-dependent solver, the inclined angle of 20° and flap stroke angle of 53° and 90° simulations is performed. The three sets of boundary conditions (flapping frequency and wind tunnel entrance wind velocity) are considered: (a) 14 Hz and 1 m/s (b) 15 Hz and 2 m/s and (c) 15 Hz and 3 m/s, respectively. The simulation results indicated that when the flapping wing is kept in the wind tunnel and actuated, the airflow around it and corresponding lift are extremely chaotic. The flapping wing lift displayed a more periodic change after three flapping cycles for the various wind velocities. It is evident from Figure 7.5(a) that, with a wind velocity of 2 m/s and for the stroke angle of 90° showed a higher average absolute lift with 5% fluctuation for the last five cycles. The average total lift (8.76 gf) is close to the body mass of Tamkang Hummingbird FWMAV (9.62 g). At the wind velocity of 3 m/s and for the stroke angle of 53°, a higher average lift with 21% fluctuation for the last six cycles is experienced, as shown in Figure 7.5(b). However, the average total lift

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FIGURE 7.4  Lift under different mesh conditions: (a) normal, (b) fine, (c) extra fine.

(3.95 gf) is less than the body mass of Golden-Snitch FWMAV (5.9 g). The transient lift data demonstrates that COMSOL Multiphysics underestimated the unsteady lift of FWMAV Golden-Snitch. Moreover, the simulation is more favorable for the case involving a larger flapping stroke angle (90°). The lift error or fluctuation generated using COMSOL Multiphysics became larger as the flapping angle becomes smaller.

7.2.4 Flow Pattern Comparison for Single Flapping Wing Smoke trace experiments are conducted for the FWMAV Golden-Snitch kept at an inclined angle of 20°; stroke angle of 53°, the upstream velocity of 1 m/s, and flapping frequency of 14 Hz. A signal interception experiment using a six-axis force

FIGURE 7.5  Average lift subjected to different flapping stroke angles: (a) 90°, (b) 53°.

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FIGURE 7.6  Vortex (smoke line) of the Golden-Snitch flapping wings: (a) downstroke, (b) upstroke.

gauge and high-speed camera to capture the flow field marked by smoke trace is performed [17–19]. The lift and thrust forces of FWMAV are obtained through processing the obtained signals using the LABVIEW platform. The smoke trace indicated an anticlockwise vortex pattern formed above the trailing edge (T.E.) during the wing downstroke, as shown in Figure 7.6(a). Conversely, a clockwise vortex pattern is formed below the trailing edge during the wing upstroke, as depicted in Figure 7.6(b). For the same boundary conditions, simulation is also performed. The simulated flow field shown in Figure 7.7 matches the smoke trace shown in Figure 7.6. The flow field is well known as the reverse Kármán vortex street, a mechanism found by von Kármán to explain lift and thrust production [20,21]. In conventional fixed wings, clockwise vortices formed above the T.E., and an anticlockwise vortex formed below the T.E., which produced a backward jet and led to the drag formation. Conversely, in flapping wings for the present investigations, an anticlockwise vortex is formed

FIGURE 7.7  Vortex (CFD analysis) of the Golden-Snitch flapping wing: (a) downstroke, (b) upstroke.

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above the T.E., and a clockwise vortex is formed below the T.E., which produced a forward jet and led to the formation of thrust. The red, yellow, and green colors on the wing surface in Figure 7.7 denote the maximum, median, and minimum displacements, respectively; red, yellow, and blue colors in the flow field in Figure 7.7 denote the maximum, median, and minimum velocities, respectively [22].

7.2.5 Aerodynamic Force Comparison for Single Flapping Wing The lift force determined from the numerical simulations for the flapping stroke angle of 53°, flapping frequency of 14–15 Hz, and wind velocity of 1 m/s, 2 m/s, and 3 m/s (solid line) and wind tunnel experiments (dotted line) are shown in Figure 7.8. Notably, the flapping lift measured by 6-axis force gauge performed in the wind tunnel experiments partially shared similar characteristics with numerical simulation (both displaying a large and small peak (bi-peak) in the positive lift stage). A similar but weakened “bi-peak” phenomenon is observed during the negative lift stage during the wind tunnel experiments, whereas the simulation results could not show this feature. Although the downstroke and upstroke motions of the flapping wing are designed with the same stroke distance, the wave patterns of positive and negative lift are not symmetrical. Within a single cycle, as shown in Figure 7.8, the time duration ratio of the downstroke and upstroke acquired from both the experiment and simulation is approximately 6:4. The high-speed photography results also confirm it, wherein the duration of downstroke is longer than that of the upstroke. Also, the peak amplitude of positive lift is larger than that of negative lift in both the experimental and numerical cases. The maximal positive lift ratio to maximal negative lift in the wind tunnel is approximately 1.4, whereas the simulation results are estimated as 1.6. The lift phenomenon depicted in Figure 7.8 shows the negative lift at the beginning of downstroke became a positive lift within a short timeframe. The lift increased continuously and reached its first peak at approximately 1/8 of the cycle (e.g., 0.48 s in Figure 7.8(c)), after which it slowly declined and then increased again to the highest peak before the end of downstroke (e.g., 0.50 s in Figure 7.8(b) or 0.505 s in Figure 7.8(c)). The subsequent decline from this peak was simultaneously marked at the end of downstroke and beginning of upstroke. The lift gradually became negative before reaching a minimum at approximately 3/4 of the cycle. After a slight recovery, the lift reached a second minimum at approximately 7/8 of the cycle and attained its maximum negative value (e.g., 0.635 s in Figure 7.8(a) or 0.525 s in Figure 7.8(c)). By restating the bi-peak waveform of lift shown in Figure 7.8, the waveform is more precisely obtained from the wind tunnel experiments. The timing of its highest peak and lowest minimum are comparable to that in the waveform of numerical simulation with monotonously up-and-down features, which can be explained by the first lift mechanism’s “delayed stall” of flapping. This translational lift mechanism achieves the largest lift peaks for the downstroke (e.g., 0.27 N at 0.505 s in Figure 7.8(c)) and upstroke (e.g., 0.13 N at 0.525 s in Figure 7.8(c)), respectively. The positive lift peak of 0.27 N is greater than the negative lift peak of 0.13 N at 20° inclined angle of the FWMAV body. The positive AOA during the downstroke always has a larger magnitude than the negative AOA during the upstroke. Hence, the global net lift for a full cycle becomes positive and supports the weight of FWMAV.

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FIGURE 7.8  Lift force for four wing beat cycles of flapping motion at various wind velocities: (a) 1 m/s, (b) 2 m/s, (c) 3 m/s

In addition to the translational lift, a rotational lift exists, which is a part of the measured lift, and it is due to the wing motion of stroke reversals. In addition to the stroke reversal characteristics, counterclockwise pronation is observed at the beginning of downstroke, and clockwise supination occurred at the beginning of upstroke. This is analogous to the Magnus effect and is known as “rotational circulation,” the second lift mechanism of flapping. Moreover, an additional lift mechanism, namely the “wake capture” of flapping, is also observed.

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However, Dickinson’s second and third mechanisms’ rotational lift is not found in the numerical simulation results. Although there is an excess lift contribution beyond the simulation waveform from the “bi-peak” measured data shown in Figure 7.8, the rotational lift contribution appears veiled, and it is comparable or coupled to the wing inertia plugging force [23–27]. The excess lift waveform or “bi-peak” phenomenon observed in Figure 7.8 must be further investigated either experimentally or numerically in the future.

7.2.6 Comparison of 3D Trajectory Using StereoPhotography for Single Flapping Wing Experiments are performed using 3D stereo photography [5] to analyze the “GoldenSnitch” wing surface, and the results are depicted in Figures 7.9 and 7.10. The

FIGURE 7.9  3D stereo photography of Golden-Snitch flapping wing.

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FIGURE 7.10  2D profile of the wing surface centerline extracted from Figure 7.9: (a) downstroke, (b) upstroke.

flexibility of overall flapping-wing-flapping-wing typically results in the deformation of FWMAV through the membrane of PET wing and carbon fiber spar at the wing’s leading edge. The measured kinematic information resulted in rich, dynamic wing profiles, including stroke reversals and aeroelastic deformation. Images of 3D simulation using COMSOL Multiphysics of the wing surface of the Golden-Snitch for one cycle of flapping motion are presented in Figure 7.11. Because of the limitations of using COMSOL Multiphysics in assigning different wing materials, the carbon fiber at the leading edge could only be configured as PET, and the same material is considered wing membrane. Also, the pre-described upstroke and downstroke sinusoidal motions are applied to the leading edge spar of the wing (in Step 13 of Table 7.2), which is equivalent to the motion of a rigid body [28]. Therefore, the 3D flow obtained herein by CFD cannot reflect the flapping wing profile observed in Figures 7.9 and 7.10. The FSI function in COMSOL Multiphysics can investigate elastic deformation of the PET wing membrane. The simulated wing profiles in Figure 7.11 obtained using COMSOL Multiphysics includes FSI to a very limited extent. Compared with the rapidly changing wing profile shown in Figure 7.10, the wing profiles shown in Figure 7.11 moves up and down with small negative camber. The sinusoidal time-varying boundary setting of the wing leading edge is passively accounted for in the simulation without streamwise vibration or pronation/supination. However, the wing deformation profiles shown in Figures 7.11 and 7.12 also failed to predict the positive-camber pattern visible during the stroke reversal moments observed in Figures 7.9 and 7.10. This may explain the difference in lift between the measured data and numerical simulation data. The following are the major observations from the numerical and experimental investigations. Firstly, the lack of wing trajectory of stroke reversal shown in Figures 7.11 and 7.12 indicate that the corresponding numerical simulation underestimated the rotational lift contribution, which often accounts for 35% of the total flapping lift. Secondly, a lack of positive camber in the wing profile shown in Figures 7.11 and 7.12 also indicate less lift in the simulation compared with the experimentally measured data. The low lift is apparent for the negatively cambered wing based on potential flow theory.

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FIGURE 7.11  3D simulation of Golden-Snitch flapping wing.

FIGURE 7.12  2D profile of wing surface centerline Golden-Snitch: (a) downstroke, (b) upstroke.

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FIGURE 7.13  3D flow structure plots for a wind speed of 1 m/s and flapping frequency of 14 Hz: (a–g) velocity field, (h–u) intercepting streamwise cross-section.

Figures 7.13 and 7.14 show the 3D velocity field during a full flapping cycle with intercepting planes in the streamwise (and spanwise) direction. The bars of “Vel.” and “Def.” denote the units and magnitudes of velocity and wing deformation. The reverse Kármán vortex sheets [29–32] can be observed at different chord cuts, as depicted in Figure 7.13. The velocity magnitude and vortex pattern are more obvious for the wingtip cut than the 0.25 chord cut. The streamwise flow cuts of 3D analysis are similar, except for the large air-jet observed in Figure 7.13(q) and (s). Also, the wingtip vortex and downwash distribution are observed in all cases in Figure 7.14. Few larger air jets are seen in Figure 7.14(c), (e), (i), (j), and (m), respectively.

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FIGURE 7.14  3D flow structure plots for a wind speed of 1 m/s and flapping frequency of 14 Hz: (a–u) intercepting spanwise cross-sections at three-chord positions.

7.2.7 Major Observations from CFD Analysis of Single Flapping Wing 1. The powerful computation abilities of COMSOL Multiphysics finite element environment for analyzing FSI of 3D flapping wing was very similar to a rear wing. According to the calculated time dependence value and

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convergence level, the simulation results indicated that a flapping wing requires at least three flapping cycles after actuation to attain a periodic flow field change. 2. According to the lift trend, the periodic changes increased with an increase in the number of elements. The finer mesh with 67,328 elements required a time frame of 154 hours and 43 mins to calculate eight flapping cycles for generating lift data. 3. Highest average lift force is obtained when the flapping wing with a stroke angle of 53°, flapping frequency of 14–15 Hz, an inclined angle of 20°, and a wind velocity of 3 m/s. 4. According to the 3D simulation of the flapping wing flow field and the images of smoke-tracking experiments using a wind tunnel, the reverse Kármán vortex street phenomenon is observed, which is also the thrust source of a flapping wing. 5. The COMSOL Multiphysics 3D flow field cannot simulate the flapping phenomenon because the FSI function could only simulate the PET wing membrane’s aerodynamic deformation. The simulation results for the lift underestimate the contribution of rotational lift, which often accounts for 35% of total lift for flapping wings [33]. Also, the lack of positive camber for the wing profiles in the simulation result implies that less lift performance is obtained in the simulation than the experimentally measured data. 6. The streamwise and spanwise wingtip vortex flow patterns and downwash are observed during the CFD analysis.

7.3  FORMATION FLIGHT OF FLAPPING WINGS FWMAVs should have good aerial maneuvers like agile cruising flight and low-speed hovering [34,35]. However, it is also reported that FWMAVs may reduce 27% flight power than their hovering counterpart [36]. Lissaman and Shollenberger discussed the flight power requirement for V-formation flight of birds in 1970 [37,38]. By their calculated induced drag and power, they found that the range of infinite birds in V-formation with their wing-tip connected has attained power of 71% higher than a single flapping bird. Meanwhile, the cruising speed of V-formation is 24% lower than a single bird. They performed calculations based on the fixed-wing aerodynamics and different from the actual flapping wings — however, CFD analysis [33,39] maybe the better choice to examine the V-formation flight characteristics of flapping wings The formation of birds, in general, has a wing gap of about a quarter. Before the realization of accurate flight control of FWMAVs like the quadrotor control of Vijay Kumar’s work [40,41], too small a wing gap may cause the air collision of FWMAVs and makes the energy-efficient flapping formation is not practical. Researchers of KAIST have ever used multiple high-speed cameras to localize the real-time position of FWMAVs, and they have achieved formation flight. However, their FWMAVS have obvious separation from one another to avoid air collision and far away from birds’ ideal flapping formation flight [42]. However, the following section discusses the V-formation of three FWMAVs and their lift generation under different wing gaps and cruising speeds using CFD analysis.

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FIGURE 7.15  (a) Three wings kept in wind tunnel, (b) position for the 3-wing formation.

7.4  CFD ANALYSIS OF FORMATION FLIGHT OF FWMAVS 7.4.1 Model Generation The COMSOL Multiphysics software platform is utilized to compute the unsteady flow field of flapping formation flight. The moving boundary coordinates and it is FSI are similar to those in the previous section of single flapping-wing CFD analysis [43–46]. A half domain of V-formation of three flapping wings is considered for the simulation studies to reduce the computational efforts. The wind tunnel of dimension 1 m long, 0.6 m wide, and 0.3 m high, as shown in Figure 7.15(a), is considered for the domain. The flapping wing with a span of 0.2 m and chord of 0.065 m is considered for a wing. The inlet velocity of the wind tunnel is varied between 2 and 4 m/s, and the corresponding Reynolds number is calculated as 6,690–13,380 at 300 K. The polyethylene terephthalate (PET) wing with a thickness of 23 μm is considered. There are two configurations for the V-formation with three flapping wings is considered for the simulation studies. Case A: The Z-Longitudinal distance of 0.2 m and X-Lateral distance of 0.3 m; Case B: Z-Longitudinal distance of 0.295 m and X-Lateral distance of 0.26 m. The definition of Z-Longitudinal distance and the X-Lateral distance are defined in Figure 7.15(b). For these cases, various types of elements are considered, which are given in Table 7.3. Accordingly, finite element mesh is created for single and three wings as

TABLE 7.3 Various Types of Finite Elements

Simulation Cases Tetrahedral elements Triangular elements Boundary elements Endpoint elements Total elements

Case A: Z-0.20 m and X-0.30 m 124,662 7,978 486 46 133,172

Case B: Z-0.295 m and X-0.26 m 125,052 8,146 486 46 133,730

Single wing 81,961 6,330 294 22 88,607

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FIGURE 7.16  Finite element mesh (a) single wing, (b) 3-wing formation.

depicted in Figure 7.16(a) and (b). Using the multiple-core work station of Intel Xeon E5-2630v4, the computation of 10 flapping cycles of three wings V-formation took 496 hours and 33 min. Compare to the single wing case in Section 7.2, the CFD computation of flapping V-formation consumed more time.

7.4.2 CFD Analysis for Single Flapping Wing The single flapping-wing subjected to the flapping frequency of 14 Hz, at an inclined angle of 20° and stroke angle of 90°, and various inlet velocities of 2 m/s, 3 m/s, and 4 m/s, the unsteady flow field is examined. At 4 m/s wind velocity, the lift waveform approaches a periodic manner after three flapping cycles, as shown in Figure 7.17. The average lift of the first ten flapping cycles for various wind velocities is shown in Figure 7.18, and they converged after 3 flapping cycles. Even though the lift at 4 m is achieved as the highest, its induced drag increases, and at the same time, the cruising speed decreased to less than 4 m/s. In other words, the inlet velocities of 2 m/s or 3 m/s may be the cases wherein the real cruising flight condition of the three wings V-formation flight is realized effectively.

FIGURE 7.17  Lift force for a single flapping-wing at 4 m/s.

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FIGURE 7.18  The average lift for a single flapping wing.

7.4.3 CFD Analysis for V-Formation with 3 Flapping Wings For the similar boundary conditions considered for the single flapping wing, CFD analysis is performed to examine the unsteady flow field for the V-formation flight with three flapping wings. It is evident from Figure 7.19 that the lift forces are unstable until the 4th cycle for both cases and the lift variation is about 6~7 gf for the inlet velocity of 4 m/s. The averaged lift converges gradually for the inlet velocities of 2 m/s and 3 m/s, similar to a single flapping wing.

7.4.4 Comparison of Averaged Lift Per Wing for V-Formation and Single Wing According to the formation flight or the single wing, the magnitude of averaged lift per wing for the three cases is more stable at 2 m/s, shown in Figure 7.20. Both in cyclic or phase change, the average lift of Case A is more similar to the case C of a single flapping wing. Meanwhile, the lift of case B is even more out of phase with case C after the 8th cycle. It may be because, in case A, the Z-distance of 0.2 m (probably related to the chord length of 0.065 m) and the X-distance 0.3 m (probably related to the wingspan of 0.2 m) may have their least common multiples (LCM) with the wing chord and wingspan, respectively. However, in case B, the Z-distance of 0.295 m and the X-distance of 0.26 m lack the smaller LCM with the wing chord and wingspan, respectively.

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FIGURE 7.19  The averaged lift per wing for the V-formation: (a) case A, (b) case B.

7.4.5 Lift Comparison for Leading Wing of V-Formation and Single Wing For cases A and B, the lift of the leading wing for the V-formation is smaller than the single flapping-wing observed in Figure 7.21. Furthermore, for comparing the two kinds of V-formation, the leading wing lift of case A is better than case B.

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FIGURE 7.20  Average lift per wing at an inlet velocity of 2 m/s.

7.4.6 Lift Comparison for Leading Wing and Follower Wing of V-Formation In comparison to the leading wing lift shown in Figure 7.21, the follower wing lift of Case A is better than case B in the high-speed region, as observed in Figure 7.22. A 3.7% of lift enhancement is attained for case A in comparison to case B at the inlet velocity of 3 m/s. It may be due to the follower wing as the leading wing to obtain the more upward stream from the former wingtip vortex. The overall V-formation pattern of case A is superior to case B from an aerodynamics perspective.

7.4.7 Comparison of Dimensionless Lift Coefficients Similar to the previous lift comparison using the dimensionless number and normalized concept, the lift coefficient for the three cases (two V-formation flapping motions and single flapping motion)is compared and shown in Figure 7.23. During the inlet velocity range of 2–4 m/s, the lift coefficients for all three cases are below 1.4, and their changing trends concerning the advance ratio are similar. The single flapping-wing achieved a better lift coefficient than the two cases of V-formations. It means the position arrangement of V-formation flapping flight is not optimized and needs revision in the future. Figure 7.23 also depicts that case A formation is still better than case B in the dimensionless domain.

Computational Fluid Dynamics Analysis

FIGURE 7.21  Lift of leading wing of V-formation: (a) 4 m/s, (b) 3 m/s, (c) 2 m/s.

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FIGURE 7.22  Lift of the follower wing of V-formation: (a) case A, (b) case B.

FIGURE 7.23  Lift coefficient for the three flapping cases.

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7.5  SUMMARY ON THE V-FORMATION FLAPPING FLIGHT 1. The side views and the isometric views of V-formation case A for a full flapping cycle subject to 3 m/s and flapping frequency of 14 Hz is shown in Figures 7.24 and 7.25. It is observed that all three flapping wings are synchronized in-phase.

FIGURE 7.24  3D flow field plots (side view) of V-formation case A for a full flapping cycle.

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FIGURE 7.25  3D flow field plots (isometric view) of V-formation case A for a full flapping cycle.

2. The average lift for all the cases is gradually converged after 3 flapping cycles. 3. The averaged lift of case A is more similar to the lift of the single flapping wing. Meanwhile, the change in the lift of case B is even more degraded and out of phase with the single wing after the 8th cycle. 4. The averaged lift of leading wings of two V-formations is smaller than the single flapping wing. The leading wing of case A experienced superior lift performance than case B, especially at the inlet velocity of 3 m/s. 5. The averaged lift of follower wings of two V-formations is also smaller than the single flapping wing. The follower lift of case A is better than case B in the high wind speed region of 3 m/s with 3.7% lift enhancement. 6. For the inlet velocity range of 2–4 m/s, the lift coefficients of all three cases are below 1.4 and their changing trends for the advance ratio is similar.

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7. The dealt unsteady lift behavior of V-formation flight using CFD is more time consuming, and optimization of wing spacing for the V-formation flight based on Taguchi method or other techniques are crucial to CFD study. Besides, evaluating net thrust force and power consumption is the future scope of formation flight.

7.6 SUMMARY Computation fluid dynamic (CFD) analysis of three-dimensional (3D) flapping-wing having 20 cm wingspan through varying mesh density and their fluid-structure interaction (FSI) is dealt with in this chapter. The lift performance of Golden-Snitch flapping wing (half-section) under varied wind conditions of 1 to 3 m/sec with the flapping stroke angles of 53° and 90°, flapping frequency of 14–15 Hz inclined angle of 20° using CFD and smoke trace experiments are elaborated. The stereo-photography measurements to obtain a 3D wing trajectory and the two-dimensional (2D) wing profile extraction are discussed. The V-formation flight of flapping wings and the unsteady lift characteristics are explained with CFD analysis results. Comparative evaluation of three flapping wings in formation flight and single flapping-wing lift performance is discussed in detail. The effect of the dimensionless lift coefficient on various cases of flapping wing characteristics is explained.

REFERENCES

1. Wang, Z. J. (2000) Two dimensional mechanism for insect hovering. Physical Review Letters, 85(10), 2216. 2. Wan, T. and Huang, C. K. (2008, September) Numerical simulation of flapping wing aerodynamic performance under gust wind conditions. The 26th International Congress of the Aeronautical Sciences (pp. 1–11). 3. Chuang, S. W., Lih, F. L. and Miao, J. M. (2012) Effects of Reynolds number and inclined angle of stroke plane on aerodynamic characteristics of flapping corrugated airfoil. Journal of Applied Science and Engineering, 15(3), 247–256. 4. Platzer, M. F., Jones, K. D., Young, J. and Lai, J. C. (2008) Flapping wing aerodynamics: Progress and challenges. AIAA Journal, 46(9), 2136–2149. 5. Yang, L. J., Huang, H. L., Liou, J. C., Esakki, B. and Chandrasekhar, U. (2014) 2D quasi-steady flow simulation of an actual flapping wing. Journal of Unmanned System Technology, 2(1), 10–16. 6. Niu, Y. Y., Liu, S. H., Chang, C. C. and Tseng, T. I. (2012) A preliminary study of the three-dimensional aerodynamics of flapping wings. Journal of Applied Science and Engineering, 15(3), 257–263. 7. Pornsin-Sirirak, T. N., Tai, Y. C., Nassef, H. and Ho, C. M. (2001) Titanium-alloy MEMS wing technology for a micro aerial vehicle application. Sensors and Actuators A: Physical, 89(1–2), 95–103. 8. Yang, L. J., Hsiao, F. Y., Tang, W. T. and Huang, I. C. (2013) 3D flapping trajectory of a micro-air-vehicle and its application to unsteady flow simulation. International Journal of Advanced Robotic Systems, 10(6), 264. 9. Dickinson, M. H., Lehmann, F. O. and Sane, S. P. (1999) Wing rotation and the aerodynamic basis of insect flight. Science, 284(5422), 1954–1960. 10. Hubel, T. Y. and Tropea, C. (2010) The importance of leading edge vortices under simplified flapping flight conditions at the size scale of birds. Journal of Experimental Biology, 213(11), 1930–1939.

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11. Bucur, D. M., Dunca, G., Georgescu, S. C. and Georgescu, A. M. (2016) Water flow around a flapping foil: Preliminary study on the numerical sensitivity. UPB Scientific Bulletin, Series D: Mechanical Engineering, 78(4), 175–182. 12. Kumar, A., Kaur, C. and Padhee, S. S. (2016) Analysis and optimization of dragonfly wing. Proceedings of the 2016 COMSOL Conference (User Presentations) in Bangalore, India. 13. Moriche, M., Flores, O. and García-Villalba, M. (2016) Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number. International Journal of Heat and Fluid Flow, 62, 44–55. 14. Ou, K., Castonguay, P. and Jameson, A. (2011) 3D flapping wing simulation with high order spectral difference method on deformable mesh. The 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (p. 1316). 15. Tsai, B. J. and Fu, Y. C. (2009) Design and aerodynamic analysis of a flapping-wing micro aerial vehicle. Aerospace Science and Technology, 13(7), 383–392. 16. Zimmerman, W. B. (2006) Introduction to COMSOL multiphysics. Multiphysics Modeling With Finite Element Methods. Citation Key: Zimmerman2006, World Scientific Publishing Company, 1–26. 17. Chen, H. C. (2010) Research on the Semi-Automatic Data Acquisition of MAV Wind Tunnel Testing. Master’s Thesis, Department of Mechanical and Electro-Mechanical Engineering, Tamkang University. 18. Nguyen, Q. V., Park, H. C., Goo, N. S. and Byun, D. (2010) Characteristics of a beetle’s free flight and a flapping-wing system that mimics beetle flight. Journal of Bionic Engineering, 7(1), 77–86. 19. Bomphrey, R. J., Taylor, G. K. and Thomas, A. L. (2010) Smoke visualization of freeflying bumblebees indicates independent leading-edge vortices on each wing pair. Animal Locomotion, Springer, Berlin, Heidelberg, 249–259. 20. Von Kármán, T. (1963). Aerodynamics (Vol. 9), McGraw-Hill. 21. Vandenberghe, N., Zhang, J. and Childress, S. (2004) Symmetry breaking leads to forward flapping flight. Journal of Fluid Mechanics, 506, 147. 22. Yang, L. J., Lee, H. C., Feng, A. L., Chen, C. W., Wang, J., Lo, Y. L. and Wang, C. K. (2017) The wind tunnel test and unsteady CFD of an ornithopter formation. Innovative Design and Development Practices in Aerospace and Automotive Engineering, Springer, 9–16. 23. Sun, M. and Tang, J. (2002) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. Journal of Experimental Biology, 205(1), 55–70. 24. Wu, J. H. and Sun, M. (2004) Unsteady aerodynamic forces of a flapping wing. Journal of Experimental Biology, 207(7), 1137–1150. 25. Vest, M. S. and Katz, J. (1996) Unsteady aerodynamic model of flapping wings. AIAA Journal, 34(7), 1435–1440. 26. Sun, M. and Yu, X. (2006) Aerodynamic force generation in hovering flight in a tiny insect. AIAA Journal, 44(7), 1532–1540. 27. Sun, M. and Wu, J. H. (2003) Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion. Journal of Experimental Biology, 206(17), 3065–3083. 28. He, W., Wang, T., He, X., Yang, L. J. and Kaynak, O. (2020) Dynamical modeling and boundary vibration control of a rigid-flexible wing system. IEEE/ASME Transactions on Mechatronics, 25(6), 2711–2721. 29. Schnipper, T., Andersen, A. and Bohr, T. (2009) Vortex wakes of a flapping foil. Journal of Fluid Mechanics, 633, 411. 30. Bergmann, M., Cordier, L. and Brancher, J. P. (2006) On the generation of a reverse von Kármán Street for the controlled cylinder wake in the laminar regime. Physics of Fluids, 18(2), 028101.

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31. Zhang, J. (2017) Footprints of a flapping wing. Journal of Fluid Mechanics, 818, 1–4. 32. Tzezana, G. A. and Breuer, K. S. (2019) Thrust, drag and wake structure in flapping compliant membrane wings. Journal of Fluid Mechanics, 862, 871–888. 33. Yang, L. J., Feng, A. L., Lee, H. C., Esakki, B. and He, W. (2018) The three-dimensional flow simulation of a flapping wing. Journal of Marine Science and Technology, 26(3), 297–308. 34. Mellinger, D., Shomin, M. and Kumar, V. (2010, October) Control of quadrotors for robust perching and landing. Proceedings of the International Powered Lift Conference (pp. 205–225). 35. Michael, N., Fink, J. and Kumar, V. (2011) Cooperative manipulation and transportation with aerial robots. Autonomous Robots, 30(1), 73–86. 36. Pesavento, U. and Wang, Z. J. (2009) Flapping wing flight can save aerodynamic power compared to steady flight. Physical Review Letters, 103(11), 118102. 37. Lissaman, P. B. S. and Shollenberger, C. A. (1970) Formation flight of birds. Science, 168(3934), 1003–1005. 38. Portugal, S. (2016) Lissaman, Shollenberger and formation flight in birds. Journal of Experimental Biology, 219(18), 2778–2780. 39. Ghommem, M. and Calo, V. M. (2014) Flapping wings in line formation flight: A computational analysis. The Aeronautical Journal, 118(1203), 485–501. 40. Fink, J., Ribeiro, A. and Kumar, V. (2011) Robust control for mobility and wireless communication in cyber–physical systems with application to robot teams. Proceedings of the IEEE, 100(1), 164–178. 41. Fink, J., Ribeiro, A. and Kumar, V. (2013) Robust control of mobility and communications in autonomous robot teams. IEEE Access, 1, 290–309. 42. Kim, H. Y., Lee, J. S., Choi, H. L. and Han, J. H. (2014) Autonomous formation flight of multiple flapping-wing flying vehicles using motion capture system. Aerospace Science and Technology, 39, 596–604. 43. Nakata, T. and Liu, H. (2012) A fluid–structure interaction model of insect flight with flexible wings. Journal of Computational Physics, 231(4), 1822–1847. 44. Hamamoto, M., Ohta, Y., Hara, K. and Hisada, T. (2007) Application of fluid–structure interaction analysis to flapping flight of insects with deformable wings. Advanced Robotics, 21(1–2), 1–21. 45. Schwab, R., Johnson, E. and Jankauski, M. (2019) A novel fluid–structure interaction framework for flapping, flexible wings. Journal of Vibration and Acoustics, 141(6), 061002. 46. Olivier, M., Morissette, J. F. and Dumas, G. (2009) A fluid-structure interaction solver for nano-air-vehicle flapping wings. The 19th AIAA Computational Fluid Dynamics (p. 3676).

8

Soap Film Flow Visualization of Flapping Wing Motion

8.1 INTRODUCTION Investigation of unsteady flow characteristics of FWMAVs through flow visualization techniques is one of the prominent techniques compared to the conventional smoke tracing observation. In smoke tracing, by using a laser, a two-dimensional (2D) flow is sliced from the real three-dimensional (3D) flow field. The main drawback of this method is hard to calculate the aerodynamic forces with numerical values, and it provides only the qualitative flow feature in general [1,2]. Other techniques like the pressure-sensitive painting (PSP) are particularly outstanding in demonstrating the high-resolution pressure distribution on the wing or body surface of aircraft in a quantitative manner. The pressure field on the wing surface is integrated to determine the resultant global force applied on the wing [3–5]. However, the high resolution of PSP rich in spatial domain with high-bit cameras and not good in the time domain. It is very difficult to capture high-bit images of the flapping wing surfaces during their high wingbeat frequencies. Regarding the quantitative flow visualization subjected to the high-frequency flapping wing is seems to be a major concern [6]. The majority of the flow visualization work used particle image velocimetry (PIV) with high-speed photography to measure the unsteady flow field, including the flapping wing case [7,8]. In the past, the soap-film is used to visualize the steady-state flow patterns induced by a stationary cylinder or other 2D objects. The observation is only categorized as one of the qualitative methods, similar to the smoke tracing technique [9–13]. However, in soap-film visualization, a 3D flow field around a flapping wing of a 10 cm-span FWMAV is recorded using a high-speed camera herein [14–17]. With the experimental inferences, the relationship between the color (thickness) field of the soap-film and the corresponding 3D downwash will be derived. Based on this relationship, the quantitative analysis of soap-film flow visualization around a flapping wing is possibly performed [18–21]. Table 8.1 summarizes the various flow visualization methods, and it is evident that the soap film and PIV methods are comparatively better than other methods in the unsteady flow issues [22–27].

DOI: 10.1201/9780429280436-8

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TABLE 8.1 Comparison of Various Flow Visualization Methods Method Smoke tracing PSP PIV Soap-film (this chapter)

Quantitative Result × ○ ○ ○

Appliance to Unsteady Flow Problems ○ × ○ ○

Running Cost Low Medium High Low

8.2 METHODOLOGY 8.2.1 Working Principle In order to solve the flow field of a soap-film, the conservation of mass is initially considered. The kinematic viscosity of soap-film (kinematic viscosity = viscosity/ density = μ/ρ) 1.95 × 10 −5 m2/s is similar to that of air 1.6 × 10 −5 m2/s at 25°. Also, the Reynolds number and viscous flow behavior of soap-film are similar to air. The contact points of soap-film with a wing airfoil follow the non-slip boundary condition, and the local velocity of the contact point can be assumed the same as the air mass dragging the soap-film. In other words, the velocity field shown on the soap-film is the airflow field adjacent to it. From an infinitesimal control volume, Δx × Δy × h of soap-film shown in Figure 8.1, the 2D flow field along x-, y-directions inside the soap-film (u,v) and soap film thickness field h is considered. Let us assume the volumetric inlet and outlet of an infinitesimal soap-film element at the location of (x,y) about the control volume Δx × Δy × h(x,y,t), the net volumetric flow rate of this volume is equal to the time change of the volume of it:

[u( x , y) − u( x + ∆x , y)] h ⋅ ∆y + [ v( x , y) − v( x , y + ∆y)] h ⋅ ∆x =

∆(h ⋅ ∆x ⋅ ∆y) (8.1) ∆t

FIGURE 8.1  Image of an FWMAV in a soap-film using a high-speed camera (1,000 fps).

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Subject to Eq. (8.1), take the Taylor expansion of u(x + Δx, y) and v(x, y + Δy) about (x,y), the nonhomogeneous continuity equation with a source term is given as,  ∂u ∂v 1 dh (8.2) + = ∇⋅u = − ∂x ∂ y h dt



When a solid boundary such as a wing slides along the soap-film in Figure 8.1, the instantaneous air velocity (u,v) relative to the wing would leave a trace on the soapfilm. Due to the change in soap-film thickness field h, the appeared fringe color can be observed in the soap-film through an appropriate light source and a high-speed camera to record.

8.2.2 Differential Approach about a Soap-Film Traditional soap-film flow visualization, which is rarely used for FWMAVs, is mainly used for steady-state flow fields [28–31]. However, the study on unsteady flow fields by their instantaneous imaging of a soap-film is a novel flow visualization method around a flapping wing. In order to successfully solve the soap-film flow field (u,v), the incompressible momentum equations may be needed.

u

∂u ∂u 1 ∂ P µ  ∂2 u ∂2 u  +v =− +  +  (8.3) ∂x ∂y ρ ∂x ρ  ∂x 2 ∂ y2 



u

∂v ∂v 1 ∂P µ  ∂2 v ∂2 v  (8.4) +v =− +  +  ∂x ∂y ρ ∂ y ρ  ∂x 2 ∂ y2 

Equations (8.2)–(8.4) are used to predict the pressure field around the flapping wing and calculate the lift and drag through solving of (u,v) field [32]. However, due to the lack of high-resolution images unable to determine the thickness fields in the soap-film and it may not be possible to solve the partial differential equations (PDEs) (8.2)–(8.4). It is difficult for the velocity and pressure fields to converge iteratively. Hence, it is necessary to adopt yet other methods to solve the soap film problem.

8.2.3 Integral Approach about a Soap-Film Using Stokes Theorem The whole idea herein is not to solve the complicated velocity field using PDEs in the previous section but rather to calculate the lift force generated by the wing without tedious integral around the wing contour. Hence, the Stokes or Gauss theorem can be utilized to avoid solving the velocity field and directly calculate the lift. The Stokes theorem is given by,

Γ=

 ∫∫ (∇ × u) ⋅ ds (8.5) ∫ u ⋅ d  =  c

s

 The curl ( ∇ × u ) of the velocity field is calculated directly from the soap-film shown in Figure 8.2. Utilizing that, the circulation Γ is calculated by substituting it

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FIGURE 8.2  Integral of the flow field around a 2D wing.

into Eq. (8.5). Further, the lift force L of a 2D wing is calculated using the KuttaJoukowski law, which is given by, L = ρUΓ (8.6)  Unfortunately, the only velocity divergence ( ∇ ⋅ u ) is grasped in Eq. (8.1) rather  than the curl ( ∇ × u ) of the velocity field. So, the above approach does not work.

8.2.4 The Integral Approach of a Soap-Film Using Gauss Theorem Gauss theorem is given by,

∫ u ⋅ dA = ∫ (∇ ⋅ u ) dV (8.7) A

V

 The reason to apply the Gauss theorem is that there is a divergence ( ∇ ⋅ u ) in Eq. (8.7). Substitute dV = h ⋅ dA and Eq. (8.2) into the right-hand side of Eq. (8.7), gives

∫ u ⋅ dA = ∫ − dhdt  dA, (8.8) A

A

where h is a reference fixed thickness of soap-film and assume the soap-film area A = (height a*) × (width b*). Due to the Gauss theorem’s higher dimension than the Stokes theorem, the lift that the Gauss theorem can predict is supposed to have a higher dimension than the 2D lift in the previous case. It means that the analysis using the Gauss theorem herein is supposed to solve the 3D lift directly, rather than the 2D lift shown in Figure 8.2. The ideal wing motion direction of the soap-film thickness field is not parallel to soap-film shown in Figure 8.1. However, the vertical soap-films penetrated through by a fixed wing or a flapping wing are shown in Figure 8.3(a–b).

8.2.5 Soap-Film Thickness Interpreted to 3D Downwash of a Wing In the actual operation of Figure 8.3, a high-speed camera is used to capture the soapfilm color images of a flapping wing. The soap-film can be maintained without breaking for several seconds, long enough to capture many flapping cycles (132 ms for one cycle). Moreover, the thickness of a soap-film is only a few hundreds of nanometers,

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FIGURE 8.3  (a) The soap-film in y-z plane and penetration of fixed wing, (b) flow field around a 3D flapping wing.

which may not cause any obstruction to the flapping wing. Therefore, it can record the velocity flow field. Furthermore, the wings’ arrangement in Figure 8.3 of penetrating through the soap-film allows us to capture few characteristics of the 3D flow field, such as wing tip vortex or downwash, exactly different from the previous 2D case in Figure 8.2 that only intercepts a local 2D flow fields across a wing section. Referred to Figure 8.3(a), the volume flow rate of the six surface planes are for calculating about the left-hand side (LHS) of Eq. (8.7) as below (i, j, k denotes the unit vector of x-, y-, z-direction, respectively): • Normal planes ⑤ and ⑥ (cross-sectional area A = a* × b; a*: height of selected area on the wing; b*: width of a selected area on the wing): The normal vectors dA of entrance plane ⑥ and exit plane ⑤ are vertical to the freestream or the flapping wing. Hence, the contribution of a volume flow rate of planes either ⑤ or ⑥ is automatically zero.

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• Side planes ①, ②, and ③ with the reference thickness h0 of the soap film: It is assumed that no volume flow rate due to zero momentum transfer by the wing disturbance at these “far-field” boundaries, and the contribution of these three surfaces is assumed zero, too. • Bottom plane ④: Assume −Wkˆ denotes the non-vanished downwash increment due to the momentum transfer by the wing disturbance, which contributes to the volume flow rate on plane ④ as follows: −Wkˆ ⋅ (−kˆ)b* h0 = h0 b*W (8.9)



Therefore, Eq. (8.9) is used to account for the average downwash velocity as follows:  1   dh  W =  *  ∫ −  dA (8.10)  b h0  A  dt 



After the average downwash is obtained from Eq. (8.10) of the soap-film thickness field, the remaining lift and induced drag can be directly obtained by the RankineFroude axial momentum jet theory. The lift due to the downwash effect is the vertical momentum rate, which is given by,

L=

d dm (mW ) = W = WρU∞ A (8.11) dt dt

U∞ is the free stream velocity. Additionally, the induced drag is defined as the work, which is the kinetic power due to the downwash effect, divided by the free stream velocity, which is given as,



Dind

1 dm 2 W L2 = 2 dt = (8.12) U∞ 2 ρU∞ 2 A

The overall procedure for the soap-film flow visualization analysis is shown in Figure 8.4.

8.3 SOAP-FILM IMAGING EXPERIMENT OF A 10 CM-SPAN FLAPPING WING 8.3.1  10 cm-Span Flapping Wing In order to investigate the unsteady lift behavior of a flapping wing, a 10 cm-wingspan FWMAV shown in Figure 8.5 has a total weight of 4.28 gf is considered for the ­soap-film flow visualization analysis [33].

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FIGURE 8.4  Methodology of soap-film flow visualization.

FIGURE 8.5  The 10 cm-wingspan MAV Micro Snitch: (a) the assembled MAV, (b) the wing design (unit: mm), (c) total weight.

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Flapping Wing Vehicles

8.3.2 Experiment Setup The experimental setup for the soap-film visualization is shown in Figure 8.6. It consists of: a. Prepare a plastic frame for setting soap-film; b. Build up an expandable polystyrene (EPS) unit as the black box for containing the soap film inside;

FIGURE 8.6  The experimental setup of soap-film visualization for an FWMAV.

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c. Set up the illumination and high-speed camera system; d. Light up the inner space of EPS box; e. Place the black cloth in the background and insert the FWMAV (holding by a trailer in the back) into the soap-film; f. Simultaneously turn on the flapping wing, push FWMAV forward, and switch on the high-speed camera to capture the color fringe image about the soap-film. The whole screen of soap-film is to be placed in a dark space with non-reflective inner walls so that the background glare on the soap-film could be minimized. The dark-space wall material is selected as EPS. The orientation of the incident light for the high-speed camera is adjusted appropriately.

8.3.3 High-Speed Photography for Capturing Soap-Film of a Flapping Wing Motion The color fringe images are captured using the experimental setup shown in Figure 8.6 with a time interval of 2 ms. Hundreds of soap-film tries give only several successful videos of FWMAVs. Figure 8.7 shows 8 snapshots of them to demonstrate one flapping cycle. The feature of the wing tip vortex is very obvious to be found.

8.3.4 RGB-Thickness Field Conversion The next step is to understand the color distribution of the captured frame. In specific, analyzing the color spectrum using a standard color chart and removing the reflective error pixels (as the black color formed in the image) using the image processing technique is performed [34–41]. Figure 8.8 depicts the procedure of image processing analysis. Every two successive frames are taken differentiated to obtain the change in thickness for each pixel. As shown in Figure 8.9(a), a rectangular domain is marked on the region of interest, and the corresponding thickness value of each pixel as Figure 8.9(b) is obtained from the thickness matrix during post-processing of selected images. Later they are used in the calculation of the thickness variation Δh. From Frame 1 to the desired Frame N, a similar procedure is followed. Each pixel in the frame is processed using mean square error and spectrum colors of soap-film with a standard color template of n = 1.33. Illuminant D65 [28] is utilized to find the closest color match for each pixel. For each pixel concerning the standard color template, the wavelength is assigned. The stored wavelength value of each pixel up to the Nth frame is given in the form of a matrix. The time-space limitation should be considered before the flapping wing test in this work for verifying the quantitative soap-film flow visualization. The soap film’s water molecules subside downward and cause the upper film to thinner and thinner until being broken. Due to this phenomenon, the soap film can be sustained only for 25 seconds. The sedimentation downwash is calculated as 0.25 cm/s, which is much smaller than the downwash values in Figure 8.9 and can be ignored for the downwash calculation. The overall size of the soap film is also confined within the frame size of

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Flapping Wing Vehicles

FIGURE 8.7  Soap-film images of the 10 cm-span FWMAV: (a–d) downstroke, (e–h) upstroke.

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FIGURE 8.8  Image processing and analysis of soap-film images.

30 × 30 cm. Even the agitation and disturbance from the flapping wing, the sustaining time of soap film even more shortened to several seconds. However, it is enough to capture many cycles of flapping images for downwash and lift analysis afterward.

8.3.5 Calculation of 3D Downwash, Lift, and Induced Drag of a Flapping Wing The time-varying downwash W in Eq. (8.10) can be discretized and given as below.

 1  W = *   b h0 





∫ (− dhdt )dA ≈  b−h1  ∆∆t ∑∑h ⋅ ∆y ∆z (8.13) *

A

ij

0

j

i

j

i

which the time interval is assigned as Δt = 2 ms. Based on the thickness matrix derived from the soap-film image processing analysis, the downwash for one flapping cycle is compared to the measured data by the force gauge in the wind tunnel shown in Figure 8.10. The downwash result of the Nth frame is compared with the measurement of force gauge from the wind tunnel experiments (U∞ = 0.15 m/s and the inclined angle of 20°) and shown in Figure 8.10. The time-averaged downwash for the soap-film and windtunnel is calculated as 0.507 m/s and 0.768 m/s, respectively. The white background is

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FIGURE 8.9  A soap film frame: (a) defining a rectangular domain (A = a* × b*: a* = 20.683 cm, b* = 14.541 cm) (b) convert into a thickness field (matrix 559 × 393) (unit: Nm).

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FIGURE 8.10  Comparison of downwash.

for downstroke flapping and the dark background is for the upstroke flapping, wherein the downwash is calculated. The unsteady lift of FWMAV is measured in a blow-down wind tunnel [14]. The length and cross-section area of the wind tunnel test section is 100 cm × 30 cm × 30 cm. The turbulence intensity of the wind tunnel is evaluated as 0.05–0.028%. The wall effect can be neglected as the blockage ratio is less than 7.5%. A calibrated 6 degrees-of-freedom load cell (Bertec, OH, USA) for lift measurement has a maximum error of 0.2% of the full-scale due to nonlinearity or hysteresis. The data-acquisition rate of the load-cell is set as 1,000 points per second. The downwash data of the soap-film experiment shown in Figure 8.10 is supposed to have a trend agreement with the twin-peak phenomenon during flapping [29]. However, it still lacks the accuracy of measurement compared to the forcegauge data from the wind-tunnel experiments. It is observed that for a single cycle, time-averaged downwash of soap-film (0.507 m/s) is 66% of force-gauge data (0.768 m/s). The main reason may be due to the scenario difference between the soap-film experiment and the force-gauge measurement of FWMAV. The former (soap-film) moves forward with quiet air and soap-film and measures the downwash values from the leading edge to the trailing edge locally; the latter (wind tunnel) lets FWMAV keep stationary but drives the air blowing across the FWMAV and the force gauge detects the whole lift globally, not locally.

8.4 SUMMARY In this chapter, a 10cm wingspan FWMAV flapping wing motion is visualized with a soap film aid. An experimental setup using high-speed photography is utilized to capture the flapping motion passing it through a soap film. A 3D downwash induced

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with a flapping wing is determined using a mathematical model. The thickness of the flow field is measured using image processing and analysis. The developed analytical and soap-film flow visualization technique can effectively record the unsteady lift behavior of an FWMAV quantitatively.

REFERENCES

1. Williamson, C. H. (1996) Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28(1), 477–539. 2. Bryant, M., Mahtani, R. L. and Garcia, E. (2012) Wake synergies enhance performance in aeroelastic vibration energy harvesting. Journal of Intelligent Material Systems and Structures, 23(10), 1131–1141. 3. Liu, T., Campbell, B. T., Burns, S. P. and Sullivan, J. P. (1997) Temperature-and pressure-sensitive luminescent paints in aerodynamics. Applied Mechanics Reviews, 50, 227–246. 4. Engler, R. H., Klein, C. and Trinks, O. (2000) Pressure sensitive paint systems for pressure distribution measurements in wind tunnels and turbomachines. Measurement Science and Technology, 11(7), 1077. 5. Egami, Y., Iijima, Y., Amao, Y., Asai, K., Fuji, A., Teduka, N. and Kameda, M. (2001) Quantitative visualization of the leading-edge vortices on a delta wing by using pressure-sensitive paint. Journal of Visualization, 4(2), 139–150. 6. Shin, T. S. (2010) Application of Pressure Sensitive Paint (PSP) on the Polymer Flexure Wing, Master’s Thesis, Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, Taiwan (in Chinese). 7. Ramasamy, M. and Leishman, J. G. (2006) Phase-locked particle image velocimetry measurements of a flapping wing. Journal of Aircraft, 43(6), 1867–1875. 8. Flint, T. J., Jermy, M. C., New, T. H. and Ho, W. H. (2017) Computational study of a pitching bio-inspired corrugated airfoil. International Journal of Heat and Fluid Flow, 65, 328–341. 9. Couder, Y., Chomaz, J. M. and Rabaud, M. (1989) On the hydrodynamics of soap films. Physica D: Nonlinear Phenomena, 37(1–3), 384–405. 10. Zhang, J., Childress, S., Libchaber, A. and Shelley, M. (2000) Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature, 408(6814), 835–839. 11. Rutgers, M. A., Wu, X. L. and Daniel, W. B. (2001) Conducting fluid dynamics experiments with vertically falling soap films. Review of Scientific Instruments, 72(7), 3025–3037. 12. Fayed, M., Portaro, R., Gunter, A. L., Abderrahmane, H. A. and Ng, H. D. (2011) Visualization of flow patterns past various objects in two-dimensional flow using soap film. Physics of Fluids, 23(9), 091104. 13. Rivera, M. K., Aluie, H. and Ecke, R. E. (2014) The direct enstrophy cascade of twodimensional soap film flows. Physics of Fluids, 26(5), 055105. 14. Huang, H. L. (2014) 2D Quasi-Steady Flow around a Flapping Wing and Its BubbleFilm Flow Visualization, Master’s Thesis, Department of Mechanical and ElectroMechanical Engineering, Tamkang University, Taiwan (in Chinese). 15. Yang, L. J., Esakki, B., Chandrasekhar, U., Hung, K. C. and Cheng, C. M. (2015) Practical flapping mechanisms for 20 cm-span micro air vehicles. International Journal of Micro Air Vehicles, 7(2), 181–202. 16. Yang, L. J. (2012) The micro-air-vehicle Golden-Snitch and its figure-of-8 flapping. Journal of Applied Science and Engineering, 15(3), 197–212.

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17. Yang, L. J., Hsiao, F. Y., Tang, W. T. and Huang, I. C. (2013) 3D flapping trajectory of a micro-air-vehicle and its application to unsteady flow simulation. International Journal of Advanced Robotic Systems, 10(6), 264. 18. Shang, J. K., Combes, S. A., Finio, B. M. and Wood, R. J. (2009) Artificial insect wings of diverse morphology for flapping-wing micro air vehicles. Bioinspiration and Biomimetics, 4(3), 036002. 19. Truong, Q. T., Nguyen, Q. V., Truong, V. T., Park, H. C., Byun, D. Y. and Goo, N. S. (2011) A modified blade element theory for estimation of forces generated by a beetlemimicking flapping wing system. Bioinspiration and Biomimetics, 6, 036008. 20. Keennon, M., Klingebiel, K. and Won, H. (2012, January) Development of the nano hummingbird: A tailless flapping wing micro air vehicle. The 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2012-0588. 21. Yang, L. J., Kao, A. F. and Hsu, C. K. (2012) Wing stiffness on light flapping micro aerial vehicles. Journal of Aircraft, 49(2), 423–431. 22. Vorobieff, P., Rivera, M. and Ecke, R. E. (1999) Soap film flows: Statistics of twodimensional turbulence. Physics of Fluids, 11(8), 2167–2177. 23. Rutgers, M. A., Wu, X. L., Bhagavatula, R., Petersen, A. A. and Goldburg, W. I. (1996) Two-dimensional velocity profiles and laminar boundary layers in flowing soap films. Physics of Fluids, 8(11), 2847–2854. 24. Gharib, M. and Beizaie, M. (1999) Visualization of two-dimensional flows by a liquid (soap) film tunnel. Journal of Visualization, 2(2), 119–126. 25. de Croon, G. C., Groen, M. A., de Wagter, C., Remes, B., Ruijsink, R. and van Oudheusden, B. W. (2012) ) Design, aerodynamics and autonomy of the DelFly. Bioinspiration and Biomimetics, 7(2), 025003. 26. Haque, M. R., Fayed, M., Gunter, A. L., Smadi, O., Kadem, L. and Ng, H. D. (2011) Numerical simulation and flow visualization using soap film of the self-organized vortex structure in the wake of an array of cylinders. Journal of Visualization, 14(4), 311–314. 27. Georgiev, D. and Vorobieff, P. (2002) The slowest soap-film tunnel in the Southwest. Review of Scientific Instruments, 73(3), 1177–1184. 28. Hunt, R. W. G. and Pointer, M. R. (2011) Measuring Colour. John Wiley and Sons. 29. Dickinson, M. H., Lehmann, F. O. and Sane, S. P. (1999) Wing rotation and the aerodynamic basis of insect flight. Science, 284(5422), 1954–1960. 30. Yang, L. J., Feng, A. L., Lee, H. C., Esakki, B. and He, W. (2018) The three-dimensional flow simulation of a flapping wing. Journal of Marine Science and Technology, 26(3), 297–308. 31. Karásek, M., Muijres, F. T., De Wagter, C., Remes, B. D. and de Croon, G. C. (2018) A tailless aerial robotic flapper reveals that flies use torque coupling in rapid banked turns. Science, 361(6407), 1089–1094. 32. Patankar, S. V. (1980) Numerical Heat Transfer and Fluid Flow, CRC Press. 33. Chen, Y. S. (2011) The Improvement on the Miniaturization of Flapping Micro Aerial Vehicles, Master’s Thesis, Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, Taiwan (in Chinese). 34. Leon, K., Mery, D., Pedreschi, F. and Leon, J. (2006) Color measurement in lab units from RGB digital images. Food Research International, 39(10), 1084–1091. 35. Almadhoun, M. D. and Palestine, G. (2013) Improving and measuring color edge detection algorithm in RGB color space. International Journal of Digital Information and Wireless Communications, 3(1), 19–24. 36. Broadbent, A. D. (2004) A critical review of the development of the CIE1931 RGB color-matching functions. Color Research and Application: Endorsed by Inter-Society Color Council, 29(4), 267–272.

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37. Chang, C. (2006) U.S. Patent No. 6,992,803. Washington, DC: U.S. Patent and Trademark Office. 38. Zneit, R. A., AlQadi, Z. and Zalata, M. A. (2017) A methodology to create a fingerprint for RGB color image. International Journal of Computer Science and Mobile Computing, 16(1), 205–212. 39. Yang, J., Ye, X., Li, K., Hou, C. and Wang, Y. (2014) Color-guided depth recovery from RGB-D data using an adaptive autoregressive model. IEEE Transactions on Image Processing, 23(8), 3443–3458. 40. Gil, S., Seok, Y., Park, K., Yoo, J. and Chin, S. (2019, November) Soap film flow and thickness for soap bubble rendering. The 25th ACM Symposium on Virtual Reality Software and Technology. 41. Afanasyev, Y. D., Andrews, G. T. and Deacon, C. G. (2011) Measuring soap bubble thickness with color matching. American Journal of Physics, 79(10), 1079–1082.

9

Dynamics and ImageBased Control of Flapping Wing Micro Aerial Vehicles

9.1  INTRODUCTION TO STEREOVISION SYSTEM Stereovision systems are developed to mimic the eyes of human beings. In general, the crossing method in Figure 9.1(a) and similar parallel method [1] in Figure 9.1(b) of stereovision are widely used, and the latter is easy to manipulate. Let us discuss the working principle of the stereovision system. Let P be the target in the stereovision analysis, as shown in Figure 9.2. A point P is considered as the target from the origin at the center of these two cameras. When it is viewed from the right end, the X is at the left, Y is toward the target, Z is orthogonal to XY, and C is the dispersion of these two cameras. The point P is seen from the left, and the right camera is depicted in Figures 9.3(a) and (b), respectively. From the central line, the largest pixel numbers are given as Pmax and θmax is the half field of view in the horizontal direction as shown in Figure 9.4. The target in the X coordinate is given by [2],

1 1  X = C  +   (9.1)  2 ρ −1

P1 and P2 are the pixels focused by the left and the right cameras away from the center and β = P1 / P2 . The depth γ = L is obtained by

L = 

C , (9.2) γ ( β − 1) tan φmax

where γ = P2 / Pmax The target height in Figure 9.5 is calculated as,

z =  µ tan φmax , (9.3)

where µ =  q / qmax , and qmax and q denote the maximal pixels and pixels of target counted from the center of the picture in the vertical direction of Figure 9.6. Based on these relationships, the stereo vision system calculates three-dimensional coordinates of a pixel, and for each image, based on the resolution of a camera, the number of pixels is varied. DOI: 10.1201/9780429280436-9

283

284

Flapping Wing Vehicles

FIGURE 9.1  Geometries of the stereo cameras: (a) crossing (b) parallel.

FIGURE 9.2  Camera with the coordinate system.

FIGURE 9.3  (a) Left camera, (b) right camera.

FIGURE 9.4  Half-field view of the camera.

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285

FIGURE 9.5  Geometry of camera.

FIGURE 9.6  Vision of a camera.

9.2  SIMPLIFIED DYNAMIC MODEL In order to understand the flapping wing motion characteristics, a simplified dynamic model is developed. By considering Newton’s second law of motion, the equations of motion of FWMAV are formulated.

9.2.1 Equations of Motion In order to formulate the equations of motion for FWMAV [3,4], various coordinate frames are assigned. A body-fixed frame shown in Figure 9.7 is attached to the FWMAV body. The Xb is represented along the fuselage, which lies in the FWMAVs symmetrical plane, Yb is normal to the symmetrical plane toward the right-side wing, and Zb is pointing downwards completes the right-hand Cartesian coordinate system. However, the inertial frame is represented as ( X f , Yf , Z f ). The transformation between these two frames is achieved through establishing a rotational matrix R,

Vf = RVb



∼ R = R ω,

(9.4) (9.5)

where Vf and Vb are velocities are represented in inertial and body-fixed frames, respec∼

tively. ω is the cross product operator for the angular velocity ω = (ωX , ωY , ωZ ) .

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Flapping Wing Vehicles

FIGURE 9.7  Body fixed coordinate frame.

The general equations of motion of the FWMAV through using Newton’s second laws is given by,

d V + ω  × ( mV ) (9.6) dt  d   ∑ M = I ω  + ω  × ( Iω ) , (9.7) dt ∑F = m

where I denote the inertia tensor. The external forces are the vehicle’s weight, aerodynamic forces, horizontal and vertical tail forces. They also produce moments about the center of gravity (CG)

9.2.2 Averaging Theory and Formulation of Forces 9.2.2.1  Applicability of Averaging Theory The averaging theory is used to analyze the periodic flapping motion and dynamics of FWMAV [5,6]. It is assumed that the wing is much lighter than the fuselage structure under this theory. The vertical motion of the flapping wing vehicle is affected

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287

FIGURE 9.8  The cruise flight of Golden-Snitch.

slightly. To understand the flapping motion, the cruising flight of Golden-Snitch FWMAV is captured using a high-speed camera. As we observed from Figure 9.8 that, it flies at a forward velocity of ∼3 m/s, and the fuselage maintains a specific altitude when the wings are flapping. In general, the lift and thrust forces can be expressed as a function of advance ratio J, which is given by [7],

1 Flift =    ρU 2 SC L ( J ) (9.8) 2 1 Fthrust =    ρU 2 SCT ( J ) , (9.9) 2

where CL(J) and CT (J) are J’s functions, denote the lift coefficient and thrust coefficient, respectively. The forces calculated from the lift or thrust coefficient with J’s function can be considered an averaged force. The proof is explained below. Consider a very thing rectangular wing, as shown in Figure 9.9(a), with length b, width W, stroke angle Φ, and flapping frequency ω = 2πf. Assume the setting angle is zero so that the angle of attack (AOA) is determined by the attacking angle of the incoming air stream completely. Consider an elemental area on the wing whose flapping motion is shown in Figure 9.9(b). According to the theory of aerodynamics, the lift force generated by this element is given by, 1 dF =  ρV 2C L (α ) dA, (9.10) 2  lω  2 where  V 2 = U 2 +  (lω ) ,  dA = Wdl , and α = arctan   U 



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FIGURE 9.9  Wing parameters.

To simplify the notation, we define l /b  = γ . Introducing the advance ratio J, we obtain γπ lω = U (9.10a) JΦ As a result, Eq. (9.10) can be redefined as,

1 dF =  ρV 2C L (α ) ds 2   π 2 2  1 =  ρU 2Wb 1 +   γ C L (α ) dγ 2   JΦ  

  π 2 2  1 =  ρU 2 S 1 +   γ C L (α ) dγ (9.11) 2   JΦ  

S = Wb is the wing’s total area, and α   =  α ( J ,γ ) . Consider the average force during the downstroke during time interval Td, which is given by,

F = 

1 Td

∫



= 

1 Td

∫ ∫

= 

ρU 2 S 2Td



Td 0

F (t ) dt

Td

0

F 0

dF dt

∫ ∫ Td

0

  π 2 2  γ C L (α ) d γ dt 1 +   JΦ  0  1

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Since the integrant is not an explicit function of time, we can integrate time first and null out Td. Therefore, F = 



ρU 2 S 2

∫

1 0

  π 2 2  γ C L (α ( J ,γ )) d γ 1 +    JΦ  

Define C L' ( J ) =



∫

1 0

  π 2 2  γ C L (α ( J , γ )) d γ 1 +    JΦ  

We obtain that

1 Fd =  ρU 2 SC L' d ( J ) , (9.12) 2

where the subscript d denotes downstroke. Similarly, the average force during the upstroke is given by



1 Fu =  ρU 2 SC L' u ( J ) (9.13) 2 As a result, the average force generated during flapping motion is given by, F =  Fd + Fu 1 1 =  ρU 2 SC L' d ( J ) + ρU 2 SC L' u ( J ) 2 2 1 =  ρU 2 SC L' ( J ) , (9.14) 2



where C′L(J) = C′Ld(J) + C′Lu(J). We can see that the average force has the same formulation as Eqs. (9.9) and (9.10). This is not rigorous proof because many aerodynamic characteristics such as wing flexibility and wind flow stability are not accounted for in the analysis. However, it can still be used as a simplified theory to analyze the flapping wing behavior based on the lift and thrust co-efficient curves determined from the experimental analysis. 9.2.2.2  Formulation of Forces and Moments The average forces are calculated by using Eq. (9.14). Moreover, Eq. (9.15) for one flapping cycle is independent of time can be applied to analyze both fixed and flapping wing vehicles. Analyzing the flapping-wing dynamics of vehicles, set angle, and stroke angle are used instead of attack angle. The aerodynamic forces are resolved in the X and Z direction, as shown in Figures 9.10(a) and (b). They are given by,

Fzbwing =  Fthrust sin (α ) −  Flift cos (α ) (9.15)



Fxbwing =  Fthrust cos (α ) + Flift sin (α ) , (9.16)

where α is the set angle of FWMAV.

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FIGURE 9.10  The aerodynamic force distribution during (a) downstroke, (b) upstroke.

Also, the moments due to these forces can be calculated by summing up all the individual moments and torque. The geometric parameters to determine the moments are shown in Figure 9.11. The calculated forces and moments are substituted in the Eq. (9.6). Moreover, Eq. (9.7) and the position, velocity, and attitude of the FWMAV are determined. 9.2.2.3  Coefficients of the Main Wing The coefficient of lift and coefficient of thrust can be modeled as,

C Lwing =  ae− bj + c (9.17)



CTwing =  a′e− b′j + c′ (9.18)

For the Golden-Snitch, these parameters are determined by performing a wind tunnel test and given as a set angle function given in Table 9.1. After determining the lift and thrust coefficients, the corresponding forces can be calculated by using Eqs. (9.9) and (9.10). These forces are the average forces calculated for a single flapping cycle.

FIGURE 9.11  Geometric parameters of the fuselage.

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TABLE 9.1 Parameters in Force Coefficients for a Flapping Wing Set angle

a b c a′ b′ c′

10° 19.07

20° 20.22

30° 35.35

40° 42.09

50° 58.25

5.471 0.6914

4.174 1.181

4.851 1.404

4.823 2.051

6.107 2.346

109.8 7.878 0.3139

103.9 8.168 0.1475

153.2 11.05 –0.1054

156.2 10.58 –0.5002

92.43 9.154 –0.8389

9.2.2.4  Coefficients of the Horizontal Wing According to aerodynamics, lift and drag coefficients shown in Table 9.2 are given by 2 Ltail (9.19) ρU 2 Stail 2 Dtail =  , (9.20) ρU 2 Stail



C Ltail = 



C Dtail

where ρ is the density of air, Stail is the tail wing area, Ltail and Dtail denote the lift and drag of the tail wing, respectively. For Golden-Snitch, the tail wing area is about 6013.715 mm2, and the density of air is 1.23 kg/m3. Hence,

C Ltail U 2 = 2.65  Ltail (9.21)



C Dtail U 2 = 2.65  Dtail , (9.22)

where the unit of U and Ltail ( Dtail ) are m/s and gf, respectively. The formulation of various coefficients and their responses for varied AOA is useful for performing preliminary analysis on understanding the flapping motion. However, to formulate a control problem in a linearized domain, further analysis is necessary for formulating transfer function, which is discussed in the forthcoming Section 9.3.2.

TABLE 9.2 Coefficients for a Tail Wing 0

−10

0

0

0

0

0

0

0

AOA

−20

C Ltail C Dtail

–1.242

–0.2808

0.3571

0.5963

0.6881

0.8148

0.9025

0.8868

–0.4868

–0.695

–0.4938

–0.5229

–0.5974

–0.6971

–0.8186

–1.04

0

10

20

30

40

50

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9.3  CONTROL LAW DESIGN 9.3.1 Linearized Dynamics For linearized analysis, the Golden-Snitch is cruising at the height of z = z0 with a speed of U = U 0 and the flapping frequency f = f0 . A small perturbation of FWMAV is encountered during the cruising condition causes non-linear behavior of the system, which was linearized about the nominal conditions. Assume that the vehicle is initially operating under cruise conditions, namely, z = z0 , z = 0U = U 0 and f = f0 . Let Θ ( t ) be the fuselage’s pitch angle and assume that Θ =  Θ0 at cruise. The set angle for the main wings is approximately α w =  Θ0 + cw , while the angle of attack (AOA) of the tails is α t =  Θ0 + ct , where cw and ct are constants that depend on the installation angle of the wings. The vehicle moves upward with a vertical speed of z then, and the AOA decreases, as shown in Figure 9.12. z Θ = tan −1 (9.23) u′ Let

Fw = Fw ,0 + δ Fw (9.24)



Ft = Ft ,0 + δ Ft (9.25)



z = z0 + δ z (9.26)

Fw,0 and Ft,0 denote the required lift forces, δ Fw and δ Ft is the perturbations in lift forces generated by the main and tail wings. δ z is the offset of FWMAV from the nominal altitude. The equation of motion for one flapping period is given by,

··

Fw + Ft − mg = m z (9.27)

FIGURE 9.12  Vertical motion of the vehicle.

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293

Linearized equation is resulted in, ¨

δ Fw + δ Ft = mδ z (9.28)



Equations (9.9) and (9.18) represent the force generated by the main wings as a function of U , ζ ,η ,ξ , and J. Besides, J itself is a function of the flapping frequency f. Therefore, the dependencies can be written as Fw = Fw (U ,ζ ,η ,ξ , f ) (9.29)



so that the perturbation δ Fw can be formulated as:

δ Fw =

∂Fw ∂F ∂F ∂F ∂F δ U + w δζ + w δη + w δξ + w δ f (9.29a) ∂u ∂ζ ∂η ∂ξ ∂f

According to the wind tunnel tests, the parameters (ζ ,η ,ξ ) are functions of the set angle and the vehicle’s vertical position and speed with a small variation is denoted as δ z and δ z . The deviation leads to various parameters by changing the direction of flow, which is equivalent to changing the set angle, as shown in Figure 9.12. Accordingly, the variations of those parameters are obtained as,

δU =



∂U ∂ δ z   = U 20 + z 2   |U =U0 ,  Z =0 = 0 (9.30) ∂z ∂z



δζ =

∂ζ ∂ζ ∂Θ δΘ = δ z (9.31) ∂Θ ∂Θ ∂z



δη =

∂η ∂η ∂Θ δΘ = δ z (9.32) ∂Θ ∂Θ ∂z



δξ =

∂ξ ∂ξ ∂Θ δΘ = δ z (9.33) ∂Θ ∂Θ ∂z

Equations (9.31)–(9.34) represent that the variation of these parameters is given as the function of set angle variation induced by the speed perturbation. Hence, it is ∂Θ easy to determine analytically. It is given as per Figure 9.12, ∂z  



∂Θ d  = −  tan −1 ∂z dz 

z  1  =− (9.34)  u u0

However, the variation of J with respect to the perturbation of flapping frequency δ f is given by

δJ =



∂J −U 0 δf = δ f (9.35) ∂f 2bΦ f02

Then, the perturbation of Fw is given by,

δ Fw = −

1  ∂Fw ∂ζ ∂Fw ∂η ∂Fw ∂ξ  −u 0 ∂Fw + + δf   δ z + U 0  ∂ζ ∂Θ ∂η ∂Θ ∂ξ ∂Θ  2bΦ f02 ∂ J

 −U 0 ∂Fw ∂ζ ∂η ∂ξ  = −K w U 0 e−η J − Jζ e−η J + δf δ z +  ∂Θ ∂Θ ∂Θ  2bΦ f02 ∂ J

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Flapping Wing Vehicles

Similarly, the perturbation of Ft is obtained,

δ Ft =



∂Ft ∂C ∂Θ ∂C δΘ = K t U 20 Lt δ z = −K t U 20 Lt δ z (9.36) ∂Θ ∂Θ ∂z ∂Θ

Finally, the linearized equations of motion are given by, mδ z + Bδ z = Rδ f , (9.37)

where

B = K w U 0 (e−η J ζ ,Θ − Jζ e−η Jη,Θ + ξ ,Θ ) + K w u 0C Lt ,Θ (9.38) R = K w U 20ζηe−η J

u0 (9.39) 2bΦf02

9.3.2 Formulation of the Transfer Function The linearized equation representing the vertical motion of the Golden-Snitch is given in Eq. (9.38) can be represented as a transfer function which is given by

δ z (s) R = (9.40) δ f ( s ) ms 2 + Bs

This open-loop system has one pole at the origin and the other pole in the lefthand plane. It can be controlled using a simple P-control with unity feedback regardless of feedback gain K. However, in order to maintain the FWMAV at a nominal height, the reference command has to be set as zero in the linearized dynamics. The reference command in the linearized system considers the offset dynamics by

δ zr = z − zo = 0 (9.41) The control law for the linearized system is given as,



δ f ( s ) = −Kδ z ( s ) + δ zr = −Kδ z ( s ) (9.42)

or  δ f (t ) = −Kδ z (t ) in the time domain. Numerical simulations are performed, and convergence of the system to the desired state is guaranteed.

9.4  NUMERICAL SIMULATIONS Simulation is performed for the Golden-Snitch by considering various parameters listed in Table 9.3. The variables defined in Eqs. (9.39) and (9.40) are computed as R = 2.0541 and B = 102.0409. From the root-locus analysis, the damping ratio is about 0.7 when K = 300.

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TABLE 9.3 Physical Parameters of Golden-Snitch Item m (g) b f0

Value   8   0.2   12.66

ζ ζ0 CL Sw

  20.22   57.43   2.19   0.014   1230

ρ

Item ϴ η ηϴ St U0 Ф ξ ξϴ

Value 0.35 4.17 1.10 0.006 3.5 0.93 1.18 2.39

The simulation results show that the vehicle has an initial offset of +10 cm, as observed in Figure 9.13, and the control history is shown in Figure 9.14. The solid line is regular P-control, and the dashed line is developed control law. The stabilization of the system is quicker within 1 sec in the case of developed control. There is a discontinuity in control, and the closed-loop system is slower in response.

FIGURE 9.13  Altitude control.

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FIGURE 9.14  Control history.

9.5  EXPERIMENTS AND DISCUSSION The experimental setup shown in Figure 9.15 is utilized to perform an indoor flight test [8–10], and the altitude of FWMAV is measured using a stereovision system. The snapshots of video recorded during the experiments are shown in Figures 9.16 and 9.17. Because of the space constraints, the Golden-Snitch FWMAV was attached

FIGURE 9.15  Indoor stereovision flight test setup.

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297

FIGURE 9.16  Flight tests in the laboratory.

to the ceiling with a string of negligible mass flying in a restricted range. The length of the string is maintained so that the vertical motion of FWMAV is not affected. However, it generates the centripetal force during flying action, and if there is any deviation from the nominal altitude, then corrective control actions are provided by the designed controller. It can fly at a designated altitude by adjusting its motion, and it was flying at the predefined desired altitude of 1.5 m. The black strips are placed on the wall (Figure 9.16) at an altitude of 1.2, 1.4, 1.6, and 1.8 m to provide the information on FWMAV flying that gives visual display to the human operators. The nominal altitude of flying is maintained at 1.5 m in Figure 9.18(a) and 1.2 m in Figure 9.18(b), respectively, and the results show that there is more noise in the

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FIGURE 9.17  Flight tests in the indoor environment.

measurement and hence the data around the nominal altitude is not attained the designated altitudes effectively. The control action was limited to –2.5 Hz with an excursion of 250/K cm, where K is the feedback gain. That is, any excursion measurement larger than 250/K cm is going to be filtered, and it triggers the largest control signal. Due to this, the noisy measurement has not attained a large variation in the flight tests. Also, Figure 9.19 shows that the altitude of FWMAV data fluctuates around the set point of 1.5 m, and there is still more noise from the stereovision measurement. The transition from 1.5 m to 1.2 m and corresponding control actions are given in Figure 9.19(b). These experimental studies are performed to understand the linear control architecture for controlling the FWMAV. However, image-based control of FWMAV is

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299

FIGURE 9.18  Position data acquired by the stereovision system for the nominal altitude of (a) 1.5 m, (b) 1.2 m.

FIGURE 9.19  Altitude transition from a height of 1.2 m to 1.5 m.

considered to be a novel and interesting topic. Hence, the following section discusses image-based control of an FWMAV and a swarm of FWMAVs.

9.6  VISION-BASED CONTROL Vison-based navigation systems are efficient choice to control the FWMAVs autonomously as it only requires a light weight camera system [11–16]. A typical visionbased control system [17–20] is depicted in Figure 9.20 through integrating FWMAV transmitter system, Ardunio circuitry, color detection algorithm, video receiver, and flapping wing system. Based on the images captured from FWMAV, the control interface sends an appropriate signal to actuate the FWMAV. The images obtained are processed using the developed image algorithms, and the respective target is identified based on its color. The predefined target color and corresponding actuation of FWMAV are performed. For example, any predefined color is considered for actuating the motors to achieve flapping motion and accounted for controlling the direction of FWMAV. The color detection algorithm is optimized for its time detection and sturdiness to

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FIGURE 9.20  Block diagram of the vision-based FWMAV control.

obtain swift color detection for enhanced navigation. The hue-based color models are preferably used due to their accuracy and simplicity for color detection. Other color models, such as RGB, Normalized RGB, HSV, YUV, YCbCr, YIQ, CIELAB, and CIELUV are also explored to improve the efficiency of color detection as per the algorithm that is schematically depicted in Figure 9.21. The color detection time comprises effective time conversion from the actual color model to process color model (TC) and thresholding time (Tp) to perform the selection of a color element, and also, the time is taken for the thresholding process (Tt). During the real-time experiments, the user can define any color of their interest and train the algorithm for actuation and direction control. Several experiments are conducted using real-time images, standard database images, and synthetic images to optimize time for color model conversion (Table 9.4) and thresholding. The image and video frames are resized to 320 × 240 for convenience during post-processing. It is evident from Table 9.5 that Y and RGB-based color models are performing efficiently in detecting the colors. However, RGB-based models are not being used because of their high sensitivity to the illumination and noise, and hence Y-based

FIGURE 9.21  Color recognition algorithm.

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Dynamics Image-Based Control of Flapping Wing

TABLE 9.4 Color Model Conversion (TC) Color Model N RGB HSV YUV YIQ YCbCr CIELUV CIELAB

Conversion Time 0.0025 0.0455 0.0133 0.0135 0.0136 0.1213 0.1673

TABLE 9.5 Average Threshold Time for Various Colors Colors Blue Green

RGB 0.031 0.032

NRGB 0.031 0.031

HSV 0.047 0.048

YIQ 0.037 0.037

Yellow Red Orange

0.03 0.031 0.034

0.031 0.031 0.032

0.048 0.046 0.047

0.036 0.036 0.037

YUV 0.037 0.037 .037 0.036 0.036 0.037

YCbCr 0.037 0.036

CIELAB 0.09 0.089

CIELUV 0.07 0.072

0.036 0.036 0.037

0.092 0.093 0.091

0.072 0.074 0.074

color model is considered. Experiments are conducted to verify its robustness of various color models under the various noises, and the results are given in Table 9.6. The threshold time is performed using the test image with various possible noises, and root mean error is evaluated. It is observed from these results that Y-based color models are performing better and robust for various noises. The color detection algorithm using the optimal color model is integrated into the control interface, enhancing the processing of real-time images received from the on-board micro camera mounted on FWMAV. TABLE 9.6 Color Model Sturdiness toward Various Noises Noises White Noise Gaussian Blue Fast Fading Jp2k Jpeg

HSV 0.088 0.025 0.044 0.035 0.046

YIQ 0.088 0.012 0.025 0.019 0.020

YUV 0.089 0.013 0.026 0.018 0.029

YCbCr 0.084 0.013 0.026 0.018 0.029

CIELAB 0.1168 0.017 0.060 0.039 0.059

CIELUV 0.115 0.011 0.024 0.017 0.028

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Flapping Wing Vehicles

FIGURE 9.22  Video transmission system: (a) flapping wing vehicle with a micro camera (b) video receiver unit, (c) Arduino-based FWMAV transmitter system.

9.7 EXPERIMENTAL STUDIES USING DEVELOPED IMAGE PROCESSING ALGORITHMS The experimental setup shown in Figures 9.22(a–c) is used to perform real-time experiments by incorporating a developed image algorithm. A micro camera is mounted on the FWMAV as shown in Figure 9.22(a), transceiver system in Figure 9.22(b) and (c), and processing of images in the developed graphical user interface. Experiments are conducted through the user-based signaling using a colored object. As per the earlier assumption, a predefined color is programmed in Figure 9.23(a) to activate the throttle, which flaps the wings at the vehicle’s predefined frequency.

FIGURE 9.23  (a) Flapping activation, (b) controlling directivity, (c) detection of object.

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Dynamics Image-Based Control of Flapping Wing

TABLE 9.7 Control of Flapping Frequency Arduino Ref PWM (Duty Cycle: 0:255) 226 211

Input Voltage (V) 3.7 0.74

Flapping Frequency (Hz) 20 4

Results about controlling the flapping frequency are shown in Table 9.7. Another predefined color is used to control the vehicle’s directionality, which is shown in Figure 9.23(b).

9.8  DEVELOPMENT OF GRAPHICAL USER INTERFACE 9.8.1 Manual Mode In this mode, the control of FWMAV is performed through the user signals with an aid of Graphical User Interface designed in MATLAB as shown in Figure 9.24. The motor’s speed is directly controlled using a throttle control wherein the variation of voltage leads to the FWMAV’s flapping frequency. To control the vehicle’s direction, push buttons are provided that provide a left and right turn of the vehicle, so that simple maneuvering characteristics are achieved.

FIGURE 9.24  Graphical user interface with manual and autonomous modes.

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Flapping Wing Vehicles

9.8.2 Hardware Setting This panel provide options for the users to select the specifications of the electronic hardware elements associated with the control interface. The main interconnected circuits have Arduino supported FMV transmitter system and camera sensors. Two types of Arduino hardware are supported through these modules, and it can be expandable for the latest boards. The camera selection involves selecting a camera type (NTSC, PAL), its color output (RGB, YUV), and the camera resolution. This setting panel helps avoid acquisition errors and enables the control interface to synchronize with the vision sensors.

9.8.3 Vision-Based Control Mode This module makes use of visual information sent from the FWMAV to generate a control signal. The initiation of vision mode executes the following sequence • • • •

Deactivate all the manual switches; Activate the vision devices equipped with the FWMAV; Run the color recognition algorithm for each acquired frame; Send the corresponding output signal based on the detected color.

The right panel on the GUI is used to perform the navigation based on the color information through activating the autonomous mode. A visualizing display panel is also provided to obtain the real-time pictures captured while performing indoor surveillance. During experiments, in the manual mode, a different PWM signal will be generated by the Arduino board as the user slide and the flapping frequency control unit. The generated PWM signal proportionally affects the input voltage to the BLDC motor used to obtain flapping motion. The experimental results provide insight into the PWM signal, the input voltage to the BLDC, and the flapping frequency of FWMAVs. Table 9.7 provides the details on these aspects after successful experimental studies using the developed hardware and software modules that could be used to control the vehicle in real-time.

9.9  VISION SYSTEM FOR FWMAV FWMAV (or ornithopter) equipped with the vision sensor as shown in Figure 9.25 can serve multiple applications such as surveillance, reconnaissance, target tracking, obstacle avoidance, and thus it forms the crucial building block of any autonomous systems. A CMOS imaging sensor of resolution 640 × 480 is used to acquire images and videos. The captured information is interfaced to the 5.8 GHz transmitter, and both the units are powered using a 160 mAH Lithium polymer battery. A tunable 5.8 GHz receiver setup receives the video signals in the ground station, which are sampled and quantized by an ADC and then interfaced to the system through a USB port. The payload of 4.7 gf is provided an endurance of 4 mins of transmission of video signals. The configured vision system can acquire images

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305

FIGURE 9.25  Vision setup for FWMAVs.

processed with the developed image algorithms to estimate the ego-motion characteristics of FWMAV and the control group of FWMAVs. A control interface is developed to achieve communication between the ground station and FWMAV, as shown in Figure 9.26. This system consists of Arduino Uno, BLDC motors, and virtual COM ports. The control signal from the control interface is sent to the RXD port, which confirms the signal’s reception, and then it redirects into the microcontroller for the next sequence of operations. During the manual mode of operation, the output voltage of port 11 is changed through varying the throttle in the user slide shown in Figure 9.24, which causes varying the flapping frequency. However, ports 12 and 13 are utilized to control the flight’s direction, which is achieved by reversing the polarity. In vision-based control, a similar control sequence is executed through color information, which was calibrated initially for achieving desired operations. Simulations are conducted to control the flapping frequency and directions using image processing tools in a MATLAB environment. The connectivity of BLDC motors is interchanged with Arduino-based wireless transmitter system for real-time processing.

FIGURE 9.26  Hardware and software development for image-based control of FWMAV.

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FIGURE 9.27  Arduino controlled FWMAV transmitter system.

The developed hardware system shown in Figure 9.27 has a control interface integrated with an Arduino-based transmitter system that will be used to achieve the communication. Output ports are interlinked to the FWMAV through a developed hardware transmitter system through 6 terminal cables. One pair is used to control the flapping frequency, and the rest is used for maneuvering control in achieving the desired flight direction. For controlling flapping frequency, pulse width modulated (PWM) signals are sent from the Arduino to the FWMAV transmitter.

9.10 MOTION ESTIMATION USING FREQUENCY DOMAIN APPROACH Vision-based motion estimation is developed, utilizing only the visual information acquired from the image sensor. A simplified approach to estimate the motion characteristics of FWMAVs based on the structural information present in the scene is considered [21]. In this approach, the images are first converted into gray scale, and then frequency transform using Fourier and cosine transforms are performed. The block-wise transformation is used, and the frequency coefficients are sorted in ascending order. The term structural index (SI) has been computed in each block, which corresponds to the ratio of 20% (13 terms) of significant coefficients to the overall intensity of the block (64 terms). 13



SI  =

64

∑ ∑Y (9.43) Yib /

i =1

ib

i =1

where Xib corresponds to the sorted DCT coefficients in an 8 × 8 block, based on the structural index swift, the motion translation and rotation are computed using the following relations:

Translation = ( m2 − m1) *8 and ( n2 − n1) *8 (9.44)

Dynamics Image-Based Control of Flapping Wing



307

Rotation = cos−1 ( x1*x2 / x1 |x2|) , (9.45)

where vector x1 (m1,n1) – index of the highest SI block in ith frame; vector x2 (m2,n2) – index of the highest SI block in the (i+1)th frame.

9.11  GROUP ACTUATION AND CONTROL Multiple FWMAVs formation control is an on-going research challenge and requires multifaceted investigation in control theory, MEMS sensor, imaging devices, and processing hardware. Electronic hardware development integrated with vision sensors and intelligent image processing algorithms to control multiple FWMAVs has endeavored in this work [22]. The “N” number of FWMAVs is shown in Figure 9.28, in which the foremost member in the group acts as a master. It is equipped with a camera unit, which sends the real-time captured video to the ground station and facilitates the group’s control using the vision-based commands. All the FWMAVs are controlled through a common frequency channel of 2.4 GHz, and two-way control strategies are formulated. The first approach involves control through a keyboard using MATLAB and a graphical interface. As the flapping frequency depends on the voltage, the sliding unit in the GUI is calibrated regarding the voltage, and thereby flapping frequency is controlled. In the second approach, the control commands are generated based on the vision information processed in the ground control station through developed image algorithms. As FWMAVs have much future military application scope, controlling aerial vehicles through color or gesture recognition ensures reliable and secure systems. In this development, control of FWMAVs through arbitrary color codes has been proposed. As depicted in Figure 9.29, the graphical control interface takes the video input and applies the robust color algorithm for rapid color detection. The signals are

FIGURE 9.28  Multiple FWMAVs.

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FIGURE 9.29  Ground station modules.

TABLE 9.8 Port Status and Corresponding Action Port Status P5, P6 +Ve P7, P8 –Ve P5, P6 –Ve P7, P8 +Ve P5, P6, P7, P8 +Ve or –Ve P9, P10

Action Right turn Left turn Deactivate direction control Flapping speed

transmitted from the corresponding Arduino ports to the driver circuit based on the detected color. The port usage and their corresponding status for control action are provided in Table 9.8 and Figure 9.30. A simple experimental setup consists of a master FWMAV equipped with a vision sensor (green color), and the other three FWMAVs are shown in Figure 9.31. Users can define the color code in the image algorithm for the activation and deactivation of FWMAVs that can be kept secured. Once the color is shown to the vision sensor, images are processed in the ground control station, and the corresponding control signal will be sent to other FWMAVs with a developed Arduino circuit. Here, a yellow color is used to actuate, and the red color is configured to stop FWMAVs’ group in real-time. The color detection algorithms also use an optimized color space

FIGURE 9.30  GUI and Arduino controlled interface circuit.

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309

FIGURE 9.31  Group of FWMAVs actuation and control.

model for faster performance. Experiments are performed through changing the color codes, and swarm control of FWMAVs is effectively achieved with developed image algorithms and hardware modules.

9.12 SUMMARY This chapter initially discussed the development of stereo vision systems and control of FWMAVs in indoor and outdoor environments through a custom-built experimental setup. The dynamics of FWMAV based on averaging theory is derived. Further, a linearized control law is developed to control FWMAVs, and simulation results are presented. Also, vision-based control algorithms are discussed to control the FWMAVs, and a GUI-based system is developed to perform image-based control in manual and autonomous modes. Finally, controlling group of FWMAVs (SWARM) is performed through integrating a hardware and software tool is explained with experimental results.

REFERENCES

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6. Schenato, L., Campolo, D. and Sastry, S. (2003, December) Controllability issues in flapping flight for biomimetic micro aerial vehicles (MAVs). The 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475) (Vol. 6, pp. 6441–6447). 7. Hsu, C. K. (2008) The Preliminary Design, Fabrication, and Testing of Flapping Micro Aerial Vehicles, Doctoral dissertation, Ph. D. Dissertation, Tamkang University. 8. Hsiao, F. Y., Yang, L. J., Lin, S. H., Chen, C. L. and Shen, J. F. (2012) Autopilots for ultra lightweight robotic birds: Automatic altitude control and system integration of a sub-10 g weight flapping-wing micro air vehicle. IEEE Control Systems Magazine, 32(5), 35–48. 9. Zhou, K., Zillich, M. and Vincze, M. (2009, July) Attitude acquisition using stereovision methodology. Proceedings of the Ninth IASTED International Conference (Vol. 652, No. 102, p. 122). 10. Flight test of Golden - Snitch [Online]. Available: http://www.youtube.com/ watch?v=bexOl4YNnd0. 11. de Croon, G. C. H. E., De Clercq, K. M. E., Ruijsink, R., Remes, B. and de Wagter, C. (2009) Design, aerodynamics, and vision-based control of the DelFly. International Journal of Micro Air Vehicles, 1(2), 71–97. 12. Todorovic, S. and Nechyba, M. C. (2004) A vision system for intelligent mission profiles of micro air vehicles. IEEE Transactions on Vehicular Technology, 53(6), 1713–1725. 13. De Wagter, C., Tijmons, S., Remes, B. D. and de Croon, G. C. (2014, May) Autonomous flight of a 20-gram flapping wing MAV with a 4-gram onboard stereo vision system. 2014 IEEE International Conference on Robotics and Automation (ICRA) (pp. 4982–4987). 14. Moore, R. J., Dantu, K., Barrows, G. L. and Nagpal, R. (2014, May) Autonomous MAV guidance with a lightweight omnidirectional vision sensor. 2014 IEEE International Conference on Robotics and Automation (ICRA) (pp. 3856–3861). 15. Shen, S., Michael, N. and Kumar, V. (2011, May) Autonomous multi-floor indoor navigation with a computationally constrained MAV. 2011 IEEE International Conference on Robotics and Automation (pp. 20–25). 16. Hsiao, F. Y., Hsu, H. K., Chen, C. L., Yang, L. J. and Shen, J. F. (2012) Using stereo vision to acquire the flight information of flapping-wing MAVs. Journal of Applied Science and Engineering, 15(3), 213–226. 17. Sankarasrinivasan, S. and Esakki, B. (2015, March) Vision based algorithms for MAV navigation. 2015 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT) (pp. 1–4). 18. Sankarasrinivasan, S., Balasubramanian, E., Hsiao, F. Y. and Yang, L. J. (2015, May) Robust target tracking algorithm for MAV navigation system. 2015 International Conference on Industrial Instrumentation and Control (ICIC) (pp. 269–274). 19. Sankarasrinivasan, S., Balasubramanian, E., Yang, L. J. and Hsiao, F. Y. (2015, August) Autonomous control of Flapping Wing Vehicles using graphical user interface. 2015 IEEE International Conference on Advances in Computing, Communications and Informatics (ICACCI) (pp. 2217–2220). 20. Seshadri, S., Esakki, B., Yang, L. J., Chandrasekhar, U. and Packiriswamy, S. (2015) A novel vision based protocol for controlling flapping wing vehicles in indoor surveillance mission. Journal of Applied Science and Engineering, 18(4), 331–338. 21. Ismael, B., Seshathiri, S. and Esakki, B. (2017, February) A comparative analysis on image translation and rotation algorithms towards implementations in micro aerial vehicles. Proceedings of the 3rd International Conference on Mechatronics and Robotics Engineering (pp. 172–175). 22. Sankarasrinivasan, S., Esakki, B. and Yang, L. J. (2017) Image processing framework towards motion estimation and control of multiple FWMAVs. International Conference on Intelligent Unmanned Systems (ICIUS 2017), Tamsui, Taiwan on 21–24 August.

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Arduino-Based Flight Control of Ornithopters

10.1 ESTIMATION OF ATTITUDE, ALTITUDE, AND DIRECTION OF FWMAV The design of a control system for FWMAV necessitates establishing an inertial reference system regarding this, and all sensor data, can be measured [1]. The inertial frame of reference is one that is time-independent and describes the space homogeneously. A schematic representation of the inertial frame of reference is shown in Figure 10.1. The direction of x  is along the magnetic north, the direction of the positive z − axis is toward the direction of gravity of earth, and the   y − axis is indicative of the horizon level. The angle subtended by the body axes of the vehicle on x, y, z axes may be defined as the pitch ( θ ), roll ( φ ), and yaw (Ψ), respectively. While examining the absolute quantities that are available to the design of attitude heading reference system (AHRS) [2], the direction of gravity, sea level, and direction of magnetic north are favorable set, as the positional relation to all these three quantities can be measured by a suitable microelectromechanical-systems (MEMS)-based sensors [3]. The MEMS sensors, namely accelerometer, digital altimeter, and magnetometer, are available to measure the parameters mentioned above. In the case of an accelerometer, the output along three axes (x, y, and z) indicates the direction of the acceleration of gravity. The perpendicular direction to these vectors is considered as the horizon level, as shown in Figure 10.2. Any variation of downward body axes for gravity direction is measured as the shift in the resultant gravity vector that is resolved as separate accelerations along with the three axes’ accelerometer. Measuring these accelerations and the resultant can be considered pitch and roll angles, illustrated in Figure 10.2. The accelerometer measures the projection of the gravity vector on the sensing axis [4,5]. The amplitude of sensed acceleration changes as the sin of the angle α between the sensitive axis and horizontal plane. The acceleration along the sensing axis is given by: A = g   [ sin sin  α   ] (10.1)



 A α =   (10.2) g If A x, Ay, Az are the raw accelerations measured along x, y, and z axes respectively, then the pitch and roll can be given by:





 Ax Pitch = α =  2  Ay +  Az 2

DOI: 10.1201/9780429280436-10

  (10.3)  311

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FIGURE 10.1  Inertial frame of reference.



 Ay Roll =  β =  2  Ax +  Az 2

  (10.4) 

As far as the yaw angle is concerned, using accelerometer data is not a practical one because the gravity vector is insensitive to the change in the direction of measurement along its axis. For this purpose, a magnetometer sensitive to the earth’s magnetic field along three axes of measurement is a better alternative. A 3D vector pointing toward the direction of maximum magnetic strength while also measuring its magnitude is formed. In such a scenario, the 3-axes gyroscope can be integrated to measure the angular rotation rates.

FIGURE 10.2  Measurement of acceleration.

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FIGURE 10.3  Attitude, altitude, and direction measurement.

However, the altitude reference is a fairly simple principle [6] in understanding, and it is based on the fact that the pressure varies inversely with the gain in altitude [7]. A digital barometer is used to measure the pressure at a particular height and be able to estimate the altitude based on the following relation established by the National Atmospheric and Oceanic Administration:

  Pressure 0.190284  Altitude = 1 −    [ 44307.694 ] , (10.5)   1013.25  

where the measured pressure is in millibar and the altitude is given in meters. It is also important to note that the pressure is subjected to change in various weather conditions, varied temperature, and flight location (indoor/outdoor). It is one of the reference systems that can be used in tandem with rotational sensing. Hence, based on these discussions, the data measured from the accelerometer, gyroscope, magnetometer, and digital barometer are acceleration, moments about the body axes, magnetic field along the three measurement axes, and altitude [8–10] respectively, as shown in Figure 10.3 Given zero initial conditions, if the three axes’ accelerations and moments are zero, the vehicle can be considered stationary with the constant pose (position and orientation).

10.2 DIRECTIONAL CONTROL OF FWMAV WITH MICROCONTROLLER AND ON-BOARD AVIONICS A prototype circuit assembly consisting of a 9-axis inertial measurement unit (IMU)-LSM9DS0 by STMicroelectronics is paired with an ATMEGA 328P microcontroller [11–13]. Initially, a comparison of magnetometer sensor data with a given

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FIGURE 10.4  Block diagram for auto direction control.

target is made to identify the current direction. Further, a small motor with a propeller attached to the rear end of FWMAV is actuated. The direction of rotation of the motor and direction of the propeller’s thrust depended on the error’s polarity from the comparison. For instance, the positive error is considered as clockwise rotation and vice-versa. In turn, this rotation is used to generate yaw motion about the center of gravity (C. G.) of FWMAV. The schematic of the direction control scheme is illustrated in Figure 10.4. As a pilot work to implement the direction control system, preliminary experiments are conducted. Magnetometer sensor is connected to an Arduino UNO, which is used to turn on LEDs of different colors based on the polarity of error. A 20° tolerance with 10° on each side is included, implying that the FWMAV did not have to take corrective measures in the marked region, as shown in Figure 10.5(a). Whenever the FWMAV’s heading went beyond the tolerance, an LED went ON, as illustrated in Figure 10.5(b).

FIGURE 10.5  (a) Tolerance for the direction control of FWMAV; (b) LED-based indication.

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TABLE 10.1 Pin Connections for Direction Control Setup LSM9DS0 VCC GND SDA SCL – –

ATmega 328P 3V3 GND A4 A5 D3 D2

Motor – – – – Terminal 1 Terminal 2

The connection ports of the Arduino UNO board and 9 axes IMU are given in Table 10.1. I2C two-wire protocol is used because of its flexibility to add more sensors to the microcontroller. Since the number of pins available on a microcontroller unit (MCU) is limited, fewer pins are always preferred. The actuating motor’s direction of rotation is controlled by connecting the terminals to two digital pins of the ATmega microcontroller. Bypassing a HIGH output signal on one terminal and a LOW signal on the other, the motor is made to rotate. Also, by changing the terminals of HIGH and LOW, the direction of rotation is altered. This setup is performed well on the test bench, and as a further step, the prototype is made small enough to fit on an FWMAV and directly prepared for flight test. In prototyping for the flight test, it is observed that conserving weight while preserving the same functionality as the larger MCU is crucial for the successful implementation of auto-control. It is found from the bench test that the proximity of the magnetometer to the main motor driving the flapping mechanism influenced the reading as depicted in Figure 10.6. A safe distance of 65 mm from the main motor is identified for positioning the magnetometer by measuring the obtained reading to a known reference reading.

FIGURE 10.6  Ferromagnetic disturbance.

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FIGURE 10.7  (a) On-board avionic elements mounted in FWMAV; (b) enlarged view of a microchip.

A scaled-down version of ATmega328P and LSM9DS0 weighing 0.3 gf and 0.4 gf, respectively, are integrated and powered through a 1S Lithium-Polymer battery weighing 0.9 gf. The avionic elements are shown in Figure 10.7(a) weighed a total of 0.7 gf. The ATmega microcontroller (Figure 10.7(b)) carried the program to monitor the magnetometer reading and control the motor connected to it. The connections between the components are made through soldering 23AWG enamel insulated copper wire to have strict control of weight. In order to control the throttle of FWMAV, a separate system consisting of an Infrared receiver motor speed controller is used with its battery. The sensor is mounted at the tail of FWMAV to avoid ferromagnetic interference from the main motor. The relative locations of sensors and other components are indicated in Figure 10.7(a). A 6mm diameter motor for the actuating mechanism and a smaller 4 mm motor for the tail rotor are utilized. A 75 mAH Li-Poly battery is considered the main source of energy for the flight trails. The weight distribution of FWMAV is given in Table 10.2, and also their percentage contribution is depicted in Figure 10.8. TABLE 10.2 Mass Distribution of Avionic Elements and Other Components Component Motor battery Wings Mechanism Support frame Main motor Tail motor Carbon fiber reinforced fuselage IR receiver Logic Battery ATmega328P + LSM303 (Acc+Magneto) Total

Mass (g) 1.96 1.64 1.82 0.68 1.60 0.58 2.80 0.36 0.98 0.70 13.12

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FIGURE 10.8  Weight distribution of FWMAV.

10.3  FLIGHT TEST The flight test [14] is performed by launching the FWMAV in North, South, East, and West. The flight trajectories are shown in Figures 10.9(a–d), respectively. The flight test results have proven that the microcontroller-based control system was effectively controlling the FWMAV in the desired direction. The deviation from the actual trajectory for the North, South, West, and East launch are 30.6°, 28°, 26.6°, and 20.9° are observed.

FIGURE 10.9  (a) North launch; (b) South launch; (c) West launch; (d) East launch.

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FIGURE 10.10  Motor driver, MCU, BMP180, and motor mechanism.

10.3.1 Altitude Measurement In order to measure the altitude [15], a digital barometer is inculcated into the sensor suite. The sensor BMP180 manufactured by Bosch Sensortec has a resolution of 10 cm integrated into the I2C protocol. During the altitude control of FWMAV, it is essential to have fine control over the throttle of FWMAV, which is achieved by controlling the driving motor’s speed. Since a brushless DC motor drives the FWMAV, a motor driver circuit DRV8837 supplied by Texas Instruments is considered to control the speed based on the digital Pulse Width Modulation (PWM) signal generated from the microcontroller. It is in the range of (0–255) where 0 represents that the motor is at minimum throttle (zero voltage passing to the motor) and 255 is considered the maximum throttle with the peak supply voltage. The IMU provided the inertial data to steer the vehicle, and the digital barometer is used to control the altitude. Both the motor controls are implemented by controlling the motor’s speed and rotation of the tail rotor. All the tiny parts for on-board controlling the FWMAV mentioned as above are shown in Figure 10.10.

10.3.2 Measurement of Flight Data Free flight data measurement is one of the key parts in building numerical models of FWMAV [16,17]. So far, wind tunnels have been conventionally used to measure the lift and thrust forces of FWMAVs. With the use of motion capture systems, it is possible to record and analyze the accelerations and rotation rates at an unprecedented rate. With a known value of the mass of FWMAV, it is possible to estimate forces from the data obtained through the motion capture system. The flight data measurement is important to develop computational models for flapping flight. To record all the data associated with the flight, a small data logging system weighing 1 gf is placed in the airframe, and the data passing through the Microcontroller is routed to the data logger and recorded on a timely basis. The IMU data is primarily the most important data, with which the overall flight path, instantaneous forces, and velocities are estimated with reasonable accuracy. The various flight data are shown in Figures 10.11–10.14, respectively.

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FIGURE 10.11  Accelerometer data log.

Because of vibration in the airframe, the data is filled with noise and requires a filtering mechanism to rectify the spikes and obtain useable values. In the past, trials with the Kalman filter have proven successful, and it is recommended that in the future, the same can be used as a post-processing tool to analyze the data and minimize noise and drift arising from the sensor values. The Kalman filter algorithm

FIGURE 10.12  Gyroscope data log.

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FIGURE 10.13  Magnetometer data log.

is incorporated for removing the noise from the roll data shown in Figure 10.14, and after the removal of noise, it is shown in Figure 10.15. Although the trace is discernible, it must be noted that the plot is largely offset from the drift of the sensor. The blue line indicates the Kalman filtered, fused sensor values with minimal drift and noise. The red line indicates the smoothed Kalman value, offset on the x-axis as there is a delay of 10 microseconds between Kalman and smoothed Kalman values.

FIGURE 10.14  Pitch, roll, yaw data log.

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FIGURE 10.15  Kalman filtered and smoothed Kalman values for roll log.

10.4  DESIGN OF PRINTED CIRCUIT BOARD A printed circuit board (PCB) [18–19] is used to house all the vital electronic components to implement an autopilot system for FWMAV. During the prototyping phase, several drawbacks are met with, notably the intricate connections that consumed enormous time to make, their delicate nature making them susceptible to disconnection after a crash landing, and so on. More importantly, the sensors occupied with their weights, and it is clear from the preliminary design evaluation that much weight could be saved if these sensors could be laid out on a single PCB. The electronic components are to be integrated into the PCB areas discussed in the previous section: • • • •

ATmega328P microcontroller LSM9DS0 9-axis inertial measurement unit BMP 180 digital barometer DRV8837 1.8A DC motor driver

The weight of the PCB and overall dimensions of the board are paid close attention during the conceptual design phase. The PCB should be as small as possible without sacrificing the functional aspects. As a result of which, a tight packing and component density on the PCB is desired. The schematics and the layout files for those electronic components are readily available on the vendor sites as it is a common trend to license these designs under Open source guidelines. These files are made extensive use of to design the PCB. As the ATmega328P is a part of the Arduino compatible microcontroller range, the brain of PCB could still be programmed via the Arduino IDE. Since it is easy to program and debug, C language programming skills are sufficient, and higher-level object-oriented programming (OOP) is not required for interpreting the sensor data. Moreover, each of the components has a well-built, constantly updated Arduino library, which can be loaded to the programming computer to massively cut down on creating a data acquisition framework to obtain data from the sensors.

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FIGURE 10.16  Computer to autopilot board connection.

As mentioned previously, the PCB needs to be compact and light in weight. In order to address this need, the universal serial bus (USB) interface that connects the ATmega microcontroller to a host computer for programming is conceived as an extra attachment that is not on-board. So the FTDI chip interface consists of its exclusive circuitry and is required when the ATmega microcontroller needs to be programmed by a computer. During the flight time, the FTDI interface is not involved in data handling or decision making of any sort. Hence, it is excluded from the PCB design and made as an extra adapter. It connects to the ATmega 328P microcontroller on one side and a micro USB port on the other. The micro USB port can be directly connected to the USB interface of the programming computer via a micro USB male to standard USB male connector as shown in Figure 10.16 that is commonly used for mobile phone charging and a host of other utilities. Based on the previous test results of the ferromagnetic influence of the main motor on the magnetometer data, it is observed that the motor connection terminal and IMU sensor have to be placed at the opposite ends of PCB to avoid deviations in magnetic field data. Also, to avoid the influence of other components on the inertial data, the IMU is designated to occupy the edge of PCB, far from the motor as depicted in Figure 10.17. The FTDI USB interface is placed along the sides as it would be possible to reprogram the microcontroller without having to unmount the PCB from the carrier vehicle. The MAV “head” is placed toward the upper end, and IMU is kept at the lower side toward the tail end. The I/O pins located at the right side of the microcontroller

FIGURE 10.17  Integration of electronic components in PCB.

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TABLE 10.3 ATmega328P to GPS Connections ATmega328P 3.3 V GND TX (I/O pin 1) RX (I/O pin 0)

GPS Receiver VCC GND RX TX

enables pairing of 2.4 GHz radio to the PCB, and I/O pins located at the lower left are programmable pins that can be used to control other devices. One of the best features of extra programmable pins is that the serial transmitter and receiver pins are made available as open ports. These can be connected to a Micro SD card to log the sensory data, enabling an unprecedented view of the dynamics of FWMAV. The logged data can be used to recreate the trajectory of FWMAV in 3D space, and such data also find a part in numerical analysis to describe the system’s control laws. On the other hand, the microcontroller’s data stored on a Micro SD card can also be read. For instance, elaborate missions can be scripted in the future and stored on the Micro SD card. These missions can be read from the SD card and also executed by the FWMAV. To maximize the applications of PCB, the serial pins are considered as programmable utility pins. These pins can also be used to attach a GPS receiver to the microcontroller. Table 10.3 provides the GPS connection with the ATmega controller. It makes the autopilot board open to a host of other applications. With such a functionality, it is possible to maintain a detailed log of take-off location, the GPS path, and they can be used to trace back the earlier path in case the control signals are lost. It would constitute a basic fail-proof system with an auto-return-home function. If the GPS points can be stored on the FWMAV beforehand, waypoint navigation principles can also be used to steer the carrier vehicle in the desired locations. For the design of the PCB, free software called CADSOFT Eagle PCB is used. The software offers two separate design avenues where the schematic connections with labels are made first, and on the other front, the PCB layout and routing are carried on. During the first iteration, PCB is designed for a dimension of 45 mm × 15 mm as Figure 10.18. Standard breadboard size connectors are considered the design guideline for the first iteration, and due to the consumption of more space, it is not accounted for further. In the next iteration, 1.5 mm pitch solder pads substituted the standard breadboard connectors, and there is a considerable amount of space saved. 10 mils/0.254 mm line width is used for the routing process, and the drills are designed at 0.5 mm. As an additional possibility, the PCB design can also be printed on a flexible substrate offering the ability to twist, roll, and bend. The finished board would be suitable for mounting in any direction, but it requires minor programming to indicate the new body axis of FWMAV. The fabricated PCB with the soldering of connecting pins has resulted in the gross weight of 0.85 gf.

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FIGURE 10.18  PCB layout of M1AP chip.

10.4.1 Uploading Firmware A software interface is essential to connect with a computer and recognize it as a program uploader for the Atmel Microcontroller. Without this, it is not possible to upload the program from an external device. It is called the Bootloader and helps recognize devices trying to upload code into it and accept it. The code for ATmega328p is available with the Arduino Integrated Development Environment (IDE), and it can be directly used as the firmware for the microcontroller without any modification. The flashing of firmware into the chip is considered a one-time activity, and the chip mounted with ATmega328p microcontroller can be used as an Arduino chip by connecting to the computer with an FTDI interface. To flash the firmware, an external In-System Programmer (ISP) prescribed by Atmel is required. The ISP is connected to PCB, and the firmware is uploaded, which is further transferred to the microcontroller via Atmel Studio software.

10.4.2 Sensor Data The sensors can be accessed via the I2C protocol, and it must bear a unique I2C address as prescribed by the sensor manufacturer. The I2C addresses of the sensors are: a. LSM9DS0 - 1000 b. BMP180 - 10085 The pitch, roll, and heading data are measured, and they are shown in Figures 10.19– 10.22, respectively. The error observed from these data are ±0.5°, which is very small and acceptable.

Arduino-Based Flight Control of Ornithopter

FIGURE 10.19  Pitch accuracy.

FIGURE 10.20  Roll accuracy.

FIGURE 10.21  Magnetic heading accuracy.

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FIGURE 10.22  Altitude accuracy.

The accuracy is about ±1 m at altitude, which is very high, and it occurs due to the environmental conditions. It is recommended that the accelerometer and gyroscope data can be used for measuring the altitude. However, it can only serve as a rough reference and not suitable for computing altitude changes, considering the operating height of FWMAVs.

10.5  FLIGHT TEST To apply in the real world, the data obtained from the chip and direction control test is conducted. The FWMAV is retrofitted with PCB, and launching the FWMAV in East and West is performed. The mass of individual components as given in Table 10.4 after incorporating the sensor unit is increased to 13.38 g, and earlier it was 13.32 g. The weight distribution of each unit of FWMAV is shown in Figure 10.23.

TABLE 10.4 Mass Distribution of FWMAV with M1AP Chip Component Motor battery Wings Mechanism Support frame Main motor Tail motor Carbon fiber reinforced fuselage Control chip (with headers and connectors) M1AP Logic battery Total

Mass (g) 1.96 1.64 1.82 0.68 1.60 0.58 3.02 1.10 0.98 13.38

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FIGURE 10.23  Mass distribution of FWMAV with PCB structure.

As per the given program, FWMAV is set to seek South direction upon the launch. It involved autonomously controlling the rudder motor to regulate the heading of FWMAV by comparing the heading data from M1AP. The real-time test flight results are shown in Figure 10.24. It is observed from these results that the average deviation angle varied from 11°–60°. In an east launch, the average deviation angle is found to be 29°, and in a west launch, it is measured as 47.5°. They are influenced by the forward speed of the vehicle and altitude gain. These results confirm that the sensor architecture successfully provides the MCU with the necessary data to control the FWMAV according to the desired target. In addition to the directional control, an altitude control experiment is devised to utilize the pressure sensor’s altitude data. The altitude is calculated based on the pressure data, and it is important to note that it can vary depending on weather, temperature, and even the building’s architecture if the FWMAV is flown indoors. In

FIGURE 10.24  FWMAV flight test with MIAP chip: (a) launch toward East, (b) launch toward West.

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FIGURE 10.25  Altitude control of FWMAV with MIAP chip.

this test, the FWMAV is designated to reach a target altitude from the ground level and land by slowing down and yawing downward. The ground level is noted from the sensor data as 53 m above sea level, and the target altitude is set as 60 m. It is only a partial success as the FWMAV tried to yaw as it reached 58 m as depicted in Figure 10.25, which is close to the target altitude of 60 m. It is then spiraled sideward and crashed. In order to successfully control the altitude, a tail rotor or an aileron structure is recommended. It is suggested that PID control be used for controlling the altitude of the FWMAV.

10.6  BIONIC ACTUATORS FOR FWMAVS In the direct control of FWMAVs, more energy is consumed because conventional tail actuators are operated by electro-magnetic solenoids and expend more power. Hence, bionic-based actuators that work on the principle of water evaporation are

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FIGURE 10.26  Working principle of comb-shaped bionic actuator: (a) flap up without liquid; (b) flap flat with liquid and surface tension.

developed [20,21]. A bionic actuator made of steel is fabricated, and it can deliver a swift response of actuation in comparison to PDMS and SU-8 materials-based bionic actuators [22].

10.6.1 Working Principle of Bionic Actuators The bionic actuator is initially kept in the folded position, as shown in Figure 10.26, which is originally filled with water. When the water is filled using a filling channel positioned at the FWMAV, water’s surface tension minimizes the water surface [23–25]. During maneuvering, a current impulse is fed into the steel actuator to evaporate the water absorbed in the comb structure [26–28]. It causes the comb structure’s retraction in the upward direction, as shown in Figure 10.26(a). A schematic representation of the bionic actuator channel placed at the FWMAV is shown in Figure 10.27.

10.6.2 Design of Bionic Actuator The capillary cantilever structure’s design is necessary to ensure that sufficient attraction force exists in the actuation device [22,29,30]. We first simplified our device as a single cantilever beam with working liquid, as shown in Figure 10.28. All the surface energy is summarized, and the surface tension torque can be analytically derived for the actuation angle. Based on the small elastic deformation assumption, the angular surface tension torque or moment M0 and spreading angle or stroke angle change β due to the capillary water force of the comb-shaped bionic actuator is given by,

M 0 = K β β = −γ la R( R + H ); K β =

EI β Hb 3 ; Iβ = (10.6) 12 w

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FIGURE 10.27  Bionic actuator placed at the tail of FWMAV.



β=

12γ la NR( R + H ) w , (10.7) EHb 3

where γla is water surface tension (γla = 0.073 N/m); N is the number (N = 50) of the comb-shaped beams; R is the length (R = 3,000 μm) of the comb; H is the depth (H = 40 μm) of the multi comb structure; w is the root gap between two comb beams (w = 50 μm); E is Young’s modulus (E = 200 GPa) of the steel comb; b is the root

FIGURE 10.28  A single pair of beam structure of bionic actuators driven by the surface tension force.

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FIGURE 10.29  Performance of bionic actuator due to surface tension: (a) steel actuator without water, (b) steel actuator with water, (c) parylene-coated actuator without water, (d) parylene-coated actuator with water.

width (b = 50 μm) of the comb beams. With these given dimensions, the actuation area of the comb-shaped cantilevers can be confined within 5 mm. By utilizing Eq. (10.7), the actuation stroke angle change is estimated at 1.14°. Even though this angle change is small and less than the micro air vehicles of 5–15°, it fits the small deformation assumption of elasticity theory applied to deriving Eqs. (10.6) and (10.7).

10.6.3 Fabrication and Testing The SUS-304 stainless steel foil of 40 μm thick has a larger Young’s modulus and yield strength than PDMS, and SU-8 is considered for the fabrication of the actuator. An Nd-YAG laser cutting (355 nm UV) is used to machine the comb-shaped contour path 15 times with the scan speed of 400 μm/s on the steel foil. The minimum line width of laser cutting is kept as 50 μm, and each actuating unit has 50 pitches of comb fingers. Many identical units could be assembled into the FWMAV control surface to provide the necessary flight control force. After fabrication, preliminary experiments are performed to understand the performance of the bionic actuator. The change in the steel-based actuators’ comb angle to water surface tension is examined, depicted in Figure 10.29. It is evident from Figures 10.29(a–b) that the actuating comb has a rotating stroke of 3° (from 38° to 35°), which is large in comparison to a theoretical value of 1.14°. Two arguments may be responsible for this error. Firstly, the mechanical property (e.g., Young’s modulus E) of the steel after the laser cutting might be changed. Secondly, the steel surface is hydrophobic (contact angle is 105.5° given in Table 10.1), and hence the water is hard to fill into the gaps among the comb structure. Therefore, a surface modification is performed through coating parylene on the steel surface. The surface roughness is measured by using KLA-Tencor Alphastep-500, and contact angle is measured by

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TABLE 10.5 Surface Roughness and Contact Angles for Bionic Actuating Units Steel Parameters Surface roughness (angstrom) Contact angle

Before Laser After Laser Cutting Cutting 473 1405 60.5° 105.5°

Steel Coated with Parylene Without Oxygen Plasma Treating 541 68.7°

With Oxygen Plasma Treating 832 21.9°

using First Ten Angstroms-125. The data is arrived at by averaging the collection of three samples at three different locations. After being coated, the bionic actuator’s contact angle is increased to 68.7°, as given in Table 10.5. The actuation force is also enhanced because of the change in stroke angle, which is increased to 10° (from 37° to 27°), as shown in Figures 10.29(c–d). Besides, the surface modification with and without oxygen plasma on the device is also tested, and the results are given in Table 10.5. The surface appears to be more hydrophilic, but the actuation stroke is almost the same as without plasma treating. It is observed from Eq. (10.7) that the w, b, and H are directly related to the elastic deformation of the bionic actuator. Even the steel is coated with parylene, the steel material has more Young’s modulus than parylene, and still, it dominates the deformation behavior. The stroke angle of 10°, in this case, might be explained by a modified Young’s modulus (22.9 GPa) of the laser-machined steel foil under the assumption that 100% of water enters into the gap of a comb. The bionic actuator is installed on the FWMAV’s vertical stabilizer, and testing is performed. The effective stroke angle again decreases to 4° due to the vertical stabilizer’s large mass loading. The scanning electron microscopy (SEM) analysis is performed to visualize the fabricated comb structure’s surface morphology, shown in Figure 10.30. It is found that the cross-section appears to be trapezoidal instead of rectangular. Further, the

FIGURE 10.30  (a) Single cantilever beam; (b) top view of the comb device.

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contact angle relation is given in Eq. (10.7) is modified as per the new shape which is given by,

β=



γ la NR( R + H ) w (10.8) EI β

Iβ =

H 3 (3a + b) (10.9) , 12

where a is the top width and b is the bottom width of the trapezoidal cross-section of the comb structure. Interestingly, the refined Young’s modulus E (4.65 GPa) of the steel comb given in Table 10.2 is close to SU-8 (4.4 GPa) or parylene (4 GPa). However, the device is now at least electrically conductive, and it can be heated for evaporating the water inside. The steel comb’s total resistance is measured as 2.12 Ω which is sufficient for generating heater power of 0.47 W for the given driving voltage of 1 V. The water among the 50 comb structures is accordingly estimated as 0.3 mg only. Such a tiny amount of water needs 0.678 J to be evaporated exactly. In other words, this device needs only 1.44 s to complete the water vaporizing process. Table 10.6 compares the experimental and theoretical methods of calculating Young’s modulus under various contact angles for the bionic actuator’s finalized dimensions. TABLE 10.6 Design Parameters, Actuation Angles, Deduced Young’s Modulus No. 1

2

β (degree) 1.14° (Theoretical)

γla ( N/m) 0.073

N 50

R H w (μm) (μm) (μm) b(μm) 3000 40 50 50

3° (Experimental)

0.073

50

3000

40

50

0.073

50

3000

56.5

70

10° (Experimental)

3

3° (Experimental)

10° (Experimental)

E (GPA) 200

Remark Rectangular cross-section; design value 50 76.3 × 30% Rectangular cross section; without parylene; 0.0% water 22.9 Rectangular cross-section; with parylene; 100% water a b 15.5 × 30% Trapezoidal cross-section, without parylene; 30.0% water

44 60

4.65

Trapezoidal cross-section, with parylene; 100% water

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10.7 SUMMARY The direction control of FWMAV with an estimation of the roll, pitch, yaw, and altitude using various sensors are elucidated. The flight trials and their flight trajectory and sensor data are explained by launching the FWMAV in North, South, East, and West. The design of PCB M1AP chip through integrating the autopilot system is enlightened. The flight test data and control of FWMAV in the desired direction by employing the developed PCB M1AP board provided a greater insight into the control of FWMAV using microcontrollers. Further, the development of bionic actuators and their actuation performance are discussed by comparing the experimental and theoretical analyses.

REFERENCES







1. Yang, L. J., Marimuthu, S., Hung, K. C., Ke, H. H., Lin, Y. T. and Chen, C. W. (2015) Development scenario of micro ornithopters. Journal of Aeronautics, Astronautics and Aviations, 47, 397–406. 2. Cordero, M., Alarcón, F., Jiménez, A., Viguria, A. and Ollero, A. (2014, May) Survey on attitude and heading reference systems for remotely piloted aircraft systems. 2014 IEEE International Conference on Unmanned Aircraft Systems (ICUAS) (pp. 876–884). 3. Keennon, M., Klingebiel, K. and Won, H. (2012, January) Development of the nano hummingbird: A tailless flapping wing micro air vehicle. The 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (p. 588). 4. Panchal, N., Yang, L. J., Zheng, X. Y., Marimuthu, S. and Esakki, B. (2018) Arduinobased altitude and heading control of a flapping wing micro-air-vehicle. Journal of Unmanned Systems Technology, 5(2), 24–30. 5. Chang, C.-C., Chen, C.-H., Peng, Y.-H., Lee, Y.-S., Hou, C.-Y., Huang, K. F., Shih, H.-T., Tseng, F.-S., Hsieh, M.-T. and Chen, J.-F. (2007) Development of stable microcrystalline silicon AMLCD. IDW’07: Proc. of the 14th International Display Workshops (vol. 1–3, p. 1921). 6. Yeo, D., Atkins, E. and Shyy, W. (2011) Aerodynamic sensing as feedback for ornithopter flight control. Proc. 49th AIAA Aerospace Sciences Meeting, January 2011, Orlando, Florida. (AIAA 2011-552). 7. Oppenheimer, M. W., Sigthorsson, D. O., Weintraub, I. E., Doman, D. B. and Perseghetti, B. (2013) Wing velocity control system for testing body motion control methods for flapping wing MAVs. The 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, January 2013. 8. Chen, C. L. and Hsiao, F. Y. Attitude acquisition using stereo-vision methodology. Proc. Visualization, Imaging, and Image Processing (VIIP 2009), Cambridge, UK, Paper 652–108. 9. Caetano, J. V., Verboom, J., de Visser, C. C., de Croon, G. C. H. E., Remes, B. D. W., de Wagter, C. and Mulder, M. (2013) Near-hover flapping wing MAV aerodynamic modelling – a linear model approach. International Journal of Micro Air Vehicles Conference and Flight Competition (IMAV2013), Sep., Toulouse, France (pp. 17–20). 10. Anderson, M., Sladek, N. and Cobb, R. (2011, January) Design, fabrication, and testing of an insect-sized MAV wing flapping mechanism. The 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (p. 549). 11. Ananda, C., Akula, P. and Kumar, K. P. (2013) Design and development of integrated micro autopilot module with 10 state sensor suite and data logger for micro air vehicle. The 9th International Conference on Intelligent Unmanned Systems, ICIUS (pp. 25–27).

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12. King, P. S. (2014) System Design Methodology and Implementation of Micro Aerial Vehicles, Doctoral dissertation. 13. Whitney, J. P. (2012) Design and Performance of Insect-Scale Flapping-Wing Vehicles, Doctoral dissertation. 14. How, J. P., Bethke, B., Frank, A., Dale, D. and Vian, J. (2008, April) Real-time indoor autonomous vehicle test environment. IEEE Control Systems Magazine, pp. 51–64. 15. Doman, D., Oppenheimer, M., Bolender, M. and Sigthorsson, D. (2009, August) Altitude control of a single degree of freedom flapping wing micro air vehicle. AIAA Guidance, Navigation, and Control Conference (p. 6159). 16. Armanini, S. F., de Visser, C. C., de Croon, G. C. H. E. and Mulder, M. (2016) Timevarying model identification of flapping-wing vehicle dynamics using flight data. Journal of Guidance, Control, and Dynamics, 39(3), 526–541. 17. Armanini, S. F., Karásek, M., de Croon, G. C. H. E. and de Visser, C. C. (2017) Onboard/ offboard sensor fusion for high-fidelity flapping-wing robot flight data. Journal of Guidance, Control, and Dynamics, 40(8), 2121–2132. 18. Jones, D. L. (2004) PCB Design Tutorial. June 29, pp. 3–25. 19. Chen, C., Tang, Y., Wang, H. and Wang, Y. (2013) A review of fabrication options and power electronics for flapping-wing robotic insects. International Journal of Advanced Robotic Systems, 10(3), 151. 20. Jin, X. Y., Yan, J. P. and Fan, H. J. (2007) Investigation and application of electrostriction appliance for bionics flapping aircraft. Machine Building and Automation, (1), 12. 21. Zhang, M., Fang, Z. and Zhou, K. (2007) Research on bionic machine of FMAVs. Machine Tool and Hydraulics, 35(6). 22. Yang, L. J., Jan, D. L. and Lin, W. C. (2013) Steel-based bionic actuators for flapping microair-vehicles. Micro and Nano Letters, 8(10), 686–690. 23. Borno, R. T. and Maharbiz, M. M. (2005) A distributed actuation method based on Young-Laplace forces. Tech. Dig. of 13th Int. Conf. on Solid-State Sensors, Actuators and Microsystems (Transducers’05), Seoul, South Korea (pp. 125–128). 24. Yang, L. J. and Liu, K. C. (2007) Surface tension-driven microvalves with large rotating stroke. Journal of Applied Science and Engineering, 10, 141–146. 25. Gere, G. and S, P. (1984) Mechanics of Materials, 2nd ed., Wadsworth, 724–726. 26. Yang, X., Yang, J. M., Tai, Y. C. and Ho, C. M. (1999) Micromachined membrane particle filters. Sens. Actuators A, Phys, 73, 184–191. 27. Zhou, S., Zhang, W., Zou, Y., Ou, B., Zhang, Y. and Wang, C. (2018) Piezoelectricdriven self-assembling micro air vehicle with bionic reciprocating wings. Electronics Letters, 54(9), 551–552. 28. Chen, C. and Zhang, T. (2019) A review of design and fabrication of the bionic flapping wing micro air vehicles. Micromachines, 10(2), 144. 29. Phan, H. V. and Park, H. C. (2019) Insect-inspired, tailless, hover-capable flappingwing robots: Recent progress, challenges, and future directions. Progress in Aerospace Sciences, 111, 100573. 30. Deng, H., Xiao, S., Huang, B., Yang, L., Xiang, X. and Ding, X. (2020) Design optimization and experimental study of a novel mechanism for a hover-able bionic flappingwing micro air vehicle. Bioinspiration and Biomimetics, 16(2), 026005.

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11.1  INTRODUCTION OF SERVOMOTORS Servo consists of several parts [1,2] such as the output axis, angle sensor, control circuit sensor, gears (plastic or metal), DC motor, and serial interface power supply. The schematic representation of servo motor is shown in Figure 11.1(a) and the dismantled servo motors are shown in Figure 11.1(b). A digital servo is an exciting device that can turn to any specific position within 180 degrees of motion, and some can rotate 360 degrees in a clockwise and counterclockwise manner. The difference between this and other motors is that it has a builtin gearbox and the circuit board inside, so it is far more precise than the other motor. Servos are mostly found in RC toys like RC plane (rudder, elevator, and ailerons), RC boat (direction), and cars (steering). Servos can only work when they are commanded via a microcontroller. Servo works on the pulse width modulation (PWM), the process of switching ON and OFF digital voltage quickly to actuate a range of voltage. For example, if the digital output pin of a microcontroller is 3.3 V, and the PWM is set for a 50% duty cycle, the output voltage would be approximately 1.65 V. The microcontroller turns the digital 3.3 V pin ON and OFF swiftly, producing an actuation concerning the voltage. This basic example of PWM variation can be used in ornithopter to actuate the wing rotation for achieving the flapping motion [3–5]. Torque in servo operation is an essential factor. Torque can be defined as how much power the servo has. The different applications will require higher or lower torque according to the need in the servo motor. A typical servo motor employed for actuating the right and left-wing of an ornithopter is shown in Figure 11.2. It is a high torque servo on which carbon fiber rods can be attached to serve as a standard flapping mechanism for ornithopter.

Specification of the Servo • • • •

Weight: About 20 gf Size: 23 mm × 12 mm × 26.3 mm Speed: 0.087 sec/60° @4.8 V Torque: 2.8 [email protected] V 0.10 S/60° 3.5 [email protected] V 0.09 S/60° 4.3 [email protected] V 0.09 S/60° 4.8 [email protected] V 0.07 S/60° • Working Frequency: 1520 μs/333 Hz • Motor: Φ12 mm Coreless • Ball Bearing: 2 BB

DOI: 10.1201/9780429280436-11

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FIGURE 11.1  (a) Schematic of servo motor, (b) parts of typical servo motor.

During the initial selection of servo motors, the earlier selected servo was too heavy for the wing rotation mechanism. To overcome this issue, Tower Pro MG90s was found to be promising for this application, and specifications are given below: • • • • • • •

Weight: 13.4 gf Dimension: 22.8 mm × 12.2 mm × 28.5 mm Stall torque: 1.8 kg/cm (4.8V); 2.2 kg/cm (6.6 V) Operating speed: 0.10 sec/60° (4.8 V); 0.08 sec/60° (6.0 V) Operating voltage: 4.8 V Temperature range: 0°C–55°C Dead bandwidth: 1 μs

FIGURE 11.2  Flapping wing servo.

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FIGURE 11.3  Design of servo mount.

11.2  DESIGN OF SERVO MOUNT The servo mount with a provision to insert a carbon fiber rod is designed [6], shown in Figure 11.3. The servo mounts are integrated into the ornithopter structure, and the assembly is shown in Figures 11.4(a) and (b). Table 11.1 provides the dimension and other details of the servo-driven ornithopter. The servo mount is 3D printed using HIPS (high impact polystyrene) material in the Fused Deposition Modeling (FDM) system, and the final assembly is shown in Figure 11.5.

FIGURE 11.4  Assembly of servo mount in the ornithopter structure: (a) front view of servodriven ornithopter, (b) isometric view of servo-driven ornithopter.

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TABLE 11.1 Details of Servo-Driven Ornithopter Specification Wingspan Chord length Wing area Mass

Value 0.96 m 0.2965 m 0.2541 m2 121 g

To measure the flapping angle and flapping frequency with the servo-based ornithopter, preliminary measurements are performed with a simple protractor, as shown in Figure 11.6(a). Besides, for the digital angle measurement (Figure 11.6(b)) directly from the video captured, Kinovea software is used. The measured flapping angle and flapping frequency for the various voltages are given in Table 11.2.

FIGURE 11.5  3D printed servo mount assembly.

FIGURE 11.6  Measurement of flapping angle for servo-driven ornithopter: (a) front view of a main flapping servo, (b) side view of wing rotation servo.

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TABLE 11.2 Measurement of Kinematic Parameters for Servo-Driven Ornithopter Voltage 2.2 V 5.5 V 8.8 V

Frequency 1.4 Hz 1.6 Hz 2.7 Hz

Flapping Angle 127° 102° 62°

Wing Rotation Angle 120° 101° 62°

11.3  FLIGHT CONTROL OF SERVO-DRIVEN FLAPPING WINGS Arduino microcontroller [7] is an open-source development board, which has been used by many researchers worldwide. Arduino is lightweight, small in size, and has a dedicated connection port to burn the code into it. These advantages of Arduino set the best platform to be used in the servo-driven ornithopter. The Atmega328p based Arduino microcontroller is used for different boards like Arduino Uno for testing the batch of codes, Arduino micro for prototype, and Arduino Nano for tethered flight test. The specification of Atmega328p is given in Table 11.2. The typical servo motor connected to the microcontroller and receiver unit is shown in Figure 11.7, and connection pins are listed in Table 11.3.

FIGURE 11.7  Circuitry connection for servo control.

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TABLE 11.3 Specification of Atmega328p Parameter CPU type Performance Flash memory SRAM EEPROM Pin count Maximum operating frequency Number of touch channels Hardware touch acquisition Maximum I/O pins External interrupts USB Interface

Value 8-bit AVR 20 MIPS at 20 MHz 32 kB 2 kB 1 kB 28 or 32 pin: PDIP-28, MLF-28, TQFP-32, MLF-32 20 MHz 16 No 23 2 No

An Arduino flight system is used to achieve the wireless control and communication protocol because of its light in weight structure. Arduino Uno is used as a test bench in the early stage to understand each servo’s controls, as shown in Figure 11.8, and the connections are given in Table 11.4. The servo motor is set to move from 0° to 180° and vice versa. The sweep moment can be effectively used for mimicking the flapping motion of an

FIGURE 11.8  Arduino-based control of servo motor.

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TABLE 11.4 Connection Pins SERVO SIGNAL GND POSITIVE --

ARDUINO D5 GND 5V D2

RX -GND 5V THRO

ornithopter. The schematic representation of the connection of various components is shown in Figure 11.9. A DC-DC regulator is used to power Arduino for achieving 5 V. All four servos can be powered directly using a LiPo battery, and the connection of various pins in the microcontroller is given in Tables 11.5 and 11.6 respectively. The overall architecture of servo-based control for achieving the required angle of rotation and corresponding flapping motion is shown in Figure 11.10. The flow chart depicts that the pulse width modulated (PWM) signal from the TX transmitter is received by the RX with the threshold of 1,100 µs and sent to the microcontroller. The microcontroller executes the transmitted signals to the connected hardware, and the two main flapping servos get actuated.

FIGURE 11.9  Schematic of servo motors control.

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TABLE 11.5 Connections for Servos ARDUINO UNO GND +5V DIGITAL PIN D9

SERVO GND Positive Signal

TABLE 11.6 Connection for Servo-Driven Ornithopter Wing Rotation Control Components SERVO 1 SERVO 2 SERVO 3 SERVO 4 RX (THROTTLE)

Arduino D5 D6 D10 D11 D2

11.4  TETHERED FLIGHT The tethered flight test [8–10] is a flight testing technique in which a tether connects to the servo-driven ornithopter. During this test cruising performance of ornithopter can be evaluated. Figure 11.11 shows the tethered flight test of servodriven ornithopter moving on the circular trajectory as depicted in Figure 11.12. The tethered wire is about 2.5 m in length, and the cruising circular radius is about 1.5 m. To test the tethered flight of servo-driven ornithopter, which is connected to the ceiling of the room or building with a height of about 6.4 m, and PVC pipes are used to hold the thread building as shown in Figure 11.13. The tethered wire is held tight near the center of mass of the ornithopter to minimize the vibration. The top view of the ornithopter’s circular trajectory is shown in Figures 11.14 (a)–(c).

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FIGURE 11.10  Flow chart for flapping and wing rotation motion.

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FIGURE 11.11  Tethered flight of servo-driven ornithopter.

FIGURE 11.12  Cruising circular trajectory of servo-driven ornithopter tethered with wire.

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FIGURE 11.13  Tethered flight with wing rotation of ornithopter.

FIGURE 11.14  Tethered flight of ornithopter with wing rotation in a circular trajectory.

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FIGURE 11.15  Prototype of USTB ornithopter USTBird.

11.5  ATTITUDE CONTROL OF SERVO-DRIVEN ORNITHOPTER University of Science and Technology, Beijing (USTB) developed a servo-driven ornithopter structure [11,12], shown in Figure 11.15. The specification of the ornithopter is given in Table 11.7. It can control the flutter of the left and right wings of the FWMAV independently. It has two servo motors, as shown in Figure 11.16 wherein the left and right wings of FWMAV are connected and actuated. Component A is 3D printed using polylactic acid (PLA), a degradable and environmental material. The A′ is a circular hole having a diameter of 3 mm, and A″ is a

TABLE 11.7 Specifications of USTB Ornithopter USTBird Parameter Mass (g) Wingspan (m) Length (m) Chord (m) Flutter Frequency (Hz) Flight Endurance (min)

Value 85 0.8 0.52 0.28 1–5 >=10

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FIGURE 11.16  Servomotors assembly.

square hole of 3 mm. Structure A is connected to the two servos (B and B′) by screws and nuts that actuate the ornithopter’s left and right wings. To control the roll angle, a simple mechanical structure is designed as shown in Figure 11.17. The component I is 3D printed using PLA. The I′ is a square hole of 3 mm, and I″ is a circular hole of 6 mm in diameter. Also, the component M is 3D printed by PLA. The M′, I″, and N′ are circular holes of 2 mm in diameter. The M and N can be connected through these two holes by screws and nuts.

FIGURE 11.17  Mechanism structure for control of roll motion.

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FIGURE 11.18  A servo-driven ornithopter mounted on a fixed bed.

11.6  EXPERIMENTAL ANALYSIS An experimental setup is developed to achieve roll angle control of ornithopter. The experimental platform shown in Figure 11.18 includes 1. Airfoil; 2. Carbon rod of the fuselage; 3. Servo-driven mechanical structure; 4. Roll angle control mechanism structure; 5. Telescopic vertical bar; 6. Pedestal. A Proportional Integral and Derivative (PID) control algorithm is implemented to control the roll angle, and the block diagram is shown in Figure 11.19. Since the FWMAV is fixed on the experimental platform, the friction force, supporting force of the vertical bar, the fuselage’s sway, and other uncertain factors must be considered. After accounting for it, the incremental PID controller is designed as:

∆u(t ) = K p (e(t ) − e(t − 1)) + K i e(t ) + K d (e(t ) − 2e(t − 1) + e(t − 2)),

(11.1)

where K p , K i , and K d are proportion coefficient, integral coefficient, and derivative coefficient respectively, ∆u(t ) is an increment of the control input, e represents feedback information of angle. Simulation is performed through selecting the simulation parameters as K p = 0.3, K i = 0.015, and K d = 0. The simulation results of incremental PID control are shown in Figures 11.20 and 11.21, respectively. Based on the simulation results, the tracking trajectory is almost in line with the desired trajectory. It means that the simulation platform is feasible to control and measure the roll angle of FWMAV.

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FIGURE 11.19  Roll angle control using PID.

FIGURE 11.20  Tracking performance.

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FIGURE 11.21  Tracking error.

The experiments are conducted using the developed experimental platform for controlling the roll motion of ornithopter [13–16], and the experimental setup with a hardware unit is shown in Figure 11.22. The experimental setup consists of a software and hardware processing unit to receive and transmit the data to the ornithopter test platform for controlling the roll angle. The deflection angle or roll motion is sensed by the attitude sensor on the minimum system. The acquired angle is transmitted to Personal Computer (PC) through a wireless transmitting module after preliminary processing by the minimum system. Then, the control input and feedback of the roll angle are processed in the PC, and a signal is generated. It is transmitted to a minimum system, which in turn actuate the servo motor that controls the roll motion of the ornithopter. It completes the closed-loop attitude control of ornithopter [17–19]. The tracking performance is studied through experiments, and it is observed from Figure 11.23 that the PID controller has attained good tracking performance concerning the target. The influence of sway of the fuselage affected the accuracy of tracking for a short period. However, the roll motion of FWMAV can be effectively controlled in real-time.

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FIGURE 11.22  Experimental setup for control of roll angle of ornithopter.

FIGURE 11.23  Tracking performance based on experiment.

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FIGURE 11.24  USTBbird with long wingspan.

11.7 DESIGN OF LONG WINGSPAN SERVO-DRIVEN ORNITHOPTER The earlier UST bird-like structure wingspan is increased to 1.2 m, and its length is modified to 0.7 m. The aesthetic elements of the bird-like structure are also improved, as shown in Figure 11.24, and its specification is shown in Table 11.8. Wing airfoil is made using chlorinated Polyethylene (CPE) membrane to have sufficient rigidity to produce enough lift and certain flexibility to generate thrust. Hollow carbon tubes are used as supporting material for attaching the wing from the front wing tip to the rear wing root. The servo motors are attached to the left and right wings of USTBird independently, as shown in Figure 11.25. The USTBird can carry out various possible motions. As shown in Figure 11.25, the USTBird flaps its wings with synchronous phase and amplitude to produce balanced lift and thrust for take-off and cruising

TABLE 11.8 Specification of the Modified Ornithopter USTBird Parameter Mass (g) Wingspan (m) Length (m) Chord (m) Flutter Frequency (Hz) Flight Endurance (min)

Value 145 1.2 0.7 0.28 1–5 ≈10

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FIGURE 11.25  Driven with synchronous phase and amplitude.

flight. When it flaps the wings with the same amplitude and asynchronous phase, as shown in Figure 11.26, the body will roll in the opposite phase, making it steer. However, when it flaps with both asynchronous phases and different amplitude (Figure 11.27), then it adjusts the attitude quickly. It increases the flapping frequency of both left and right wings to climb or keep wings flattened to glide.

11.8  LIGHTWEIGHT BATTERIES FOR FWMAVS In general, Lithium Polymer (Li-Po) batteries are used as a power source for FWMAVs due to the following reasons [20–24]: • They are compact and light in weight. It can be made into any desired shape and size depending on the design of FWMAV; • They hold much amount of energy in a small compact size with high energy density; • They possess very good charging and discharging capacity by maintaining a constant power without fluctuation;

FIGURE 11.26  Driven with the same amplitude and asynchronous phase.

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FIGURE 11.27  Driven with different amplitude and asynchronous phase.

• They have no memory effect in comparison to the Ni-Cd and Ni Mh batteries; • It is safe because it is more resistant to overcharging, and very few leaks in an electrolyte. The LiPo battery used for the present FWMAV is a 70 mAH 20C Lithium battery that weighs about 2.34 g. It occupies 24% of the overall mass of 9.62 g of Golden – Snitch ornithopter. Table 11.9 illustrates typical battery capacities and their sizes for the maximum voltage capacity of 3.7 V.

TABLE 11.9 Various Capacities of LiPo Batteries Sl. No 1 2 3 4 5 6 7 8 9 10 11 12 13

Capacity (mAH) 40 45 55 60 70 75 80 85 95 130 160 210 250

Thickness (mm) 4 4 3.5 4 3 3.8 4 4 4 3.5 4 3 4

Width (mm) 12 12 9 11 23 12 10 12 12 23 20 30 25

Length (mm) 14 15 26 20 23 30 30 25 30 23 30 30 30

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11.9 SUMMARY This chapter discussed the development of servo-driven ornithopter and attitude control through simulation and experimental studies. Tamkang University develops a 0.96 m wingspan servo-driven ornithopter is discussed in detail. The flight control unit for the servo-driven mechanism and control strategy on achieving the synchronous motion by using servo mechanism-based actuation is discussed. The real-time tethered flight to attain a circular trajectory for the servo-driven ornithopter is illustrated. Further, discussion on an USTBird structure and its attitude control on tracking the desired trajectory showed a good demand for FWMAVs in autonomous missions. Improvement of existing USTBbird structure through increasing its wingspan to 1.2 m to carry more payloads and their simplified version of servobased actuation to achieve synchronous and asynchronous motion characteristics with varying amplitude is explained in detail. The lightweight Li-Po batteries for FWMAVs of various sizes and energy densities are provided.

REFERENCES





1. Voss, W. (2007) A Comprehensible Guide to Servo Motor Sizing, Copperhill Media. 2. Firoozian, R. (2014) Servo Motors and Industrial Control Theory, Springer. 3. Gerdes, J., Bruck, H. A. and Gupta, S. K. (2015, August) A systematic exploration of wing size on flapping wing air vehicle performance. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 57137, p. V05BT08A012). American Society of Mechanical Engineers. 4. Nguyen, Q. V. and Chan, W. L. (2018) Development and flight performance of a biologically-inspired tailless flapping-wing micro air vehicle with wing stroke plane modulation. Bioinspiration and Biomimetics, 14(1), 016015. 5. Phan, H. V., Kang, T. and Park, H. C. (2017) Design and stable flight of a 21 g insectlike tailless flapping wing micro air vehicle with angular rates feedback control. Bioinspiration and Biomimetics, 12(3), 036006. 6. Panchal, N. (2019) Wing Rotation Effect on an Ornithopter Using Servo Control, Master Thesis, Tamkang University, Department of Mechanical and Electro-Mechanical Engineering. 7. Barrett, S. F. (2013) Arduino microcontroller processing for everyone! Synthesis Lectures on Digital Circuits and Systems, 8(4), 1–513. 8. Baek, S. S. and Fearing, R. S. (2010, September) Flight forces and altitude regulation of 12 gram i-Bird. 2010 The 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (pp. 454–460). 9. Caetano, J. V., Percin, M. U. S. T. A. F. A., De Visser, C. C., Van Oudheusden, B., De Croon, G. C. H. E., de Wagter, C. and Mulder, M. (2014, May) Tethered vs. free flight force determination of the DelFly II flapping wing micro air vehicle. 2014 International Conference on Unmanned Aircraft Systems (ICUAS) (pp. 942–948). IEEE. 10. Baek, S. S. (2011) Autonomous Ornithopter Flight With Sensor-Based Behavior. University California, Berkeley, Tech. Rep. UCB/EECS-2011-65. 11. Kang, Y., Lu, Z., Huang, K., Chen, Y., Yang, L. J. and He, W. (2017) An all servo-driven ornithopter. International Conference on Intelligent Unmanned Systems (ICIUS-2017), Taipei, Taiwan.

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12. Feng, F., Huang, K., Huang, H., Liu, H., Mu, X. X., Fu, Q. and He, W. (2019) Video stabilization system development for a servo-driven flapping wing aerial vehicle. International Conference on Intelligent Unmanned Systems (ICIUS 2019), Beijing, China. 13. Gerdes, J. W., Gupta, S. K. and Wilkerson, S. A. (2012) A review of bird-inspired flapping wing miniature air vehicle designs. Journal of Mechanisms and Robotics, 4(2), 021003. 14. Jackowski, Z. J. (2009) Design and Construction of an Autonomous Ornithopter, Doctoral dissertation, Massachusetts Institute of Technology. 15. He, W., Huang, H., Chen, Y., Xie, W., Feng, F., Kang, Y. and Sun, C. (2017) Development of an autonomous flapping-wing aerial vehicle. Science China Information Sciences, 60(6), 063201. 16. De Croon, G. C., Groen, M. A., De Wagter, C., Remes, B., Ruijsink, R. and van Oudheusden, B. W. (2012) Design, aerodynamics and autonomy of the DelFly. Bioinspiration and Biomimetics, 7(2), 025003. 17. Verboom, J. L., Tijmons, S., De Wagter, C., Remes, B., Babuska, R. and de Croon, G. C. (2015, May). Attitude and altitude estimation and control on board a flapping wing micro air vehicle. 2015 IEEE International Conference on Robotics and Automation (ICRA) (pp. 5846–5851). 18. Baek, S. S., Bermudez, F. L. G. and Fearing, R. S. (2011, September) Flight control for target seeking by 13 gram ornithopter. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 2674–2681). 19. Shigeoka, K. S. (2007) Velocity and Altitude Control of an Ornithopter Micro Aerial Vehicle, Doctoral dissertation, Department of Electrical and Computer Engineering, University of Utah. 20. Salameh, Z. M. and Kim, B. G. (2009, July) Advanced lithium polymer batteries. 2009 IEEE Power and Energy Society General Meeting (pp. 1–5). 21. Overview of Lithium Batteries, Kokam Co., Ltd. http://www.kokam.com. 22. Jung, H. K., Choi, J. S., Wang, C. and Park, G. J. (2015) Analysis and fabrication of unconventional flapping wing air vehicles. International Journal of Micro Air Vehicles, 7(1), 71–88. 23. Jones, K., Bradshaw, C., Papadopoulos, J. and Platzer, M. (2003) Development and flight testing of flapping-wing propelled micro air vehicles. The 2nd AIAA Unmanned Unlimited Conference and Workshop and Exhibit (p. 6549). 24. Avanzini, G., de Angelis, E. L. and Giulietti, F. (2016) Optimal performance and sizing of a battery-powered aircraft. Aerospace Science and Technology, 59, 132–144.

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Figure-of-Eight Motion and Flapping Wing Rotation

12.1 INTRODUCTION One of the major obstacles in the research framework of unsteady flow mechanisms is the difficulty in directly measuring the aerodynamic forces produced by a flapping insect or a flapping bird [1]. A free-flying butterfly has ever been attracted into a wind-tunnel, and an unconventional lift-generating mechanism based on in-situ [2] measurement is cumbersome [2]. Besides, a MEMS-based micro force sensor using capacitive detection is developed for characterizing the flight behavior of a tethered fruit fly (Drosophila melanogaster) [3]. Recently images of the wake vortices of bats (Glossophaga soricina) are analyzed by means of a digital particle image velocimetry (DPIV) method [4]. Generally speaking, the researchers studied the unsteady flow mechanisms by observing the living natural flyers. Even though this obtained flight information is firsthand and precious, two shortcomings are still inevitable. First, living natural flyers are hard to control. Constrained by the human-made environment with limited fidelity, the living animals’ measured gestures are even questioned with their reality. Second, these experimental data from the same species of animals are usually without good repeatability. Therefore, the corresponding summary of the flight behaviors or mechanisms is hard to conclude from natural flyers’ massive experimental data. Several groups developed FWMAVs with different configurations and actuation principles [5–7]. In this chapter, discussions on the design of novel passive wing rotation flapping mechanisms, fabrication, assembly, and wind tunnel testing to evaluate their aerodynamic performance are given.

12.2  PASSIVE WING ROTATION OF FLAPPING 12.2.1 Review on Tamkang’s Golden-Snitch Based on the observation of the prior works about flapping MAVs, including the Golden-Snitch of Tamkang University, a research framework and development is shown in Figure 12.1. It consists of gear-transmission mechanism and flapping wings, manufacturing, mechanism assembly, wind-tunnel test, flight test, flight stability and control, computational fluid dynamics (CFD), and final product of FWMAV. DOI: 10.1201/9780429280436-12

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FIGURE 12.1  The research framework for the development of FWMAV.

As the first step toward constructing the complete framework, it adopts the scaling laws of natural flyers to relate the body mass m with the wingspan b and wingbeat frequency f as follows:

b = (1.17) ⋅ m 0.39 (12.1)



f = (3.98) ⋅ m −0.27 (12.2)

Take the example of a 0.2 m-span MAV (b = 0.2), the body mass m cannot surpass 0.011 Kg, and the wingbeat frequency f must be faster than 13.5 Hz. Hence designing

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FIGURE 12.2  The Eagle-II FWMAV assembly with FBL mechanism.

and fabricating the key mechanism component to accomplish light in weight FWMAV is not easy. In other words, the gear transmission mechanism for flapping motion should be tiny and less weight. The corresponding wingbeat frequency should also be fast enough, and most importantly, the flapping gesture ought to mimic the natural flyers accordingly. These problems have been investigated in Chapter 5. In this chapter, the authors initially discussed how to use the conventional four-bar linkage (FBL) mechanism to fabricate an ultra-light driving mechanism for wing flapping and found out the passive wing rotation motion termed as “oblique Figure-of-8” from the original simple flapping induced by the flexible wing frame [8]. The author’s group employed an FBL gear transmission mechanism to Eagle-II shown in Figure 12.2 with only one DOF flapping motion for the excuse of very lightweight and low technical complexity. The wing skin is made of parylene foil, which is clued to the Balsa-wood leading-edge beams with a simply supported boundary condition instead of a clamped boundary condition. As a result, the wing skin can be rotated freely according to the up-and-down plugging, and the instantaneous angle-of-attack of the flapping wing could almost have a simple harmonic motion. The lift and net thrust coefficients CL and CT (divide lift L and net thrust T with dynamic pressure and wing area respectively that gives lift coefficient CL and net thrust coefficient CT with respect to advance ratio J) extracted from a wind-tunnel test of Eagle-II. It has a parylene film of 20–30 μm thick, a wingspan of 25 cm, flapping frequency of 7.2–15.7 Hz, and stroke angle =35° with a semi-rigid leading-edge subject to a fixed inclined angle of 20°, and various advance ratios are shown in Figure 12.3. Regarding the details of wind tunnel testing, please refer to Chapter 2. In general, the time-averaged lift coefficient CL of the FWMAV shown in Figure 12.3(a) is larger than 3.0 in the regime of J below 0.4, which has a counterbalancing force to the weight of FWMAV. The net thrust coefficient CT subjected to a J value below 0.4 is always positive, as observed in Figure 12.3(b), which is signified as the continuous forward pushing without a decrease in speed during the real flight conditions.

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FIGURE 12.3  The aerodynamic coefficients of Eagle-II: (a) lift coefficient CL, (b) net thrust coefficient CT.

12.2.2 Joint Wearing of Flapping Mechanism It can be seen from Figure 12.3 that, at a certain period of the operation time, the thrust data for small advance ratio or high flapping-frequency region of J < 0.4 revealed the trend of diversity or data fluctuation (e.g., U = 0.4 m/s). Such a diversity

Figure-of-Eight Motion and Flapping Wing Rotation

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FIGURE 12.4  Worn FBL (black dash line) mechanism for Eagle-II.

of thrust data is traced back, and it is due to the worn of the gear transmission module. In other words, the wear of the power transmission mechanism impeded the smooth flapping and induced corresponding unpredictable aerodynamic forces. Figure 12.4 shows the detailed FBL (black dash line) mechanism for the Eagle-II. The extremely worn (reaming) gear condition is marked with a red circle in the Balsa leading-edge frame (motor is not shown in Figure 12.4). It signifies an aging issue of FWMAVs and reveals certain uncommon penalty forces resulting from the improper assembly of semi-rigid wing structures in the flapping mechanism. Based on the concept of miniaturization of FWMAVs, the design methodology is to use much lighter and more flexible materials as the key structures for the new version of Golden-Snitch FWMAV. For instance, shortening the wingspan from 30 cm to 20 cm, the authors replaced the Balsa-wood leading edge frame with fine carbon-fiber rods. Meanwhile, the aluminum-alloy FBL mechanism is reconstructed by using the EDWC technique. The new mechanism made of aluminum alloy shown in Figure 12.5 has attained 1.2 g in mass which is far less than the case of Caltech’ Microbat [9] of 2.8 g. The assembled Golden-Snitch FWMAV is shown in Figure 12.6. It has a carbonfiber leading-edge beam/rib and parylene skin. A 7 mm-diameter electrical motor is mounted on an aluminum-alloy holder and a Li-Poly battery of 30–50 mAh is used for power supply. The total mass including flexible wing frame, motor, gear assembly, wing, fuselage, tail, battery, and receiver is about 5.9 g. Chapter 5 discussed the aerodynamic force data gathered using wind tunnel experiments. It is apparent that the net thrust force of Golden-Snitch is superior to Eagle-II with 35% enhancement.

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FIGURE 12.5  Four-bar (black dash line) gear transmission module for Golden-Snitch.

The flapping frequency of Golden-Snitch is also increased to 20 Hz from 15 Hz of Eagle-II. As also mentioned in Chapter 5, the author’s group has succeeded in two folds of precision injection molding (PIM) manufacture for constructing the polyoxymethylene (POM) flapping mechanism and the expandable polystyrene (EPS) fuselage for

FIGURE 12.6  The Golden-Snitch FWMAV.

Figure-of-Eight Motion and Flapping Wing Rotation

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FIGURE 12.7  Tamkang’s Golden-Snitch Pro in 2010.

the Golden-Snitch Pro shown in Figure 12.7 [10]. It has achieved the following: (1) The flight endurance is extended to 480 s in 2010. (2) The fabrication time using PIM is about 1 min which is much shorter than 30 min by EDWC. (3) It can land safely for 100 times with the protection of EPS fuselage.

12.2.3 Oblique Figure-of-8 Flapping Characteristics of Golden-Snitch As the Golden-Snitch Pro exalts in free flight, the author found that a streamwise vibration of carbon-fiber leading edge due to increasing in wingbeat frequency from 15.6 to 21.7 Hz for the wings with 30° ribs. It is much smaller than the natural frequency of 85 Hz for the wing structure. It means that the occurred vibration is not relevant to the resonance of the wing frame. By combining the induced coherent streamwise vibration of the wing frame and the vertical reciprocating flapping motion, a 3D Figure-of-8 flapping motion of FWMAV is evident. It can be also seen even by human naked eyes. The streamwise vibration of the wing frame is originated due to the Knoller-Betz effect and interpreted as coherent forward locomotion. By using a basic video camera with 30 frames per second the Figure-of-8 motion is captured. Since the speed is too slow the full flapping cycle of FWMAV is unable to be captured. Hence, a high-speed CCD camera (Phantom v. 4.2) having 1,000 frames per second is utilized to capture the Figure-of-8 trajectory of the wingtip of Golden-Snitch Pro in quiet ambient conditions. It is installed in the wind-tunnel and the real-time images of flapping wings subjected to two cases such as with and without 30° rib are captured which is shown in Figure 12.8. The angle of attack is maintained at 20° and flapping frequencies are varied from 9.4–25 Hz for without rib and 15.6–21.7 Hz for the stiffened 30°−rib. The surface morphology of the wing skin showed a wavy profile from the leading edge to the trailing edge and from the wingtip to the inner wing root simultaneously.

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FIGURE 12.8  The front views from (a) to (h) corresponds to the side views without rib from (i) to (p), and side views with 30° rib from (q) to (x).

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It accorded the flexible wing design with a sinusoidal change of the leading-edge angle-of-attack.

12.2.4 Symmetry Breaking of Flapping Dynamics According to the genetic design aspects of FWMAVs, the structure of small natural flyers has rigid leading edges and flexible trailing edges. The leading edge should be hard to bend, but easy to twist [11]. The trailing edge of Golden-Snitch is made of parylene or other polymer films and agreeable to the aforementioned rules of thumb’s flexible requirement. The carbon-fiber beam’s leading-edge is also easy to twist but vulnerable to bending along streamwise or up-and-down directions. However, the bending of the leading edge due to large wind loading or high-frequency flapping, on the one hand, resulted in phase lag. The leading-edge vortices have weakened the mechanism resulted in a “delayed stall.” On the other hand, the coherent movement of elastic, leading-edge created the Figure-of-8 flapping and made up for the earlier lift loss due to unsteady mechanisms, e.g., “wake capture” or “rotational circulation.” Due to chaotic reasons, e.g., bifurcation’s duality, including Vandenburghe’s flat paddle [12] or Alben’s flapping body [13], the Figure-of-8 contours could not match with an identical trajectory. Their geometry is related to the wingbeat frequency unaffectedly. The classical Figure-of-8 motion of Golden-Snitch is evaluated for width-to-height ratios (W/H) with respect to various wingbeat frequencies, depicted in Figure 12.9. The width-to-height (W/H) ratio is regarded

FIGURE 12.9  Figure-of-8 trajectories of Golden-Snitch and extracted W/H ratio.

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as equivalent to the thrust or forward locomotion in real flying. For the 30°-rib wing, the (W/H) ratios around 0.81 ± 11% depict similar traces at all wingbeat frequencies except that the lower loop is bigger than the upper loop at the high-speed region. Without rib condition of the wing, the (W/H) ratio is around 0.46 ± 28% denotes a much larger variation in the Figure-of-8 traces with different speeds. In the event of non-identical Figure-of-8 contours, the authors would like to address the horizontal movement of 2-D vertically oscillating plate foil of Vandenburghe’s experimental work and Alben’s theoretical work. A verticallyoscillating plate’s ideal case ruined its symmetry in dynamics and started to move forward or backward freely. Besides, the forward or backward speed coherently matched linearly with the original oscillating frequency. However, a hysteresis or bifurcation existed intrinsically. In other words, the oscillating frequencies for starting and ending during the forward/backward locomotion are not similar. Compared to prior studies, the FWMAV in this work could be regarded as a non-ideal but more complicated. Also, the wing frame is very flexible, and the airfoil is not symmetric. Therefore, the 3D flow field is not similar to a 2D profile of Vandenburghe’s work. The following arguments are made for the comparative purpose: 1. Vandenburghe’s work is an ideal simplified model of FWMAV with the Figure-of-8 flapping. However, the Figure-of-8 flapping motion would gradually disappear if the FWMAV increases its rigidity of the wing frame structure. It is observed from Figure 12.9 that a more flexible wing frame (the case of without rib) has achieved a wide range of frequency (9.4–25 Hz). 2. The Figure-of-8 flapping comprises all the characteristics mentioned in the ideal model of Vandenburghe’s work, of course including the bifurcation phenomena. The Figure 12.10 demonstrated the Figure-of-8 trajectories of the Golden-Snitch for the increase and decrease in voltages for the range of 3.7 to 9 V. Even under the same driving voltage, the wingbeat frequency of increasing trend in voltage is smaller than the decreasing of voltage case and the Figure 12.11(a) depicts those cases. The starting wingbeat frequency showing the Figure-of-8 (13.51 Hz) is higher than the frequency where the Figure-of-8 disappears (9.62 Hz). The pathway of the complete up-and-down operation loop depicts the bifurcation duality. The W/H ratio of the Figure-of-8 increase and decrease in the flapping frequency trend is also shown in Figure 12.11(b). It is observed that it acts as an equivalent index of coherent motion like the rotating frequency or the driven Reynolds number in Vandenburghe’s work. It is found to be that the Figure-of-8 motion of Golden-Snitch regarded as nonsymmetrical behavior in the nonlinear dynamics. As a matter of fact, it is categorized as a passive wing rotation and needs improvement. Hence, a few examples of active wing rotation are discussed in the following section.

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FIGURE 12.10  The trajectories of Figure-of-8 for Golden-Snitch (a) increasing trend of voltage, (b) decreasing trend of voltage.

FIGURE 12.11  The bifurcation or hysteresis phenomena of Golden-Snitch: (a) variation of voltage in increasing and decreasing case, (b) W/H ratio for the Figure-of-8 of flexible wing.

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12.3  ACTIVE WING ROTATION OF FLAPPING 12.3.1 Lift-Generation Principle for Wing Rotation of Flapping There are many arts in the literature that dealt with flapping mechanisms with wing rotation [14–16], collision recovery [17–22], hummingbird hovering [23–25], flapping-wing using artificial muscle [26], morphing wing [27], and fly’s banked turn [28]. However, Dickinson et al. [1] conducted a systematic study about the wing rotation lift. Due to difficulty in measuring insect’s or birds’ aerodynamic characteristics in a wind tunnel setup [29,30], they developed a robot model of fruit-flies, as shown in Figure 12.12(a), to mimic the flapping motion. Figure 12.12(b) shows the various components of the lifting phenomenon captured during the wing rotation. The total lift is shown in Figure 12.12(b) includes the main contribution from the translational lift called delayed stall and the additional peaks correspond to wing rotation. He stated that the solid dots signifies rotation circulation and the peaks of hollow dots represent the wake capture. Besides yet another phenomenon, namely, the Magnus effect, is generally observed in insects. The Magnus effect for a baseball case is depicted in Figure 12.13(a) is yielded based on Bernoulli’s theory. The clockwise circulation Γ as shown in Figure 12.13(b) combines the relative freestream speed V∞ to generates a positive lift L by the KuttaJoukowski law (L = ρV∞Γ) potential theory. It can be seen from Figure 12.13(b) that there are a flow attachment and detachment on the entry and exit of airflow. The increase in velocity is observed upper surface regime of the ball compared to underneath. Similar to baseball, Insects’ have horizontal Figure-of-8 motion, as shown in Figure 12.13(c). It has two-stroke reversals called pronation and supination at both sides [31]. The wing rotation motion of supination at the end of the downstroke is the same as the clockwise circulation in Figure 12.13(b). The left-side flow field just before the supination naturally creates additional lift. Similarly, regarding the rightside flow field just before the pronation or at the end of the upstroke, the velocity direction is negative, as observed in Figure 12.3(b). Also, the wing rotation has a counter-clockwise direction with negative circulation is attained. Therefore, the generated lift is still positive due to the rotation circulation. The developed wing rotation is one of the categories proposed by Dickinson. Moreover, there are symmetric and delayed wing rotations occur in the insects.

FIGURE 12.12  (a) Fruit-fly robot model, (b) time history of flapping lift (solid dots denoting rotation circulation and hollow dots denoting wake capture).

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FIGURE 12.13  (a) Magnus effect in A baseball; (b) circulation Γ relative freestream velocity v∞, (c) horizontal Figure-of-8 of insects.

• Advanced wing rotation Before the stoke reversal due to the advanced wing rotation, the flow field has generated an additional positive lift, shown as the solid peaks in Figure 12.12(b). The active wing rotation motion needs extra power, which can be produced through the actuation of servo motors or a special mechanism. • Symmetric wing rotation This lift generation is similar to the advanced wing rotation, except the wing rotation moment is exactly happened at the stroke reversal. In the hovering flight, the first and last half of the wing rotation is supposed to increase and decrease the lift characteristics without forward speed. As we know, the air drag and power dissipation increase with lift. However, during the symmetric wing rotation, power consumption is less than the case of advanced wing rotation. In other words, the higher frequency symmetric wing rotation may be a more efficient way to perform a low-speed hovering or forward flight. • Delayed wing rotation It happens after the stroke reversal and creates a negative V∞, as denoted in Figure 12.13(b), leading to a negative lift. The delayed wing rotation is shown in the oblique Figure-of-8 of Golden-Snitch in Section 12.2 [32]. It is generated naturally and passively due to the fluid-structural interaction between the wing frame and the unsteady flow field. It is not contributed to enhancing the lift characteristics of flapping wings.

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Although Dickinson claimed that the horizontal wing rotation, including the rotational circulation and wake capture, could provide an extra 35% lift relative to the flapping lift without wing rotation, we need to evaluate whether the advanced (or symmetric) wing rotation can provide it. The following section addresses this issue.

12.3.2 Flapping Mechanisms with Wing Rotation In an attempt to achieve the active wing rotation, the authors’ group surveyed various flapping mechanisms that can actively rotate their wings along with the flapping motion [33,34]. Most of them focused on the flapping mechanism design with multiple degree-of-freedoms and not dealt with aerodynamic force measurement for the case of flapping with wing rotation. Hence, several flapping mechanisms are designed, which are given in Table 12.1. Among them, the type A1 (normal-servo) and Golden-Snitch’s FBL are without active wing rotation for comparison. The configuration features are briefly mentioned in the remark, and their performance is discussed in the following sections.

12.3.3 Type A: All Servo Mechanism The first attempt to achieve such a mechanism is shown in Figure 12.14. It has two pairs of servos [35], and one pair is used for achieving flapping motion, and the other one is for wing rotation. The advantage of using servos as the main driving mechanism is that servos have high power to torque ratio, which is good for instant flapping motion and wing rotation. In order to reduce the weight and make it easy to manufacture, all the parts are fabricated using the 3D printing technique. Carbon fiber rods are used as a fuselage to keep the total weight as minimal as possible and make the machine a compact one. Servo ornithopter works on the principle of PWM (pulse width modulation) controlled by the Arduino microcontroller as a flight control board. Unlike conventional Ornithopters contain mechanical gears and DC brushless motors, the servo ornithopter operates on a set of digital servos controlled by PWM pulses, as discussed in Chapter 11. A wind tunnel experiment is conducted for the ornithopter having a wingspan of 96 cm and a wing area of 0.2541 m2, and the wing rotation mechanism shown better performance than the normal mechanism. Even though the Type-A mechanism’s performance is better, few factors can be improved, such as weight reduction (larger than 100 g), reducing the number of servo actuators, and requirement of less energy. Hence, in order to improve on these aspects, new flapping mechanisms are designed.

12.3.4 Type A1: Normal Servo Mechanism In order to compare the newly designed wing rotation mechanisms, a normal servo mechanism is designed and fabricated, which has identical specifications as like other wing rotation mechanisms. The Type-A1 mechanism shown in Figure 12.15 utilizes one pair of servos for achieving flapping motion. For a clear understanding of the design, an exploded view is shown in Figure 12.16. The servos are installed

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Figure-of-Eight Motion and Flapping Wing Rotation

TABLE 12.1 Flapping Mechanisms for Investigating Wing-Rotation Effect [36] Mechanism Type Type A All-servo

Schematics

Remarks Two pairs of servo motors; one pair for flapping; one pair for wing rotation.

Type A1 Normal-servo

One pair of servo motors for flapping only.

Type B Servo-Bevel gear Hybrid

Servo flapping linked with one pair of bevel gears for continuous wing rotation.

Type B1 Servo-Bevel gear hybrid with stoppers

Servo-bevel gear hybrid with stoppers for discontinuous wing rotation (rotating only at stroke reversals).

Golden-Snitch’s FBL without servo

DC motor-driven flapping with four-bar linkage (FBL).

Type C FBL-Bevel gear Hybrid

DC motor-driven flapping hybrid with four-bar linkage (FBL) and bevel gear for continuous wing rotation.

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FIGURE 12.14  Type-A: all servo flapping mechanism.

FIGURE 12.15  Type-A1 mechanism using one pair of servos: (a) front view, (b) top view, (c) isometric view.

FIGURE 12.16  Exploded view of Type-A1: normal servo mechanism.

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FIGURE 12.17  Assembled Type-A1 mechanism: (a) front view, (b) top view.

FIGURE 12.18  Dimensions of the PET wing (unit: cm).

in the servo mount to make the mechanism more compact and reduce vibration. The fuselage is attached at the servo mount’s backside, and the wings are attached to the wing bar. The wing connector holds the wing bar and the servo tightly. The wing bars can be adjusted to get the equal stroke angles and maintain zero phase lag between the two wings. After the fabrication of the required parts using a 3D printer, all the parts are assembled, as shown in Figure 12.17. The flapping wing (Figure 12.18) is made using PET, and the wing membrane is attached to the flapping mechanism, as shown in Figure 12.19. The wing parameters are given in Table 12.2.

FIGURE 12.19  Wing membrane attached to the flapping mechanism.

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TABLE 12.2 Wing Parameters of Normal Servo Mechanism Type-A1 Parameters Wingspan Chord length Wing area Aspect ratio

Metric 70 cm 22.5 cm 1406.8 cm2 3.48

After successful fabrication and assembly of the mechanism, a wind tunnel experiment is conducted by varying the wind speed 1.5–4 m/s and inclined angles from 10º to 35º and the driving voltages of 1.25 V, 2.5 V, and 5 V. The wind tunnel details are given in Table 12.3. An FWMAV with a 70 cm wingspan having a semielliptical area of 1406.8 cm2, and with a Type-A1 flapping mechanism is mounted on a six-axis force gauge as shown in Figure 12.20 to measure the aerodynamic lift and net thrust at different inclined angles as shown in Figure 12.21. About 10,000 points of unsteady data of lift and net thrust forces are collected and taken on average to one data point. Instrument World software is used to acquire the unsteady data. After finishing the experiment, the raw data is averaged to one data point. Similarly, many single data points are collected for each case. The flapping frequencies with respect to given voltages are given in Table 12.4. As observed in Figure 12.22, the lift increases when the voltage and wind speed increase. However, it is also noticeable that the net thrust decreases with an increase in the wind speed (due to increasing air drag). The maximum lift is experienced at the wind speed of 4 m/s and the highest voltage of 5 V (2.5 Hz) irrespective of inclined angles. The cruising speed where the net thrust is zero is found for different inclined angles and the driving voltages given in Table 12.5. From the aerodynamic force data shown in Figure 12.22, it is evident that even though the maximum lift observed is about 70–74 gf at 35° and 4 m/s, the corresponding net thrust is negative. Hence, the flying speed of 4 m/s will be automatically reduced to a cruising speed near 3 m/s with a lower cruising lift of 63 gf. The best cruising condition for the FWMAV is 25°, 5 V, and 3 m/s, as given in Table 12.5.

TABLE 12.3 Dimensions and Details of the Medium-Size Wind Tunnel Parameters Length Width Height Wind speed range Lowest turbulence intensity

Metric 15 m 2.2 m 1.8 m 1 ~ 28 m/s 0.5%

Figure-of-Eight Motion and Flapping Wing Rotation

FIGURE 12.20  A servo ornithopter mounted on a wind tunnel.

FIGURE 12.21  FWMAV at inclined angles: (a) 0°, (b) 15°.

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TABLE 12.4 Flapping Frequency with Respect to the Applied Voltage Voltage (V) 1.25V 2.5V 5V

Flapping Frequency (Hz) 1.5 Hz 2.0 Hz 2.5 Hz

Compared to the total weight of 80.9 gf of FWMAV, the best cruising lift of 63 gf is apparently not large enough. As we know the Dickinson’s three lift mechanisms, such as delayed stall, rotational circulation, and wake capture, that has to be identified in the lift data shown in Figure 12.23(a). We found that the sine wave that signifies the delayed-stall without wing rotation effect. (No double-peak phenomena, as shown in Figure 2.7(a) was not found inside the lift curve.) However, the net thrust data are shown in Figure 12.23(b) has two positive actions per one flapping cycle that matched with the trend of Figure 2.7(b). In summary, there is a necessity to add the wing rotation motion to the servo-based flapping wing motion.

12.3.5 Type B: Servo-Bevel Gear Hybrid Mechanism Compared to the two-pair servo mechanism for attaining the wing rotation motion, the one-pair servo mechanism has advantages in coupling or engaging a bevel gear for flapping and rotating of wings at the same time. The bevel gears’ rotational motion purely depends on the servo motors’ flapping angle and the number of teeth of bevel gears. The CAD model of the mechanism is shown in Figure 12.24, and for better understanding, the exploded view is shown in Figure 12.25. The Type-B mechanism comprises a rotating bevel gear and a fixed auxiliary bevel gear fixed to the central base. The rotating axes of these two pairs of bevel gears are perpendicular to each other, and the rotating bevel gears drive the wing spars as an output. When the servo is powered, the flapping arm connected with the servo connectors’ help starts swinging, and the rotating bevel gear connected to the flapping wing also swings synchronously. Because of the mating between the rotating bevel gear and the fixed auxiliary bevel gear, the rotating bevel gear starts following the fixed auxiliary gear path, thereby creating a rotation motion. Therefore, whenever the servo is driven, then the wing motions’ flapping and rotation occur synchronously. Further, the designed mechanism parts are fabricated using a 3D printer and assembled, as shown in Figure 12.26. The wing profile used in Type A1 is incorporated for the present mechanism as well. However, the wing membrane is fabricated slightly larger than the designed one to generate wing rotation and avoid interference during flapping. The wing area is increased from 1406.8 cm2 to 1473.8 cm2 by maintaining the same wingspan and chord length with an aspect ratio of 3.32.

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FIGURE 12.22  Lift and net thrust by Type-A1 mechanism at different inclined angles: (a–b) 10°, (c–d) 15°, (e–f) 20°, (g–h) 25°, (i–j) 35°.

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TABLE 12.5 Cruising Speeds of Type A1 Mechanism Inclined Angle 10º 15º 20º 25º 35º

Voltage 5V 5V 5V 5V 5V

Cruising Speed × 4.0 m/s 3.2 m/s 3.0 m/s 1.8 m/s

Cruising Lift × 49 gf 45.5 gf 63 gf 35 gf

The wind tunnel setup and the measurement are retained the same as the case of Type A1. The lift and the net thrust by taking the time average are shown in Figure 12.27 for the varied inclined angles, wind speeds, and the driving voltages. As per the earlier discussion, the cruising flight conditions are determined from the Figure 12.27, and they are given in Table 12.6. The Type-B mechanism’s best cruising lift is found to be 51.13 gf at 35°, 5 V, and 1.5 m/s. The classical waveforms of lift and net thrust are shown in Figure 12.28. It is observed that the total weight of the Type-B mechanism is 88.1 gf, which is lesser than the Type A (more than 100 gf). However, it is still larger than the best cruising lift (51.13 gf) experienced by the Type-B mechanism. Moreover, we found that Type-B’s best cruising lift with wing rotation is also smaller than Type-A1 (63.17 gf) without wing rotation. While comparing these two mechanisms, in the case of the Type-A1 mechanism (Figure 12.23(a)), the double-peak is not seen at the stroke reversal, whereas in the Type-B mechanism, it occurs, which is observed from Figure 12.28(b). Besides, there is only one positive peak per cycle in the net thrust shown in Figure 12.28(b), and in

FIGURE 12.23  The classical time-changing signals of a flapping wing using Type-A1 mechanism: (a) lift force, (b) net thrust force.

Figure-of-Eight Motion and Flapping Wing Rotation

FIGURE 12.24  Type-B mechanism: (a) front view, (b) top view, (c) isometric view.

FIGURE 12.25  Exploded view of Type B: servo-bevel gear hybrid mechanism.

FIGURE 12.26  Assembled Type-B mechanism: (a) front view, (b) top view.

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FIGURE 12.27  Lift and net thrust of Type-B mechanism at different inclined angles: (a–b) 10°, (c–d) 15°; (e–f) 20°, (g–h) 25°, (i–j) 35°.

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TABLE 12.6 Better Cruising Lift Values at Their Cruising Speeds of Type-B Mechanism Inclined Angle 10º 15º 20º 25º 35º

Voltage 5V 5V 5V 5V 5V

Cruising Speed 3.0 m/s 2.6 m/s 2.25 m/s 1.6 m/s 1.5 m/s

Cruising Lift 27 gf 42 gf 48 gf 46 gf 52 f

Type A1 has two positive peaks as observed in Figure 12.23(b). If the net thrust force reduces, it diminishes the cruising speed to 1.5 m/s, and it can achieve less cruising lift. Therefore, a rational way to comfort this situation is that the servo mechanism should be modified to improve the net thrust forces. Hence, we need to adjust the wing rotation by redesigning the servomechanism to engage and disengage the bevel gears at a specific period to reduce friction and power loss.

12.3.6 Type B1: Hybrid Servo-Bevel Gear Mechanism with Stoppers It is a servo-powered mechanism with rotating bevel gears connected to the flapping wing spars, auxiliary bevel gears (non-fixed) coupled with stoppers, a servo mount, and a central base, which is shown in Figure 12.29. The difference between Type-B1 and Type-B mechanism is that the non-fixed auxiliary bevel gear for controlling the wing rotation is fixed and engaged at stroke reversals. When the flapping arm swings during the downstroke or upstroke, the rotating bevel gear driving the flapping spars also swings synchronously. The auxiliary bevel gear did not engage with the rotating bevel gear (without wing rotation) until it touched the stopper and switch to perform the wing rotation motion. The bevel gears’ rotation can be designed by the position

FIGURE 12.28  Classical signals generated by Type-B mechanism: (a) lift, (b) net thrust.

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FIGURE 12.29  Type-B1 mechanism: (a) front view, (b) top view.

of the stoppers before the stroke reversals to attain advanced wing rotation, and the rest of the wing sweeping path will have without rotation. The exploded view of the Type-B1 mechanism assembly is shown in Figure 12.30. The fabricated Type-B1 mechanism using a 3D printer and the snapshots of a single cycle of operation are shown in Figures 12.31 and 12.32, respectively. The following are the descriptions for the downstroke and upstroke motion of Type-B1 mechanism depicted in Figure 12.32. (a): The black marks on the base and the rotating gear are exactly aligned at the beginning of downstroke (b–c): The black marks keep the same aligned position during the downstroke (d–e): Wing rotation occurs as the stopper works and the marks are misaligned at the stroke reversal of supination (f–g): The misaligned angle keeps the same during the upstroke without wing rotation (h): Wing rotation occurs again as the stopper works and the marks are recovered to the aligned position at the stroke reversal of pronation. By considering a similar wing profile, wind tunnel testing is performed. The lift and net thrust data are collected and time-averaged profile are shown in Figure 12.33.

Figure-of-Eight Motion and Flapping Wing Rotation

385

FIGURE 12.30  Exploded view of Type-B1 mechanism.

The increasing trend of lift and decreasing trend of net thrust with respect to increase in wind speed can be seen. The cruising conditions are identified and given in Table 12.7. The best cruising condition occurs at 35°, 5 V, and 3 m/s which generates the highest lift of 84 gf. The cruising speed recovers again at a wind speed of 3 m/s. Hence, the modified wing-rotation Type B1 mechanism reduces the drag or increase the thrust effectively by its switchable stoppers to trigger the wing rotation motion at right time. However, due to the addition of stoppers screws and the pins of non-fixed auxiliary bevel gears, the weight of the Type-B1 mechanism is increased to 93 gf. Even though the cruising lift is substantially improved to 84 gf, still it is hard to counterbalance the bodyweight of FWMAV. Hence, the weight reduction of 70-cm span servo-driven FWMAV will have to be attempted in near future. Besides, the classical signals of lift and the net thrust generated by the Type-B1 mechanism are shown in Figure 12.34. The lift signal is shown in Figure 12.34(a) has a double-peak phenomenon that seems not apparent. However, the main positive

FIGURE 12.31  Assembled Type-B1 mechanism with four stoppers: (a) front view, (b) top view.

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FIGURE 12.32  Single cycle of operation of Type-B1 mechanism.

peak from the pronation moment to the downstroke period contributes a much larger lift than the wings driven by other previous servo mechanisms. Moreover, the net thrust signal is shown in Figure 12.34(b) has two peaks per flapping cycle, and it promotes the flapping wing to generate a higher net thrust force. Also, the higher cruising speed back to 3 m/s provides more cruising lift.

12.3.7 FBL-Bevel Gear Hybrid Mechanism Basically, the large wingspan of 70 cm servo-driven FWMAVs may not be designated as MAVs. Miniaturization of flapping wings is indeed and design philosophy of this book. Authors are developing miniaturized FWMAVs, similar to the size of non-servo-based Golden-Snitch with wing rotation characteristics. In other words, the FBL mechanism as light as the POM model shown in Figure 3.1 has to be added with small bevel gears, and their housing can be modified accordingly to make it compact. However, due to manufacturing difficulties of tiny mechanisms, the authors included the FBL mechanism with wing rotation and not used switchable

Figure-of-Eight Motion and Flapping Wing Rotation

387

FIGURE 12.33  Lift and net thrust data of Type-B1 mechanism at different inclined angles: (a–b) 10°, (c–d) 15°, (e–f) 20°, (g–h) 25°, (i–j) 35°.

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Flapping Wing Vehicles

TABLE 12.7 Cruising Conditions of Type-B1 Mechanism Inclined Angle 10º 15º 20º 25º 35º

Voltage 5V 5V 5V 5V 5V

Cruising Speed 3.6 m/s 3.9 m/s 3.25 m/s 3.1 m/s 3 m/s

Cruising Lift 34 gf 58 gf 64 gf 66 gf 84 gf

function by stoppers in the development of FWMAV. The 70 cm wingspan FWMAV can also achieve a 3 Hz flapping frequency, which needs switching for wing rotation. However, a 25 cm wingspan FWMAV can provide a 10–15 Hz flapping very high frequency. The CAD model FBL mechanism is shown in Figure 12.35(a), and the Type C: FBL with bevel gear hybrid wing rotation mechanism is shown in Figure 12.35(b). The 25 cm span, chord length of 6.5 cm, wing area of 155.73 cm2, and the FBL mechanism with aspect ratio of 4.01 are 3D printed, and the assembled structure is shown in Figure 12.36. Further, the PET wing membranes are attached to the 3D-printed mechanisms, as shown in Figures 12.36 and 12.37. The reason to use a long wingspan is to create more lift and compensate for the added weight (~1.5 g) of 3D-printing and bevel gear parts. Table 12.8 lists the individual parts and their weight of both the mechanisms. The flapping frequency is compared for both the mechanisms and given in Table 12.9. Since the FBL mechanism with bevel gears has more weight than the normal FBL mechanism, it has achieved a lower flapping frequency. Wind tunnel experiments are conducted, and the time-averaged lift and net thrust data for the normal FBL mechanism are shown in Figure 12.38.

FIGURE 12.34  Classical force signals generated by Type-B1 mechanism: (a) lift, (b) net thrust.

Figure-of-Eight Motion and Flapping Wing Rotation

389

FIGURE 12.35  (a) Normal FBL mechanism, (b) front view of Type C: FBL with wing rotation mechanism, (c) top view, (d) exploded view.

FIGURE 12.36  Assembly of Type-C mechanism with wing rotation function: (a) front view, (b) side view.

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FIGURE 12.37  Wing membrane attached to the 3D-printed mechanisms: (a) Normal FBL mechanism; (b) Type-C mechanism with wing rotation.

TABLE 12.8 Mass Distribution of FWMAV with Wing-Rotation FBL Mechanism Component Base Connecting rod (⋅2) Small gear Big gear Flapping arm (⋅2) Rotating bevel gear (⋅2) Wing with carbon rods Styrofoam body Motor Battery Receiver Miscellaneous Total weight of FWMAV

FBL Mechanism (g) 1.30 0.24 0.38 0.54 0.40 1.06 1.65 2.65 2.32 2.41 0.90 13.85

Type-C FBL Mechanism (g) 1.63 0.35 0.38 0.54 0.58 0.42 1.09 1.65 2.65 2.32 2.41 1.33 15.35

391

Figure-of-Eight Motion and Flapping Wing Rotation

TABLE 12.9 Comparison of Flapping Frequency (Hz) for Normal FBL and Type-C Mechanisms Voltage (V) 2.4 2.7 3 3.4 3.7

Normal FBL Mechanism – Flapping Frequency (Hz) 10.68 11.41 12.15 12.76 14.85

Type C Mechanism – Flapping Frequency (Hz) 9.46 10.5 11.72 12.82 13.61

Similarly, the cruising conditions are determined for the normal FBL mechanism without wing rotation, given in Table 12.10. The best cruising condition is at 20°, 3.7 V, 2.7 m/s, which generated the highest lift of 11 gf, which is less than the total weight of the FWMAV of 13.85 gf.

FIGURE 12.38  Lift and net thrust for the normal FBL mechanism at different inclined angles: (a–b) 10°, (c–d) 20°, (e–f) 30°.

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TABLE 12.10 Cruising Conditions of Normal FBL Mechanism Inclined Angle 10º 20º 30º

Voltage 3.7 V 3.7 V 3.7 V

Cruising Speed 4 m/s 2.7 m/s 1.8 m/s

Cruising Lift 6.9 gf 11 gf 10.5 gf

Besides, the time-averaged data of lift and net thrust generated by the FBL mechanism with wing rotation is shown in Figure 12.39. The cruising conditions for the FBL mechanism with wing rotation are given in Table 12.11. The best cruising condition is at 20°, 3.7 V, 3.3 m/s, which generates the highest lift of 16 gf, and it exceeded the total weight of the FWMAV of 15.35 gf. Why can the FBL mechanism of 25 cm wingspan with bevel gears but without switchable characteristics generate high lift, than the 70 cm wingspan? The following are the major observations from the wind tunnel test data:

FIGURE 12.39  Lift and net thrust for the FBL mechanism with wing rotation at different inclined angles: (a–b) 10°, (c–d) 20°, (e–f) 30°.

393

Figure-of-Eight Motion and Flapping Wing Rotation

TABLE 12.11 Cruising Conditions of FBL with Bevel Gear Mechanism Inclined Angle 10º 20º 30º

Voltage 3.7 V 3.7 V 3.7 V

Cruising Speed 3.2 m/s 3.3 m/s 1 m/s

Cruising Lift 9.2 gf 16 gf 7.3 gf

It is observed from Figure 12.40(b) that the lift signal of the mechanism with wing rotation has got similar features of Dickinson’s three lift mechanisms, including the rotation lift at the pronation moment (4.14 s) and the wake capture peak at the beginning of downstroke (4.09 s). Hence, it has resulted in a high lift force of 16 gf. Meanwhile, the net thrust signal preserves two peaks per flapping cycle, ensures a notable propulsion performance, and achieves a high cruising speed of 3.3 m/s.

FIGURE 12.40  The classical lift and net thrust signals: (a) lift for Normal FBL mechanism, (b) net thrust for Normal FBL mechanism, (c) lift for FBL mechanism with wing rotation, (d) net thrust for FBL mechanism with wing rotation.

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12.3.8 Major Inferences The authors summarized the best cruising conditions for the five flapping mechanisms and provided them in Table 12.12. The first three mechanisms are actuated using servo motors and digital control; the last two FBL mechanisms are actuated using DC motors and analog control. It is evident that the highest lift generated by the servo mechanism with bevel gears and stoppers still can hardly afford the total weight of the 70 cm-span FWMAV. On the contrary, the maximum lift generated by the non-servo FBL mechanism with bevel gears can afford the total weight of 25 cm-span FWMAV. Specifically, if we look at the best cruising speed, almost all of the mechanisms have achieved nearly 3 m/s except the Type-B mechanism, which has attained 1.5 m/s due to smaller net thrust. The following are the comparisons with respect to lift and lift-to-weight ratio for the servo-based mechanisms • The lift of Type B1 is 33% [(84/63)-1]higher than the Type-A1 mechanism, which is close to the 35% contribution due to the wing rotation of Dickinson’s work • The lift-to-weight ratio of Type B1 is 15% [(0.9/0.78)-1] higher than Type-A1 mechanism. With regard to the DC-motor based FBL mechanisms of 25-cm span: • Type C achieved 45% [(16/11)-1] higher lift than the normal FBL mechanism • Type C is 32% [(1.04/0.79)-1]better than the normal FBL mechanism with respect to the lift-to-weight ratio, which is close to the 35% contribution due to wing rotation of Dickinson’s work.

12.4  POWER CONSUMPTION OF FLAPPING-WING FLIGHT In general, the power can be estimated by measuring the current consumption for the given input voltage, which is given by,

Total ( electrical ) Power = Driving Voltage × Driving Current (12.3)

An experimental method to estimate the total power of FWMAV is from the given capacity of the battery. The following relation holds for estimating the current consumption:

Driving Current = Total battery capacity / Flight Endurance (12.4)

For example, if we use a Li-Po battery with a capacity of 70 mAh = 0.07 A × 3600 s = 252 C, and it can provide a flight endurance of 480 s, then the averaged driving current is 0.525 A. For the given driving voltage of 3.7 V, the consumed power is 1.94 W.

395

Figure-of-Eight Motion and Flapping Wing Rotation

TABLE 12.12 Summary of the Best Cruising Conditions of Designed Mechanisms Driving Voltage, Flapping Cruising Frequency Speed

Parameters Mechanisms

Total Weight

Wingspan

Inclined Angle

Cruising Lift (Lift/Weight)

Type-A1: servo

80.9 gf

70 cm

25º

5 V, 2.5 Hz

3 m/s

63 gf (63/80.9 = 0.78)

Type-B: servo + bevel gear 88.1 gf

70 cm

35º

5 V, 2.5 Hz

1.5 m/s

52 gf (52/88.1 = 0.59)

Type-B1: servo + bevel gear + stopper

93 gf

70 cm

35º

5 V, 2.5 Hz

3 m/s

84 gf (84/93 = 0.90)

DC motor + FBL

13.85 gf

25 cm

20º

3.7 V, 14.85 Hz

2.7 m/s

11 gf (11/13.85 = 0.79)

Type C: DC motor + FBL + bevel gear

15.35 gf

25 cm

20º

3.7 V, 13.61 Hz

3.3 m/s

16 gf (16/15.35 = 1.04)

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TABLE 12.13 Estimated Flight Parameters of Normal FBL Mechanism dD/du Inclined [gf/(m/s)] Angle [°] Lift [gf] Speed [m/s] (Figure 12.38) 30 10.5 1.8 5.5 20 11 2.7 3.1 10 6.9 4 1.95 D is from the data fitted given as D = −0.781u2 + 7.943u

Drag D [gf] 11.8 15.8 19.3

Fly Power [W] 0.21 0.42 0.76

The total (electrical) power is the summation of flight power, thermal dissipation of motors, and the flapping mechanism’s friction loss. Flight power is given by,

Flight Power = Flight Speed × Total Drag, (12.5)

where

Total Drag = Induced Drag + Friction Drag + Others (12.6)

Unfortunately, the total drag along the airflow direction may not be measured from the force gauge during the wind tunnel experiments. The force gauge provides the net thrust (= thrust – drag) rather than the drag along the airflow direction. One approximation to deduce the drag from the net thrust data is to use the data close to the zero net thrust (thrust = drag) corresponding to different cruising speeds. Based on the assumption of equal thrust around the cruising points, the drag changing rate with respect to airspeed, i.e. dD/du, are curve fitted, and the slope at the cruising points of net thrust data are determined. For example, consider the FBL mechanism shown in Figure 12.35 and the net thrust data shown in Figures 12.38 and 12.39, the flight power is estimated as 0.36–0.42 W subject to the best cruising speed conditions of 3.3–2.7 m/s. The calculated values are given in Tables 12.13 and 12.14, respectively.

TABLE 12.14 Estimated Flight Parameters of Type-C Mechanism dD/du Inclined [gf/(m/s)] Angle [°] Lift [gf] Speed u [m/s] (Figure 12.39) 30 7.3 1 2.6 10 9.2 3.2 7 20 16 3.3 3.2 D is from the data fitted given as D = 0.527u2 + 1.634u

Drag D [gf]  2.2 10.6 11.1

Fly Power [W] 0.02 0.33 0.36

Figure-of-Eight Motion and Flapping Wing Rotation

397

It is evident that the Type C mechanism with wing rotation function shows better flight performance. However, if we measure the total (electrical) power during flapping and prove that the friction loss in the flapping mechanism with wing rotation is not more than the normal FBL mechanism (0.42 – 0.36 = 0.06 W), then we can probably conclude that the modified mechanism is a successful one.

12.5  SUMMARY AND FINAL CONCLUSION This chapter initially recollected the Golden-Snitch and Eagle-II mechanisms, and the wearing behavior of balsa wood-based mechanism assembly is explained. In order to alleviate this issue, EDWC is employed to fabricate the parts of the mechanism after a few modifications in the mechanism assembly, and the new configuration is named Golden-Snitch Pro. A typical flapping motion characteristic, namely “Figure-of–8,” is realized through performing high-speed photography measurements, is discussed. Based on the Figure-of-8 motion, the W/H ratio for increasing and decreasing voltage trend is studied, and with and without rib condition is also explained in detail. The principle of wing rotation and various flapping mechanisms to achieve wing rotation are designed, and their aerodynamic performance through performing wind tunnel experiments are exploited in detail. Comparative evaluation with respect to identifying their best cruising conditions and corresponding lift-toweight ratios of various developed servo and DC motor-driven mechanisms is made. The results are compared with well-known Dickinson’s work. Finally, the estimation of power consumption of selected the best configurations of flapping mechanisms and their flight parameters are calculated and provided. Based on the aerodynamic observation of the flapping wings in this book, the following concluding remarks were drawn: 1. The scaling law of flapping wingspan and weight shows that the flapping wingspan (m0.39~m0.59) is more obvious than the body length (m0.33), and the flapping wings must be lighter due to the weight constraint. Henceforth, birds use feathers and insects use membrane wings. 2. The body size and shape of natural flyers maintain certain features to reduce the weight and the following are the major observations for various kind of natural flyers: i. The lightweight feathers of birds are due to the fulfill of air gaps, and their opening and closing actually guide the airflow to penetrate the feather gaps for enhancing lift. However, the feather size is too large to ignore its inertia which is related to the closing movement of the feathers. ii. Even though the corrugated wing has no obvious thickness, the aerodynamic effect deduced by the airflow vortices is comparable with that of flapping wings with thickness. Hence, the wing corrugation is an added advantage to reduce the weight without downgrading the lift performance. iii. The finger-like wing bristles of fairyflies has ultra-low Reynolds number flow with superior viscous characteristics. The gap is too small to let the airflow easily penetrate the bristle gaps and attained comparable aerodynamic performance of the insect membrane wings.

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3. Natural flyers are having multiple wings without connected as single piece except the bat with a membrane-connected wing. Therefore, the individual rigidity of the double wings must be high enough and not as soft as a membrane to support the flapping wing itself. Hence, the aerodynamic lift and thrust can be smoothly transmitted to the fuselage body through the wing frames. Therefore, various strategies are adopted individually with different wingspans of high stiffness for the design of feather wings, corrugated wings, or even finger-like wing bristles. 4. For the given flapping wing area and unfolding of wings, the aerodynamic performance of flapping mechanisms of FWMAVs has tremendous impact with respect to stroke angle amplitude, the phase difference between the two wings, and the wing rotation. Large stroke angle, zero phase difference and advanced wing rotation are effectively improving the lift force. Under different flight modes the following are majorly observed: i. During hovering, a very large stroke angle is required (preferably 180°). Due to this phenomenon, the torque and power requirements are higher and the motor becomes larger and heavier correspondingly. ii. In the case of forward flying, the priority is given to increase the flapping frequency and minimize the weight of FWMAVs. The stroke angle in the range of 50°–60° can also be acceptable for achieving steady flight. If necessary, the wing rotation motion coupled with a bevel gear and stoppers can be added. 5. From an experimental point of view, the manufacturing cost of a FWMAV is not high, and the lift and net thrust of FWMAV original size (1:1) can be directly used for aerodynamic studies. The various measurement methods are as follows: i. If the wind tunnel force gauge is utilized to measure the time-varying signal of the lift and net thrust of a FWMAV, there will be more noises in the acquired signal. Using a low-pass filter, the high-frequency noises are eliminated and the resulted time-varying waveform is the superimposed aerodynamic forces and the inertial force of the flapping wing. By further time averaging, the inertial force component can be filtered out if the flapping motion is periodic and the average lift and net thrust can be obtained. ii. By analyzing the zero average net thrust data, the cruise speed and corresponding lift can be calculated. The cruise lift is compared with the total weight of a FWMAV and decision can be made whether it can fly or not and also the payload carrying capacity will be determined. However, cruise speed is a determining factor to resist gust wind. The higher the cruise speed, the better capability to resist the gust wind for FWMAVs. iii. MEMS technology is used to integrate on-site lift force sensors, such as PVDF, on the flapping wings for direct lift measurement rather than the wind tunnel force gauge. It can be directly used for airborne flight control in the future. iv. The use of soap-film flow visualization technique with high-speed stereo photography can complement the aforementioned wind-tunnel force gauge measurement. The former soap-film records the time-varying

Figure-of-Eight Motion and Flapping Wing Rotation

399

information of the flow field around a flapping wing, and the latter highspeed stereo photography measures the real-time deformation trajectory of the flexible flapping wing. Based on various numerical simulation analyses, it was observed that the flapping wing flow field coupled with multiple physical phenomenon. The problem complexity and the solution cost are high. At present, the numerical simulations of singlewing flapping and three-wing V-formation flight are discussed. Still, the comparison between CFD numerical results and the aforementioned experimental data are not exploited rigorously. In future, the numerical and experimental results will be compared and the flapping flow field characteristics can be effectively determined.

REFERENCES



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Index A Acceleration 39, 41, 53, 313, 318 Accelerometer 311-313, 326 Acetone 57, 206 Acrylic 69, 70, 91, 158, 164 Added-mass 53 Advance ratio 10, 37, 62, 79, 173 Aerodynamics 1, 4, 47 Aesthetic elements 354 Affinity transformation 13 Aileron 31, 45 Alben 367 Aluminum alloy 363 Amoeba proteus 219 Angle of attack (AOA) 86 Angle sensor 337 Anisotropic wings 203 Annular ring 194 Anti-wear 137 Arburg 220S 140 Arduino micro 341, 372 Arduino Nano 341 Arduino-based 302, 306, 311, 342 Aspect ratio 33, 34, 35, 179 Asymmetry angle 78, 81, 90 Asynchronous phase 355 Atmega328p 321, 324, 341 Autopilot 321, 334 Auxiliary bevel gear 378, 383, 385 Averaging theory 286, 309 Avionics unit 111

B Balsa wood 69, 91, 361 Barometer 313, 318, 321 Bernoulli equation 7 Bernoulli’s theory 370 Bevel gear 371, 383 Bifurcation 367, 368 Bio-natural flyers 33 Bionic actuator 141, 193, 329, 331 Bird-like 11 Blade element theory 39–41 Blockage ratio 50, 161, 279 Blow-down wind tunnel 49, 279 Body axes 311 Boot loader 324

Boundary condition 6, 8, 241, 256, 361 Boundary-layer 11–12, 219 Brushless 77, 208, 318 Bubbles 205 Buckling 203 Butterfly 42

C Carbon fiber 337, 339, 363, 365, 372 Cartesian coordinate 285 Center of gravity 42, 127, 286, 314 Center of mass 4, 45, 344 Centrifugal 39 Centripetal force 297 Centroid 45 Check-valve 55, 193 Chemical vapor deposition (CVD) 61 Chitin 203 Chlorinated polyethylene (CPE) 354 Chord 8, 340, 376, 378, 388 Cicada 203 Circular trajectory 344, 357 Clap and fling 38, 41, 219, 234, 235 Closed loop 295, 352 CNC machine 134 Color detection algorithm 299, 301, 308 Comb 219, 329, 331 Compressible flow 6, 10, 12–13, 19 Computational fluid dynamics (CFD) 45, 239, 359 Computer aided design (CAD) 141, 156, 378, 388 COMSOL 203, 239–242 Contact angle 331–333 Control algorithms 309 Control board 372 Control law 292, 294–295, 309 Convergence 239–240, 253, 294 Coriolis force 10, 39 Corrugated 202–203 Cosine transform 306 Crash landing 321 Cruising condition 95, 100, 122, 124, 127 Cruising flight 176, 227, 228–230 Cruising lift 197–199, 208, 227 Cruising speed 227–231 Cut-in speed 4 Cyclic loading 66, 132–133

401

402 D Delfly 220 De-molding 205 Derivative coefficient 350 Dickinson 53–54 Didel 77, 176 Digital altimeter 311 Dihedral angle 77, 86 Dimensional analysis 8, 10, 47 Dimensionless parameter 176, 185, 213, 232, 235 Discharging capacity 355 Discontinuity 295 Double-FBL 225 Downstroke 77 Drag 227, 245, 253, 255, 269, 272 Dragonfly 203–205, 214 Drone 1 Drosophila melanogaster 40, 219, 359 Dutch roll 30–31 Dynamic pressure 9, 62, 95, 117, 361

E Eagle-II 69, 73, 77, 83, 85 Eeprom 342 Elasticity theory 331 Electric discharge wire cutting (EDWC) 91 Electrical discharging machining (EDM) 131 Elevator 25, 28, 45 Enamel 316 Energy equation 6, 13 Equations of motion 20, 285–286, 294 Euler angle 19, 23 Euler equation 12–13 Evans mechanism 109, 115, 117, 134, 156 Excursion 156, 160–161, 166, 208 Expandable polystyrene (EPS) 91–92, 141, 146 Explicit function 289 External force 6, 18–19, 240, 286

F Flapping frequency 85–86, 102, 104, 109 Flapping mechanism 42, 59, 65, 109, 127 Flapping stroke angle 62, 77, 87, 100, 219 Flapping wing micro air vehicle (FWMAV) 1, 77 Flash memory 342 Flexibility 203 Flight power 13, 16, 17, 253 Flight stability 68, 111, 359 Flight test 123, 127, 315, 317, 326 Flight trajectories 3, 43, 69 Flow visualization 219, 239, 267, 268, 272 Fluid dynamics 45, 204, 239 Fluid structural interaction (FSI) 18–19, 213, 239, 249

Index Fluorinated ethylene propylene (FEP) 193 Fly-by-wire 42 Force gauge 50–52, 376, 396 Forward flight 16, 18, 36, 37 Four bar linkage (FBL) 64, 77, 90, 95, 101 Fourier transform 5 Freestream velocity 5, 14, 38, 40 Friction coefficient 137, 156 Fused deposition modeling (FDM) 131, 154, 167, 339 Fuselage 16, 350, 352, 372, 375

G Gain 194, 295, 298, 313, 327 Gauge 50–52, 56, 64 Gauss theorem 269, 270 Gear ratio 102, 108–109,115, 117 Gear transmission 359, 361, 363 Gearbox 337 Glide angle 1 Glider 1 Golden-Snitch 4, 40, 77, 90, 356 Golden-Snitch Pro 92, 95 Gravity 1, 3, 5, 42, 311 Grinding 131, 135 Gross weight 323 Ground station 304, 305, 307

H Harmonic motion 361 Heading data 324, 327 High impact polystyrene (HIPS) 339 High-speed camera 72, 102, 112, 206, 225 High-speed photography 225, 247, 267, 279, 397 High-speed stereo photography 18, 53, 240 Horseshoe vortex 14 Hot-wire anemometer 49, 79 Hovering 18, 37, 44, 45, 54 Hummingbirds 78, 85, 35, 36 Hydrophilic 332 Hypersonic 12 Hysteresis 112, 157, 158, 279, 368

I Inertial frame 285, 311–312 Inertial measurement unit (IMU) 95, 313 Infrared receiver 316 Initiator 58–59, 68–69, 72 Inkjet 158 Insect wing 202–203, 205, 206 In-situ measurement 55, 71 Integrated development environment (IDE) 324 Intelligent image processing 307

403

Index Interface 302–303, 307, 322, 324 Interference 133–134, 154, 316, 378

Joint wearing 362 Joukowski airfoil 7, 8, 13

Milling 131 Mobile phone 322 Modal analysis 195, 200 Multicopter 193 Multifaceted 307 Multijet 131, 158, 163, 166, 167 Mylar 185

K

N

KAIST 253 Kalman filter 319–321 Kapton (polyimide) 193 Kármán vortex 38–39, 47, 240, 245 Kelvin’s theorem 13 Kinovea 340 Kite 1–2 Knoller-Betz effect 365 Konkuk Beetle 100–101 Kutta-Joukowski law 7, 13, 270, 370

National atmospheric and oceanic administration (NAOA) 313 Natural frequency 27, 44, 194, 200, 365 Navier–Stokes equation 6, 11, 19, 200, 239 Nerves 203 Net thrust 51, 92, 161, 263, 361 Neutral-point 43 Newton’s law 20, 45, 285, 286 Norberg 34–35 Nose-up 42–43 Nozzle 154, 156, 158, 205 Numerical control (NC) 131

J

L Labview 245 Laminar flow 12 Laplace equation 7, 13 Laser cutting 331–332 Lateral mode 28 Latex 193 Leading edge 38, 63, 139, 185, 361 Leading edge vortex (LEV) 39, 67 Lift coefficient 38, 81, 173, 180, 185 Light-weight 69, 203, 215 Linearized analysis 292 Lithium polymer (Lipo) battery 102, 122, 144, 304, 316 Load cell 79, 81, 161, 279 Locomotion 365, 368 Longitudinal cross veins 203 Longitudinal mode 25, 47

M Mach number 12–13, 16 Magnetometer 311, 313, 315, 322 Magnus effect 41, 248, 370–371 Maneuverability 35, 193 Master mold 205 Mechanical strength 137, 141, 146, 154, 163 Membrane wing 148, 193, 207, 213, 215 Mems-based 58, 359 Micro actuator 55, 193 Micro-camera 301–302 Microcontroller 305, 313, 321, 337, 372 Micro electro mechanical systems (MEMS) 49, 71, 156, 193, 307 Micro-molding 205

O Object-oriented programming (OOP) 321 “Oblique Figure-of-8” 18, 361, 365, 371 Oil tank experiment 54 On-board 301, 313, 316, 318, 322 Open-loop 294 Optimization 128, 194, 263, 335, 398 Orientation 81–82, 182, 275, 313 Ornithology 193, 216 Ornithopter 18, 129, 236, 304, 398 Orthogonal 283 Outdoor 69, 72, 116, 127, 309 Oxygen plasma 332

P Polyamide 66 (PA66) 137 Polydimethylsiloxane (PDMS) 205 Polyethylene terephthalate (PET) 85, 193, 240, 254 Polyjet 131, 158, 163, 166, 171 Polylactic acid (PLA) 156 Polymethyl methacrylate (PMMA) 158 Polyoxymethylene (POM) 77, 137, 169, 364 Poly-para-xylylene (parylene) 61, 170 Polyvinylidene fluoride (PVDF) 55 Post-processing 205, 275, 300, 319 Potential flow theory 7, 11, 13, 249 Prantl–Glauert rule 13 Printed circuit board (PCB) 321 Pronation 40, 248, 370, 384, 393 Proportional integral and derivative (PID) 350 Protozoa 219

404 Pulse width modulating (PWM) 303, 318, 337, 343, 372

Q Quasi-steady flow 6, 39, 173, 237, 263

R Reaming 363 Recirculation zone 203 Rectangular wing 287 Relative flow velocity 2, 3 Resonance 194, 365 Reynolds number 9, 193, 219, 239, 268 Rib reinforcement 179, 215 Rigidity 91, 141, 203, 354, 368 Roll mode 30–31 Root mean error 301 Root-locus 294 Rotation lift 53, 370, 393 Rotational circulation 41, 248, 367, 372, 378 Rotational matrix 285 Rudder 36, 42, 95, 327, 337 Rudder angle 25, 31, 45

S Starting vortex 13, 14 Static pressure 13, 240 Steady-state 11, 21, 45, 62, 232 Stephenson mechanism 100, 116, 127, 136, 153 Stereolithography 131, 159 Stereovision 283, 296, 298, 309, 310 Stiffness 55, 75, 184, 213, 281 Stopper 373, 384, 388, 394, 395 Stream function 11 Streamlined 13, 204 Stroke angle 85, 152, 213, 243, 375 Stroke reversal 40, 206, 219, 248, 370 Strouhal number 38 Styrofoam 208, 390 Subsonic 12, 161–162 Supersonic 12 Surface morphology 332, 365 Surface tension 329–331, 335 Swarm 299, 309 Symmetric breaking 264 Synchronize 127, 261, 304

T Teflon 134 Tensile strength 57, 132, 163, 167 Tensor 6, 240, 286 Terminal cables 306

Index Test platform 352 Test rig 129, 131, 161, 168, 171 Tethered flight 341, 344, 346, 357, 398 Texas instruments (TI) 318 Thermal stability 137 Threshold time 301 Thrust 3, 51, 92, 122, 164, 245 Time averaged 54, 380 Titanium-alloy 57, 59, 69, 74, 263 Tolerance 95, 109, 133, 141, 314 Trachea 203 Transfer function 27, 291, 294 Transmission angle 78, 106, 109, 221 Transmission module 66, 77, 363, 364 Transonic 12 Trapezoidal tape 185 Trim 43 Turbulent flow 10, 242

U Ultraviolet (UV) 158 University of Science and Technology, Beijing (USTB) 348 Unmanned air vehicle (UAV) 1 Unsteady aerodynamics 215, 203 Unsteady state 9, 37, 52, 62, 203 Upstroke 2, 77, 193, 245, 370

V Vandenburghe 367–368, 398 Vertical stabilizer 332 Video receiver 299, 302 Viscous flow 6, 9, 11, 268 Visijet-SL-Flex 159 Vision based 310 Vision sensor 304, 307–308, 310 Von Kármán vortex 38–39, 47

W Waypoint navigation 323 Wearing 134, 362, 397 Weather conditions 313 Weight distribution 316–317, 326 Weight reduction 141, 169, 203, 372, 385 Weis-Fogh lift-generation 219 Width-to-height ratio 367 Wind speed 95, 162, 176, 225, 252 Wind tunnel 49, 66, 239, 246, 388 Wing area 33–34, 57, 207, 376 Wing beat frequency 34–35, 115, 360, 367 Wing loading 33–35, 113 Wing rib 57, 63, 173, 180, 185 Wing root 37, 57, 63, 91, 354

405

Index Wing rotation 40–41, 340, 341, 365 Wing span 33, 348, 354, 395 Wingspan 10, 33, 77, 200, 360 Wingtip vortex 13, 14, 39, 251, 258 Wing–wake interaction 41, 74 Wireless control 342 Wireless transmitter 305 Wrinkling 203

Y Yaw control 46 Yield strength 57, 132, 331 Young’s modulus 185, 330–333