Aerodynamic Force Characteristics of 3D Flapping Wings LAI KENG CHUAN (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 Acknowledgements Acknowledgements I would like to express many thanks to my supervisor, Professor Lim Tee Tai for his guidance and support in the project. Meetings with Prof. Lim left me feeling motivated to break new grounds in research and I want to thank him once again for clearing many obstacles along the way. A special mention goes out to research fellow Dr. Lua Kim Boon for imparting his valuable knowledge and his relentless pursuit in perfecting the force transducer despite the various frustrations and delays. I would like to thank all the Laboratory Officers of the Fluid Mechanics Laboratory for their help in constructing, advising on, and modifying the apparatus design. Finally, I would like to thank to my parents for their care and support. Far above all, I am grateful for God’s provision of joys, challenges, and grace for growth. This Master of Engineering programme in the Department of Mechanical Engineering is supported by a National University of Singapore research scholarship. i Table of contents TABLE OF CONTENTS ACKNOWLEDGEMENTS I TABLE OF CONTENTS . II SUMMARY VIII LIST OF TABLES . X LIST OF FIGURES XI NOMENCLATURE XXI CHAPTER 1. INTRODUCTION . 1.1. Assumptions 1.2. Objective of this study 1.3. Organization of thesis . CHAPTER 2. LITERATURE REVIEW ON FLAPPING WINGS . 2.1. A brief history of flapping flight development . 2.2. Wingbeat kinematics . 2.2.1. Reynolds number 2.2.2. Flapping frequency . 2.2.3. Flapping angles . 10 2.2.4. Flapping rhythm 11 ii Table of contents 2.2.5. Stroke ratio 11 2.3. Aerodynamic mechanisms 12 2.3.1. Added mass effect . 14 2.3.2. Wagner effect 15 2.3.3. Delayed stall and leading edge vortex 17 2.3.4. Rotational effect (Kramer’s effect) . 22 2.3.5. Wake capture 25 2.3.6. Summary of aerodynamic mechanisms 27 2.4. Quasi-steady estimates 28 2.5. Wing detail and flexibility 29 2.6. Force measurement experiments and motivation . 31 CHAPTER 3. EXPERIMENTAL APPARATUS AND PROCEDURES . 33 3.1. Definition of angles . 35 3.2. Mechanical system 37 3.2.1. Motor control 37 3.2.2. Motors . 40 3.2.3. Motion transmission 40 3.3. Force measurement system . 42 3.3.1. Strain gages . 43 3.3.2. Wheatstone bridge 44 3.3.3. Force transducer design 45 3.3.4. Summing and differential amplifiers 49 iii Table of contents 3.3.5. Noise filter 51 3.3.6. Analog to digital converter . 52 3.4. Synchronization 52 3.5. Statistical functions . 52 3.6. Wings 54 3.6.1. Fabrication of wings . 54 3.6.2. Derivation of second moment of wing area 55 3.6.3. Quantification of wing elasticity . 60 3.6.4. Evaluation of deflection angle, γ . 63 3.7. Experimental Procedure 64 3.7.1. Calibration . 64 3.7.2. Verification . 71 3.7.3. Alignment of the wing 77 3.7.4. Elimination of buoyancy forces 77 3.7.5. Measurement of weight and buoyancy force 80 3.7.6. Measurement of forces 81 3.7.7. Resolving of forces . 85 3.7.8. Non-dimensional parameters 85 3.7.9. Presentation of results . 87 3.8. Potential errors 88 CHAPTER 4. 4.1. REVOLVING WING EXPERIMENTS 89 Kinematics of the revolving motion . 89 iv Table of contents 4.2. Revolving wing experiments results and discussion 92 4.2.1. Time history of the measured forces . 92 4.2.1.1. Discussion . 96 4.2.2. Mean force coefficients for rigid wing . 97 4.2.2.1. Discussion . 100 4.2.3. Mean force coefficients of flexible wings 103 4.2.3.1. Discussion . 106 4.2.4. Comparison of the force characteristics of flexible wings 108 4.2.5. Deflection angles 110 4.2.6. Discussion on the force coefficient ratios and deflection angles 112 4.3. Comparison with past experiments . 113 4.4. Conclusion 115 CHAPTER 5. 5.1. OSCILLATING MOTION EXPERIMENTS . 117 Motion . 118 5.1.1. Sinusoidal motion . 119 5.1.2. Hawkmoth motion 120 5.2. Results and discussion 121 5.2.1. Rigid wing results . 122 5.2.1.1. Sinusoidal motion . 122 5.2.1.2. Hawkmoth motion 124 5.2.1.3. Discussion of rigid wing results 126 5.2.2. Mean force coefficients for rigid wing . 127 5.2.3. Flexible wings results . 128 v Table of contents 5.2.3.1. Sinusoidal motion . 128 5.2.3.2. Hawkmoth motion 134 5.2.3.3. Discussion on the time histories of flexible wings . 135 5.2.4. Mean force coefficients for flexible wings . 138 5.2.5. Deflection angles of flexible wings 141 5.2.6. Discussion . 142 5.3. Comparison with numerically predicted results . 145 5.4. Conclusion 148 CHAPTER 6. ADVANCED AND DELAYED FEATHERING EXPERIMENTS 151 6.1. Motion . 152 6.2. Time histories of force coefficients 156 6.2.1. Results and discussion 156 6.2.1.1. Case U30 . 156 6.2.1.2. Case U45 . 159 6.2.1.3. Case U60 . 159 6.2.1.4. Case V30 . 159 6.2.1.5. Case V45 . 165 6.2.1.6. Case V60 . 165 6.2.2. Discussion on the time histories . 165 6.3. Mean force coefficients . 171 6.3.1. Discussion . 174 vi Table of contents 6.4. Conclusion 175 CHAPTER 7. FLAPPING RHYTHM EXPERIMENTS 176 7.1. Motion . 177 7.2. Results and discussion 181 7.2.1. Time histories of force coefficients 181 7.2.1.1. Discussion . 184 7.2.2. Wake interaction effects . 188 7.2.2.1. Discussion . 192 7.2.3. Mean force coefficients . 192 7.2.4. Discussion . 194 7.3. Conclusion 195 CHAPTER 8. CONCLUSION AND RECOMMENDATION 196 8.1. CONCLUSION . 196 8.2. RECOMMENDATION 198 REFERENCES . 199 APPENDIX A. TECHNICAL DRAWING OF FORCE TRANSDUCER . 216 APPENDIX B. TANK BOUNDARY EFFECTS . 217 vii Summary Summary In this project, the aerodynamic characteristics of insect flapping wings are assessed by measuring the forces acting on them. A 3D flapping wing mechanism capable of mimicking the motion of insect flight is developed to measure forces acting on model wings flapping according to various motions. It consists of a pair of wings connected to gear boxes driven by stepper motors. On each side of the wing, three stepper motors actuate the positional, feathering and elevation motions via coaxial shafts and gearboxes which are immersed in a tank filled with water so that hovering characteristics can be modelled. Forces acting on the flapping wing are measured by an in-house developed force transducer consisting of strategically arranged strain gages, attached to the base of the flapping wing. By connecting the strain gages to Wheatstone bridges, the response of the strain gages to forces and moments can be determined. An accompanying calibration procedure is carried out to determine a calibration matrix that relates the raw signals into forces and moments. The flight of a hawkmoth Manduca sexta which has a Reynolds number of approximately 7000 is investigated by mimicking its motion and wing shape. Measured mean force coefficients are in good agreement with results derived from free-flying hawkmoths but the time course of force coefficients differs from numerically predicted results. For the fixed incidence steadily revolving wing cases, the maximum mean force coefficients are large (CL =1.84 and CD =3.6). Furthermore, flapping wings not stall for all the tested incidence angles up to 100o, suggesting that delayed stall and leading edge vortices are mainly responsible for the enhanced performance of insect flight. viii Summary Application of flexible wings lowers the force coefficients. However, flexible wings are able to sustain relatively large force coefficients despite larger than real wing estimated wing deflection angles of 10o, which are higher than that observed in hawkmoth wings. Wing flexure can passively alter the wing flapping motion such that different force generation patterns are produced. On a separate note, the force coefficients for rigid wings are insensitive to changes in Reynolds number ranging from 3600 to 11000. Moreover, a study of wing kinematics suggests that large positional and feathering amplitudes are vital for increasing aerodynamic performance. Finally, as the flapping rhythm tends towards a triangular-like wave, wake capture effects are found to increase force coefficients by at least 10%. Conversely, wake capture effects are insignificant but overall aerodynamic performance increases as the flapping rhythm tends towards a sinusoidal-like wave. ix Chapter Revolving wing experiments 2.5 wing wing wing wing wing wing wing 2.0 1.5 CL 1.0 0.5 0.0 -0.5 -1.0 -20 20 40 60 80 100 120 α [deg] Figure 4.14: Lift coefficients for wings with a range of flexibility under high Re conditions. 4.0 wing wing wing wing wing wing wing 3.5 3.0 2.5 CD 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -20 20 40 60 80 100 120 α [deg] Figure 4.15: Drag coefficients for wings with a range of flexibility under high Re conditions. 105 Chapter Revolving wing experiments 4.2.3.1. Discussion The positive lift at α = 90o shown in the lift coefficients of wing is likely due to the deflected shape of the soft wing causing the actual angle of attack to be lower than the undeflected angle of attack of 90o thus generating lift as illustrated in the side view of the wing in figure 4.16. This change in geometric angle of attack is confirmed from the visual observations from the experiment (see figure 4.17), the wing was observed to deflect from its plane, furthermore there was a decrease in geometric angle of attack due to the fluid forces acting on the wing. Such suggestions are further confirmed from the calculated force angles acting on the force transducer. Calculated force angles based on measured FC and FN for wing at α = 90o (undeflected) is 77o and 75o for the low and high Re cases, respectively. Note that this difference in force angle is due to the deflection of the wing and is unlikely due to the change in the aerodynamic mechanisms. The aerodynamic force vector is assumed to act in a direction normal to the wing surface, and therefore as the wing surface is deflected as shown in the side view of figure 4.16, it follows the direction of the deflected wing plane and hence registers as lift in the measurements of the force transducer. Finally, the reduction in CD may be caused by the decrease in the effective wing area facing the flow, thereby reducing the aerodynamic forces acting on the wing as shown in the top view of figure 4.16. 106 Chapter Revolving wing experiments Wing motion Top view FD Effective area decreased after deflection Deflected wing Wing length Aerodynamic force Undeflected plane Side view Wing motion FN FC Pressure force α = 90o Wing chord Deflected wing Aerodynamic force Angle of attack of wing modified by aerodynamic force Undeflected angle of attack Figure 4.16: Illustration of wing deflection decreasing angle of attack. 107 Chapter Revolving wing experiments Figure 4.17: Photograph of wing flexing under fluid dynamic forces for high Re case at α = 50o. 4.2.4. Comparison of the force characteristics of flexible wings Figure 4.18 and figure 4.19 compare the force coefficients of the flexible wings by expressing them as a fraction relative to that of the rigid wing (wing 1). Results of both low and high Re cases are presented in the figures. The ratios are plotted against each individual wing’s elasticity values with the wing numbers labelled accordingly in the graph. For the comparison of C L , α is chosen to be 40o which is among the range of α that produces maximum C L . The lift coefficient ratio (mean CL/CL rigid) is defined as the C L of each flexible wing divided by the C L of the rigid wing, both for α = 40o. Next, for the comparison of C D , α = 90o is chosen as it produces the maximum C D . The drag coefficient ratio (mean CD/CD rigid) is defined as the C D of each flexible wing divided by the C D of the rigid wing at α = 90o. 108 Chapter Revolving wing experiments Figure 4.18 shows that the lift coefficient ratios are higher than 0.9 for wings to in both Re cases. Figure 4.19 shows that the drag coefficient ratios are higher than 0.8 for wings to for both Re cases. It can be seen from figure 4.18 and figure 4.19 that wings to are insensitive to changes in Re and variations in wing elasticity. Wing which is the softest among all the wings tested, has large reductions in force coefficients shown by the low values of force coefficient ratios in both figures. Furthermore, wing showed sensitivity to Re between the low and high Re cases. As a result, it has a larger reduction of force coefficients in the high Re case with extremely low drag coefficient ratio of 0.2. For the same wing flapping at low Re, the drag coefficient ratio is 0.46. mean CL/CL rigid 0.9 0.8 0.7 0.6 Low Re High Re 0.5 0.4 0.3 0.2 10 20 30 40 50 60 70 Elasticity [N/m] Figure 4.18: Comparison of mean lift coefficients for wings of various flexibilities plotted against the elasticity of each wing. 109 Chapter Revolving wing experiments mean CD/CD rigid 0.9 0.8 0.7 Low Re High Re 0.6 0.5 0.4 0.3 0.2 10 20 30 40 50 60 70 Elasticity [N/m] Figure 4.19: Comparison of mean drag coefficients for wings of various flexibilities plotted against the elasticity of each wing. 4.2.5. Deflection angles Estimated wing deflection angles (γ) corresponding to the results in figure 4.18 and figure 4.19 for the flexible wings are plotted in figure 4.20. These angles are estimated from their flexibility data and the normal aerodynamic force acting on each wing. The calculation method is explained in section 3.6.4. Note that these angles illustrate the bending of the wing along the span wise axis only. To further illustrate the effects of wing deflection on the force coefficients, the force coefficient ratios from figure 4.18 and figure 4.19 are plotted against γ from figure 4.20 into figure 4.21. For all wings, γ followed two general trends, first, lower elasticity results in higher γ and second, high Re cases also results in higher γ. These findings are hardly surprising. The lowest γ is found at low Re lift for wing with γ = 1.94o, and the largest γ is found at high Re drag for wing with γ = 73.3o. 110 Chapter Revolving wing experiments Figure 4.21 also shows the mean force coefficient ratios having values of above 0.8 when the deflection angles are less than 30o. A drastic decrease in the force coefficients occurs after the deflection angles are greater than 47o. 80 70 High Re lift Low Re lift High Re drag Low Re drag γ [deg] 60 50 40 30 20 10 0 10 20 30 40 Elasticity [N/m] 50 60 70 Figure 4.20: Estimated deflection angle (γ) versus elasticity of each wing. Mean force coefficient ratio Low Re lift 0.9 High Re lift 0.8 Low Re drag 0.7 High Re drag 0.6 Wing 0.5 Wing 0.4 Wing 0.3 Wing 0.2 Wing 0.1 Wing 10 20 30 40 50 60 70 80 γ [deg] Figure 4.21: Force coefficient ratios plotted against estimated wing deflection angles (γ). 111 Chapter Revolving wing experiments 4.2.6. Discussion on the force coefficient ratios and deflection angles From the results obtained, force coefficients seem to be loosely correlated with deflection angles with lower force coefficient ratios for higher values of γ, suggesting that deflections have direct effect on force generation. Interestingly the force coefficient ratios are relatively unchanged at values of γ lower than 20o. Lower force coefficients for the most flexible wing (wing 7) under high Re condition suggests the penalty of flapping at higher angular velocities using soft wings, as this causes the wing to deflect to an extent that reduces its effective area against the flow. Furthermore, the deflections may cause the airflow to be redirected by the lower surface of the wing into the span-wise direction. Interestingly, wing deflections lower than 40o have relatively slight effects on aerodynamic properties. According to Combes and Daniel (2003b), hawkmoth insects have a maximum wing deflection angle of 10o in the course of flapping in hovering flight. This production of higher force coefficients in flexible wings than would be expected in the translating flow in wind tunnels (Willmott and Ellington, 1997c) appears to be remarkably robust, and is relatively consistent over quite a dramatic range of wing flexure. Hence, it is postulated that the LEVs continue to exist over deflected wings under such conditions. Therefore, insects and birds can afford wing deformations in exchange for a light wing, but this is a very difficult question to answer quantitatively. 112 Chapter Revolving wing experiments 4.3. Comparison with past experiments Figure 4.22 to figure 4.24 compare the mean coefficients of our low Re results with prior experiments performed under similar conditions. In the figures, the ‘propeller’, ‘fruit fly’, ‘wind tunnel’ results were obtained from Usherwood and Ellington (2002a), Dickinson et al. (1999) and Willmott and Ellington (1997c), respectively. Note that the ‘propeller’ results are obtained from experiments with Re = 8071, which is of similar value as the low Re case in this study. Next, the ‘fruit fly’ results are modeled after the fruit fly insect at a lower Re of 120, which is much lower than the Re of the current study. Lastly, the ‘wind tunnel’ results are steady-state force coefficients from real hawkmoth wings in steady, linear flow at Re = 5560 which excludes 3D unsteady flow effects. The differences are remarkable: the revolving wings here produce much higher force coefficients than the ‘wind tunnel’ results. The large disparity of results of measuring forces from wings placed in steady flow is emphasized again in the drag polars of figure 4.24. As can be seen in figure 4.22, C L measured here is consistent with the two prior sets of results except for the wind tunnel results. However, there is a significant difference in C D with past experiment results (see figure 4.23). The low Re of the fruit fly experiment resulted in higher C D at low values of α, presumably due to relatively larger viscous shear forces. The comparisons show that only experiments that considered the 3D effects of flow past flapping wing are able to produce realistic values of C L to support a hovering hawkmoth. 113 Chapter Revolving wing experiments 2.0 1.5 CL 1.0 0.5 Low Re Propeller Fruit fly Wind Tunnel 0.0 -0.5 -1.0 -20 20 40 60 α [deg] 80 100 120 Figure 4.22: Comparison of lift coefficients with past experiments for low Re case. 4.0 3.5 Low Re Propeller Fruit fly Wind Tunnel 3.0 2.5 CD 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -20 20 40 60 α [deg] 80 100 120 Figure 4.23: Comparison of drag coefficients with past experiments for low Re case. 114 Chapter Revolving wing experiments 2.0 1.5 CL 1.0 0.5 0.0 Low Re Propeller Fruit fly Wind Tunnel -0.5 -1.0 -1.5 -1 CD Figure 4.24: Comparison of drag polars with past experiments for low Re case. 4.4. Conclusion Based on the time histories of the revolving motion, three unsteady aerodynamic mechanisms are assumed to be present in the steadily revolving rigid wing. They occur in the following order, starting with the added mass effect during acceleration, followed by the Wagner effect at the beginning of the steady motion and finally the LEV. Steadily revolving model rigid wings produce large force coefficients due to the postulated presence of unsteady aerodynamic mechanism, the leading edge vortex. Both lift and drag forces, at angles of attack greater than 20o, are dominated by the pressure difference between upper and lower wing surfaces; separation at the leading edge produces a suction force located slightly rear of the wing’s leading edge. 115 Chapter Revolving wing experiments Moreover, the force coefficients are insensitive to changes in Reynolds number from 8170 to 14700. Wings of various flexibilities undergoing revolving motions were tested. Maximum force coefficients are remarkably unaffected when the wing deflection angles are lower than 47o. The softest wing (wing 7) underwent a significant loss in force coefficients. Furthermore, the high Re case caused greater wing deflection of wing and resulted in lower force coefficients. Based on the magnitudes of the forces coefficients, all the wings (except for wing 7) are able to produce large force coefficients, indicating the robustness of the high lift mechanism, LEV, being present in the wide range of conditions tested here. Furthermore, there is no evidence of stall at high angles of attack for all the tested wings, suggesting the remarkable ability of flapping wings to produce large force coefficients in the presence of wing flexure. 116 Chapter Oscillating motion experiments Chapter 5. Oscillating motion experiments As a goal of studying the aerodynamics of flapping flight, the approach here is to establish the time history of instantaneous force production. At this point of the project, the aim is to investigate the effect of wing deflection on the resultant aerodynamic forces acting on model wings undergoing oscillating motions. Wings of various flexibilities defined in chapter are applied. Furthermore, the force production of the flapping wing accurately mimicking the three-dimensional movements of the wing of a hovering hawkmoth is examined. Two flapping motions will be used in the study, the sinusoidal motion and the hawkmoth insect motion. Force measurement results of both motions will be compared to gain a better understanding as to why the hawkmoth adopts a unique flapping motion. The two flapping motions used in this study were cited by Weis-Fogh (1973) as being typical of ‘normal hovering’, a flight mode characteristic of many insects in which the stroke plane is approximately horizontal and the two down- and up-strokes make similar contributions to the overall lift force. The existing asymmetries in the trajectory of the hawkmoth motion mean that it may not perfectly fit the definition of ‘normal hovering’ from Weis-Fogh (1973). However, Liu et al. (1998) suggest four reasons why it is still a good species to use as a flapping model. First, it displays long periods of positional motion during which the wing angle of attack is relatively constant. Second, each wing stroke is separated by a rapid rotation about the span-wise axis located close to the leading edge. Third, the positional amplitude is close to the value of 120o that is cited by Weis-Fogh (1973) as typical for insects. Fourth, the kinematics is not complicated by the exaggerated wing flexion observed in some 117 Chapter Oscillating motion experiments Diptera (Nachtigall, 1979; Ennos, 1989b) or by the Z-shaped wing deformations noted for locusts (Jensen, 1956). The hawkmoth, therefore, offers a reasonably generalized wing beat. 5.1. Motion Three flapping frequencies were considered for both motions in the present study and hence three Reynolds numbers. For ease of reference, they were labelled as low Re, medium Re and high Re with their relevant data tabulated in table 5.1. Note that real hawkmoths were observed to flap at 26 Hz by Willmott and Ellington (1997b). For the conditions employed here, the dynamic scaling reduces the flapping frequency to match the Reynolds number. The Reynolds number identified as the ‘medium Re’ case is typical of free-flying hovering hawkmoths based on measurements from Willmott and Ellington (1997b). The six motions will test seven wings of various flexibilities and this works out to a total of 42 sets of experiments in this chapter. Table 5.1: Experimental parameters relating to the sinusoidal flapping motion. Motion Sinusoidal Description Re Flapping frequency, n [Hz] Low Re 3900 0.05 Medium Re 7800 0.10 High Re 11700 0.15 Low Re 3627 0.05 7254 0.10 11000 0.15 Hawkmoth Medium Re High Re 118 Chapter Oscillating motion experiments 5.1.1. Sinusoidal motion Free-flight data of many insects (Ellington, 1984c; Ennos, 1989b) showed that their flapping rhythms are sinusoidal. For the design and development of MAVs, sinusoidal motions can be implemented easily. In these experiments, generic sinusoidal motion is used to simulate hovering flight of insects. The results, although an idealized motion, may nevertheless be related to the forces generated by real flying insects. This motion features a high positional velocity and an optimal angle of attack of 45o at the middle of a half-stroke. The sinusoidal motion shown in figure 5.1 is modelled by the following functions: φ (t ) = Aφ cos(2πnt ) , (5.1)   α (t ) = 90° + Aα cos 2πnt + π  2 (5.2) where Aφ and Aα are the amplitudes of positional and angle of attack motion respectively, n is the flapping frequency (Hz) and t is the time (s). In this study, a positional amplitude of Aφ = 120o typical of many insects was applied. It is equivalent to approximately six chord lengths, calculated by projecting the arc length of the middle section of the wing’s trajectory onto a straight line. Also, the amplitude of the angle of attack motion Aα is 45o. The phase timing of the angle of attack motion is 90o with respect to the positional motion which is considered symmetrical and there was no stroke deviation which means that the wing tip was always moving on the horizontal stroke plane. Based on a flapping time normalized to the stroke period, the motion is down-stroke from T = to T = 0.5, followed by the up-stroke from T = 0.5 to T = 1. 119 Chapter Oscillating motion experiments 180 Positional Angle of attack 150 Angle [deg] 120 90 60 30 -30 -60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 cycle Figure 5.1: Time histories of sinusoidal motion in this study. Note that the elvation angle θ is zero. 5.1.2. Hawkmoth motion The flapping wing apparatus was programmed to mimic the hawkmoth insect hovering flight. Hawkmoth motion was obtained by curve-fitting the traces of the hovering motion of a male hawkmoth from Liu et al. (1998), which consists of the time history of positional angle, elevation angle and angle of attack. A spline interpolation routine written in LabVIEW was used to fit the curves. Subsequently, another custom program calculates the required Transistor-Transistor Logic (TTL) pulse patterns for commanding the stepper motors that drove the gears in the flapping wing gearbox to actuate the hawkmoth flapping motion. The fitted hawkmoth motion curves are plotted in figure 5.2. Positional stroke amplitude of 111.816o is used to calculate Uref for the purpose of determining Reynolds 120 [...]... real hawkmoth The flapping frequency is reduced from 26 Hz in a real hawkmoth to 0.1 Hz in the robotic apparatus2 The higher density of water allows a more reliable measurement of forces acting on the wings using a dynamic force transducer By obtaining the time accurate measurements of the forces acting on a 3D flapping wing, the aerodynamic characteristics and performance of 3D flapping wings can be analyzed... result, the bending of wings due to its weight is excluded The aerodynamic forces measured on the bending wings are assumed to be relevant to bending owing to other types of forces 1.2 Objective of this study The primary objective of this study is to investigate the aerodynamic forces acting on flapping wings that mimic insect flight Another area of concern is the lack of flapping wings experiments with... on the aerodynamic force generation This part of the study is motivated by the lack of knowledge about wing flexure on the aerodynamic force generation on flapping wings and aims to benefit the scientific community by filling this knowledge gap The time histories of force coefficients measured from flapping wings will be analyzed for better understanding of the force production through flapping wings. .. means of understanding the aerodynamic forces of 3D flapping wings Here, a mechanical robotic 3D flapping wing apparatus, that mimics insect hovering flight, is developed in this project The model wings are tested in water and the scale of the wings is five times larger than that of a real hawkmoth Such conditions allow the similarity parameter, the Reynolds number1, to approximately match that of a... Interference FC Chord-wise force acting on the wing xxi Nomenclature FD Drag force FL Lift force FN Normal force acting on the wing FN Mean normal force g Acceleration of wing GF Strain gage factor h Width of trapezium jN y-coordinate of leading edge marker N of wing kN y-coordinate of trailing edge marker N of wing K Wing stiffness lα Arc length of positional stroke l Span-wise length of wing Lsection Sectional... flapping wings Corresponding mean values serve to compare the aerodynamic forces between different sets of experiments Finally, a comparison of the aerodynamic force generation between various flapping motions is carried out to examine the effect of the parametric and rhythmic changes in the motion on force generation of flapping wings 1.3 Organization of thesis This thesis is divided into 8 chapters Chapter... Figure 5.16: Time histories of drag coefficients for wings with a range of flexibilities flapping according to hawkmoth motion at medium Re case 136 Figure 5.17: Time histories of lift coefficients for wings of various flexibilities flapping according to hawkmoth motion for high Re case 136 Figure 5.18: Time histories of drag coefficients for wings of various flexibility flapping according to hawkmoth... The bending here is of the passive type and is generated by fluid dynamic forces acting on the flexible wings The estimated degree of bending due to flexibility will be examined Performance of flexible wings will be compared with the rigid wings This includes the measurement of the time history of lift and drag, which are essential for the understanding of aerodynamic mechanism of insect flight 1.1... case 137 Figure 5.19: Comparison of mean lift coefficients for wings of various flexibilities flapping according to sinusoidal motion 139 Figure 5.20: Comparison of mean drag coefficients for wings of various flexibilities flapping according to sinusoidal motion 140 Figure 5.21: Comparison of mean lift coefficients for wings of various flexibilities flapping according to hawkmoth motion... number of above 5000 Therefore, this study will focus on the upper range of Reynolds number to investigate the characteristics of flapping wings with low viscous effects 3 Chapter 1 Introduction However, this cannot be completely achieved without knowing the influence of wing flexure on the aerodynamic force production Hence the initial part of the study is dedicated to the examination of influence of . Aerodynamic Force Characteristics of 3D Flapping Wings LAI KENG CHUAN (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING. 3.7.3. Alignment of the wing 77 3.7.4. Elimination of buoyancy forces 77 3.7.5. Measurement of weight and buoyancy force 80 3.7.6. Measurement of forces 81 3.7.7. Resolving of forces 85 3.7.8 by measuring the forces acting on them. A 3D flapping wing mechanism capable of mimicking the motion of insect flight is developed to measure forces acting on model wings flapping according