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Hummingbirds use banking to achieve faster turns and asymmetrical wingstrokes to achieve tighter turns Read, Tyson J Gavin 2015

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Hummingbirds use banking to achieve faster turns and asymmetrical wingstrokes to achieve tighter turns  by Tyson J Gavin Read B.A., University of California, Berkeley, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Zoology)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2015  © Tyson J Gavin Read, 2015  ii Abstract  Flying animals are hypothesized to direct the lateral force necessary to execute turns through two methods. The first is force vectoring, which is accomplished by banking the wing stroke plane and body in concert. Through this method, centripetal force is provided by the lateral component of aerodynamic force that is directed into a turn. An alternative hypothesis is that they generate lateral force through asymmetries in wingbeat kinematics between the left and right wings without varying body position. Examples of asymmetrical kinematics could include differences in angle of attack, stroke plane angle, or stroke amplitude. We studied turning hummingbirds as they tracked a revolving feeder to distinguish between these mechanisms. Comparing hovering and turning flight revealed that hummingbirds bank their stroke plane and body into turns and maintain the position of the stroke plane relative to their bodies, supporting a force vectoring mechanism. However, several wingbeat asymmetries were observed during turning, such as the outer wing tip path being higher and flatter, and the inner wing tip path being lower and more scooped than in hovering. Because the centripetal force necessary to complete a turn is determined by translational velocity and turn radius, we created four balanced turning treatments where these aspects of a turn were varied with a revolving feeder to determine how wing and body kinematics change in order to compensate for these challenges. We found that three asymmetric wingbeat kinematic variables were associated with changes in turn radius and two body kinematic variables related to force vectoring were associated with changes in translational velocity. There were no kinematics influenced by both radius and velocity. This suggests wingbeat asymmetries compensate for changes in turning radius and force vectoring is used to compensate for changes in velocity. Thus, rather than force vectoring and wingbeat asymmetries  iii being mutually exclusive, our results indicate that the two mechanisms are used simultaneously and independently to meet different aerodynamic challenges.    iv Preface  Tyson Read conceived of the experimental design in this thesis under the guidance of Paolo Segre and Professor Douglas Altshuler. Mr. Read developed the experimental apparatus and collected the data. Mr. Read, Mr. Segre, and Professor Kevin Middleton analyzed data. Mr. Read wrote the introductory and concluding chapters. Mr. Read wrote initial drafts of the research chapter and final drafts were written with Professor Altshuler.       v Table of Contents  Abstract ........................................................................................................................................... ii	  Preface............................................................................................................................................ iv	  Table of Contents............................................................................................................................ v	  List of Tables ................................................................................................................................ vii	  List of Figures .............................................................................................................................. viii	  List of Abbreviations ..................................................................................................................... ix	  Acknowledgments........................................................................................................................... x	  Introductory Chapter....................................................................................................................... 1	  Research Chapter: Hummingbirds use banking to achieve faster turns and asymmetrical wingstrokes to achieve tighter turns ............................................................................................... 5	  Introduction................................................................................................................................. 5	  Material and methods.................................................................................................................. 7	  (a) Animals and marking techniques ...................................................................................... 7	  (b) Measurements of banking turns ........................................................................................ 7	  (c) Kinematic analysis............................................................................................................. 9	  (d) Statistical analysis ........................................................................................................... 10	  Results....................................................................................................................................... 11	  Discussion ................................................................................................................................. 13	  Concluding Chapter ...................................................................................................................... 27	  References..................................................................................................................................... 31	   vi Appendices.................................................................................................................................... 36	  Table 4. Bird morphometrics ............................................................................................ 36	       vii List of Tables  Table 1. Mixed model ANOVA between the wing kinematics of hovering and turning ............ 21 Table 2. Mixed model ANOVA between the whole body kinematics of hovering and turning .. 23 Table 3. Two-way mixed model ANOVA of whole body and wing kinematics among turning treatments.............................................................................................................................. 24 Table 4. Bird morphometrics ........................................................................................................ 36               viii List of Figures  Figure 1. Filming apparatus .......................................................................................................... 16	  Figure 2. Instantaneous wing measures ........................................................................................ 17	  Figure 3. Analysis of kinematics between hovering and turning.................................................. 18	  Figure 4. Average wing kinematics .............................................................................................. 19	  Figure 5. Kinematic changes across turning treatments ............................................................... 20	   ix List of Abbreviations US  upstroke   DS  downstroke L  left wing R  right wing χGR,XZ  body pitch angle χGR,YZ  body angle frontal χSP,XZ  body roll angle RWBA relative wing bank angle WBA  wing bank angle β  stroke plane angle GR  average elevation angle, relative to ground θGR  instantaneous elevation angle, relative to ground ΦSP  wingstroke amplitude, relative to stroke plane ΘSP  elevation amplitude, relative to stroke plane  φGR  instantaneous position angle, relative to ground WDT  wingtip distance travelled tip   average wingtip speed αmid  geometric angle of attack, mid-stroke αend  geometric angle of attack, end-stroke € θ€ U  x Acknowledgments  I am grateful to the post-doctoral fellows and graduate students of the Altshuler Lab. They are exceptional scientists and wonderful friends. I am honored to have been one of them.   I owe a great deal to Professor Douglas Altshuler. I am grateful to have been one of his students and have learned a tremendous amount from our collaborations. I am thankful for the guidance Professor Robert Shadwick and Professor Darren Irwin provided me in crafting my thesis project. I thank Peter Credico, Nandhini Sankhyan, Soroush Safa, Hannah Visty, Simon Plath, Janet Li, and Justin Sheppard for assistance with data digitization and data collection.  At the University of California, Berkeley, I thank Dr. Yonatan Munk for introducing me to research and Professor Jim McGuire for encouraging me to pursue graduate school.   To my colleagues at the Pacific Gas and Electric Company, I thank Ken DiVittorio, Dr. J Mark Jenkins, and Laura Burkholder for encouraging me to pursue my interest in ornithology and Pamela Money and Megan Lum for enabling me to start my graduate work.   Lastly, I thank my parents, Emy Daniel, and Aaron and Emily Read for whom I have much to be grateful for.  1 Introductory Chapter   Animal flight has a rich evolutionary history and has arisen in multiple taxonomic lineages [1]. Given the diversity of flying animals, it is unsurprising that there are several mechanisms for flight, including directed aerial descent, gliding, and flapping flight. Directed aerial descent and gliding are controlled conversions of gravitational potential energy into lift and thrust and can be differentiated by glide angles steeper and shallower than 45 degrees, respectively. Both mechanisms can be seen in a variety of species, but notable examples of each are arboreal ants that employ directed aerial descent [2] and gliding arboreal frogs [3]. In contrast, flapping flight actively produces lift and thrust and modulates aerodynamic force production through adjustments in wing and body kinematics. A significant focus within the field of flapping flight has been maneuverability, the importance of which is evidenced by its function in behaviors that are fundamental to an individual’s survival, such as establishing and defending territories [4] and avoiding predators [5]. A broad definition of maneuverability is an organism’s agility along the x, y, and z axes of space and its ability to rotate on these axes [6]. Maneuverability studies within flapping flight have encompassed a diversity of species and maneuvers of varying complexity including forward flight in bats [7], turning flight in dragonflies [8], and tandem flight in cliff swallows [9]. When identifying maneuvers in flight, it is useful to consider the duration of a maneuver and the way air flows over the wings. Transitory maneuvers, such as rapid turns that have been observed in dragonflies [10], occur over the span of a few wingbeats and are in contrast with  2 sustained maneuvers, which employ the same kinematic pattern over many wingbeats. The aerodynamic mechanisms employed in a maneuver can be explained through steady state, quasi-steady state, or unsteady state aerodynamics. Maneuvers which employ changing wing orientations and velocities are characterized by unsteady air-flow and constant wing orientations and velocities experience steady air-flow. In addition to defining maneuverability as axial and torsional agility [6], another common definition for flying animals is the smallest radius for which a given individual or species can make a turn [11].  Different types of turns include yaw turns, where there is no component of translational velocity, and arced turns, which combine yaw and forward flight to follow a curving trajectory. Level arced turns, which require aerodynamic force to provide lift, thrust, and lateral force in the direction of the turn, can be accomplished through different mechanisms. One mechanism to orient force into a turn and produce centripetal force is force vectoring. In this method, an animal reorients its body and strokeplane to direct a component of total aerodynamic force in the direction of a turn. Force vectoring, which is accomplished through banking, is a common strategy employed by insects [12] and birds [13] during turning maneuvers. Force vectoring is also the only mechanism which birds have been shown to implement during arcing turns. The other distinct mechanism that could accomplish an arced turn is via asymmetrical wingbeats. Instead of banking the body and wings, wingbeat asymmetries, such as differences in stroke amplitude and angle of attack between the left and right wings, produce aerodynamic force in the direction of the turn. Wingbeat asymmetries have notably been observed in yaw turns in hummingbirds [14] where there was rotation around the yaw axis, but no translation. Given the asymmetries seen in yaw turns and the distinct horizontal wingstroke of hummingbirds, they may not be constrained to the force vectoring strategy seen in other birds.  3 By identifying the body and wing kinematics of arcing turns, we can identify whether hummingbirds are reorienting their bodies and wings like other birds to use force vectoring, if they are orienting force via wingstroke asymmetries, or they are using a combination of these strategies.  Because hummingbirds are capable of slow maneuvering flight and can be trained to track a feeder following defined trajectories, they provide an opportunity to examine the wing and body kinematics employed in sustained arcing turns. In addition, hummingbirds are a well established model organism for studying maneuverability [16], for which several maneuvers have been previously examined, including hovering [17], display dives [18], forward flight [19], backward flight [20], and yaw turns [14]. Expanding this list to include a new maneuver ensures that the results of this study are applicable to an active research community. Hummingbirds’ ability to hover provides another advantage as a model organism. By comparing the wing and body kinematics of hovering and turning, the kinematic changes necessary to produce lift, thrust, and lateral force towards a turn can be can be compared to the kinematics employed in hovering, where force is only needed to counteract gravity. In addition to describing how hummingbirds orient force into a turn, this study asks how turning kinematics change to produce faster or tighter turns. The kinematics of turning have been explained for many species, but it is unknown how kinematics respond to each aspect of a turn. The centripetal force (Fc ) necessary for an object to complete a turn is determined by its mass (m), translational velocity (v), and turning radius (r) and can be calculated through the equation:  Fc=mv2/r   4 By training a hummingbird to track a revolving feeder that moves at slow and fast velocities as well as small and large radii, the kinematics used to control speed and turning radius can be determined. Also, by having experimental treatments with the same centripetal velocity, but different translation velocities and turning radii, we can determine whether kinematics are dictated solely by centripetal force or by the radius and velocity of a turn. The levels of translational velocity used in this study were chosen after preliminary trials determined the fastest velocity hummingbirds were capable of tracking a feeder. The levels of turning radius were constrained by the size of the flight chamber where filming occurred. Having a single set of kinematics that are modulated to supply different centripetal forces would be the simplest explanation for how birds orient force into a turn. However, the alternative method for directing force into a turn would be though one set of kinematics that are related to changes in translational velocity and another set that are related to changes in turning radius. Determining the kinematic changes that produce faster and tighter turns will significantly expand upon the findings of previous studies to identify how different aspects of a turn are controlled in flapping flight. If hummingbirds use separate sets of kinematics to control for turning radius and translational velocity, future studies could determine if there are different energetic costs associated with these kinematics. The findings of this study will also provide researchers that study other species an opportunity to explore whether their model organisms have a single set of kinematics for orienting force into a turn, or separate kinematics to control changes in turning radius and translational velocity.  5 Research Chapter: Hummingbirds use banking to achieve faster turns and asymmetrical wingstrokes to achieve tighter turns   Introduction  Arced turns are of particular interest for flying animals because they are employed in many fundamental maneuvers such as predator-prey interactions [5] and intra-specific competition [18]. During a level arced turn, the total aerodynamic force must be reoriented to provide forward thrust, lift, and inward centripetal force. An example of this maneuver is an airplane increasing its total aerodynamic force and banking its wings toward the turn, directing a component of lift laterally and producing centripetal force via force vectoring. This bank angle increases during faster or tighter turns because the centripetal force necessary to complete the turn increases. Despite the aerodynamic differences between flapping flight and aircraft, turning studies of rose-breasted cockatiels [21], pigeons [13], and fruit flies [12] have shown that these species employ largely the same banking strategy as fixed-wing aircraft during arcing turns. If turning is accomplished through force vectoring as seen in pigeons [13] and cockatiels [21], the wingstroke of steady-state turns should be reoriented into the turn to produce centripetal and translational force. Alternatively, centripetal force for an arced turn may be produced via  6 asymmetrical wing strokes that are not determined by body orientation. Hummingbirds are known to execute yaw turns via asymmetrical wing strokes [14],  and have the potential to employ a similar kinematic pattern to produce lateral and centripetal forces during an arced turn. To identify the mechanism hummingbirds use to orient force into a turn, we compared the wingbeat kinematics employed by Anna’s hummingbirds (Calypte anna) during hovering and when performing an arcing turn of small radius and fast translational velocity. Determining that hummingbirds reorient their wing stroke plane angle and bodies into the turn would support the hypothesis that force is oriented through force vectoring. A consistent body orientation between hovering and turning treatments would indicate that hummingbirds use wing beat asymmetries instead of force vectoring to orient force into a turn.  Previous studies have analyzed the wing kinematics of arced turns [15,21,22] and identified adjustments in angle of attack and wing trajectory as important mechanisms for initiating and controlling turns. However, it is unknown how aspects of a turn, such as its radius or translational velocity, impact an organism’s wingbeat kinematics or body orientation. Varying these features allows us to ask if force vectoring, or sustained kinematic asymmetries are used separately or in combination to meet the challenges imposed by translational velocity, turning radius, angular velocity, and centripetal force. In our study, we compare kinematic changes across four arcing turns that represented four angular velocities and required three levels of centripetal force generation. These turns combined slow and fast translational velocities with large and small radii to achieve a balanced design for statistical comparison. By implementing this experimental design, our study can identify if there is one set of kinematics that controls changes in centripetal force, or separate sets of kinematics that control a turn’s radius and translational velocity 7 Material and methods (a) Animals and marking techniques Six adult male Anna’s hummingbirds were captured at the University of British Columbia with drop-door traps [23] and housed in a vivarium with a 12 h:12 h light:dark lighting cycle. Each individual was kept in a cage measuring 0.91x0.61x0.61 m and fed ad libitum with 13% Nektar-Plus (Nekton, Pforzheim, Germany) or 15% sucrose solutions. Immediately prior to filming, Wite-Out correction fluid (Bic, Toronto, ON, Canada) markers were applied to the head, back, and rump of the birds to facilitate tracking. Wite-Out was reapplied whenever markers showed signs of wear, typically three times for each individual. The Animal Care Committee of the University of British Columbia approved all animal procedures.  (b) Measurements of banking turns Flight was filmed in April and May of 2014 within a 0.91 x 0.91 x 0.84 m acrylic chamber that contained a feeder assembly and wooden perch (Fig. 1). The feeder assembly consisted of a 10 ml syringe attached to an adjustable arm that was rotated by a stepper motor (MDrive 23 Plus, Schneider Electric Motion, Marlborough, CT, USA) in a clockwise circle. Two 0.50 m aluminum bars (80/20, Columbia City, IN, USA) supported the motor and feeder arm. Three high-speed cameras (Miro 120, Vision Research, Wayne NJ, USA) were positioned to provide dorsal and posterior views of individuals during feeding and one camera (Miro 4, Vision Research, Wayne NJ, USA) recorded a lateral view. These cameras were synchronized at 1000 Hz with a function generator (AFG3021B, Techtronix, Beaverton, OR, USA) and triggered with a common external end trigger. All cameras recorded video at 1000 frames/sec with an exposure  8 of 200 µsec. Lighting was supplied with four to six 800 W halogen lights configured to minimize shadows over wings and body markers.  Prior to the start of filming, all individuals were given time to acclimate to the flight chamber. The amount of time spent acclimating varied with each individual, but took no longer than two hours. After a hummingbird fed regularly from a 10 ml syringe, access to the feeder was restricted with a cover and the individual was allowed to feed only while the feeder revolved. After a successful feeding event, the feeder was stopped and covered for 15 to 20 minutes. The feeder’s angular velocity increased incrementally with each successful feeding session until individuals were capable of feeding at the experimental speeds. Training took approximately four hours per individual.  Individuals were filmed feeding while hovering and performing four different turns. The four turning treatments had a balanced design with two levels of turn radius (0.23 m, 0.33 m) and two levels of translational velocity (0.626 m/s, 0.750 m/s). These combinations were selected to illustrate the relative roles of radius and velocity on kinematics. The angular velocity of these turns was calculated as:  ω=v/r  where ω is angular velocity, v is translational velocity, and r is the radius of a turn. Turning treatments had angular velocities of 1.89 rad/s, 2.27 rad/s, 2.72 rad/s, and 3.26 rad/s. The centripetal force of the treatments was calculated as:   Fc=mv2/r  9  where Fc is centripetal force, m is mass, v is translational velocity, and r is the radius of a turn. The values were 1.19 N at 1.89 rad/s, 1.70 N at 2.27 rad/s and 2.72 rad/s, and 2.45 N at 3.26 rad/s. Centripetal force was matched for the treatments with angular velocities of 2.27 rad/s and 2.72 rad/s because one turn had a radius of 0.33 m and was completed at 0.750 m/s and the other had a radius of 0.23 m and a translational velocity of 0.626 m/s. Video of hovering was captured on each day of filming to facilitate body roll calculations, but the order of turning and hovering was alternated among individuals to ensure treatment order was not a confounding variable. At the start of each day and whenever a new individual was used, cameras captured footage of a calibration object and the feeder arm was checked with a level to ensure it was horizontal.   (c) Kinematic analysis Sections of video where the bird was at the feeder and maintained a consistent body position were selected for digitization. Fifteen total wingbeats were analyzed for each bird in each treatment. These wingbeats were drawn from two to six consecutive wingbeats from three or four different trials. Camera views were calibrated after filming a 36-point calibration object and with a direct linear transformation from DLTcal5 software [24]. Ten points distributed on the head, rump, shoulders, wingtips, fifth primaries, and two body points were digitized in every frame of the 15 wingbeats with DLTdv5 software [24].  Digitized points describe 14 kinematic variables during the upstroke and downstroke of each wingbeat. Body angle lateral (Body pitch, χGR,XZ), body angle frontal (body bank angle, χGR,YZ), wing bank angle (WBA), relative wing bank angle (RWBA), average elevation angle (GR), average wingtip speed ( tip), wingtip distance traveled (WDT), instantaneous position angle € θ€ U  10 (φGR), instantaneous elevation angle ( GR), angle of attack (α), and the stroke plane angle (β) were calculated with a gravitational frame of reference. A wingstroke-centered frame of reference was used to calculate the stroke amplitude (ΦSP), elevation amplitude (ΘSP), and body roll angle (χSP,XZ). Frames of reference and kinematic calculations are described in detail in previous studies [14] with the exception of body roll angle, wing bank angle, relative wing bank angle, and angle of attack. Roll along the long axis of a bird’s body was calculated as a vector extending perpendicularly from a plane comprised of the rump and two markers on each individual’s back. Body roll was averaged over each wingbeat. To ensure marker placement did not adversely affect roll calculations, body roll was adjusted by subtracting the average roll observed during a given day’s hovering trials from the recorded roll. Wing bank angle was calculated by taking the mean difference of the absolute values of the outside (left) and inside (right) wings. Relative wing bank angle was calculated by adding wing bank angle and body angle frontal. A value of 0º indicates the wings are perpendicular to the body. Angle of attack is calculated as the angle between the plane of the wing and the horizontal for a given wing elevation. The plane of each wing was defined by the shoulder, wingtip, and fifth primary. The wing is oriented parallel to the horizon at 0º or 180º and perpendicular at 90º.  (d) Statistical analysis Changes in kinematics between hovering and turning were analyzed with turning data from the treatment that required the greatest centripetal force (0.23 m, 0.750 m/s). Kinematic parameters for hovering were a mean of the left and right wing. Wingstroke differences between hovering and turning were identified with a one-way mixed model ANOVA that used wing motion (left wing turning, right wing turning, hovering) as the fixed effect and bird as the € θ 11 random effect [25–27]. Models with significant overall ANOVAs (α=0.05) received pairwise post-hoc comparisons that assessed differences between each treatment [28]. A separate one-way mixed model ANOVA quantified changes in parameters related to body kinematics and both wings. This ANOVA used flight mode (hovering versus turning) as the fixed effect and bird as the random effect.   Kinematic changes among the four turning treatments were analyzed with a factorial two-way mixed model ANOVA. The two levels of translational speed and turning radius were used as categorical variables in this analysis. These variables, as well as the interaction between the two, also served as the fixed effects in the mixed model, and bird was the random effect.  After completing our statistical analyses, a positive false discovery rate (pFDR) analysis was used to control family-wise error rate [29–31] at 0.05. Our pFDR analysis used the “smoother” option in the R [27] package qvalue [32]. We determined that an adjusted α-level of 0.028 controlled family-wise error at 5% for our 396 statistical tests, and subsequent inferences (Tables 1-3) use this adjusted α-level.  Results  Comparing hovering flight to the turning treatment with the highest angular velocity and centripetal force revealed multiple changes in wingbeat and body kinematics. The time course of the three wing angles revealed substantial asymmetries for the elevation amplitude and angle of attack and minor differences between the left and right wings in stroke position angle (Fig. 2). Wingstroke asymmetries in turning flight apparent in instantaneous wing measures translated  12 into statistically significant differences for several kinematic parameters (Fig. 3). Asymmetries in stroke position angle resulted in a small, but significant increase in stroke amplitude in the outer wing and a decrease in the inner wing, relative to hovering (Fig. 3a).  The outer wing also had a higher average elevation angle and lower elevation amplitude, whereas the inner wing has a lower average elevation angle and higher elevation amplitude (Fig 3d,e). These two measures of wing elevation varied in concert, as has been previously shown for yaw turns [14]. The stroke plane angle of the outer wing was indistinguishable from the hovering wingbeat, but the stroke plane angle of the inner wing was essentially horizontal during the downstroke and was pitched up during the upstroke (Fig. 3f), such that it was higher at supination than at pronation (Fig. 4). The time course of angle of attack was analyzed by considering it at four phases. Overall, the inner wing had advanced timing in wing rotation and the left and right wings were significantly different at all phases except for mid-downstroke (Fig 3b). P-values for kinematic parameters related to this analysis can be found in Table 1. The analysis of body kinematics demonstrated that body roll angle, body angle frontal, and wing bank angle all tilted into the turn with similar magnitude (Fig 3h,j,k). As a consequence, there was no significant change in relative wing bank angle between hovering and turning (Fig. 3l). P-values for these kinematic parameters can be found in Table 2.  Comparing the four different arcing turns revealed that some wingbeat kinematic measures varied with radius, some body kinematics varied with velocity, but no kinematic measures varied with both radius and velocity. Tighter turns (r = 0.23 m) were associated with an increase of the elevation amplitude of the inner wing’s downstroke (Fig. 5c), tilting of the outer wing’s stroke plane angle forward (pronation higher than supination; Fig. 5a,b), and decreasing angle of attack of the inner wing at mid-downstroke (Fig. 5d). Within a radius treatment,  13 translational velocity had no significant effect on these variables. In contrast, faster turns were accomplished by banking the wings and the body (Fig. 5e-h) farther into the turn. As a result, relative wing bank angle remained consistent across the turning treatments, just as it did between hovering and the arcing treatment with highest angular velocity and centripetal force (Fig. 4). P-values for these kinematic parameters can be found in Table 3.  Discussion  Whereas numerous changes in wingbeat kinematics were observed between hovering and turning, wing bank angle is a key parameter for resolving the mechanism through which flying animals orient aerodynamic force into a turn. Force vectoring is indicated by maintaining the relative wing bank angle in the same direction as acceleration and has been demonstrated in numerous studies of transient maneuvers in insects [12,33] and birds [13,21]. In our study, hummingbirds performed arced turns by banking their stroke plane (wing bank angle) into the turn for all four turning treatments. They also banked their body (body angle frontal) into the turns and maintained the position of the stroke plane relative to the body (the relative wing bank angle) for hovering and all four turning treatments. The consistency in relative wing bank angle across our treatments supports the hypothesis that hummingbirds accomplish arced turns via force vectoring and joins a recent study of pigeons [22] in expanding force vectoring to include sustained maneuvers.  An alternative hypothesis to force vectoring is that flying animals can orient aerodynamic force using left-right asymmetries in wingbeat kinematics without changing body position. Our  14 results show several wingstroke asymmetries during arced turns with a higher and flatter outer wing tip path and a lower, more scooped inner wing tip path, relative to each other and to hovering. However, the presence of these asymmetries alone does not preclude force vectoring from being a mechanism hummingbirds implement to orient aerodynamic force into a turn. Indeed, recent studies of pigeons [22] observed that force vectoring is modulated by wing stroke asymmetries. Intriguingly, several of the asymmetries that were not found to effect force vectoring in pigeons, such as angle of attack, stroke amplitude, and wingbeat timing, were observed in our study. The changes in wing elevation and elevation amplitude found in our study were also seen in a study of fruit flies [15] where the wing bank angle did not fully correspond to the direction of motion. This emphasizes the difficulty in resolving the function of wingbeat asymmetries from examining a single maneuver. By comparing kinematic changes across several turns, our study identifies the function of several wingbeat asymmetries. In addition, it answers the question of whether force vectoring or sustained kinematic asymmetries are used separately or in combination to meet the challenges imposed by changes in translational velocity and turning radius. Unlike all previous studies of detailed wingbeat kinematics during maneuvering flight, ours is the first to use a balanced treatment design, which allows for independently testing the influence of radius and translational velocity. The mixed model analysis revealed that three features of asymmetrical wingbeat kinematics (elevation amplitude, stroke plane angle, and angle of attack) were associated with changes in turn radius, and two body kinematic variables (body angle frontal and wing bank angle) that control force vectoring were associated with changes in translational velocity. These kinematics were associated with changes in turning radius or translational velocity, but none were influenced by both aspects of a turn and there was no interaction between turning radius or  15 translational velocity for any of our ANOVAs (Table 3). This analysis suggests that wingbeat asymmetries are used to compensate for changes in turning radius and force vectoring is used to compensate for changes in velocity. Thus, rather than force vectoring and wingbeat asymmetries being mutually exclusive hypotheses, our results indicate that the two mechanisms are used simultaneously and independently to meet different aerodynamic challenges of turns. The coordinated changes in average wing elevation, elevation amplitude, and wing rotation timing during arced turns were previously observed during yaw turns [14], which raises the question of how can a similar kinematic pattern be used to generate different motions? One potentially important wingbeat kinematic that has varied among these maneuvers is the stroke plane angle, which is a two-dimensional representation that is relative to the horizontal plane. In hovering flight, the stroke plane angle is pitched down 7-11° in both wings, such that supination is lower than pronation. During yaw turns [14] and arced turns, the stroke plane of the elevated wing is statistically indistinguishable from hovering and the stroke plane of the lowered wing is pitched up, relative to hovering. While the stroke plane angle of the lowered wing is essentially horizontal during a yaw turn, it is pitched up even farther during the upstroke of an arced turn, such that it is higher at supination than during pronation. This pattern suggests that stroke plane modulation may be an important mechanism for orienting aerodynamic forces in maneuvers with left-right differences in wing elevation.  In addition, further study of other sustained maneuvers employing similar asymmetries may demonstrate that stroke plane angle is critical for orienting aerodynamic force laterally.  16 Tables and Figures Figure 1. Filming apparatus    Hummingbirds fed from a 10 ml syringe while hovering and turning within an acrylic chamber. The radius and translational velocity of turns varied by adjusting the length of the feeder arm and the speed of the stepper motor’s rotation. Experimental treatments and their respective turning radii (r), translational velocities (v), angular velocities (ω), and centripetal forces (Fc) are high speed camerasZXYFigure 1. apparatus and treatments33 cm0.626 m/s1.89 rad/s1.18 N33 cm0.750 m/s2.27 rad/s1.70 N23 cm0.626 m/s2.72 rad/s1.70 N23 cm0.750 m/s3.26 rad/s2.45 NrvωFchovering 17 provided and represented by five symbols. Four high-speed cameras provided dorsal, posterior, and lateral views of hummingbirds.   Figure 2. Instantaneous wing measures  Kinematics averaged across all individuals are presented for two wingbeats of hovering (left column) and the turn with the highest centripetal force (middle column). The right column depicts position angle (top), angle of attack (middle), and elevation angle (bottom). The left wing is given in red and the right wing is in blue. Lines indicate average values and transparent bands are the standard error of the mean. Downstroke is shaded in gray. Scale bars are representative of 25 milliseconds for all graphs in this panel. 900-90elevationangle (º)angle ofattack (º) 180900outer winginner wing30-300positionangle (º) 18 Figure 3. Analysis of kinematics between hovering and turning   Kinematic parameters describing hovering are shown in green. Box plots from parameters related to the left and right wings of the turning treatment with the highest centripetal force are presented in red and blue, respectively. Parameters related to the body or both wings are shown in purple for turning. Downstroke is shaded in gray.   −20020body roll (º)body pitch (º)body angle frontal (º)wing bank (º)relative wing bank (º)204060−20020−20020−20020−20020wingtip velocity (m/s)stroke plane (º)elevation amplitude (º)average elevation (º)120160stroke amplitude (º)endstrokemidstrokeangle of attack (º)endstrokemidstrokeFigure 3. analysis of kinematics between hovering and turningboth wingsor bodyleft wingright wingboth wingsor bodywing kinematic parametersbody kinematic parameters02040−20020−2002040801201600bad e f gh i j k lwingtip distance traveled (mm)80120160c 19 Figure 4. Average wing kinematics    Hovering kinematics are presented in the left column and turning kinematics are arranged in order of increasing angular velocity from left to right. Anterior, lateral, and superior views are provided in the first, second, and third rows, respectively. The left wingtip path is given in red and the right wingtip is in blue. The left shoulder is given in orange and the right shoulder is given in green. The rump is given in purple. The fourth row presents the angle of attack at seven points in the wingstroke with the downstroke shaded in gray. Circles represent the leading edge of the wing.   Figure 4. averaged wingtip paths1 cm 20 Figure 5. Kinematic changes across turning treatments  210-1-2-3210-1-2-3210-1-2-3velocityradius210-1-2-3-8-6-4-200123401230123outer stroke plane angledownstroke  (º)outer stroke plane angleupstroke (º)abcdefghFigure 5. kinematic changes across turning treatmentsbody angle frontalupstroke (º)40353025200.626  0.750velocity (m/s)0.626  0.750velocity (m/s)0.33  0.23radius (m)0.33  0.23radius (m)10503025201050-5inner elevation amplitudedownstroke (º)wing bank angledownstroke (º)wing bank angleupstroke (º)body angle frontaldownstroke (º)inner angle of attackmid-downstroke (º)-5-10-15-20-5-10-15-20181614121081412108(Δº)(Δº)(Δº)(Δº)(Δº)(Δº)(Δº)(Δº)velocityradiusvelocityradius0.626  0.750velocity (m/s)0.626  0.750velocity (m/s)0.33  0.23radius (m)0.33  0.23radius (m) velocityradius 21  Kinematic parameters that are significantly influenced by turning radius (sub-figure a-d) and velocity (sub-figure e-h) are presented on the left and right, respectively. Plots showing the influence of radius and velocity are shown on the left and middle of each sub-figure. Averages for each level of radius or velocity are presented for each bird and are connected across changes in radius or velocity by lines. Bar plots indicating the average change in degrees across all individuals are presented with the standard error of the mean in the right plot for each kinematic.  Table 1. Mixed model ANOVA between the wing kinematics of hovering and turning Means are presented with P-values from the mixed model for stroke plane angle (β), average elevation angle ( GR), stroke amplitude (ΦSP), elevation amplitude (ΘSP), wingtip distance traveled (WDT), average wingtip speed ( tip), and geometric angle of attack at mid-stroke (αmid) and end-stroke (αend) during upstroke (US) and downstroke (DS) while hovering (h) and turning (0.23 m, 0.750 m/s) for the left (l) and right (r) wings. Flight mode (hovering and turning) is the fixed effect and the random effect is bird. The degrees of freedom for all ANOVAs are 2, 10. Three post-hoc comparisons tested for significant differences between the left wing and hovering, the right wing and hovering, and the left and right wings when the overall model was significant (α=0.05). Significant P-values are presented in bold.   x¯   P value  l h r  overall model l-h r-h l-r βUS (º) 6.9 8.6 -10.8  3.76E-06 0.681 <1.0E-04 <1.0E-04 € θ€ U  22  x¯   P value  l h r  overall model l-h r-h l-r βDS (º) 10.2 11.1 -0.8  4.47E-04 0.914 1.07E-07 1.35E-06 GR,US (º) 17.9 3.1 -9.2  2.15E-09 <2.0E-16 <2.0E-16 <2.0E-16 GR,DS (º) 20.2 5.9 -5.1  4.90E-10 <2.0E-16 <2.0E-16 <2.0E-16 ΦSP,US (º) 144.6 136.9 131.5  2.31E-03 1.23E-02 0.113 3.18E-06 ΦSP,DS (º) 146.5 137.4 127.4  9.28E-05 1.33E-03 3.90E-04 3.67E-13 ΘSP,US (º) 5.5 16.1 31.1  2.99E-07 4.12E-08 1.78E-15 <2.0E-16 ΘSP,DS (º) 9.3 11.2 24.6  3.37E-06 0.441 <1.0E-04 <1.0E-04 WDTUS (mm) 120.5 123.2 122.3  0.706 - - - WDTDS (mm) 122.8 124.4 120.3  0.455 - - - tip,US (m/s) 9.8 10.2 9.9  0.159 - - - tip,DS (m/s) 10.6 10.9 10.4  0.158 - - - αmid,US 124.2 133.1 143.5  1.74E-03 5.14E-02 1.76E-02 1.09E-06 αmid,DS 25.4 29.7 25.5  0.257 - - - αend,US 85.1 76.7 71.3  4.07E-04 4.00E-04 6.38E-02 2.37E-09 αend,DS 70.6 93.1 111.3  4.29E-09 <2.0E-16 <2.0E-16 <2.0E-16   € θ€ θ€ U € U  23  Table 2. Mixed model ANOVA between the whole body kinematics of hovering and turning  Means are presented with P-values from the mixed models for body pitch angle (χGR,XZ), body angle frontal (χGR,YZ), body roll angle (χSP,XZ), relative wing bank angle (RWBA), and wing bank angle (WBA)  during upstroke (US) and downstroke (DS) in hovering and turning (0.23 m, 0.750 m/s). Flight mode (hovering and turning) is the fixed effect and individual is the random effect. The degrees of freedom for all ANOVAs are 1, 5. Significant P-values are presented in bold.   x¯   P value  hover turning   χGR,XZ,US (º) 52.7 48.9  0.059 χGR,XZ,DS (º) 48.8 45.6  0.069 χGR,YZ,US (º) -2.2 -16.3  8.00E-06 χGR,YZ,DS (º) -2.3 -16.1  2.14E-05 χSP,XZ,US (º) 2.22E-11 -9.4  0.012 χSP,XZ,DS (º) -3.33E-11 -9.6  0.014 RWBAUS (º) -2.2 -2.8  0.423 RWBADS (º) -2.3 -3.4  0.162 WBAUS (º) -0.018 13.5  4.98E-06 WBADS (º) -0.021 12.7  6.36E-07   24  Table 3. Two-way mixed model ANOVA of whole body and wing kinematics among turning treatments Means are presented with P-values from the two-way mixed model ANOVA for body pitch angle (χGR,XZ), body angle frontal (χGR,YZ), body roll angle (χSP,XZ), relative wing bank angle (RWBA), wing bank angle (WBA), stroke amplitude (ΦSP), stroke plane angle (β), elevation amplitude (ΘSP), average elevation angle ( GR), average wingtip speed ( tip), wingtip distance travelled (WDT), and geometric angle of attack at mid-stroke (αmid) and end-stroke (αend) for the left (L) and right (R) wings during upstroke (US) and downstroke (DS) for all turning treatments. The levels of turning radius and translational velocity are the fixed effect and the random effect is bird. The degrees of freedom for all ANOVAs are 1, 15. Significant P-values are presented in bold.   x¯   P value  0.23 m 0.33 m 0.23 m 0.33 m   0.626 m/s 0.626 m/s 0.750 m/s 0.750 m/s  radius velocity interaction χGR,XZ,US (º) 50.1 50.6 48.9 51.6  0.134 0.921 0.289 χGR,XZ,US (º) 46.8 47.5 45.6 48.4  0.107 0.859 0.352 χGR,YZ,US (º) -12.4 -12.8 -16.3 -13.8  0.189 0.008 0.079 χGR,YZ,DS (º) -12.5 -12.5 -16.1 -13.4  0.086 0.007 0.072 χSP,XZ,US (º) -7.2 -7.6 -9.4 -6.7  0.500 0.721 0.381 χSP,XZ,DS (º) -7.5 -8.7 -9.6 -7.1  0.732 0.899 0.377 RWBAUS (º) -1.7 -2.6 -2.8 -2.3  0.812 0.638 0.384 RWBADS (º) -2.4 -3.3 -3.4 -2.9  0.832 0.663 0.390 WBAUS (º) 10.8 10.2 13.5 11.5  0.108 0.017 0.343 € θ€ U  25  x¯   P value  0.23 m 0.33 m 0.23 m 0.33 m   0.626 m/s 0.626 m/s 0.750 m/s 0.750 m/s  radius velocity interaction WBADS (º) 10.1 9.3 12.7 10.5  0.061 0.020 0.343 ΦSP,L,US (º) 140.4 140.8 144.6 144.2  0.992 0.093 0.850 ΦSP,L,DS (º) 142.1 142.2 146.5 146.1  0.945 0.080 0.912 ΦSP,R,US (º) 131.1 127.8 131.5 131.0  0.332 0.371 0.478 ΦSP,R,DS (º) 127.8 125.8 127.4 128.7  0.872 0.550 0.421 βL,US (º) 6.8 4.1 6.9 4.9  0.015 0.600 0.715 βL,DS (º) 9.6 7.8 10.2 8.1  0.016 0.543 0.824 βR,US (º) -8.2 -11.1 -10.8 -10.8  0.467 0.567 0.495 βL,DS (º) -0.7 -4.6 -0.8 -2.6  0.185 0.661 0.615 ΘSP,L,US (º) 6.2 7.5 5.5 6.4  0.073 0.115 0.705 ΘSP,L,DS (º) 6.7 8.4 9.3 7.8  0.910 0.268 0.100 ΘSP,R,US (º) 28.7 26.6 31.1 28.2  0.047 0.098 0.726 ΘSP,R,DS (º) 22.8 19.5 24.6 21.9  0.004 0.036 0.757 GR,L,US (º) 15.3 14.5 17.9 16.0  0.126 0.032 0.534 GR,L,DS (º) 17.2 16.9 20.2 18.2  0.239 0.031 0.372 GR,R,US (º) -6.2 -5.9 -9.2 -7.0  0.204 0.040 0.323 GR,R,DS (º) -2.9 -1.7 -5.1 -2.7  0.036 0.063 0.477 tip,L,US  (m/s) 9.8 9.8 9.8 9.9  0.402 0.675 0.671 tip,L,DS  (m/s) 10.6 10.7 10.6 10.7  0.505 0.828 0.894 tip,R,US  (m/s) 10.0 9.7 9.9 9.8  0.069 0.710 0.233 tip,R,DS  (m/s) 10.5 10.3 10.4 10.4  0.443 0.889 0.380 WDTL,US   119.2 120.8 120.5 122.9  0.306 0.371 0.841 € θ€ θ€ θ€ θ€ U € U € U € U  26  x¯   P value  0.23 m 0.33 m 0.23 m 0.33 m   0.626 m/s 0.626 m/s 0.750 m/s 0.750 m/s  radius velocity interaction (mm) WDTL,DS   (mm) 121.5 122.4 122.8 125.4  0.331 0.250 0.620 WDTR,US   (mm) 122.2 119.1 122.3 122.2  0.393 0.394 0.406 WDTR,DS   (mm) 120.8 117.9 120.3 122.2  0.806 0.362 0.243 αmid,L,US (º) 125.0 128.5 124.2 125.6  0.098 0.194 0.449 αend,L,US (º) 82.9 85.3 85.9 86.5  0.391 0.226 0.595 αmid,R,US (º) 143.2 146.9 143.5 143.9  0.215 0.399 0.297 αend,R,US (º) 73.4 74.5 71.3 72.7  0.331 0.135 0.891 αmid,L,DS (º) 25.8 26.7 25.4 26.2  0.476 0.694 0.956 αend,L,DS (º) 74.6 74.1 70.6 73.8  0.390 0.173 0.248 αmid,R,DS (º) 26.2 33.0 25.5 30.6  0.005 0.423 0.644 αend,R,DS (º) 107.7 109.7 111.3 110.5  0.797 0.360 0.555      27 Concluding Chapter   The research presented in this thesis identifies the methods hummingbirds use to orient aerodynamic force into a turn and describes how kinematics vary in response to changes in turning radius and velocity. Notably, hummingbirds control turning radius through wingbeat asymmetries and translational velocity through force vectoring. Both of these mechanisms have been previously described during turns in other taxa [13,15], but their combination to simultaneously control separate aspects of a single maneuver is unprecedented. This thesis compliments published literature and expands upon recent findings [22] to offer the first description of how changes in turning radius and velocity are accomplished through adjustments in kinematics. In addition to contributing to our understanding of turning mechanics, these findings are also relevant to maneuverability in a broad context by identifying a clear relationship between behavior and physical challenges. While feeder tracking represents a powerful mechanism for studying maneuverability in hummingbirds, it suffers from some limitations. The first is that it is unknown whether the trajectories and velocities in a given study are representative of flight in natural conditions. It is possible that the average arced turn of a hummingbird has a larger turning radius or a faster translational velocity. Similarly, the range of translational velocities where the feeder elicited a sustained turn from the hummingbird was limited. For slowly revolving feeders used in preliminary research and training, hummingbirds implemented a series of maneuvers where an individual would hover while feeding and fly forward in a straight line to intercept the feeder as  28 it moved away from them. At high velocities, hummingbirds were incapable of consistently tracking the feeder and would accelerate and decelerate during feeding. This limited the range of velocities that could be examined with our methods and it is possible that new kinematic mechanisms may emerge at higher turning velocities. These limitations, however, are not likely to extend to changes in turning radius. Our smallest turning radius, at 0.23 m, represents a relatively tight arcing turn in the context of a hummingbird’s wingspan. The average wing length of the individuals used in this study was 0.053 m (Appendix Table 4), meaning that the turning radius represented just over four wing lengths. In addition, arced turns featured marked similarities in average wing elevation, elevation amplitude, and wing rotation with yaw turns [14], where the turning radius was zero. Despite the limitations of feeder tracking, the results obtained in this study illustrate the kinematics over the range of experimental treatments and offer a set of mechanisms that can be tested at higher centripetal forces and translation velocities. Several avenues for future research on turning mechanics are suggested by the results of this study. One potential direction would be to repeat the experimental treatments with the addition of flow visualization techniques that would identify the direction of the vortices generated by each wing [34]. Such a study could provide additional insight for the function of force vectoring and asymmetrical wing kinematics in turning. Care would have to be taken, however, to ensure that the revolving feeder did not create a wake that obscured the jets produced by each wing. A second topic that could be explored is whether there is an energetic difference between force vectoring and asymmetrical wingbeats. Previous studies of flight energetics and thermogenesis in hummingbirds [35,36] have established methods for measuring oxygen consumption in hummingbirds and similar methods could be used to determine the energetic costs of each mechanism of lateral force production. A third question that could be  29 addressed is how arced turns are initiated and concluded in hummingbirds and whether these transitional periods are affected by a turn’s radius or translational velocity. To answer this question, flight corridors similar to those used in other turning studies [13,21,22] could be constructed that would require different turning radii. A feeder could then travel down these corridors at specified speeds. High-speed cameras would record the kinematic transition from forward flight to turning and from turning to forward flight. Lastly, another potential area of research is diving, which is related to turning. Instead of requiring lateral force to conduct an arcing turn, a dive would require vertical force to counteract gravity and provide centripetal force. A similar apparatus to the one used in this study could incorporate a feeder that revolved perpendicular to the horizon. This experiment could detail the wing kinematics required to execute a dive and explain how the kinematics change with variations in dive radius, velocity, and centripetal force. While the limitations of feeder tracking would likely preclude recording the accelerations observed during free flight [18], such a study could provide valuable insights into how dives are initiated, controlled, and concluded. Our results demonstrate that hummingbirds control turning radius and velocity by adjusting left-right wingbeat kinematics and body and wing bank angle, respectively. However, it is unknown if other flying animals control these aspects of a turn in a similar manner. Because previous studies of turning have not varied turning radius or velocity, it is unknown how these aspects of a turn are controlled by body and wing kinematics. Many species of insects, birds, and bats have a more vertically oriented wingstroke, and they may alter different aspects of their wingbeat kinematics to modulate turning radius in particular. One challenge posed by studying turning in other taxa is that it can be difficult to train individuals to follow defined trajectories and speeds. To resolve this issue within insects, similar methods to previous studies [15,33]  30 could record a large number of turns and those meeting specific criteria for turning radius and velocity could be selected for kinematic analysis. Among other bird species, individuals could be trained to fly at two velocities through multiple flight corridors that are similar to those used in previous studies [13,21,22] but would require different turning radii. A recent study of turning pigeons [22] found several wingstroke asymmetries, and it is possible that these asymmetries are important in modulating turn radius in addition to initiating turns and controlling force vectoring. Similar experimental treatments could also prove informative for studies of bat flight. A previous study of bats [37] determined that bats rotated their bodies into a turn without changing trajectory during upstroke and used force vectoring to orient force into a turn during downstroke. Comparing different turns within bats could provide insight into the role the upstroke and downstroke have in controlling turning radius and speed. These studies would provide valuable insight into how body and wingstroke orientation influence turning mechanics and offer opportunities to further explore how turns are accomplished during flapping flight.   31 References  1. Dudley, R. & Yanoviak, S. P. 2011 Animal Aloft: The Origins of Aerial Behavior and Flight. Integr. Comp. 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Chai, P. 1998 Flight thermogenesis and energy conservation in hovering hummingbirds. J. Exp. Biol. 201, 963–968.  37. Iriarte-Diaz, J. & Swartz, S. M. 2008 Kinematics of slow turn maneuvering in the fruit bat Cynopterus brachyotis. J. Exp. Biol. 211, 3478–3489. (doi:10.1242/jeb.017590)   36 Appendices Table 4. Bird morphometrics average body mass (M), wing length (R), wing area (S), aspect ratio (AR), and the non-dimensional radii of the first [ (S)], second [ (S)], and third [ (S)] moments of wing area for each bird.  bird M (g) R (mm) S (mm2) AR (S) (S) (S) 1 4.26 55.445 1620.070 7.593 0.423 0.496 0.549 2 4.38 54.228 1653.012 7.130 0.447 0.521 0.573 3 4.15 52.549 1518.295 7.278 0.433 0.507 0.561 4 4.56 53.641 1524.945 7.557 0.434 0.506 0.558 5 4.09 52.132 1483.544 7.345 0.420 0.495 0.549 6 4.48 53.521 1559.219 7.366 0.430 0.506 0.560  Body mass is averaged across trials. Wing measurements are an average of both wings, with the exception of non-dimensional radii of wing area, which were calculated from a digital photograph of a single wing.   € ˆ r 1€ ˆ r2€ ˆ r3€ ˆ r 1€ ˆ r2€ ˆ r3

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