This thesis presents a method for designing a flapping wing stroke for a flapping wing vehicle. A flapping wing vehicle is a vehicle such as a bird or an insect that uses its wings for propulsion instead of a conventional propeller or a jet engine. The intent of this research is to design a wing stroke that the wings can follow which will maintain the vehicle at a desired longitudinal flight path angle and velocity. The cost function is primarily a function of the flight path angle error, velocity error and control rate. The objective maneuver is to achieve a flight condition similar to the trim of a conventional fixed wing aircraft. Gliding configurations of the vehicle are analyzed to better understand flight in minimal energy configurations as well as the modes of the vehicle. A control law is also designed using Lyapunov’s direct method that achieves stable tracking of the wing stroke. Results are presented that demonstrate the ability of the method to design wing strokes that can maintain the vehicle at various flight path angles and velocities. The results of this research show that an optimal control problem can be posed such that the solution of the problem results in a wing stroke that a flapping wing vehicle can use to achieve a desired maneuver. The vehicle velocity is shown to be stable in controlled gliding flight and flapping flight.

Flapping wing propulsion has the potential to revolutionise the field of Micro Aerial Vehicles (MAVs), but little is known about the effect of flapping motion on the performance of flapping wings. Prototype MAVs have achieved flight with passive flapping wings moving in a sinusoidal flapping motion, but the possible benefits of alternative flapping motions have not been studied in detail. This thesis presents the development of an Integrated Testing System (ITS), which allows the evaluation of flapping wing performance for different flapping motions. A detailed parametric study of the effect of flapping motion on wing performance is performed, and the optimal flapping motion for several passive flapping wings is determined by hardware-in-the-loop optimisation of two wing performance metrics. The developed ITS was able to automatically test a variety of passive flapping wings, and demonstrated precise control of the flapping motion and accurate and repeatable measurements of average lift force, mechanical power, and wing twist angle. The parametric study revealed that of the three flapping motions tested, the sinusoidal flapping motion generated the highest lift force, but a smoothed triangular motion was able to generate lift significantly more efficiently under load. The optimal flapping motion was successfully determined for three flapping wings, and was found to increase the loaded effciency of the wings by an average of 31% over a sinusoidal flapping motion. The determined optimal motion was almost identical for the three tested wings, and was found to strongly resemble the flapping motion of insects These findings demonstrate that significant improvements in the performance of passive flapping wings can be achieved by relatively minor variations of the flapping motion. This increased understanding will ideally lead to more efficient flapping wing MAVs with higher payloads, longer flight times, and improved performance.

Highly agile, hover capable flapping wing flight is a relatively new area of study in engineering. Researchers are looking to flapping flight as a potential source for the next generation of reconnaissance and surveillance vehicles. These systems involve highly complicated physics surrounding the flapping wing motion and unusual characteristics due to a hover requirement not normally associated with conventional aircraft. To that end this study focuses on examining the various models and physical parameters that are considered in various other studies. The importance of these models is considered through their effect on the trim and stability of the overall system. The equations of motion are modeled through a quasi coordinate Lagrangian scheme while the aerodynamic forces are calculated using quasi-steady potential flow aerodynamics. Trim solutions are calculated using periodic shooting for several different conditions including hover, climb, and forward flight. The stability of the trim is calculated and examined using stroke-averaged and Floquet theory. Inflow and viscous effects are added and their effects on trim and stability examined. The effects of varying hinge location and the inclusion of stroke deviation in the wing kinematics are also explored. The stroke-averaged system was not found to be a direct replacement for the periodic system as the stability was different for the two systems. Inflow and viscosity were found to have large effects on the stability of the system and models accounting for the two should be included in future flight dynamic models. / Master of Science

Micro Air Vehicles (MAVs) are defined as a class of vehicles with their larger dimension not exceeding 15 cm and weighing 100 gm. The three main approaches for providing lift for such vehicles are through fixed, rotating and flapping wings. The flapping wing MAVs are more efficient in the low Reynolds-number regime than conventional wings and rotors. Natural flapping flyers, such as birds and insects, serve as a natural source of inspiration for the development of MAV. Flapping wing design is one of the major challenges to develop an MAV because it is not only responsible for the lift, but also propulsion and maneuvers. Two important issues are addressed in this thesis: (1) an equivalent beam-type modeling of actual insect wing is proposed based on the experimental data and (2) development of the numerical framework for design and analysis of insect scale smart flapping wing. The experimental data is used for structural modeling of the blowfly Calliphora wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. It is found that natural frequency in bending and torsion are 3.17 and 1.57 times higher than flapping frequency of Calliphora wing, respectively. The results provide guidelines for the biomimetic structural design of insect-scale flapping wings. In addition to the structural modeling of the insect wing, development of the biomimetic mechanisms played a very important role to achieve a deeper insight of the flapping flight. Current biomimetic flapping wing mechanisms are either dynamically scaled or rely on pneumatic and motor-driven flapping actuators. Unfortunately, these mechanisms become bulky and flap at very low frequency. Moreover, mechanisms designed with conventional actuators lead to high weight and system-complexity which makes it difficult to mimic the complex wingbeat kinematics of the natural flyers. The usage of the actuator made of smart materials such as ionic polymer metal composites (IPMCs) and piezoceramics to design flapping wings is a potential alternative. IPMCs are a relatively new type of smart material that belongs to the family of Electroactive Polymers (EAP) which is also known as “artificial muscles”. In this work, structural modeling and aerodynamic analysis of a dragonfly inspired IPMC flapping wing are performed using numerical simulations. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. Later, a comparative study of the performances of three IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens is conducted. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. In addition to the IPMC, piezoelectric materials are also considered to design a dragonfly inspired flapping wing because they have several attractive features such as high bandwidth, high output force, compact size and high power density. The wings of birds and insects move through a large angle which may be obtained using piezofan through large deflection. Piezofan which is one of the simple motion amplifying mechanisms couples a piezoelectric unimorph to an attached flexible wing and is competent to produce large deflection especially at resonance. Non-linear dynamic model for the piezoelectrically actuated flapping wing is done using energy method. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. Subsequently, a comparative study of the performances of three piezoelectrically actuated flapping wings is performed. Numerical results show that the flapping wing based on geometry of dragonfly Sympetrum Frequens wing is suitable for low speed flight and it represents a potential candidate for use in insect scale micro air vehicles. In this study, single crystal piezoceramic is also considered for the flapping wing design because they are the potential new generation materials and have attracted considerable attention due to superior electromechanical properties. It is found that the use of single crystal piezoceramic can lead to considerable amount of wing weight reduction and increase of aerodynamic forces compared to conventional piezoelectric materials such as PZT-5H. It can also be noted that natural fliers flap their wings in a vertical plane with a change in the pitch of the wings during a flapping cycle. In order to capture this particular feature of the wingbeat kinematics, coupled flapping-twisting non-linear dynamic modeling of piezoelectrically actuated flapping wing is done using energy method. Excitation by the piezoelectric harmonic force generates only the flap bending motion, which in turn, induces the elastic twist motion due to interaction between flexural and torsional vibrations modes. It is found that the value of average lift reaches to its maximum when the smart flapping wing is excited at a frequency closer to the natural frequency in torsion. Moreover, consideration of the elastic twisting of flapping wing leads to an increase in the lift force.

Flapping-wing micro air vehicle (MAV) is an emerging micro-robotic technology, which has several challenges toward its practical implementation. Inspired by insect flight, researchers have adopted bio-mimicking approach to accomplish its engineering model. There are several methods to synthesize such an electromechanical system. A piezoelectric actuator driven flapping mechanism, being voltage controlled, monolithic, and of solid state type exhibits greater potential than any conventional motor driven flapping wing mechanism at small scale. However, the demand for large tip deflection with constrained mass introduces several challenges in the design of such piezoelectric actuators for this application. The mass constraint restricts the geometry, but applying high electric field we can increase the tip deflection in a piezoelectric actuator. Here we have investigated performance of rectangular piezo-actuator at high electric field. The performance measuring attributes such as, the tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically calculated for the actuator at high electric field. The analytical results suggest that the performance of such an actuator can be improved by tailoring the geometry while keeping the mass and capacitance constant. Thereby, a tapered piezoelectric bimorph cantilever actuator can provide better electromechanical performance for out-of-plane deflection, compared to a rectangular piezoelectric bimorph of equal mass and capacitance. The constant capacitance provides facility to keep the electronic signal bandwidth unchanged. We have analytically presented improvement in block force and its corresponding output strain energy, energy density and energy effi- ciency with tapered geometry. We have quantitatively and comparatively shown the per- formance improvement. Then, we have considered a rigid extension of non-piezoelectric material at the tip of the piezo-actuator to increase the tip deflection. We have an- alytically investigated the effect of thick and thin rigid extension of non-piezoelectric material on the performance of this piezo-actuator. The formulation provides scope for multi-objective optimization for the actuator subjected to mechanical and electrical con- straints, and leads to the findings of some useful pareto optimal solutions. Piezoelectric materials are polarized in a certain direction. Driving a piezoelectric actuator by high electric field in a direction opposite to the polarized direction can destroy the piezo- electric property. Therefore, unipolar high electric field is recommended to drive such actuators. We have discussed the drawbacks of existing switching amplifier based piezo- electric drivers for flapping wing MAV application, and have suggested an active filter based voltage driver to operate a piezoelectric actuator in such cases. The active filter is designed to have a low pass bandwidth, and use Chebyshev polynomial to produce unipolar high voltage of low flapping frequency. Adjustment of flapping frequency by this voltage driver is compatible with radio control communication. To accomplish the flapping-wing mechanism, we have addressed a compatible dis- tributed compliant mechanism, which acts like a transmission between the flapping wing of a micro air vehicle and the laminated piezoelectric actuator, discussed above. The mechanism takes translational deflection at its input from the piezoelectric actuator and provides angular deflection at its output, which causes flapping. The feasibility of the mechanism is investigated by using spring-lever (SL) model. A basic design of the com- pliant mechanism is obtained by topology optimization, and the final mechanism is pro- totyped using VeroWhitePlus RGD835 material with an Objet Connex 3D printer. We made a bench-top experimental setup and demonstrated the flapping motion by actuating the distributed compliant mechanism with a piezoelectric bimorph actuator.

Unlike conventional propellers, flapping wings may generate large amplitude oscillating forces, which can make them difficult to incorporate into a craft design. This is particularly true for a single, vertically oscillating hydrofoil, as part of a surface water craft where the cyclic lift of the hydrofoil disrupts the craft stability. This thesis begins by reviewing the history of human-powered watercraft with a focus on those having flapping foil propellers. This review combined with a review of the literature provides a balanced overview on how flapping wing propellers are currently designed. Current literature shows that although the mean performance of an oscillating foil has been determined in terms of the Strouhal number and the angle of attack, relatively little describes performance directly in terms of the foil motion. Hence, predicting temporal hydrodynamic forces acting on an oscillating foil is difficult. This provides motivation for research investigating the temporal performance of an oscillating foil directly in terms of its motion. In this thesis, experimental equipment designed to measure the hydrodynamic forces on a heaving object is presented. Key features of the equipment are analysed to show how measurement accuracy is maintained. Experimental measurements of unsteady hydrodynamic forces acting on a heaving cylinder, flat plate, symmetrical foil, and an asymmetrical foil are analysed with respect to the heaving motion. Firstly, the object motion is limited to one degree of freedom; pure heaving with zero forward velocity, to investigate the start-up conditions of the oscillating hydrofoil propeller. Secondly, these results are expanded on by adding a steady forward velocity component to the object motion to investigate how the hydrodynamic forces on the object are affected by the cross-flow. Experimental temporal hydrodynamic force measurements presented in this thesis show how the relative composition of hydrodynamic drag and inertia forces change with oscillating frequency, and forward velocity, affecting the phase, magnitude, and profile of the force cycles. This composition is also influenced by the cross-section of the oscillating object and the presence of a free surface. Current marine engineering equations for unsteady hydrodynamic forces on an object in an oscillating flow are validated for a cylinder. However, they are found to contain significant error when predicting the unsteady hydrodynamic forces on an oscillating hydrofoil. Contributions of this thesis link oscillating foil propulsion research to common marine engineering equations with the intent of making flapping wing propeller design more accessible to the general engineering community.

In this study a mechanism which produced flapping and pitching motions was designed and fabricated. These motions were produced by using a single electric motor and by exploiting flexible structures. The aerodynamic forces generated by flexible membrane wings were measured using a two degree of freedom force balance. This force balance measured the aerodynamic forces of lift and thrust. Two sets of wings with varying flexibility were made. Lift and thrust measurements were acquired as the mechanism flapped the wings in a total of thirteen cases. These thirteen cases consisted of zero velocity free stream conditions as well as forward flight conditions of five meters per second. In addition, flapping frequency was varied from two Hertz to four Hertz, while angle of attack offsets varied from zero degrees to fifteen degrees. The four most interesting conditions for both sets of wings were explored in more detail. For each of these conditions, high-speed video of the flapping wing was taken. The images from the video were also correlated with cycle averaged aerodynamic forces produced by the mechanism. Several observations were made regarding the behavior of flexible flapping wings that should aid in the design of future flexible flapping wing vehicles.

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Research efforts in this dissertation address aerodynamics and flight performance of flapping wing aircraft (ornithopters). Flapping wing aerodynamics was studied for various wing sizes, flapping frequencies, airspeeds, and angles of attack. Tested wings possessed both camber and dihedral. Experimental results were analyzed in the framework of momentum theory. Aerodynamic coefficients and Reynolds number are defined using a reference velocity as a vector sum of a freestream velocity and a stroke-averaged wingtip velocity. No abrupt stall was observed in flapping wings for the angle of attack up to vertical. If was found that in the presence of a freestream lift of a flapping wing in vertical position is higher than the propulsive thrust. Camber and dihedral increased both lift and thrust. Lift-curve slope, and maximum lift coefficient increased with Reynolds number. Performance model of an ornithopter was developed. Parametric studies of steady level flight of ornithopters with, and without a tail were performed. A model was proposed to account for wing-sizing effects during hover. Three micro ornithopter designs were presented. Ornithopter flight testing and data-logging was performed using a telemetry acquisition system, as well as motion capture technology. The ability of ornithopter for a sustained flight and a presence of passive aerodynamic stability were shown. Flight data were compared with performance simulations. Close agreement in terms of airspeed and flapping frequency was observed.

Numerical models of insect flapping flight have previously been developed and used to simulate the performance of insect flight. These models were commonly developed via Blade Element Theory, offering efficient computation, thus allowing them to be coupled with optimisation procedures for predicting optimal flight. However, the models have only been used for simulating hover flight, and often neglect the presence of the induced flow effect. Although some models account for the induced flow effect, the rapid changes of this effect on each local wing element have not been modelled. Crucially, this effect appears in both axial and radial directions, which influences the direction and magnitude of the incoming air, and hence the resulting aerodynamic forces. This thesis describes the development of flapping wing models aimed at advancing theoretical tools for simulating the optimum performance of insect flight. Two models are presented: single and tandem wing configurations for hawk moth and dragonfly, respectively. These models are designed by integrating a numerical design procedure to account for the induced flow effects. This approach facilitates the determination of the instantaneous relative velocity at any given spanwise location on the wing, following the changes of the axial and radial induced flow effects on the wing. For the dragonfly, both wings are coupled to account for the interaction of the flow, particularly the fact that the hindwing operates in the slipstream of the forewing. A heuristic optimisation procedure (particle swarming) is used to optimise the stroke or the wing kinematics at all flight conditions (hover, level, and accelerating flight). The cost function is the propulsive efficiency coupled with constraints for flight stability. The vector of the kinematic variables consists of up to 28 independent parameters (14 per wing for a dragonfly), each with a constrained range derived from the maximum available power, the flight muscle ratio, and the kinematics of real insects; this will prevent physically-unrealistic solutions of the wing motion. The model developed in this thesis accounts for the induced flow, and eliminates the dependency on the empirical translation lift coefficient. Validations are shown with numerical simulations for the hover case, and with experimental results for the forward flight case. From the results obtained, the effect of the induced velocity is found to be greatest in the middle of the stroke. The use of an optimisation process is shown to greatly improve the flapping kinematics, resulting in low power consumption in all flight conditions. In addition, a study on dragonfly flight has shown that the maximum acceleration is dependent on the size of the flight muscle.