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With the aim to understand the synergistic roles played by kinematics, aerodynamics, and inertia in flapping wing maneuvers, this thesis first investigates the plunging motion of a simple flat plate as it is a fundamental motion in the kinematics of many flying animals. A wide range of frequency (k) and amplitude (h) is investigated to account for a robust kinematic characterization in the form of plunge velocity (kh). Leading Edge Vortices (LEVs) are found to be responsible for producing thrust while Trailing Edge Vortices (TEVs) produce drag. The vortex dynamics becomes nonlinear for higher kh and three main vortex-vortex interactions (VVI) are identified in the flow-field. To estimate the sole effect of LEVs on thrust coefficient, TEVs are eliminated by introducing a splitter plate. This resulted in reduced non-linearity in VVI and facilitated a parametrization of aerodynamic thrust coefficient with key kinematic features, frequency (k) and amplitude (h) [C_T= A.k^1.4 h-B where A and B are constants]. This is followed by investigating the more direct problem of bio-inspired MAV research – the interplay of kinematics, aerodynamics, and inertia on maneuvering bat flights. At first, an ascending right turn of a H. pratti bat is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Deceleration in flight speed, an increase in flapping frequency, shortening of the upstroke, and thrust generation at the end of the upstroke is observed during this maneuver. The turn is initiated by the synergisytic implementation of roll and yaw rotation where the turning moments are generated by drawing the inside wing closer to the body, by introducing phase lags in force generation between the two wings and by redirecting force production to the outer part of the wing outside of the turn. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) in order to establish the complete motion dynamics of a maneuver in action. The individual effects of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory trend is mostly driven by the aerodynamic forces and moments, whereas inertial effects drive the intricate intra-cycle fluctuations as well as the vertical velocity and altitude gain during ascent. Additionally, inertial moments play a dominant role for effecting yaw rotations where the importance of the Coriolis and centrifugal moments increase with increasing acuteness of the maneuver, with the largest effect of centrifugal moments being evidenced in the U-turn. / Doctor of Philosophy / The study of flapping wing is of paramount interest in the field of small aerial and aquatic vehicle propulsion. The intricate mechanisms acting behind a flapping wing maneuver can be explained by the synergistic roles played by 3 main components; details of the wing motion or the kinematics, how the air reacts to the wing motion or the aerodynamics, and the effort or force required to move the wings or wing inertia. This dissertation systematically reports the contribution of these components to a flapping flight maneuver. At first, the plunging motion of a simple flat plate is investigated as it is a fundamental motion in the flapping flight of many flying animals. A wide range of frequency and amplitude is investigated and their effect is characterized by a single parameter called "plunge velocity". It is found that, the resultant flow field becomes disorderly for higher plunge velocities which can be characterized by three different types of vortex interactions. The observed results facilitated a robust parametrization of aerodynamic thrust production with key kinematic features, frequency and amplitude. After this, the dissertation focuses on the bio-inspiration aspect of flapping flight by investigating the interplay of kinematics, aerodynamics, and inertia of maneuvering bat flights. At first, an ascending right turn of one species (H. pratti) is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Some characteristic features observed are – lowering of flight speed, increase in flapping rate, shortening of upstrokes, and generation of a forward force at the end of the upstroke. It is observed, that the bat turns by using synergistic body rotations in multiple directions which are effected by various techniques such as - drawing the wing inside the turn closer to the body, and changing the timing and location of the forces produced between the two wings. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed in the maneuver mechanisms. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) to establish the complete motion dynamics of a maneuver. The individual contributions of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory is mostly influenced by the aerodynamic forces and moments, whereas inertial effects are responsible for trajectory fluctuations during a flapping cycle as well contributing to altitude gain during ascent for the H. armiger bat.

Bats have many impressive flight characteristics such as the ability to rapidly change direction, carry substantial loads, and maintain good flight efficiency. For several years, researchers have been working towards an understanding of the specific aerodynamic phenomena which relate the unique wing structure of bats to their flight abilities. Computational fluid dynamics, a powerful tool used extensively across aerospace research, has led to substantial progress in the understanding of insect flight. However, due to technical challenges, numerical simulation has seen limited use in bat flight research. For this research, we develop, validate, and apply computational modeling techniques to three modes of bat flight: straight flight, sweeping turn, and U-turn maneuver. 3D kinematic data collection was achieved using a 28 camera multi-perspective optical motion capture system. The calibration of the cameras was conducted using a multi-camera self-calibration method. Point correspondences between cameras and frames was achieved using a human-supervised software package developed for this project. After the collection of kinematic data, we carried out aerodynamic flow simulations using the incompressible Navier-Stokes solver, GenIDLEST. The immersed boundary method (IBM) was used to impose moving boundary conditions representing the wing kinematics. Validation of the computational model was preformed through a grid independence study as well as careful evaluation of other relevant simulation parameters. Verification of the model was performed by comparing simulated aerodynamic loads to the expected loads based on the observed flight trajectories. Additionally, we established that we had a sufficient resolution of the wing kinematics, by calculating the sensitivity of the simulation results to the number of kinematic markers used during motion capture. For this study, three particular flights are analyzed—a straight and level flight, a sweeping turn, and a sharp 180 degree turn. During straight flight, typical flight velocities observed in the flight tunnel were 2-3 m/s resulting in a Reynolds number of about 12,000. Lift generation occurred almost exclusively during the downstroke, and peaks mid-downstroke. At the beginning of each downstroke, the effective angle of attack of the wings transitions from negative to positive and a leading edge vortex (LEV) quickly forms. LEVs are known to augment lift generation in flapping flight and allow lift to remain high at large angles of attack. During the end of each downstroke, the LEVs break up and lift drops substantially. As the wingbeat cycle transitions from downstroke to upstroke, the wings rotate such that the wing chordline is vertical as the wing moves upward. This wing rotation is critical for mitigating negative lift during the upstroke. Many of the basic flight mechanisms used for straight flight—i.e. LEV formation, wing rotation during upstrokes—were also observed during the sweeping turn. In addition, asymmetries in the wing kinematics and consequently the aerodynamics were observed. Early in the turn, the bank angle was low and elevated levels of thrust were generated by the outer wing during both the upstroke and downstroke causing a yaw moment. As the bat moved towards the middle of the turn, the bank angle increased to 20-25 degrees. Although the bank angle remained nominally constant during the middle and later portion of the turn, there was variation within each wingbeat cycle. Specifically, the bank angle dropped during each upstroke and subsequently was recovered during each downstroke as a consequence of elevated lift on the outer wing. Banking served to redirect the net force vector laterally causing a radial, centripetal force. Considering the mass of the bat, the nominal flight velocity, and the radius of curvature, the magnitude of the radial force fully explained the expected centripetal acceleration during the middle and later portion of the turn. Over the entire turn, yaw was found to be important in initiating the turn while banking was more important during the middle part of the turn. Over the course of 5 wingbeat cycles, the change in bearing angle (direction of flight) was about 45 degrees. Analysis of the U-turn flight showed many of the same characteristics as were observed during the sweeping turn, as well as a few key differences. The bat's ability to rotate its body rapidly appears to be more limited than its ability to change its trajectory. For this reason, the yaw rotation began about one to two cycles before the rapid bearing angle change and was stretched out over several wingbeat cycles. At the apex of the U-turn, the bat combined a high roll angle with a low flight velocity magnitude to very rapidly redirect its bearing direction and negotiate a low radius of curvature flight trajectory. Increases in roll angle occurred almost exclusively during the downstrokes, while both the upstroke and downstroke were active in generating yaw. Elevated thrust on the left outer wing during the end of the upstroke was observed throughout the flight, and elevated drag on the right inside wing did not appear to have an impact on the turn. We hope that this project motivates and facilitates further computational analysis into bat flight aerodynamics. Additionally, the data and findings will be useful for applications such as the design of bioinspired MAVs or flexible membrane energy harvesting technology. / Doctor of Philosophy / Bats have many impressive flight characteristics such as the ability to rapidly change direction, carry substantial loads, and maintain good flight efficiency. A better understanding of the physics of how bats fly can help scientists and engineers build more maneuverable, quieter, and more efficient bioinspired micro air vehicles. This engineering approach leverages the incredible capabilities observed in nature, but requires detailed knowledge of the animal as a prerequisite. Computational fluid dynamics, a powerful tool used extensively across aerospace research, has led to substantial progress in the understanding of animal flight broadly. However, due to technical challenges, numerical simulation has seen limited use in bat flight research. For this research, we develop, validate, and apply computer modeling techniques to the investigation of bat flight aerodynamics. Three particular modes of flight were analyzed—a straight and level flight, a sweeping turn, and a sharp 180 degree turn. During straight flight, typical flight velocities observed in the flight tunnel were 2-3 m/s. Lift generation, the force keeping the bat aloft, occurred almost exclusively during the downstroke, and peaks mid-downstroke. As the wing flap transitions from downstroke to upstroke, the wings rotate such that the wing is vertical as it moves upward. This wing rotation is critical for maximizing lift force during flight. During the sweeping turn, asymmetries in the wing kinematics and consequently the aerodynamics were observed. Early in the turn, the bank angle was low and elevated levels of thrust were generated by the outer wing during both the upstroke and downstroke causing rotation of the bat. As the bat moved towards the middle of the turn, the bank angle increased to 20-25 degrees. Banking served to redirect the net force vector laterally causing a turning force. Over the course of 5 wingbeat cycles, the change in direction of flight was about 45 degrees. Analysis of the U-turn flight showed many of the same characteristics as were observed during the sweeping turn, as well as a few key differences. At the apex of the U-turn, the bat combined a high roll angle with a low flight velocity magnitude to very rapidly redirect its bearing direction and negotiate a low radius of curvature flight trajectory. We hope that this project motivates and facilitates further computer simulations studying bat flight aerodynamics. Additionally, the data and findings will be useful for applications such as the design of bioinspired MAVs or flexible membrane energy harvesting technology.

In recent years, the design, fabrication, and control of robotic systems inspired by biology has gained renewed attention due to the potential improvements in efficiency, maneuverability, and adaptability with which animals interact with their environments. Motion studies of biological systems such as humans, fish, insects, birds and bats are often used as a basis for robotic system design. Often, these studies are conducted by recording natural motions of the system of interest using a few high-resolution, high-speed cameras. Such equipment enables the use of standard methods for corresponding features and producing three-dimensional reconstructions of motion. These studies are then interpreted by a designer for kinematic, dynamic, and control systems design of a robotic system. This methodology generates impressive robotic systems which imitate their biological counter parts. However, the equipment used to study motion is expensive and designer interpretation of kinematics data requires substantial time and talent, can be difficult to identify correctly, and often yields kinematic inconsistencies between the robot and biology. To remedy these issues, this dissertation leverages the use of low-cost, low-speed, low-resolution cameras for tracking bat flight and presents a methodology for automatically learning physical geometry which restricts robotic joints to a motion submanifold identified from motion capture data. To this end, we present a spatially recursive state estimator which incorporates inboard state correction for producing accurate state estimates of bat flight. Using these state estimates, we construct a Gaussian process dynamic model (GPDM) of bat flight which is the first nonlinear dimensionality reduction of flapping flight in bats. Additionally, we formulate a novel method for learning robotic joint geometry directly from the experimental observations. To do this, we leverage recent developments in learning theory which derive analytical-empirical potential energy fields for identifying an underlying motion submanifold. We use these energy fields to optimize a compliant structure around a single degree-of-freedom elbow joint and to design rigid structures around spherical joints for an entire bat wing. Validation experiments show that the learned joint geometry restricts the motion of the joints to those observed during experiment. / Ph. D. / In recent years, robots modeled after biological systems have become increasingly prevalent. Such robots are often designed based on motion capture experiments of the animal they aim to imitate. The motion studies are typically conducted using commercial motion capture systems such as ViconTM or OptiTrackTM or a few high-speed, high-resolution cameras such as those marketed by PhotronTM or PhantomTM. These systems allow for automated processing of video sequences into three-dimensional reconstructions of the biological motion using standard image processing and state estimation techniques. The motion data is then used to drive robotic system designs such as the SonyTM AiboTM dog and the Boston Dynamics Atlas humanoid robot. While the motion capture data forms a basis for these impressive robots, the progression from data to robotic system is neither algorithmic nor rigorous and requires substantial interpretation by a human. In contrast, this dissertation presents a novel experimental and computational framework which uses low-speed, low-resolution cameras for capturing the complex motion of bats in flight and introduces a methodology which uses the motion capture data to directly design geometry which restricts the motion of joints to the motions observed in experiment. The advantage of our method is that the designer only needs to specify a general joint geometry such as a ball or pin joint, and geometry which restricts the motion is automatically identified. To do this, we learn an energy field over the set of kinematic configurations observed during experiment. This energy field “pushes” system trajectories towards those experimentally observed trajectories. We then learn compliant or rigid geometry which approximates this energy field to physically restrict the range of motion of the joint. We validate our method by fabricating joint geometry designed using both these approaches and present experiments which confirm that the reachable set of the joint is approximately the same as the set of configurations observed during experiments.

This dissertation broadly seeks to understand the effect different kinematic parameters, external forces, and dynamic wing conformation have on the fluid dynamics of flapping flight. The primary motivation is to better grasp the fundamental fluid phenomena driving efficient flapping flight in the Reynolds number regime of birds, bats, and man made fliers of similar scale. The CFD solver (GenIDLEST) used is a Navier-Stokes solver in a finite volume formulation on non-staggered structured multiblock meshes. It has the capability for both body-fitted moving grid simulations and Immersed Boundary Method (IBM) for simulating complex bodies moving within a fluid. To that purpose we investigate the response of a rigid flapping thin surface planar wing in forward flight, at Re=10,000, subjected to frontal gusts. Gusts are a common ecological hazard for flapping fliers, especially in crowded environments. Among the various temporal and spatial scales of gust possible, we look at the phasing and duration of very large spatial scale gusts and their impact on the unsteady fluid dynamics of flapping within a single flapping cycle. The gust is characterized by a step function with time scale much smaller than the flapping time period. Having the advantage of prescribing the motion, as well as the timing and duration of the gust, this allowed the observation of the effect of angle of attack (AOA) and wing rotation on the evolution of the Leading Edge Vortex (LEV) and, hence the instantaneous lift and thrust profiles, by varying the parameters. During the downstroke, frontal gusts accelerated the flow development resulting in early separation of existing LEVs and formation of new ones on the wing surface which influenced the force generation by increasing the lift and thrust. These phenomena underscored the importance of the unsteady vortex structures as the primary force generators in flapping flight.The effect of the gust is observed to be diminished when it occurs during rapid supination of the wing. Unlike the influence of the vortices during the downstroke, the upstroke primarily reacted to effective AOA changes. A key characteristic of the kinematics of fliers in nature is stroke deviation. We investigate this phenomenon using a similar framework as above on a rigid thin surface flat-plate flapping wing in forward flight. Stroke deviation happens due to a variety of factors including wing flexion, wing lateral translation, and wing area change and here we investigate the different stroke deviation trajectories. Various trajectories were analyzed to assess the different capabilities that such kinematics might offer. The instantaneous lift and thrust profiles were observed to be influenced by a combination of the Leading Edge Vortex (LEV) and the Trailing Edge Vortex (TEV) structures existing in the flow at any given time. As an index of the cost of performance across all cases, the power requirements for the different cases, based on the fluid torques, are analyzed. Anti-clockwise figure-of-eight-cycle deviation is shown to be very complex with high power costs while having better performance. The clockwise elliptic-cycle held promise in being utilized as a viable stroke deviation trajectory for forward flight over the base non stroke deviation case. Armed with insight gained from these simple flapping structures, we are able to conduct the analysis of the flapping flight data obtained on a fruit bat. Understanding the full complexity of bat flight and the ways in which bat flight differs from that of other vertebrate flight requires attention to the intricate functional mechanics and architecture of the wings and the resulting unsteady transient mechanisms of the flow around the wings. We extract the detailed kinematic motion of the bat wing from the recorded data and then simulate the bat wing motion in the CFD framework for a range of Reynolds numbers. The Strouhal number calculated from the data is high indicating that the flow physics is dominated by the oscillatory motion. From the data the bat exhibits fine control of its mechanics by actively varying wing camber, wing area, torsional rotation of the wing, forward and backward translational sweep of the wing, and wing conformation to dictate the fluid dynamics. As is common in flapping flight, the primary force generation is through the attached unsteady vortices on the wing surface. This force output is modulated by the bat through varying wing camber and the wing area. Proper orthogonal decomposition of the wing kinematics is undertaken to compile a simpler set of kinematic modes that can approximate the original motion used by the fruit bat. These modes are then analyzed based on aerodynamic performance and power cost for more efficient flight. Understanding the physics of these modes will help us use them as prescribed kinematics for mechanical flappers as well as improve upon them from nature. / Ph. D.

Bats are some of the most agile flyers in nature. Their wings are highly articulated which affords them very fine control over shape and form. This thesis investigates the flight of Hipposideros Pratti. The flight pattern studied is nominally level and straight. Measured wing kinematics are used to describe the wing motion. It is shown that Proper Orthogonal Decomposition (POD) can be used to effectively to filter the measured kinematics to eliminate outliers which usually manifest as low energy higher POD modes, but which can impact the stability of aerodynamic simulations. Through aerodynamic simulations it is established that the first two modes from the POD analysis recover 62% of the lift, and reflect a drag force instead of thrust, whereas the first three modes recover 77% of the thrust and even more lift than the native kinematics. This demonstrates that mode 2, which features a combination of spanwise twisting (pitching) and chordwise cambering, is critical for the generation of lift, and more so for thrust. Based on these inferences, it is concluded that the first 7 modes are sufficient to represent the full native kinematics. The aerodynamic simulations are conducted using the immersed boundary method on 128 processors. They utilize a grid of 31 million cells and the bat wing is represented by about 50000 surface elements. The movement of the immersed wing surface is defined by piecewise cubic splines that describe the time evolution of each control point on the wing. The major contribution of this work is the decomposition of the native kinematics into canonical flapping wing physical descriptors comprising of the flapping motion, stroke-plane deviation, pitching motion, chordwise, and spanwise cambering. It is shown that the pitching mode harvests a Leading Edge Vortex (LEV) during the upstroke to produce thrust. It also stabilizes the LEV during downstroke, as a result, larger lift and thrust production is observed. Chordwise cambering mode allows the LEV to glide over and cover a large portion of the wing thus contributing to more lift while the spanwise cambering mode mitigates the intensification of LEV during the upstroke by relative rotation of outer part of the wing ( hand wing ) with respect to the inner part of the wing ( arm wing). While this thesis concerns itself with near straight-level flight, the proposed decomposition can be applied to any complex flight maneuver and provide a basis for unified comparison not only over different bat flight regimes but also across other flying insects and birds. / MS / Bats are some of the most agile flyers in nature. Their wings are highly articulated which affords them very fine control over shape and form. This thesis investigates the flight of Hipposideros Pratti. The flight pattern studied is nominally level and straight. Measured wing kinematics are used to describe the wing motion. The central motivation of the thesis is to characterize how the bat uses its wings to generate lift to counter gravity and thrust to move forward against drag forces. A mathematical filter based on Proper Orthogonal Decomposition (POD) is used to filter the measured wing motion to eliminate high frequency noise in the data but at the same time including including the important motions which produce lift and thrust. The filtered native kinematics is decomposed into flapping wing motions comprising of flapping mode, stroke-plane deviation, pitching motion, chordwise, and spanwise cambering. It is shown that the pitching mode harvests the low pressure region created by the Leading Edge Vortex (LEV) during the upstroke to produce thrust. It also stabilizes the LEV during the downstroke, as a result, larger lift and thrust production is observed. Chordwise cambering mode allows the LEV to glide over and cover a large portion of the wing thus contributing to more lift, while the spanwise cambering mode mitigates the intensification of LEV during the upstroke by relative rotation of the outer part of the wing (hand wing) with respect to the inner part of the wing (arm wing). While this thesis concerns itself with near straight-level flight, the proposed decomposition can be applied to any complex flight maneuver and provide a basis for unified comparison not only over different bat flight regimes but also across other flying insects and birds.