Table Of ContentFlapping Wing
Vehicles
Flapping Wing
Vehicles
Numerical and
Experimental Approach
Lung-Jieh Yang
Balasubramanian Esakki
First edition published 2022
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ISBN: 9780367232573 (hbk)
ISBN: 9781032074139 (pbk)
ISBN: 9780429280436 (ebk)
DOI: 10.1201/9780429280436
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My Beloved Father, Mother, Wife, and Children
Contents
Preface......................................................................................................................xv
Acknowledgments ..................................................................................................xvii
Authors ....................................................................................................................xix
Chapter 1 Introduction to Micro Aerial Vehicles .................................................1
1.1 Flapping Motion ........................................................................1
1.2 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
1.3 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
1.4 Scaling Laws of Flapping Wings ............................................33
1.4.1 Geometry Similarity ..................................................33
1.4.2 Scaling Laws of Bio-natural Flyers ............................33
1.5 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
1.6 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
viii Contents
1.6.3 Time-Averaging of Inertia for Flapping Wings .........45
1.6.4 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 Lift Measurement Using Wind Tunnel ....................................49
2.2 Inertial Force Effect on Lift ....................................................53
2.3 Principle of Polyvinylidene Fluoride (PVDF) .........................55
2.4 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 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
3.2 Impact of Flapping Stroke Angle on Flapping
Aerodynamics ..........................................................................85
3.3 Aerodynamic Characteristics of Golden-Snitch Pro ..............90
3.4 Watt-Stephens Mechanism ....................................................100
3.5 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
Contents ix
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 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
5.2 Carbon-Fiber Rib Effect on the Flapping Wings ..................179
5.3 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
